NIST Special Publication 988

Technical Digest:

Symposium on Optical Fiber

Measurements, 2002

Sponsored by the National Institute of Standards and Technology

in cooperation with the IEEE Lasers and Electro-Optics Society

and the Optical Society of America
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NIST Special Publication 988

Technical Digest:

Symposium on Optical

Fiber Measurements, 2002

Digest of a symposium sponsored by the

National Institute of Standards and Technology

in cooperation with the

IEEE Lasers and Electro-Optical Society

and the Optical Society of America

September 24-26, 2002

National Institute of Standards and Technology

Boulder, Colorado 80305

Edited by

P. A. Williams

G. W. Day

September 2002

U.S. Department of Commerce

Donald L. Evans, Secretary

Technology Administration

Phillip J. Bond, Under Secretaryfor Technology

National Institute of Standards and Technology

ArdenL. Bement, Jr., Director

NIST

Opttccii Society of A/norico
National Institute of Standards and Technology Special Publication 988

Natl. Inst. Stand. Technol. Spec. Publ. 988, 232 pages (September 2002)

CODEN: NSPUE2

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 2002

For sale by the Superintendent of Documents, U.S. Government Printing Office

Internet: bookstore.gpo.gov Phone: (202)512-1800 Fax: (202)512-2250

Mail: Stop SSOP, Washington, DC 20402-9325
PREFACE

This year has been a challenging one for the optical fiber telecommunications industry. In spite of that,

the 12

th Symposium on Optical Fiber Measurements has seen a significant increase in the number of

submitted papers. This year, we are bulging at the seams, having accepted 51 papers (9 invited and 42

contributed). The international participation in SOFM remains strong with a little more than half of the papers originating outside the United States.

Topically, the papers are more diverse than usual. Except for polarization-mode dispersion, which fills three sessions this year, there is a fairly even distribution across the measurement subjects of nonlinear

behavior, fiber and waveguide geometry, group delay, dispersion, wavelength, polarization, multimode

fiber, and systems modeling.

Happy reading,

Paul Williams

Gordon Day

Boulder, Colorado

September, 2002

Except where attributed to NIST authors, the content of individual sections of this volume has not been reviewed or edited by the National Institute of Standards and Technology. NIST therefore accepts no responsibility for comments or recommendations

therein. The mention of trade names in this volume by no means implies any endorsement or recommendation by the National

Institute of Standards and Technology.

iii
SYMPOSIUM COMMITTEE

G.W. Day, NIST, General Chair

P.A. Williams, NIST, Program Chair

A. Barlow, PerkinElmer

S.C. Fleming, Sydney University

D. Franzen, NIST

N. Gisin, University of Geneva

M. Hackert

T.A. Hanson, Corning

A. Inenaga, JDS Uniphase

J. Jackel, Telcordia

K. Okamoto, NEL

W. Reed, OFS Fitel

G. W. Schinn, EXFO

C. Shaar, NetTest

J. Taylor, NPL

K.K. Wong, Northstar Photonics

iv
CONTENTS

PREFACE iii SYMPOSIUM COMMITTEE iv

The Unique Measurement Challenges of Raman Amplifiers (invited)

A. Evans, S. Gray, M. Muktoyuk, Corning, Inc. 1 Pnmn^n Qr\n c\\ ^tiTniil^tpH ann ^nntitanpniic ^pat+pnticr AApciQiirpmpntc c\ "F tVip T-miII \^\j\\.\xJCiY lo\Jll KJL - j I 1 1 11 Ul U Lt. U tlllLl OLvCHld lllg IVACdoUll C111C11L& Ul 1 till AA/a VV avpI V CICIIULU pti cxtn T^pt^PTinp'npp L^L Ul. ilUCilC C nfv * 1 tnp Lilt. Ratn^'n IVulllull (^TaiTi VJalll Qt"\pp1~t~i LjUwvyll Ulll itn N.R. Newbury, K.L. Corwin, National Institute of Standards and Technology 7

FiHpr Nonlinpar Copfficipnt lVfpasiirpmpnt Schpmp RaspH on FW1VT lVTptVind with

Externally Modulate DFB Laser Source

B. Batagelj, M. Vidmar, University of Ljubljana Laboratory of Optical

Communications 11

r\. ^Ullipal lbUIl Ul olA 1 CX 1 11 1 1 C| Lit S 1UI INUIlllilCal V^UClllClCIll IVlCabUI CIIlCIllc> Ul VallUUs

ijlllglc 1V1UUC WpLlLal riUClS

Y. Namihira, K. Miyagi, K. Kaneshima, University of the Ryukyus; M.

Tadakuma, Furukawa Electric Co. Ltd; C. Vinegoni, University of Geneva; G.

Pietra, Pirelli Labs Innovation; K. Kawanami, Muroran Institute of Technology 15

Monitoring the Optical Network (invited)

Randy Giles, Lucent Technologies Advanced Photonics Research 19

Burial Depth Measurement tor Ion-Exchanged Glass Waveguides with Different

Widths

P. Madasamy, University of Arizona-Tucson Optical Sciences Center ; M. Morell,

NP Photonics; D. Geraghty, S. Honkanen, N. Peyghambarian, University of

Arizona-Tucson Optical Sciences 25

Accuracy of MFD and Aeff Measurements Using Far-Field Scanning

A.J. Barlow, R. Castle, Perkin Elmer Optoelectronics; A.G. Hallam, Halcyon

Optical Services 29

Mode-Field Diameter and "Spot Size" Measurements of Lensed and Tapered

Specialty Fibers

J.L. Guttman, PHOTON, Inc. 33

Anomalies in Online Fibre Measurements and Their Implications for Fibre Array

Manufacture

S.H. Law, T.N. Phan, Australian Photonics CRC; G.W. Barton, University of

Sydney Department of Chemical Engineering; M.J. Barton, J. Elsey, Australian

Photonics CRC 37

Performance Characterization of Components with Group Delay Fluctuations

M. Eiselt, C.B. Clausen, R.W. Tkach, Celion Networks 41

High-Resolution Group Delay Measurements of a Hydrogen Cyanide Gas Cell Using

Low-Coherence Interferometry

S.D. Dyer, R.J. Espejo, P.A. Williams, National Institute of Standards and

Technology 45

V
Group Delay and Spectral Response of Free Space Optics Mux/Demux Measurement

Using OLCR

X. Chapeleau, LPIO Universite de Nantes, NetTest; D. Leduc, C. Lupi, R. Le Ny,

C. Boisrobert, LPIO Universite de Nantes 49

High Accuracy Relative Group Delay Measurements of a Chirped Grating (NIST

Telecom Round Robin)

X. Chapeleau, D. Leduc, LPIO Universite de Nantes; M. Wicks, National Physics

Laboratory, UK; R. Le Ny, C. Boisrobert, LPIO Universite de Nantes 53

Direct Dispersion Slope Measurement by Mach-Zehnder Interferometer on Short

Length Optical Fibre

Y.C. Zhao, S. Fleming, Australian Photonics CRC J /

Dispersion Measurements on Multiple Kilometer-Length Few-Mode Fibers with an RF Spectrum Analyzer

J.W. Nicholson, S. Ramachandran, S. Ghalmi, M.F. Yan, OFS Laboratories 01

Group-Delay Measurements with RF Optical Frequency Scanning

M.C. Santos, J. Prat, M. Solar, Universitat Politecnica de Catalunya Dept. of

C ' 1

rT, 1_ _ ^ J /"""I ' i" - _ Signal A heory and Communications 65

Optical Waveform and Q-Factor Measurement Using Optical Sampling for UltraHigh Speed TDM Systems (invited)

H. Takara, I. Shake, S. Kawanishi, NTT Network Innovation Laboratories 69

Frequency-Controlled Supercontinuum Lightwave Source Applied to Optical

Measurements with High Frequency Accuracy

K. Mori, T. Morioka, A. Takada, E. Yamazaki, NTT Network Innovation

Laboratories 75

Recent Developments of Excited-State Optical Frequency Standards for Telecommunications

D.A. Humphreys, C. Campbell, F. Bernard, P. Patel, National Physical

Laboratory, UK 79

Fiber Bragg Gratings as Wavelength References - Development and Characterization

E.G. Grosche, Physikalisch-Technische Bundesantalt; J. Meissner, Advanced

Optics Solutions 83

Simultaneous Measurement or Transverse Strain and Temperature Using FBG

Written in HiBi Fiber

I. Abe, Universidade de Aveiro Dept. de Fisica, Centro Federal de Educacao

Tecnologica do Parana; M.W. Schiller, Centro Federal de Educacao Tecnologica

do Parana; R. Nogueira, Universidade de Aveiro Dept. de Fisica, Instituto de

Telecomunicacoes; P. Lopes, Universidade de Aveiro Dept. de Fisica; 0. Frazao,

J.L. Santos, INESC Porto; J.L. Pinto, Universidade de Aveiro Dept. de Fisica,

Instituto de Telecomunicacoes; H.J. Kalinowski, Centro Federal de Educacao

Tecnologica do Parana 87

A Simple and Direct Method to Estimate Long Period Grating Parameters

K. Thyagarajan, M. Das, M.N. Satyanarayan, Indian Institute of Technology

Dept. of Physics 91

A Simplified Model of Modal Dispersion in Multimode Fiber (invited)

A.J. Ritger, OFS Fiber Optics Division; S.E. Golowich, Bell Laboratories 95

vi
DMD Measurement and Simulation on Short Length, 850-nm Laser-Optimised, 50

/xm Core Diameter, GIMM Optical Fibres

F.J. Achten, Draka Fibre Technology; M. Bingle, Eindhoven University of

Technology, EM Software and Systems; B.P. de Hon, Eindhoven University of

Technology; M.J.N, van Stralen, Draka Fibre Technology 101

Determination of Skew in Multimode Ribbon Fibers

A.J. Barlow, PerkinElmer Optoelectronics; M.J. Hackert, Corning, Inc.

1 A C 105

rnase imaging ivieinoas ior upucai noer i^naracierizauon

/\. is-ODens, universny 01 ivieiDourne ocnooi 01 rnysics, \j. rjaxier, in. uragomir,

Victoria University School of Communications and Informatics; S.T. Huntington,

University of Melbourne School of Chemistry; E. Ampem-Lassen, M.L. Michna,

K.A. Nugent, University of Melbourne School of Physics 109

Measurement or Fiber Birefringence Using Lyot-Sagnac Interferometer

L.a. rum, Y.vj. Han, K.M. oova, J.U. is.ang, Johns Hopkins university Dept. 01

Electrical and Computer Engineering, U.C. Paek, Y. Chung, Kwangu Institute of

Science and Technology Dept. of Information and Communication 113

Determination 01 the Degree 01 Polarization Based on a Coherent Quantum

Measurement

M. Legre, M. Wegmiiller, N. Gisin, University of Geneva Group of Applied

Physics 117

Visualizing the Limitations of Four-State Measurement of PDL and Results of a SixState Alternative

R.M. Craig, National Institute of Standards and Technology 121

Four-State Measurement Method for Polarization Dependent Wavelength Shift

W.C. Swann, S.D. Dyer, R.M. Craig, National Institute of Standards and

Technology 125

Measurement of Dispersion in Photonic Bandgap Fibers (invited)

J. Jasapara, OFS Laboratories 129

Counting Modes in Optical Fibres with Leaky Modes

A. Argyros, I.M. Bassett, Australian Photonics CRC 135

Measurement 01 Multipath Interference and Resulting Optical Communication System

Penalty (invited)

D.L. Craig, M.G. Taylor, W. Zheng, J. Fowlkes, H.P. Sardesai 139

Predicting MPI in Raman Optical Amplifiers by Measuring the Rayleigh

Backscattering Coefficient P.B. Gaarde, Y. Qian, S.N. Knudsen, B. Palsdottir, OFS Fitel Denmark 143

Measurement of Multimode Resonances in Hexagonal Micro-Pillar Optical Cavities

N. Ma, A.W. Poon, Hong Kong University of Science and Technology Dept. of

Electrical and Electronic Engineering 147

Measurement Requirements for Optical and Optoelectronic Model Verification,

Validation, and Calibration (invited)

J. Morikuni, P. Mena, B.K. Whitlock, R. Scarmozzino, RSoft Design Group, Inc. 151
Photon-Counting OTDR at Telecom Wavelength: High-Resolution and LongDistance Measurements

F. Scholder, A. Fougeres, J.-D. Gautier, C. Barreiro, A. Haldimann, H. de

Riedmatten, M. Wegmiiller, N. Gisin, University of Geneva Group of Applied

Physics 157

Coherent Speckle in Direct-Detection OTDR

S.G. Murdoch, NetTest 161

Full Measurement of the Spatial Distribution of PMD Using Backscatter

A.J. Rogers, S.V. Shatalin, University of Surrey Dept. of Electronic Engineering 165

Polarisation Mode Dispersion in Restricted Optical Bandwidth: An Evaluation of

Measurement Techniques

S. Harris, D. Ives, National Physical Laboratory, UK 169

A/tea si irement and A/fitiPation of lVTnltmle Reflection Fffects on the Differential frroim

Delay Spectrum of Optical Components

PA. Williams, J.D. Kofler, National Institute of Standards and Technology 173

x-Shifted All-Fire Sagnac Loop for Characterization of Femtosecond Polarization

Mode Disnersion

E. Simova, I. Golub, Institute for Microstructural Sciences 177

TT<;it*io" V_JolIl^ TtYrnnTtanpf* LilliJKJL lu-llVV SlamTilincr ual 1 1L/1 1 1 lii, toIVJ ./YoOtOO Accpcs: thp U It PtfipptQ L.llk,^lo nfPlVfO Ul J. IVXi-/ onUll uYolWlll ^Ivctpm PprfV^rTnanpp 1 CI LXJk llluliV^W

f invitpH l 1 111 V IlCvlj

1WVV . Tl—i . TCath l\u 111, T^Jorthwp^fpm liUl Ul WLuLLl 11 TU1UTnivprQitv V tl oil V Dpnt !LvV_l-H. af\JL PncnnpprirnT JL^l . 1 1 1 V_ i 1 1 1 ti Spiptippq UvlvllvvO anH &11U /lUUIIvU AnnlipH

Mathematics; Gino Biondini, Ohio State University Department of Mathematics 181

TnvpQti Ul V C o LI cyntirvnQ L£,tl 1 1U>1 lo nnv ' 1 1 thp LUC Pplatirvn IXC Id 1 Rpfwppn UtLWttll P1VTT") 1 1V1 \_J (^npffipipnt V/U^lllvlWlll Qndlllirl f^aHIp V_ dUlC Tnctflll!* 11 lo Id lidtifvn U4J1 1 Vpi*r 1 vdl

in111 T^pnt^rhp V- L4 L lTj V 1 1 V Xplplcom 1 ClvlVvlll Pihpr J. 1 L/Vl Plant 1 ICXl Lv H.-J. Tessmann, D. Breuer, H.M. Foisel, H. Reiner, H. Cremer, Deutsche

Telekom 187

Pulsed Measurement of Polarization-Mode-Dispersion in Field-Installed Optical

Fibers

A.O. Kleivstul, Telenor R&D; A.S. Sudbo, University Graduate Center-UniK 191

Analysis and Comparison of Measured DGD Data on Buried Single-Mode Fibers

C Allen P K Kondamuri Universirv of Kansas Lightwave Communication

Svstems Laboratorv D L Richards D C Hat?ue Snrint Cornoration 195

Statistical Evaluation of Polarization-Dependent Losses and Polarization-Mode

Disnersion J—'1JL/L1 J1UI1 in111 anCI 1 1 Installed lllOLdliWU Piher J. lUvl Network liWlWUlIV

CJ.K. Richardson, University of Maryland Laboratory for Physical Sciences; R.J. Runser, M.Goodman, Laboratory for Telecommunication Sciences and Telecordia

Technologies; L. Mercer, Naval Research Laboratory 199

Programmable Polarization Mode Dispersion Generation (invited)

J.N. Damask, P.R. Myers, T.R. Boschi, YAFO Networks 203

Measurement of Differential Group Delay Profiles in Fibers and in LiNb03 Distributed PMD Compensator

S. Bhandare, D. Sandel, R. Noe, University of Paderborn Dept. of Optical

Commmunication and High-Frequency Engineering; H. Hermann, H. Suche, W.

Sohler, University of Paderborn Dept. of Applied Physics 209

viii
Estimation of System Outage Statistics Due to Polarization Mode Dispersion

P.J. Leo, YAFO Networks; D.L. Peterson Jr., Transmission Engineering,

WorldCom; K.B.Rochford, YAFO Networks 213

Low-Coherence Interferometric Measurement of Differential Group Delay and its Dispersion to Second-Order in Polarisation Maintaining Fibre

D.A. Flavin, Waterford Institute of Technology Dept. of Physical and

Quantitative Sciences; R. McBride, Heriot-Watt University Dept. of Mechanical

and Chemical Engineering; J.D.C. Jones, Heriot-Watt University Dept. of Physics 217

AUTHORS INDEX 221

APPENDIX I - PROGRAM 223

ix

The Unique Measurement Challenges

of Raman Amplifiers

Alan Evans, Stuart Gray, Mark Muktoyuk

Corning Inc., Science & Technology, SP-AR-01-4, Corning, NY 14831

I. Introduction

New technologies are required for the improved system performance of today's ultra long-haul 10 Gb/s and future 40 Gb/s transmission. Stimulated Raman scattering, discovered in 1925, and demonstrated as an amplifier in 1973,

[1] has emerged as a key solution to greater transmission distance and bit rate by reducing cascaded amplified

spontaneous emission build-up in the optical link. [2-5] The small gain coefficient of stimulated Raman scattering

provides long interaction lengths thereby distributing gain (and spontaneous noise) over the transmission span. It is well known that distributed amplifiers have a signal-to-noise ratio in between that of post- and pre-amplifiers. [6] Given that fiber nonlinearities limit the launch power, today's long-haul systems operate in a pre-amplified mode.

Distributed Raman amplification can reduce noise build-up by acting as a low-noise pre-amplifier to the subsequent

in-line discrete amplifier.

As an amplifier, there are similarities between Raman and erbium; however, there are unique measurement

challenges specific to using transmission fiber as the gain media. This paper reviews recent progress in Raman

measurements and is broken into three parts: the first describes standard gain measurements highlighting details that improve accuracy and reliability; the second focuses on ASE and other noise sources and why optical noise can be a misleading indicator of performance; the third addresses field-deployment issues that need consideration for practical commercial systems.

II. Raman Gain Measurements

Obtaining accurate Raman gain information is key to the design and deployment of distributed Raman amplifiers.

Gain information includes: gR/A^ff (the ratio of the Raman gain coefficient divided by effective area of the fiber at the pump wavelength) and its spectral dependence; and the spectral attenuation, GCp, of the Raman pump light in the 14xx nm wavelength band. The gain coefficient not only represents the wavelength-dependent strength of the pumpto-signal scattering-induced Raman amplification, but also the energy distribution of optical phonons. In a mechanical sense, the gain coefficient is the vibrational response to a pump impulse function. An independent measurement of the effective area could be used to obtain gR, but this is not necessary for amplifier design in optical

fiber. From the Raman gain coefficient and pump attenuation, a pump efficiency figure of merit, FOM, is derived

which is the small signal pump on/off gain versus pump power in units of dBAV:

FOM = 8r = 8rL* =

GR' 0nl0ff where l = y~ ex^~apL^ j s the effective length, L is the fiber length and

V*, Aff PP

eff oc

p L

GR,on /off= m°E>

^ P0Ul (Pump on, signal on) - P0Ul {Pump on, signal off)^

psignai ouXPumP off, signal on)

where the first term is the numerator is the signal power out of the fiber with the Raman pump(s) on, the second

term in the numerator is the>background amplified spontaneous emission and the denominator is the signal power

out of the fiber with the Raman pump(s) off. The pump on/off gain is typically given at the spectral peak of the Raman gain coefficient so that multiplying the pump FOM by pump power gives the maximum small signal Raman

on/off gain for a single pump wavelength.

An experimental setup for measuring Raman on/off gain is shown in Figure 1 . A broadband light emitting diode

signal source (ELED) provides unpolarized and low intensity signal light to the fiber under test. The low intensity avoids pump-depleted gain saturation and allows the use of analytic solutions to calculate the Raman gain

coefficient if the fiber. The LED source also allows for continuous gain measurements across greater than a 25 THz

wide gain bandwidth. For Phosphorous-doped fiber, a signal source greater than 40 THz is required as shown in Figure 2. For a 1450 nm pump, this implies an optical spectrum analyzer (OSA) scan beyond 1730 nm. A tunable

1
laser could be used as the signal source but is slower since an individual measurement has to be made at each

desired point verses a broadband, single scan capture of an OSA when using an ELED. The tunable also has a

limited tuning range and several such sources may be required to cover the desired bandwidth. A bank of fixed wavelength DFB lasers could also be used but does not give a continuous gain spectrum.

One important issue related to the source is to ensure good optical signal-to-noise ratio: As a guideline, the signal

output without pumps on should be 15 to 20 dB higher than the OSA noise floor; the measured gain should be

greater than about 2 dB; and the signal output with pumps on should be 15 to 20 dB greater than the ASE power. While this sets limits on minimum and maximum fiber length and required pump power, the setup is robust against

OSA power inaccuracy since the pump on/off gain is a relative (not absolute) measurement.

Power Meter

® Splice Loss

ELED

Switch —® Q@—

<

Source /

FUT

I Calibrated splices

Power Meter

OSA

14xx

Isolator 1

RPM

Figure 1: Ramanfiber gain experimental setup. RPMis the Raman pump module, FUT is fiber under test.

20 30 Frequency (THz)

Figure 2: Raman gain spectrumfor a P-doped opticalfiber. The gain peak near 13 THz is due to the silica glass

matrix; the gain peak near 40 THz is due to the phosphorus dopant.

Continuing with the experimental set up, the input switch is used to block the signal source so the amplified

spontaneous emission spectrum can be measured and subtracted from the amplified signal spectrum with the pumps

on. The input circulator removes unabsorbed pump while the output circulator injects the Raman pump counter- propagating with respect to the signal light. This is preferred over 14xx/1550 nm WDMs that are wavelength

dependent and make it difficult to measure the Raman spectrum close to the pump wavelength. It is important that such information can be obtained to calculate levels of pump to pump interaction in Raman amplifiers. The power

meter, with readings referenced to the power internal to the fiber under test (FUT), is used to measure pump

attenuation and as a check to make sure pump depletion has not occurred. Finally, an unpolarized fiber laser or a set of two fiber grating stablized, 14xx nm, laser diodes orthogonally polarized are used as the Raman pumps. If the Raman pump is polarized, there can be polarization dependent gain and errors in the gain spectrum. This is illustrated in Figure 3 where the gain spectrum with one of the polarization-multiplexed pumps is turned off. Fortunately, polarization effects are easily avoided since signal and pump degree of polarization can be kept small;

2
in addition, fiber lengths can be large enough and the pump is counter-propagating so that polarization evolution is randomized. Finally, the set up can be enhanced by measuring the Raman gain at multiple wavelengths. This gives

the of wavelength dependence of the Raman gain coefficient which, to a good approximation, is linear through the 14xx nm wavelength band.

4 .5 E -0 4

Frequency (THz)

Figure 3: Raman gain spectrumfor 5 km ofstandard single-modefiber with individual pumps on and both together

(shown as the middle line).

Any measurement procedure should have a number of automated steps that ensure the measurement is properly

performed. First, there should be a check that the powers of the two pumps of the same wavelength are equal.

Second, the power of the unabsorbed pump with and without the signals should be compared. If the difference is too great, either the input pump power is unstable (which can be checked with the other power meter channel) or pump-depleted gain saturation is occurring. Third, at any time, the user should be able to take a baseline pump

spectrum and calculate a new power-averaged center wavelength. This is done to account for any wavelength drift, say at the beginning of the day or when the bench is idle for more than an hour. We recommend using poweraveraged center wavelength in contrast to peak wavelength for a more stable and realistic characterization of the complex modal structure of grating-stabilized Fabry-Perot laser diodes. Finally, the pump attenuation should be

measured and used in the effective length calculation.

The last issue addressed related to Raman gain measurements is the impact of launch conditions in few-moded

fibers. For dispersion-compensating fibers (DCF), there can be additional design flexibility with selectively

launching into the lowest order mode of a few-moded fiber. Launching into the lowest mode at both the signal and

pump wavelength is required to get reliable gain spectrum data. For example, Figure 4 shows gain spectrum for two

uncontrolled launches into a DCF. Note the difference in peak value and in high frequency secondary peaks. Measurements on unpackaged DCF need to account for this effect.

4.0E-03 " 3.5E-03

'e 3.0E-03

| 2.5E-03 o

a 2.0E-03 o

o

.£ 1 5E-03

roO)£ 1.0E-03 E

a

O. 5.0E-04

0.0E+00

0 5 10 15 20 25 Frequency (THz) Figure 4: Raman gain coefficient ofafew-moded DCF under two different launch conditions

3
III. Noise Figure

Raman and EDFAs both generate amplified spontaneous emission resulting in signal-spontaneous and spontaneousspontaneous beat noise. This noise source is captured in the standard optical noise measurement technique.

However, the fast response time of Raman scattering and distributed Rayleigh scattering add terms only captured in electrical noise measurements. The fast response time allows pump power RTN (relative intensity noise) transfer to the signal [7] and pump-mediated signal cross-talk [8]. With the later, the pseudo-random signal depletes the pump,

creating pump noise that transfers onto other WDM signals. Double Rayleigh backscattering (DRBS) of the signal creates distributed multi-path interference of random phase and intensity leading to Gaussian-like noise on the

signal. [9, 10] The first two effects are mitigated by counter-propagating the pump with respect to the signal to average pump power fluctuations over the transit time of the amplifier; DRBS MPI is avoided in distributed amplifiers by keeping gain low and in discrete amplifiers by splitting gain between two, isolated stages. DRBSinduced MPI becomes a greater concern for high Raman gain in long span lengths. More recently discovered noise

effects include broadening of the DRBS interference and enhanced ASE in properly phase-matched fibers, [11, 12] and an increase in DRBS for temporally-modulated Raman pumps. [13]

However, in a well-designed Raman amplifier, ASE-induced signal-spontaneous noise is the dominant noise mechanism. It is convenient to treat noise figure as a discrete, lumped quantity to cascade it through the optical link. Since distributed Raman amplification is added to the existing transmission fiber, a differential noise figure, known

as the Raman effective noise figure is defined in terms of the amplified spontaneous noise, Pase, at the output of the transmission span: pASE = hv(GRi on/offFeff- 1)- As an example of the dependence of the effective noise figure on Raman on/off gain, consider a 48 C-band signals from 1527.6 nm to 1565.1 nm with launch power per channel of 0 dBm propagating through 90 km of non-zero dispersion-shifted fiber. Two pumps at 1426 and 1455 nm are varied

in power to sweep through a 0 to 22 dB range of Raman gain. The resulting effective noise figure for the bluest channel is shown in Figure 5, with the shortest wavelength channel having the worst noise figure of all the channels

for a number of reasons: pump-to-pump Raman power transfer allows the lower frequency pump to penetrate

deeper into the fiber so the lower frequency signals have more distributed gain than the higher frequency signals;

phonon energy distribution means that the ground state is more populated for higher frequency signals; spectral attenuation of the pump and C-band signals are greater for shorter frequency; and signal-to-signal Raman gain means for spectrally flat gain, the gain of lower frequency occurs closer to the output end of the fiber where OSNR

is lower.

0 5 10 15 20 25 Raman Gain (dB)

Figure 5: Noisefigure vs. Raman gainfor a two pump wavelength C band example. Also shown is the total noise figure including a 6.5 dB EDFA andfractional reach increase assuming reach scales inversely with noisefigure.

With this definition of noise figure, cascaded noise build up through multiple spans can easily be considered by

replacing the complicated, distance-dependent, distributed gain and noise functions with an equivalent lumped

amplifier at the end of each span just before the next in-line amplifier. Tracking noise and signal power through a

distributed Raman/EDFA hybrid amplifier gives the cascaded noise figure equation: Ftota i = Feff + FEDFa/Gr where

Fedfa is the noise figure of the EDFA, GEDFA is the gain of the EDFA, and G = GRGEDFA is the total gain. Using the Raman noif e figure of Figure 5 and assuming an EDFA noise figure of 6.5 dB independent of input power, gives the

total noise figure shown as the dashed line also shown in Figure 5. The noise improvement can be converted fo a

fractional reach increase through the amplifier Q equation, as shown by the dotted line.

4
IV. Field Deployment Issues

For EDFAs, the gain media is characterized and amplifier performance carefully measured prior to field deployment. In-service average gain changes are handled by total signal power taps at the input and output. By

contrast, Raman amplifiers have well-characterized pump properties but the gain media and resulting amplifier

performance is dependent on the transmission fiber and associated discrete losses - all of which can have significant variations in the field. In-service average gain changes may need to be handled by spectral signal power monitoring

to account for the complexity of nonlinear power transfer.

While field-deployed Raman transmission has been demonstrated, universal commercial acceptance requires

amplifier controls that ensure a known gain shape (average, ripple and tilt) over the full range of field conditions. Such conditions include variations between and within a given fiber type as well as variations in span length, signal

input power, channel loading, cabled fiber attenuation, splice losses, insertion loss between the Raman module and

the transmission fiber. Additionally, over the lifetime of the optical link there is the need to account for aging of the pumps and loss change in the components and cabled fiber. These conditions affect the launched signal and pump

power, pump effective length, pump and signal power transfer, and pump-depleted gain saturation. In the end, the key field deployment issue is to obtain and maintain the desired composite gain spectrum by adjustment and

feedback of the powers at all Raman pump wavelengths.

Given the difference between fiber types (e.g., standard single-mode fiber and various non-zero dispersion-shifted

fibers) and manufacturing differences in dopant concentration, effective area and pump wavelength fiber attenuation, some approaches try to characterize the Raman gain at individual pump wavelengths as a first step. For

example, a modified OTDR technique has been used to measure the pump effective length in the presence of pumpto-pump power transfer and pump depletion. [14] The wavelength dependence of the Raman gain is also determined. The multi-pump gain spectrum can be analytically calculated using a single gain measurement and the

effective length information. Most techniques, this one included, rely on a direct measurement of gain spectrum.

Typically this has meant the potential drawback of requiring control of remotely located launch signals to probe the

gain. Sobe and Yano have proposed using the Raman ASE itself as the probe signal. [15] They have established a

linear relationship between the normalized differential noise power and the Raman gain pump efficiency slope,

AGRaman/APpump. Normalized differential noise, measured at a single pump wavelength, is the difference in noise at two pump powers for a fixed optical bandwidth divided by the difference in pump powers, ApASE/APpump . Important

to this approach is that the slope is strongly dependent on the optical bandwidth and also weakly dependent on

temperature, so proper calibration is required. To illustrate, we modeled a 48 nm, 100 km of NZ-DSF case where

three pump powers (50, 250 and 500 mW) at the pump wavelength of 1432 nm were used to calculate differential noise (no signals present) and Raman gain slope (one signal present at 1529.2 nm). Figure 6a shows a linear relationship using the ASE power only at the signal wavelength; Figure 6b shows a linear relationship with a

different slope using the ASE power across the entire 48 nm signal band. Also shown is the dependence with

temperature. For a 60 degree change, there is a ~5% change in slope.

30 C

-30 C

Linear (30 C)

- - -Linear (-30 C)

5E-09 1E-08 1 5E-08 2E-08 Normalized Differential ASE (mW/mW)

(a)

0 1E-07 2E-07 3E-07 4E-07 Normalized Differential ASE (mW/mW)

(b)

30 C

-30 C

-Linear (30 C)

Linear (-30 C)

Figure 6: (a) Dependence ofthe peak Raman gain on differential ASE noise measured under the gain peak; (b) Same relationship with the differential ASE noise measured across a 48 nm signal band. Twofiber temperatures

shows the change in the linear relationship across 60° degrees.

5
After a measurement of the fully-loaded channel spectrum, there are several approaches to pump control - trial-and- error feedback, use of a control algorithm or gain-to-pump look-up tables. We have developed a simple yet robust algorithm to find pump powers that maintain low gain ripple (i.e., maximum gain - minimum gain / minimum gain) over a wide range of average gain. As an example, consider a 54 signals from 1521.3 nm to 1607.7 nm spaced by

200 GHz propagating through 100 km of NZ-DSF pumped at the four wavelengths, 1421 nm, 1449 nm, 1471 nm,

and 1 509 nm. The ratio of individual pump power verses average gain is shown in Figure 7. Evident from the

figure is the change in pump power ratio over the gain range due to pump-to-pump power transfer. As average gain

increases, pump power at the edge wavelengths exhibit the greatest change in fractional pump power since the Raman gain monotonically increases for this range of pump frequency spacing. The dependence is nearly linear but has some saturation effects for gain greater than 12 dB.

m

o

Jo

Q.a

E

3

Dl

rec

o

0.7

0.6

0.5

0.4

0.3

0.2

0.10 •

- -- - 1421 nm

- -* - 1449 nm

- 1471 nm

- -•- - 1509 nm

0 5 10 15 20 Average Raman Gain (dB)

Figure 7: A C+L bandpump optimization example illustrating pump power transfer over a range ofaverage Raman gain.

V. Conclusions

Raman amplification, particularly in transmission fiber, has rapidly become a critical tool in the design of high

performance transmission pushing reach, capacity, amplifier spacing or spectral efficiency. While there are

similarities in the measurement of gain and noise figure to EDFAs, there are also unique challenges particularly associated with a lack of apriori knowledge of the field-deployed gain media. Optimum design needs to consider

additional noise sources, polarization (PDG and PMD) and fiber nonlinearities.

VI. References

1. Stolen, R.H. and E.P. Ippen, "Raman gain in glass optical waveguides," Applied Physics Letters, 22(6) p. 276-281.

2. Hansen, P.B., et al, "Capacity upgrades of transmission systems by Raman amplification," IEEE Photonics Technology Letters, 9(2) p. 262.

3. Onhira, R., et al. "40 Gbits/s X 8-ch NRZ WDM transmission experiment over 80 km X 5-span using distributed Raman amplification in RDF," European Conference on Optical Communications 1999, p. 176.

4. Tanaka, T., et al. "2.1-Tbit/s WDM transmission over 7,221 km with 80-km repeater spacing," European Conference on Optical Communications 2000, p. 1.8.

5. Zhu, Y., et al. "1.28 Tbit/s (32X40 Gbits/s) transmission over 1000 km with only 6 spans," European Conference on Optical Communications

2000, p. 1.8.

6. Walker, G.R., et al., "Noise performance of distributed fibre amplifiers," Electronics Letters, 27(15) p. 1390-1391.

7. Fludger, C.R.S., V. Handerek, and R.J. Mears, "Pump to signal RIN transfer in Raman fiber amplifiers," Journal ofLightwave Technology,

19(8) p. 1140-1148.

8. Forghieri, I ., R.W. Tkach, and A.R. Chraplyvy. "Bandwidth of cross talk in Raman amplifiers," Optical Fiber Communications 1994, p. 294.

9. Lewis, S.A.E., S.V. Chernikov, and J.R. Taylor, "Characterization of double Rayleigh scatter noise in Raman amplifiers," IEEE Photonic Technology Letters, 12(5) p. 528-530.

10. Burtsev, S., W. Pelouch, and P. Gavrilovic. "Multi-path interference nose in multi-span transmission links using lumped Raman amplifiers," Optical Fiber Communication 2002, TuR4, p. 120.

11. Gray, S., M. Vasilyev, and K. Jepsen. "Spectral broadening of double Rayleigh backscattering in a distributed Raman amplifier," Optical Fiber Communication 2001, MA2, p. 1-3. 12. Vasilyev, M., S. Gray, and M. Ricci. "Pump intensity noise and ASE spectrum of Raman amplification in non-zero dispersion-shifted fibers," Optical Amplifiers and Applications 2001, p. 57

13. Artamonov, A., et al. "Enhancement of double Rayleigh scattering by pump intensity noise in fiber Raman amplifiers," Optical Fiber Conference 2002, WB6, p. 186.

14. Kim, P., J. Park, and N. Park. "Performance optimization of distributed Raman amplifier using optical pump time domain reflectometry," Optical Fiber Conference 2002, ThB5, p. 387.

1 5. Sobe, M. and Y. Yano. "Automatic pump power adjustment for gain-flattened multi-wavelength pumped Raman amplifier," Optical Fiber Conference 2002, TuJ5, p. 63.

6
Comparison of stimulated and spontaneous scattering

measurements of the full wavelength dependence of the

Raman gain spectrum

N. R. Newbury and K. L. Corwin

National Institute ofStandards and Technology, Optoelectronics Division, 325 Broadway, Boulder CO 80305

Tel: (303) 497-4227, Fax: (303) 497 -3387, E-Mail: nnewbury@boulder.nist.gov

Abstract

We present a direct comparison of the measured spontaneous Raman spectra and the measured

stimulated Raman gain from a pump laser. We confirm that the spontaneous Raman spectrum is related to the stimulated Raman gain spectrum through a simple Bose-Einstein temperature

factor. Given this simple relation, the full dependence of the Raman gain on both the signal and

pump wavelength can be extracted directly from spontaneous Raman spectra, which are easily

generated with a low-power (few milliwatts) diode laser and calibrated optical spectrum

analyzer.

Introduction

Since the early observations of Raman gain in optical fibers [1], Raman amplification has

become increasingly important in optical-fiber communication because it can provide gain with a low effective noise figure over a very large bandwidth. Clearly, accurate measurements of the

full wave'ength dependence of the Raman gain are important in view of the growing use of

Raman amplifiers. The gain will depend on both the signal and pump wavelength; however,

since the gain depends most strongly on the wavelength difference between the pump and signal

beams, the Raman gain is perhaps most usefully described in terms of its dependence on the

pump wavelength and on the wavelength difference between the pump and signal beams.

Historically, most measurements of Raman gain have used a pump-probe configuration with a fixed-wavelength pump beam to generate the Raman gain versus the pump-signal frequency

offset [2]. In a recent letter, one of the authors showed that this same general pump-probe

configuration can be used to determine not only the dependence of the Raman gain on the pumpsignal frequency offset, but also its dependence on the pump wavelength, provided the probe

light spans both the Stokes (gain) and anti-Stokes (loss) region of the Raman effect [3,4]. As a

result, a single pump-probe measurement of the Raman gain can provide the full wavelength

dependence of the Raman gain over the wavelength range of interest. An alternative method to the pump-probe configuration for measuring the Raman gain is to measure the spontaneous

Raman spectrum from a pump laser, from which one can extract the stimulated Raman gain [5]. In this paper, we demonstrate measurements of the full wavelength dependence of the stimulated

Raman gain using spontaneous Raman scattering. Using a single low-power pump laser we

determine both the stimulated Raman gain curve dependence on the signal-pump wavelength

offset and on the absolute pump wavelength.

The Raman gain spectrum and the spontaneous Raman spectrum will depend differently on

temperature. Historically, the underlying vibrations responsible for the Raman gain were assumed to be those of a simple harmonic oscillator [6], in which case the temperature correction

involves a Bose-Einstein factor. Although it has not been widely acknowledged in the literature,

7
the presence of anharmonicities will, at some level, introduce errors into the simple temperature

correction used in this model. Previous work comparing the noise figure from amplified

spontaneous emission and the gain of Raman amplifiers indicates that this simple Bose-Einstein

factor is at least accurate to a few tenths of a decibel [7,8,9]. One goal of this work is to demonstrate that this factor is accurate to better than 0.1 dB, the experimental limit on the

measurement of the absolute spontaneous Raman spectrum.

Direct measurement of the stimulated Raman gain curve typically requires a strong pump of a few hund ed milliwatts and a broad probe source. The advantage of measuring the gain from the

spontaneous Raman spectrum, as described here, is that only a very low-power pump of a few

milliwatts is needed along with a well-calibrated OSA. On the other hand, extracting the gain

from the spontaneous Raman spectrum does require calibration of the fiber attenuation and

absolute optical spectrum analyzer (OSA) power response at all wavelengths, while a direct

measurements of the stimulated Raman gain requires these calibrations only at the pump

wavelength. In practice, the choice of technique will be dictated by the available hardware.

Theory

The standard equations governing the Raman effect in single mode fiber of length L can be

written in terms of the number of pump photons per mode, np (z) , and the number of counterpropagating signal photons per mode, ns , at position z down the fiber as [10]

^- = -a(cos )ns + y(cop ,Aco)np (z)[ns +C(7\A<»)] (1)

where the fiber attenuation as a function of frequency is a{co) , the frequency offset between the

pump and signal beams is Aco = a>p -cos , and the Raman gain coefficient y(cop ,Aco) is positive

for the Stokes side ( Aco > 0 ) and negative for the anti-Stokes side ( Acq < 0 ). The factor C is responsible for the generation of spontaneous Raman photons and differs depending on whether

the signal is on the Stokes side, in which case C = 1 + ^(7

, ,|A<»|j , or on the anti-Stokes side of the

pump, in which caseC = 0>(7\|A<2)|) . The Bose-Einstein temperature-dependent correction factor

(p{T, Aco) = (exp (hA<z>/kT) - l) can be viewed equivalently as the phonon occupation number

at the temperature T, or as the thermal average of the squared matrix element between adjoining

states of the simple harmonic oscillator. This simple Bose-Einstein temperature correction

results from the assumption of simple harmonic vibrations, for which the density of states is exactly the same regardless of the initial state (i.e., the states are evenly spaced) and the matrix

elements can be easily calculated. Experimentally, if this simple-harmonic assumption were

incorrect, the measured and expected spontaneous Raman curves would deviate at frequency

offsets hAco < kT , where <p(T) > 1

.

In general, there is an equation similar to (1) that describes the pump evolution. For our

parameters, the undepleted pump approximation is valid, so the pump decays exponentially in

the -z direction. At very low pump powers of a few milliwatts, the Raman gain is low and the

spontaneously-generated Raman photons undergo negligible Raman gain. Equation (1) can then

be solved in closed form as:

Ynp C = gRM (cop , Aco)

P

ns (cos p Leff , tota,CAf (2) ) a(cop ) + a(cos )

8
where Leff Jotai , the quantity in square brackets, is the total effective length, Af is the mode

spacing so that ns /Af is the number of photons per Hz bandwidth, Pp

is the initial pump power,

and gRM {cop , Acq) is the standard Raman gain. We will assume the pump is unpolarized so that

gRM is the unpolarized gain (half the polarized gain) and ns /Af is the number of photons per

hertz per polarization mode. Solving Eq. (2) for gRM gives the Stokes Raman gain at a fixed

pump wavelength or frequency. As discussed in detail in Ref. [3,4], the pump-wavelength

dependence is contained in the asymmetry of the Raman gain spectrum; essentially, the antiStokes signal "pumps" the pump laser with a Raman gain corresponding to a pump wavelength

equal to the anti-Stokes wavelength. If we assume the Stokes Raman gain varies as ~ co

kp , then

the exponent k can be found from the solution to [3,4]

gRM (A(o) + gRM (-Aco) _ k + \ gnu (Aco)-

g

RM (-Acq) 2cot Aco (3)

Experimental Measurements

The experimental setup to measure the backward-generated Raman spontaneous spectrum is shown in Figure 1 . As discussed earlier, the OSA calibration is critical to accurate

measurements of the Raman spectrum. The OSA was calibrated for three factors: the

wavelength scale was calibrated relative to the pump-laser wavelength, the power scale was

calibrated relative to a calibrated optical power meter (OPM), and finally the effective resolution

bandwidth was measured as a function of signal wavelength. We also separately measured the

loss of the circulator and other components between the fiber end and the OSA. Finally, the

attenuation over the full wavelength range of interest was measured with a broad source and

adjusted by more accurate attenuation measurements taken over a smaller wavelength range with

the cutback method. To avoid uncertainties from polarization-dependent loss the pump

polarization was scrambled. The measured spectrum S in dBm from the OSA was converted to the number of photons per Hz per polarization as ns /Af = SV/(2hc2 AZ) , where AX is the

calibrated OSA resolution bandwidth.

1500 nm

Laser

ASE

Filter

OSA

Figure 1 : Setup for measuring the spontaneous Raman spectrum. The laser power was ~4 mW, well

below the stimulated Brillouin scattering threshold and low enough to provide negligible Raman gain.

Figure 2a shows the spontaneous Raman spectrum, in units of nfAf , measured directly for two

different fiber types and calculated directly from Eq. (2) using the calibrated Raman gain curves measured for the same exact fibers, as reported in Ref. [3]. Figure 2b shows the same data set, but in this case in terms of the directly measured stimulated Raman gain and the indirectly

measured stimulated Raman gain inferred from the spontaneous spectrum and Eq. (2). No free

parameters were used in the comparison. The difference between the measured and predicted

Raman spectra, shown in Figure 3, has an average offset of less than 0.1 dB and a standard

deviation of—O.ldB. We attribute these deviations to uncorrected wavelength dependence of the

OSA power response or to fiber and component attenuation. No discrepancies attributable to anharmonicities, which would be evident at wavelengths offsets of - 45 nm or below, were

observed, indicating the Bose-Einstein correction factor is valid to better than 0.1 dB.

9
1400 1500 1600 1400 1500 1600 Wavelength (nm) Wavelength (nm)

Figure 2: a) Comparison ofmeasured spontaneous Raman spectra with the calculated spontaneous

Raman spectrafor two typical communicationfibers, b) Comparison ofthe same data in terms ofthe stimulated Raman gain spectrum.

1400 1500 1600

Wavelength (nm)

Figure 3: The difference between the calculated and measured curves of2(a) or 2(b).

We have shown that the full wavelength dependence of the Raman gain can be obtained either

directly from measurements of the gain or indirectly from measurements of the spontaneous

Raman spectrum. In general, the uncertainty for the spontaneous-based measurement will be

larger (~0.2 db) since this measurement requires absolute power measurements at each

wavelength, whereas the direct measurement requires only relative power measurements at each

wavelength. However, if this level of uncertainty is adequate and if only a low-power pump is available, measurement of the Raman gain through the spontaneous spectrum is an attractive

choice.

1. R. H. Stolen and E. P. Ippen, Appl. Phys. Lett., 22, 276 (1973).

2. R. H. Stolen in Technical Digest: Symposium on Optical Fiber Measurements, 2000, P.A. Williams and G. W.

Day eds. (NIST Special Publication 953, Boulder CO, 2000) p. 146; F. Coch, S.A.E. Lewis, S. V. Chernikov and J.R. Taylor, ibid., p. 143; D. Hamoir, N. Torabi, A. Bergonzo, S. Borne and D. Bayart, ibid., p. 147; S. Gray, ibid., p. 151.

3. N. R. Newbury, Opt. Lett., accepted for publication (2002).

4. N. R. Newbury, "Pump-Wavelength Dependence of Raman Gain", in Optical Amplifiers and their Applications,

accepted for publication., July (2002).

5. F. Koch, S.A.E. Lewis, S.V. Chernikov, and J. R. Taylor, Electron. Lett., 37, 1437 (2001).

6. W. D. Jonnston Jr. and I. P. Kaminow, Phys. Rev., 168, 1045 (1968).

7. C. R. J. Fludger, V. Handerek, R. J. Mears, "Fundamental Noise Limits in Broadband Raman Amplifiers", paper MA5-1 in Optical Fiber Communication Conference (OFC), Vol 54 of OSA Trends in Optics and Photonics Series (OSA, Washington DC 2001).

8. S. A. E. Lewis, S. V. Chernikov and J. R. Taylor, Opt. Lett., 24, 1823 (1999).

9. K. Rottwitt, J. Bromage, M. Du, and A. Stentz, "Design of Distributed Raman Amplifiers", paper 4.4.1, in ECOC

2000, Munich Germany, 2000.

10. J. Aeuyeung and A. Yariv, IEEE J. Quantum Electron., QB-14, 347 (1978).

10
Fiber Nonlinear coefficient measurement scheme based on FWM

method with externally modulated DFB laser source

Bostjan Batagelj, Matjaz Vidmar

Laboratory of Optical Communications, Faculty ofElectrical Engineering, University ofLjubljana,

Trzaska 25, 1000 Ljubljana, Slovenia

Tel: (386) 14768423, Fax: (386) 14768424, e-mail: bostian.bataselKcvfe.uni-Ii.si ABSTRACT

In this paper, we present measurement scheme for determining the optical fiber non-linear coefficient y, using

externally modulated continuous wave DFB laser source. The measurement technique is based on Four-Wave

Mixing. The measurement source which uses one laser and one optical erbium-doped fiber amplifier only is described precisely. The proposed simple measurement scheme is polarization independent, enables high

sensitivity and accuracy, and is applicable to all currently available types of fiber. Keywords: Optical Fiber Communications, Fiber Measurements, Non-linear Coefficient, Four-Wave Mixing.

1. INTRODUCTION

Many schemes have been previously proposed to make measurement of non-linear coefficient (y) [1]. Four- Wave mixing (FWM) is a reliable technique for determining the fiber y. The well-known measuring setup [2]-

[4] based on FWM is made up of two DFB lasers, where the wavelength spacing is adjusted by temperature

tuning. It uses more than one optical erbium-doped fiber amplifier (EDFA) to raise the total optical power. One

of the biggest disadvantages of this method is that the polarisation controllers must be adjusted all the measurement time in order to obtain maximum FWM efficiency. The determination of y employing such FWM

method has a limited measurement capability due to the polarization adjustment and insufficient amplification.

We have devised and demonstrated a measurement scheme based on FWM method [5]-[6], which uses one

externally modulated DFB laser source only. The use of such source eliminates polarization dependence and

making measurement scheme simple and highly sensitive, what leads to higher accuracy. The introduced measurement scheme is applicable to all currently available fiber types including Photonic Crystal Fibers.

2. THEORY OF THE FWM METHOD

The FWM is a non-linear process induced by Kerr effect in optical fiber. It occurs when two or more

wavelengths of light propagate together through an optical fiber. Supposed the equal signal input power, the

ratio between the power of new frequencies generated through FWM at the end of the fiber and the signal output

power is written as [7]

FWM (L)

PAL) a

2 +A(3'

-ai

1 + 4- sin H

2

(1)

where Ps(0) is the signal input power, PS(L) is the signal output power and LeJj is the fiber effective interaction

length. The phase-matching condition is given by

27t-X2n AP= p- 4TA

2 D(X) + /±f—

c

\

dD

dX

-yPs (o)

\-e

-aL

eff aLeff

(2)

where Af is frequency spacing, Z)(X) is the fiber chromatic dispersion, dD/dX is the dispersion slope, and Xp

is the wavelength corresponding to the pump frequency. The second part of equation (2) corresponds to the

intensity dependence of the phase matching [8]. In our case, the measured fiber should be relatively short, in order to make measurements in the flat part of FWM characteristic and to achieve phase matching, so that sine term of equation (1) could be neglected. However, a numerical algorithm based on the above described FWM is usually used to relate the input and output fields and to determine the y.

11
3. MEASUREMENT SOURCE WITH EXTERNALLY MODULATED DFB LESER

3.1 Mach-Zehnder intensity modulator

The key element of the measurement source, which is shown in the left side of Fig. 3, is the Mach-Zehnder

LiNb03 guided-wave intensity modulator. The Mach-Zehnder modulator (MZM) transfer function shape is shown in Fig. 1 . The output optical power of an ideal MZM is given by

P~ =l/2-^n

(l + cos(A<p)), (3) where A<p is the optical phase difference, Pm and Pout are the input and output optical power of MZM. The bias voltage changes the optical phase difference between the interfering waves at the output of the Mach-Zehnder

interferometer and thus changes the output intensity. The MZM's halfwave voltage Un is defined as the change

in bias vc ltage necessary to move between a peak and null on the transfer function curve. So, the optical phase

difference can be written as A(p = n-U(t)/U7t , (4) where U{t) is the applied signal including DC bias, and UK is the modulator full-swing voltage.

Max

Phase difference A(p Modulator bias voltage

Figure 1. Plot ofthe optical output power versus the applied voltage for MZM.

There are basically two typical operation points on the MZM transfer function curve. In the first one MZM is biased at any voltage that is halfway between maximum and minimum transmission point on the transfer function curve. This point is called quadrature bias point. The second operation point is when the MZM is biased at either the maximum or minimum transmission point on the transfer function curve. At this bias point

the odd-order products are minimized and even-order products are maximized as shown in Fig. 2.

Fourth-order product

Phase difference A(p

Figure 2. MZ optical output power at thefundamental and high-orderfrequencies.

3.2 Operation of measurement source The experimental configuration for our method is shown in Fig. 3. The output from a single frequency laser is externally modulated in a LiNb03 Mach-Zehnder amplitude modulator (1 1GHz 3dB bandwidth, UK=7V) preset

to minimum transmission point. MZM is driven by pulsed RF signal of a fixed frequency 10GHz. The light source is single frequency DFB laser. In order to suppress stimulated Brillouin scattering, the continuous wave (CW) laser source is directly modulated with the signal of few MHz, which broadens the optical spectrum.

Otherwise, the Brillouin scattering limits the optical power that can be launched in the fiber under test (FUT).

12
10GHz RF

Generator 1MHz

Pulse Generator

Measurement

source

RF amplifier

24dB

Laser

diode

driver TLO

CW

laser

Isolator

LO!

Bias

1 * Curent

Feedback

circuit Photodetector

Fabry-Perot Optical

Spectrum Analyzer

FSR=100GHz

Resolution = 1MHz

Attenuator ~7

i, r

Figure 3. Experimental setup for the measurement offiber nonlinear coefficient.

The electrical pulse modulator, switched by the 1MHz pulses, produces a train of 10GHz RF pulses as shown

in Fig. 3. The train of pulses has width t and repetition time T. Pulse modulation is used to increase the optical

peak power, while the RF modulation produces sidebands in the optical spectrum. The obtained optical

spectrum is symmetrical around the incident lightwave frequency. Two sidebands are equally spaced in frequency by 20GHz. The bias of the MZM is set to the point where the carrier is maximally suppressed. Since

there is an active bias control, the desired MZM bias point occurs at specific DC bias voltage that remains

constant for all the time despite variations in environmental conditions. A typical modulated optical spectrum

with suppressed carrier is shown in Fig. 3. The output spectrum mainly consists of two sidebands, separated by

twice the RF modulation frequency. The sidebands have equal power and linear polarization parallel to each

other. The frequency separation of 20GHz, however, is chosen since the Brillouin shift for silica fibers ranges from 10,5-1 1,5GHz [9]. Because of that the Brillouin scattering is unlikely to coincide with by FWM produced

components needed for measurement. Approximately 5% of the optical power is tapped off to an active bias controller for MZM. An external modulator bias controller uses tapped optical signal to maintain a desired bias point. The method of controlling

is based on previously injected pilot tone from the local oscillator (LO) and feedback correction of bias voltage.

The remaining 95% of the optical power of modulated signal is amplified by an EDFA to the ~24dBm average power and propagated through the FUT. Thanks to the pulse modulation of the RF signal and suppressed optical

carrier, the optical signal has a much higher peak power. To avoid pulse distortion due to gain dynamics, T was

set much lower than the relaxation time of the EDFA, which thus react only to the average power (7==l|0.s). High

peak power is obtained by using low duty cycles. Higher peak power of the pulses is resulting in higher FWM

products while travelling through the FUT. Due to the short length of the lumped amplifier, the fiber nonlinearity effects such Stimulated Brillouin Scattering compared to the stimulated emission of Er

3+ ions are

negligible.

4. MEASUREMENT PROCEDURE

While travelling through the FUT the optical signal experiences FWM, which leads to the generation of

additional sidebands in the optical spectrum. The spectral analysis is performed by high dynamic and high

resolution optical spectral analyzer. Fig. 4 shows a typical experimentally measured spectrum at the output of

the FUT. By switching pulse modulation on and off, optical power at the input of FUT is changing. With power

variations of the launched signal and measuring the strength of the spectral sidebands, it is possible to determine

the magnitude of non-linear FWM product experienced by the signal and hence FUT y. The total signal input power is measured with an optical power meter. The partition of the power between the

different spectral components is evaluated using optical spectral analyzer measurements. Finally, the power of

sidebands is corrected for parameter a' and G'. Their determination is shown in Fig. 4, where a' is the

13
decreased optical power due to the duty cycle of the pulse source and G' is the increase in gain due to higher

amplification of the modulated signal.

Pulse modulation: OFF Pulse modulation: ON

Figure 4. Determination of a' and G' parameters.

5. CONCLUSIONS

We introduce the measurement scheme of the fiber y using FWM technique. Simple measurement source uses one DFB laser only, eliminates polarization dependence and enables high sensitivity. With this measurement scheme it is easy to measure the y of all types of currently available fiber including Photonic Crystal Fibers. In the further work we need to distinguish between the J4 Bessel component and the FWM components as they

are coincident. The fourth order frequency component is a systematic error which is produced by external modulation in MZM. The consideration and determination of non-linear effect in EDFA is also needed. With

additional elimination of these systematic errors the estimated error in our measurements of the fiber y is expected to be less than 5%. The higher accuracy depends on how accurately the launch and output power can

be measured and also on how important the effect of electrostriction on the measurement is. REFERENCES

[1] B. Batagelj: Review of so far Proposed Fiber n2 Measurement Schemes, in Proc. ICTON 2002, Warsaw,

Poland, April 2002.

[2] L. Prigent, J. P. Hamaide: Measurement of Fiber Nonlinear Kerr Coefficient by Four-Wave Mixing, IEEE

Photonics Technology Letters, vol. 5, pp. 1092-1095, Sep. 1993.

[3] M. Tadakuma, O. Aso, S. Namiki: Nonlinear coefficient measurement of reverse dispersion fiber using

four-wave mixing, in Proc. ECOC'99, Nice, France, September 1999, paper 11-224.

[4] J.-C. Antona, S. Bigo, S. Kosmalski: Nonlinear index measurements of various fibre types over C+L band

using four-wave mixing, in Proc. ECOC'01, Amsterdam, The Netherlands, Sept. 2001, paper We.L.1.2.

[5] B. Batagelj: A simple non-linear coefficient measurement scheme based on Four-Wave Mixing, in Proc. Optical Fiber Measurement Conference, United Kingdom, September 2001, pp. 73-76.

[6] B. Batagelj and M. Vidmar: Patent application no. P-200200029, Slovenian Intellectual Property Office,

2002, pp. 1-7.

[7] N. Shibata, et al.\ Phase-mismatch dependence of efficiency of wave generation through FWM in a SingleMode Optical Fiber, IEEE JQE, vol. 23, pp. 1205-1210, July 1987.

[8] S. Song, et al., Intensity-dependent phase-matching effects on four-wave mixing in optical fibers,/. Lightwave Technol, vol. 17, pp. 2285-2290, Nov. 1999.

[9] Agrawal, G. P., Nonlinear Fiber Optics, 2

nd ed., UK: Academic Press, 1995.

14
A Comparison of Six Techniques for Nonlinear Coefficient

Measurements of various Single Mode Optical Fibers

Y. Namihira , K. Miyagi , K. Kaneshima , M. Tadakuma , C. Vinegoni #3

, G. Pietra

#4 and K. Kawanami #5

#2: The Furukawa Electric Co. Ltd., Japan, #3: University of Geneva, Switzerland

#4: Pirelli Labs Innovation, Italy, #5: Muroran Institute of Technology, Japan

#1: University of the Ryukyus, 1 Senbaru, Nishihara, Okinawa 903-0213, Japan

Phone/Fax: +81-98-895-8700, E-mail: namihira@eee.u-ryukyu.ac.jp

Abstract A comparison of six techniques for nonlinear coefficient (nilAeff) measurements of various optical fibers using Pulsed-LD SPM, CW-LD SPM, sinusoidally modulated signal-SPM, XPM, self-aligned Interferometric, and FWM methods is first demonstrated. The (tillAeff) obtained from the six different methods were in good

interlaboratory agreement except for dispersion compensating fiber (DCF).

Introduction: Accurate determination of the nonlinear coefficient (n2/Aeff){n2 is the nonlinear refractive index,

Aeff is the effective area} of optical fibers is required for the ultra-long amplified optical transmission systems. To

date, the nonlinear coefficient of the optical fibers has been measured by using the self-phase modulation (SPM)

method with a pulsed laser diode (LD) (P-SPM)[1], the SPM method with dual CW-LDs (CW-SPM) [2], the cross- phase modulation (XPM) method [3], self-aligned Interferometric (INT) method [4], sinusoidally modulated signalSPM (S-SPM) method [5], and four wave mixing (FWM) method [6]. Heretofore, ITU-T {nilAeff) round robin measurements for various optical fibers coordinated by Prof. Y. Namihira of University of the Ryukyus (formerly KDD) have been successfully performed [7-9]. This paper first presents the results of the interlaboratory fiber nonlinear coefficient (nilAeff) measurements for various optical fibers such as standard single mode fiber (SMF), cut-off shifted fiber (CSF), dispersion shifted fiber (DSF), non-zero DSF (NZDSF) and large effective area DSF (LEDSF), and dispersion compensating fiber (DCF) using

six different techniques such as the P-SPM [1] , CW-SPM [2], XPM [3], INT[4], S-SPM [5], and FWM [6] methods at 1550nm.

Experiments: The experimental set-up of the (n2IAefj) measurements for the various single mode optical fibers are shown in Fig.l. In Fig.l, (a), (b), (c), (d) and (e) are P-SPM method, CW-SPM method, XPM method, INT method, S- SPM, and FWM methods, respectively. Here, n2 can be estimated by (n2/Ae/f) multiplying the Ae//. The Aejj was

measured by the far-field scan (FFS) technique [10]. The parameters of six kinds of single mode optical fibers are shown in Table 1. These fibers were circulated to the five Laboratories such as University of the Ryukyus (formerly

KDD), Furukawa, University of Geneva, Pirelli Labs., Muroran Institute of Technology.

P-SPM method: In Fig. 1(a), the transform limited (TL) Gaussian pulse-LD were used as a pulsed-LD [1]. The

output optical pulse due to SPM was measured by the optical spectrum analyzer (OSA). As the input optical power

increases, the maximum phase shift increases in proportion to the input peak power. The (n2 IAefj) can be obtained from

the numbers of peaks in the SPM broadened spectra [1]. CW-SPM method: In Fig. 1(b), the optical beat signal was derived from dual CW-LDs operating at around 1550nm

[2]. The beat signal was then amplified in a preamplifier (EDFA1) and transmitted through a optical band pass filter to suppress the amplified stimulated emission, and transmitted through a polarizer to a following high power EDFA2.

XPM method: In Fig; 1(c), the probe signal power is set relatively weak so that (n2/Ae/f) in FUT is dominantly caused by amplified strong pump CW-LD through XPM and that the effect of SPM is negligible. When pump CW-LD or CWSLD is modulated in its intensity, probe CW-LD is modulated in this phase through XPM [3]. INT method: In Fig. 1(d), the Interferometric method is based on the detection of the Kerr phase shift by a self- aligned interferometer. Here, the distributed feedback laser (DFB), Erbium doped fiber amplifier (EDFA), polarization

controller (PC), Farady mirror (FM), and fiber Bragg grating (FBG) were used [4]. S-SPM method: In Fig.l (e), the S-SPM method is based on SPM effect estimation. This technique consists simply

in propagating an optical signal sinusoidally modulated by means of an electro-optical LiNb03 modulator. The y -factor estimation is achieved using a simulation tool capable of reproducing the evolution of signal spectra along the fiber and

doing a comparison between acquired experimental data and simulation result [5].

15
FWM method: In Fig. 1(f), pump (DFB-LD1) and probe (DFB-LD2) sources are tunable with a temperature and

current controller. The LD1 of pump source was amplified with a EDFA to compensate an insertion loss of polarization

optics, and passed through a tunable band-pass filter (BPF) with AX=lnm to eliminate the ASE noise of EDFA. The

X/2 wave plate was used to rotate the input azimuth of linearly polarized light of LD1. In contrast, the output light of LD2 was depolarized with a depolarizer to examine the depolarization effect on FWM efficiency. Otherwise, the depolarizer was deleted in the setup so that the FWM efficiency was measured in linearly polarized states of LD1 and

LD2 [6]. Results and discussions: The results of interlaboratory (nllAeff) and n2 measurements at random polarization states (RP) using six different techniques of P-SPM, CW-SPM, XPM, INT, S-SPM, and FWM for a SMF, a CSF, two kinds of DSFs, two kinds of NZDSFs, a LEDSF and a DCF at 1550nm are summarized in Tables 2 and 3, respectively.

In Tables 2 and 3, n2(RP) = n n2(LP), n =1.0 for P-SPM, r) =8/9 for CW-SPM, S-SPM, and FWM, and the

polarization factor r\ =2/3 for XPM were used. Here, LP represents the linear polarization state. Here, concerning the results of the self-aligned Interferometric (INT) method [4], the (n2/Aeff) values were larger than that of the other methods. Then, a correction (scaling) factor of -0.8 with respect to the mean values of the other methods were used. Such a scaling could easily arise from an erroneous estimation of the absolute peak power used for

this measurements (underestimate of the power by a factor of just 0.8). Therefore, the special correction factor of k

=0.8 {(*) in Tables 2 , 3, Figs.1,2} were used for the INT method because of the experimental error. Meanwhile, in FWM method at Muroran Institute of Technology, only one (r\2/Aeff) measurement of 20 km long

DSF was measured at present, however, they will measure (n2/Aeff) of another fiber samples in the near future. Fig. 2 show estimated values of n2 at random polarization states for various optical fibers as a function of six different measurement methods. Fig. 3 indicates the estimated values of n2 at random polarization states for six different measurement methods as a function of various optical fibers. From Tables 2 and 3, it was found that the average values of n2 at RP of SMF, CSF, DSF, NZDSF, LEDSF, and DCF were -2.62, 2.43, 4.80, 4.16. 3.19 and 12.1 x

10~ [1/W], respectively. Also, the average values of n2 at RP for SMF, CSF, DSF, NZDSF, LEDSF and DCF were -2.21, 2.14, 2.25, 2.31, 2.32, and 2.78 x

10'

2° [nWW], respectively.

-20 2 The average values of n-> =2.25 x 10 [m /W] of DSFs at random polarization states are in good agreement with that

-20 2 of 2.1 - 2.3 x 10 [m fW] range of published results, respectively.

Conclusions: From the interlaboratory nonlinear coefficient {nllAeff) measurements for various optical fibers, the (nUAeff) obtained from the six different techniques such as pulsed-LD SPM method, CW-SPM method, a XPM

method, a self-aligned Interferometric (INT) method, a sinusoidally modulated signal SPM method, and FWM method

were found to be a good agreement with each methods except for DCF.

It was confirmed that the average values of n2 at random polarization state obtained from these different methods

were

-20 2 -20 2 2. 1-2.3 x 10 [m /W] for SMF, CSF, DSF, NZDSF and LEDSF except for DCF of -2.8 x 10 [m /W], respectively.

References :

[1] Y. Namihira:"Higly accurated nonlinear coefficient measurements by SPM method for DSFs and large effective area fibers at 1.55 urn," SOFM 1988, NIST, Boulder, USA, pp.83-86, 1998.

[2] A. Boskovic,et al.,:"Direct continuous-wave measurement of n2 in various types of telecommunication

fiber at 1.55 urn", Optics Letters, vol. 21, no. 24, pp. 1966-1968, 1996.

[3] T. Kato et al.,: "Measurement of nonlinear refractive index in optical fibers by cross phase modulation method using depolarized pump light," Optics Lett. ,20, p. 988, 1995.

[4] C. Vinegoni et al.,:" Interlaboratory measurements of the nonlinear coefficient of standard SMF and DSF fibers using an

interferometric method and an SPM based cw dual-frequency method", OFMC'01, pp. 59-62, Canbridge, UK, 2001.

[5] G. Pieira: "Sinusoidally modulated SPM method", Private communications, May, 2002.

[6] K. Kawanami et al., "Polarization effects on determination of nonlinear refractive index by four-wave mixing in a dispersion shifted fiber", OECC'02, Yokohama, Japan, 2002.

[7] Y. Namihira : "Nonlinear coefficient round robin measurements for various dispersion shifted fibers in Japan and UK", ECOC2000, 8.2.5, pp.97-98, 2000.

[8] Y. Namihira: "KDD nonlinear coefficient round robin measurements for various dispersion shifted fibers

in Japan and UK", SOFM 2000, Boulder Co. USA, pp.49-52, 2000.

[9] Y. Namihira et al., "Interim report of ITU-T nonlinear coefficient (n2/Aeff) round robin measurement results in Japan ", OFMC'01, pp.63-66, Canbridge, UK, 2001.

[10] Y. Namihira :"Relationship between nonlinear effective area and mode field diameter for dispersion shifted fibers", Electron. Lett., vol.30, no.3, pp.262-264, 1994.

16
Table 1 Fiber parameters for various single mode optical fibers.

Fibers SMF CSF DSF NZDSF LEDSF DCF D@550nm

[ps/(nm-km)] 163 19.4 -058 -2.19 -2.48 -109.1

Aeff@550nm

IV m

2

] 84.6 882 46.8 55.6 72.8 22.9

i

si' Mode 1.vied- LD

Gain Switcned-LD

Traniform Limited Catmun Pulse-LD

Er-Doped Optical Fiber BandPalb

Amplifier Fflter (LDFA) (OBPF)

Optical Fiber Underr—

Attenuator Test (FIT)

Optical Power Mem

(QPM)

Optical Pulsewidth Measurement

Optical Spectrum

Analyxrr tOSA)

Optical

I—1 PuUewtlLh MCHS it remen I

Q H OV-LD1

Q H CW-LD2

Er-Doped Optical Fiber Band Path

Amplifier Filler

Optical Fiber Under

Attenuator Tejl(FUT) B-CH21

Optical Spectrum 0 Annlvwr

((MA)

Upticai Power Meter (OPM)

Q : X/4 (n72), H : a/2 (it)

(a) Pulsed-LD SPM (P-SPM)

(b) CW-LD SPM (CW-SPM)

Polarization Controller <PQ Optica] Fiber Under BandPith

Teal (FIT) Filter (OBPF)

Q : a/4 (n/2), II : X/2 (n)

Se.f-Dday«l Heterodyne

Defection

Electrical Spectrum

Anfllvzer

generator) FM

FBG DELAY

50% \ PC mm

FUT

(c) XPM method (d) Self-aligned Interferometric

F.U.T. Band-paa. niter

(e) Sinusoidally modulated signal SPM (S-SPM) (f) Four wave mixing (FWM)

Fig. 1 Experimental set up for six different (n2/Aeff) measurement methods.

(a) Pulsed LD SPM(P-SPM), (b) CW-LD SPM (CW-SPM), (c) XPM

(d) Self-aligned Interferometric (INT), (e) Sinusoidally modulated signal SPM (S-SPM),

(f) Four wave mixing (FWM)

17
Table 2 Measured values of (n2/Aeff) at random polarization states for

various optical fibers using six different methods.

Fibers

(n2/Aeff)« 10' 10 [VIA)

P-SPM CWSPM XPM INT) S-SPM FYM Ave 0

SMF 2.62 260 245 253 290 2.62 0.172 CSF 245 231 214 258 2.65 2/13 0.206 DSF 476 509 4.69 4 51 505 4.70 480 0227 NZOSF 3.94 426 3.70 418 475 4.16 0395 LEDSF 3.01 325 3.00 318 3.51 319 0209 DCF 1166 1156 1300 1402 10 12 1211 1.481

(*1 : Uslna a correction factor of 08 t-) : Not Measured Table 3 Estimated values of n2 at random polarization states for various optical fibers using six different methods.

Fibers

n2» 10

25 [m2/W

P-SPM CWSPM XPM INTO S-SPM FV\M Ave o

SMF 222 220 207 214 2.45 221 0.145 CSF 216 204 189 227 234 214 0.182 OSF 223 239 219 211 236 222 225 0.105 NZDSF 220 237 205 233 2.63 231 0216 LEDSF 219 237 218 231 256 232 0155 DCF 272 266 297 321 233 278 0.331

f) : Usina a correction factor of 08 (- 1 : Not Measured

4.00

3.50 r

| 3.00

°2.50 t

7 2.00

1.50

1.00 P-SPM CWSPM XPM INTO S-SPM FWvl

Measurement Methods

Fig.2 Estimated values of n2 at random polarization states for various

optical fibers as a function of six different measurement methods.

A =1550nrn(g*andom Polarization

(*): Using a correction factor of 0.8

4.00

3.50 ?

| 3.00 8 250 r

; zoo

1.50

1.00

A =15S0nm @tendom Polarization C ): Using a correction factor of 0.8

SMF CSF DSF NZDSF

Optical Fibers

LEDSF DCF

Fig.3 Estimated values of n2 at random polarization states for six different measurement methods as a function of various single mode optical fibers.

18
Monitoring the Optical Network

Randy Giles

Advanced Photonics Research

Lucent Technologies

Holmdel, NJ 07733

randygiles@lucent.com

Introduction

The sophistication and complexity of optical transport networks is apparent from

their data capacity (Tb/s), transmission reach (1000's km), services functionality

(voice, data, video) and global connectivity. As with any complex system,

network operations are not fully deterministic, element specifications or testing

may be flawed, databases may be erroneous or incomplete, software is not

perfect, and things break. Yet through reliability analysis, redundant

architectures, protection schemes, and performance monitoring, optical

networks can be engineered to give high availability and minimal service

disruption. Examples include conventional SONET rings that have as part of

their OAMP, overhead bytes that are set and monitored to generate critical alarms (loss-of-signal, loss-of-frame etc) and are detected in less than 10ms to activate line or path protection switching in less than 50ms. Similar cause

(monitor condition) and effect (path restoration) protection schemes are used in mesh networks, often with lower costs relative to SONET rings through sharing of

protection resources and sometimes at the expense of slower restoration times.

These conventional networks of both (inter)national and metropolitan extent are

evolving from simple rings and point-to-point interconnections linked through

end-terminals and electronic switches, to ones that are substantially transparent

and perform more routing tasks in the DWDM optical layer than before. Figure 1 illustrates some features of modern transparent networks and begins to suggest

the scope of monitoring needs. Transparent networks are economically feasible

when the end-to-end demands between nodes are large enough to require the

capacity of a WDM optical channel rather a lower subrate. End-to-end demands

of OC-48 (2.5 Gb/s), OC-192 (10 Gb/s), and even OC-768 (40 Gb/s) are best

routed using optical channel add/drop multiplexers and crossconnects. The

trouble with this optical transparency is unavailability of the in-band monitor bytes

of a data stream at intermediate points along the path, requiring instead

alternate, dedicated optical monitoring methods. Furthermore, line engineering

is more involved and faults are harder to find as links are transparently

interconnected through the optical switch fabrics and accumulate optical

impairments. Optical monitoring will be imperative for these networks to be

practical.

19
Figure 1. Wide-area (core) and regional (edge) networks transparently

integrated through core- and metro- optical add/drop multiplexers, and optical

crossconnects.

Network Impairments

It is well known from point-to-point optical line systems that careful engineering is required in order to achieve the long reaches (1000's kms) and high capacities

(several terabit per seconds) required for cost-effective transport. A guide to understanding a line system is given in figure 2 starting with the electrical input

data stream Di(t) and ending in the output from the decision circuit . Omitting a

rigorous formulation, noise nT(t) is present at the transmitter (eg shot noise) and

the optical signal is propagated through the optical channel made of a series of

fiber spans that contribute additive noise term, ns (t), and respond to the input

optical field E(t) through hs (E;t). A common source of noise is the amplified

spontaneous emission, ASE, produced in optical amplifiers and a crude estimate

of the resulting optical signal-to-noise ratio measured in 0.1 nm bandwidth

around a 1550nm and expressed in dB is OSNR~58+PiN-Ls-NF-10logNs , where

Pin is the transmitter power, l_s is the span loss, NF is the amplifier noise figure

(4-5 dB typically) and Ns is the number of amplified spans. Typical requirements

have OSNR at the destination to exceed 15-20dB, though forward error correction (FEC) technology relaxes these numbers.

The response function hs (E;t) may simply be a single constant attenuation

coefficient, or it may incorporate chromatic and polarization dispersion and

nonlinear optical phenomena including self-phase modulation, cross-phase

modulation, four-wave mixing, Raman scattering and Brillioun scattering.

Fiber chromatic dispersion can cause signal distortion by temporally spreading

the optical field's frequency components and lead to reduced transmission

20
performance. The resultant optical field after chromatic dispersion is given

by E{z,t)= ^E(z,a))exp(-i(/3(a))z - cat))dco . The frequency-dependent propagation

coefficient can be expanded,

P(co) = Pq +Px {cq-co0) + ^P2 {cq-cq,) 2 +...

where the group velocity is v

g =l//?, and the dispersion coefficient is, D = -27ieP2 1 A

2

. The nominal limit to the allowable chromatic dispersion for a channel data rate B is estimated from B

2 |D|L<105 (Gb/s)2 ps/nm. This

corresponds to a residual group delay dispersion tolerance of approximately

1000ps/nm for 10 Gb/s data rates and 60 ps/nm for 40 Gb/s.

Monitor Monitor

D (t) I 1 I 1 I

1

I 1 I 1 J-K+)- hTW " E-0 -(+> h3

(E;t) -###-<+)- hs(E;t) - O-E h„(t)

nA(t) nR

(t)

hTransmitter Optical Link

Clock Recovery

Decision

Circuit

Receiver

Figure 2. An optical communications line system comprised of a transmitter,

optical link, and receiver.

Even after careful dispersion compensation of individual line systems, their

concatenation through optically transparent switch nodes may compromise the

end-to-end performance. Temperature effects are often neglected but the

increases in data rates and system reach may alter this perspective. For

example, where the temperature coefficient for the change of A,0 , the fiber's zero- dispersion wavelength, is dA.0/dT=0.03nm/°C and the dispersion slope

0.05ps/nm2/km, a 25°C change of temperature in a 1000km length optical path

could disrupt 40Gb/s systems.

Polarization mode dispersion is an impairment arising from the residual

birefringence present in optical fibers. Through PMD effects, the initial transmitter (single) polarization evolves into one that is randomly varying with the

difference of mean power in orthogonal polarizaton states steadily decreasing as

the light progresses down the line system. The differential group delay, DGD,

induced by PMD is time-varying and the impairment, expressed as an outage

probability, is a function of the fiber parameters, line length, and modulation

format. The outage probability resulting from first-order PMD is approximately

Poutage=exp[-PPenaity/K(AT)

2 B2

] where AT is the mean PMD-induced differential

delay, Ppenaity is the threshold power penalty for an outage event, and the K value

21
is a approximately 6 for RZ data and 14 for NRZ. Typical system limits have

ATB<0.1 to achieve outage probabilities below 10"7

.

Optical nonlinearities in the fiber medium create additional boundary conditions

to operating the optical line system. Very simply, with the inclusion of noise

effects, they result in the establishment of optimum signal power requirements; if the power is low, noise is the predominant degradation, if the power is high,

optical nonlinearities dominate. Only one class of nonlinearities will be discussed

here for illustrative purposes, those originating from the Kerr effect. In the Kerr

effect the refractive index of the transmission medium changes with the light

intensity, An=n2 P/Aeff, where n2 ~2.6x10"20 m

2/W in silica fiber, P is the signal

power, and Aetf is the fiber effective area. The instantaneous self-phase

modulation of a signal is A(j)spm=N s n2Q)oPI-eff/cAeff, where Leff=(1-exp(-aL))/a is the

fiber effective length for physical length L and attenuation coefficient a. Impairments from Kerr-related nonlinearities (self-phase modulation, cross phase

modulation, four-wave mixing) become important when A(j)spm approaches n.

Finally, light traversing the line system is detected with a photodiode, additional

noise is contributed from the receiver, and the signal is filtered before reaching

the clock recovery and decision circuit.

Optical Monitoring

The diversity of optical impairments and their dependence on device parameters

and system design creates the need for accurate characterization of components

and appropriate system performance monitoring and network element control. It

is clear that in addition to the optical impairments, there are many other electrical,

mechanical, and optical components that contribute to the end-to-end

performance of a data flow. With many possible culprits it may not always be

practical to identify the exact cause of deterioration or even failure of a line

system, but finding its location may be. Fault location is currently the primary reason for measuring a line system's performance, particularly as the network

becomes highly connected through transparent nodes, has large numbers of

optical signal channels, or has very long reach. However, despite current

limitations, optical monitoring needs are evolving in hand with optical networks

and can be summarized as:

1. WDM channel presence, power, and wavelength. Used for link status

verification.

2. WDM channel optical signal-to-noise ratio or Q-factor. Can sense non- alarm degradations and locate faults.

3. Feedback signal in gain equalizers, chromatic dispersion and PMD

compensators.

4. Transparent network management. Channel performance verification

after link concatenation.

22
5. In-situ link parameter extraction from detailed optical channel signatures.

Used for preplanning and preprovisioning assessment.

Commerically available optical monitoring methods cannot perform all the tasks

suggested by this list. Compact optical spectrum analyzers can report some

optical attributes and in some instances give estimates of a channel's Q-factor, a measure of the error-rate margin in digital transmission. Specialized optical

receivers can perform eye analysis and yield Q-factor numbers. However, these

limited techniques are either not adequate or cost effective for the demands of

fully transparent optical networks. Several new approaches to optical monitoring

will now be described.

Recently, a number of RF signal analysis and optical sampling techniques have

been reported, that suggest the possibility of not only indiscriminately sensing

changes in signal parameters as a fault location method, but identifying the cause. For example, PMD is well known to cause RF signal fading through

cancellation of frequency components that destructively interfere after a

birefringence-induced relative delay. The normalized fading from first-order

PMD effects measured at frequency f is F=1-4r(1-r)sin2 (7ifAT) where r is the

power ratio in the two principal orthogonal states. If the monitor can derive

PMD values from RF fading measurements, then a network operator could

recognize PMD outage events, or in severe cases, identify out-of-spec fiber

spans.

Optical sampling methods to obtain amplitude histograms or reconstructed eye

diagrams are available to analyze signals at very high data rates (>1Q0Gb/s).

Figure 3 illustrates synchronous and asynchronous sampling of a data eye

diagnm and the corresponding distribution functions. Both approaches yield

estimates of Q ( Q=|u.i-uo|/(oi+ao) ). trading off between requiring timing recovery

at the monitor (synchronous), and reduced accuracy of the Q estimate

(asynchronous). These sampling techniques offer better estimates of signal

quality than OSNR as they are sensitive to time-domain features not observed in the optical spectrum. Optical sampling may also distinguish between chromatic

dispersion-induced signal degradation and ASE noise penalties.

Figure 3. Data eye diagram and distribution functions for synchronous and

asynchronous sampling.

Synchronous

Asynchronous

23
Although conventional electrical sampling techniques can generate amplitude

histograms, optical methods through either nonlinear or coherent homodyne

detection are candidates for use at 40Gb/s and higher data rates. Figure 4

shows these sampling methods that involve mixing an incoming signal with a

narrow-width sampling (gating) pulse such that recovered signal is the

convolution of the signal and sampling pulse shapes,

^ 0Ut NONLINEAR (0 <* 1 ^DATA WgATE ~ 0^

^ 0UtHOMODYNE (0 ~ Re

\

EDATA {^)E*GATE (t - t)dl

where r\ is a conversion efficiency associated with the nonlinear interaction and

generally is very small. In contrast, the coherent homodyne method can be very

sensitive, but for eye diagram reconstruction requires two balanced receivers so

that quadrature components of the homodyne signal can be added. Either

sampling method enables detailed pulse characterization without high-speed

(expensive) photodetectors, suggesting that practical implementations as

monitors for transparent networks are possible.

(a) Nonlinear Sampling Gate (b) Coherent Homodyne Sampling

Beam Splitter

Sampling Pulse

Sampling

Pulse

Data Pulse

Receiver

Nonlinear

Material

Figure 4. Nonlinear and coherent homodyne optical sampling techniques for Qfactor histograms and eye diagram reconstruction.

Summary

Optical monitoring of optical networks is in its infancy. Channel monitoring in DWDM transmission systems and fault location in line systems are the first applications, but new requirements are arising as system architectures move to transparent ring and mesh networks. Identifying and quantifying optical

impairments (noise, chromatic dispersion, PMD) during network operation will be

needed and a variety of techniques based on RF and optical means are in development.

24
Burial depth measurement for ion-exchanged glass

waveguides with different widths

Pratheepan Madasamy, Mike Morrell*

,

David Geraghty, Seppo Honkanen and Nasser Peyghambarian

Optical Sciences Center, University of Arizona, Tucson, Arizona

*NP Photonics, Tucson. Arizona

Introduction

Buried ion-exchanged glass waveguides are used extensively for making devices for

communications because they have low loss, are mode matched with the fiber and can be

polarization insensitive. It has been reported [1] that in an arrayed waveguide grating device

having both slab waveguide regions and single mode channel waveguide regions, the two regions

get buried to different depths. This would result in a significant loss at the intersection of these

waveguide regions. In this paper we report a simple method to measure the burial depth and we

investigate the difference in burial depths for different waveguide widths ranging from 2 to 10 um. We show that the burial depth increases linearly for mask opening widths from 2 to 10 um.

Fabrication

BGG31 glass was used as the substrate material. Mask widths ranging from 2 to 10 um

were patterned on the sample. Buried ion-exchanged waveguides were prepared in two steps.

The first step involved Ag/Na ion exchange at the surface. Two different samples were prepared

using different first steps. In the first sample the first step involved thermal ion exchange

performed in a 50:50 AgNCb/Na NO3 melt at T=553K for 75 mins. A 100 nm thick titanium film was used as the mask for the first step. The second step was an unmasked field assisted burial at T=523K, with a current density of 1.15 Am"2 for 40mins. In the second sample, the first step

involved field assisted ion exchange with a 100 nm thick Ag film as the ion source. Ion exchange was done at 90°C, 300 V for 3 hours. In the first step, photoresist itself was used as the mask [2,

3]. The second step was an unmasked field assisted burial at T=523K, with a current density of

1.79 Am"2 for 26mins. Both processes have been commonly used to fabricate ion-exchanged

devices.

Measurement technique

We define the burial depth as the distance from the surface of the glass to the center of

the waveguide mode. The experiment was set up using a Newport AutoAlign system. The data was taken with a resolution of 0.1 um. The setup used to find the center of the mode is given in Fig. la. The input fiber from a 1550nm SLD (superluminescent diode) source and the output

fiber to the optical power meter are butt-coupled to the waveguide, and the throughput is maximized. Then the output fiber is scanned in the y direction to get the profile in y direction as shown in the inset in Fig. la. The center of the profile gives the center of the mode (yo). To find

the surface of the glass, the input fiber is moved about 1mm from the surface of the glass as shown in Fig. lb. This forms a Lloyd's mirror interferometer like set-up, as shown in Fig 2, with

interference fringes formed due to the direct light from the input fiber and the reflected light

from the glass surface. The intensity in y direction in the observation plane is:

25
7lC2V

I = 470 sin " () for y>0 where y=0 is the surface.

sA

The interference fringe has a minimum at the surface of the glass and there are no fringes

below the surface of the glass. In the setup in Fig lb, scanning the output fiber in the y direction

from the center of the mode gives the fringes and the first minimum gives the surface point. The

difference between the surface point and the center of the mode gives the burial depth for the

waveguide.

Output fiber

Fig. 1 Set-up for measuring the burial depth; la shows the set-up to find the center ofthe mode and lb

shows the set-up to obtain the interference fringes to get the surface point.

Fig. 2 Lloyd's mirror interferometer.

26
Results

Using this technique, the burial depth is measured for all the waveguides on both

samples. The burial depth increases linearly for mask opening widths from 2 to lOum for both of

the samples as shown in Fig. 3. This is in agreement with the observation made in [1] where

larger burial depth for the slab waveguide region as compared to the single mode channel

waveguide was obtained. The slope differs for the two samples because the burial parameters are not the same for the samples and the first step results in different Ag+ concentration in the

surface waveguides of the two samples.

Ag film S Molten salt iiimiLinear (Ag film) — — Linear (Molten salt)

4 6 8

Mask opening width (um)

10

Fig. 3 Burial depth as a function of mask opening width. The square data points are for sample 1 with

molten salt ion exchange as the first step. The dashed line is a linearfitfor this data. The diamond data

points are for sample 2 with Agfilm ion exchange as thefirst step. The continuous line is a linearfitfor

this data.

Discussion

We report a simple technique to measure the burial depth for buried ion exchange

waveguides. We measured the burial depth as a function of waveguide width for two samples

with two different but commonly used ion exchange processes. We found the burial depth to increase linearly for mask opening widths from 2 to 10 urn. The difference in burial depths for

different waveguide widths can be explained by the effect of the conductivity change in the

waveguide region on the field lines. For slab waveguides the field lines are not affected and the

27
waveguide only results in a small change in the net conductivity of the glass. For a narrow

channel waveguide the field lines are affected resulting in a smaller burial depth as opposed to when the field lines are perpendicular to the surface [4, 5]. Subsequently, in a wider waveguide

the field lines are affected less in the center part of the waveguide and only affected near the

edges of the waveguide which results in a larger burial depth for the wider waveguides compared

to the narrower waveguides. By knowing the burial depths quantitatively as reported in this paper, the loss at the intersection of narrow and wide waveguides can be eliminated by adding a proper taper at the intersection of these waveguides.

References

[1] B. Buchold and E. Voges, "Polarisation insensitive arrayed-waveguide grating

multiplexers with ion-exchanged waveguides in glass," Electron. Lett. 32, pp. 2249-2250,

1996.

[2] P. Poyhonen, S. Honkanen, A. Tervonen, M. Tahkokorpi, J. Albert, "Planar 1/8 splitter

by photoresist masked silver film ion exchange," Electron. Lett. 27, 1319-1320, 1991.

[3] P. Madasamy, G. Nunzi Conti, P. Poyhonen, Y. Hu, M. M. Morrell, D. F. Geraghty, S. Honkanen, N. Peyghambarian, "Waveguide distributed Bragg reflector laser arrays in erbium doped glass made by dry Ag film ion exchange," Opt. Eng. 41, pp. 1084-1086,

May 2002.

[4] D. Cheng, J. Saarinen, H. Saarikoski and A. Tervonen, "Simulation of field assisted ionexchange for glass channel waveguide fabrication: Effect of nonhomogenous timedependent electric conductivity," Opt. Commun. 137, pp. 233-238, 1997.

[5] Jerome Hazart and V. Minier, "Concentration profile calculation for buried ionexchanged channel waveguides in glss using explicit space charge analysis," IEEE

Journal of Quantum Electronics, vol. 37, pp. 606-612, April 2001.

28
Accuracy of MFD and Aeff Measurements using Far-Field Scanning

Arthur J Barlow, Richard Castle, PerkinElmer Optoelectronics, Wokingham RG41 2GY UK

E-mail: arthur.barlow(q)perkinelmer.com

&

Andrew G Hallam, Halcyon Optical Services, Waltham Chase UK S032 2LG

E mail: ahallam@halcyon-optical.co.uk

Abstract:

This paper describes the implementation of a high-accuracy system for the measurement of Mode Field Diameter

(MFD) and Effective Area (Ae ff) in single mode fiber manufacturing environments. Certain engineering details are described, in particular the effect of the light collection angle subtended by the detector. This is examined both

theoretically and experimentally.

Introduction

The measurement of MFD by use of far-field scanning has long been the preferred route to high accuracy and more recently has been standardised by TIA [1], [2] and IEC as the reference test method (RTM). In this paper we

describe some error sources and the engineering issues involved in designing an instrument to be both reliable and

accurate, as well as being fast enough for production measurements. We describe some engineering details that were developed in order to implement a fast, accurate test instrument for use in fiber production environments.

In the far-field method, the test fiber is cleaved and the cleaved end placed at the centre of rotation of a detector placed on a rotating table. In addition the fiber must lie in the plane of rotation of the detector. These apparently easy fiber handling issues require surprisingly high tolerances of fiber positioning [1], [2]. Furthermore, additional

issues such as light scattering can introduce a measurable experimental error [2]. To determine the MFD and Ae ff, the detector is scanned around the fiber end to detect the far field radiation pattern. Prescriptive algorithms set out in FOTP-191 [3] and FOTP-132 [4] describe how to calculate the MFD and Aeff respectively. These were updated in 2001 to cover the newer types of large Ae ff fiber being used in high-power,

high bit-rate optical transmission systems, and throughout this paper we use these latest algorithm including side lobe reversal and noise-based integration limits. A detailed analysis of the tolerances to fiber position [1], [2] reveals that the most critical parameter is the "in-out" (Z axis) position of the fiber end. In essence, the fiber must lie perfectly over the centre of rotation. Further

substantive dependence upon the fiber height (Y axis) and tilt (the fiber must "aim" horizontally at the detector) are

also evident. It is clear that in order to achieve a routine accuracy of MFD below a few percent, that a very precise

fiber positioning system is required. We examine this issue later.

Detector Design

A further parameter, so far not studied in detail in the literature, is that of the angle subtended by the detector at the fiber end (see Figure 1). The light "collection angle", d, is dependent on the radius R of the detector scan, and

the detector size D. With modern fibers, the far-field scanning system must be capable of very high dynamic range

(50dB), and so it is desirable to use a large collection angle, in order to collect more light and help speed up the measurement. Conversely, a small detector will exhibit less noise. This has to be balanced against the angular

resolution requirement of d<0.5 degrees, set by the FOTP's [3], [4]. This requirement stems historically from the

desire for high angular resolution [5]. Furthermore, the detector must be protected from any scattered light [2].

Before setting out on the design of a new instrument, we examine the collection angle dependence. It is important

to understand the effects of deliberately increasing the collection angle in the search for higher dynamic range. We

used some sample data from a standard dispersion-unshifted single mode fiber measured by NPL in London. They

state that their collection angle is 0.4 degrees, and the data is taken at 0.4-degree intervals. To synthesise the effect

29
of larger collection angles, we integrated the raw Intensity-angle data specially provided by NPL [6] over

progressively wider angles, using a rectangular filter method.

\ Detector

Collection

angle, d v

fiber ^s^Z^

R

\

: ___S

Figure 1: detector subtends an angle, d, at the fiber

radian radian

Figure 2: a) Original NPL data (solid line) compared to an effective 2°colIection angle (dashed line), b) Original NPL data (solid line) compared to an effective 3.2° collection angle (dashed line), obtained by

filtering the data. Also shown is the same fiber measured on an instrument with a 3.2° collection angle

(dotted line).

Plots of far-field intensity versus angle for a matched-clad fiber at 1310nm with different amounts of filtering are shown in Figure 2. In Figure 2a), the "depth" of the minima between the main lobe and the first side lobes is reduced, as we would expect. However, a second effect, less obvious and somewhat unexpected, is the weighting of

the data to higher angles. This becomes obvious in Figure 2b, where the collection angle has been deliberately increased to a large value. The smoothing effectively increases the width of the main lobe and thereby reduces the calculated MFD value accordingly. In addition, at the higher angles, and hence lower light levels, the smoothing can assist location of the second minima, in this case at ~ ±0.38 radians. A summary of the MFD and Ae ff values are given in Table 1

.

MFD, urn Aefr, urn

2 NPL unsmoothed 9.16 65.6 NPL 3.2 degree smoothing 8.70 59.1 Measured, 3.2 degree collection angle (Fig 2b) 8.73 59.5 Measured, <0.5 degree collection angle (Fig 5b) 9.14 65.4

Table 1. Summary of smoothing effect on MFD and Acff

In Figure 3, we show the effect of collection angle on the calculated MFD and Aeff values for this fiber at three

different wavelengths. In each case, the data calculated versus collection angle from 0.4 degrees to 6 degrees was

fitted with a third-order polynomial and the intercept at zero inserted into the data set as a synthetic "zero collection angle" data point. This value was taken as the reference point for the percentage deviation shown in Figure 3c) and

3d). Because of the different shapes of Intensity-angle curve for differing fiber types, it is not possible to correct for large collection angles.

30
MFD vs collection angle for NPL data

0 2 4 6

detector collection angle, degree

a) MFD versus collection angle

MFD error vs collection angle for NPL data

-1310mfd

-1550 mfd A 1618 mfd

0 2 4 6

detector collection angle, degree

c) Percentage MFD change with collection angle

Aeff vs collection angle for NPL data

-— 1310 Aeff -*— 1550 Aeff A -1618 Aeff

0 2 4 6

detector collection angle, degree

b) Aeff versus Collection angle

0

-5

-10

-15

-20

-25

-30

Aeff error vs collection angle for NPL data

-—1310 Aeff -*— 1550 Aeff A 1618 Aeff

1

0 2 4 6

detector collection angle, degree

d) Percentage Aeff change with collection angle

Figure 3: the effect of light collection angle on MFD and Acff

These results confirm that to maintain a high accuracy, it is necessary to maintain a collection angle under 0.5 degrees, in accordance with the latest FOTP's. At 0.5 degrees collection angle, the error in MFD and Aeff remains

well under 1%.

Instrument Design

We now turn to the design of a production instrument. The light sources chosen were three high-power fiber- coupler LEDs, centred at 1310, 1550 and 1620 nm respectively, coupled via fiber couplers and a solid-state monochromator to allow the source wavelength to be tunable over the main fiber operating wavebands. To

maximise dynamic range with these sources, the detector size was chosen as 350um to minimise the detector noise. The light sources were chopped and the signal measured using a digital lock-in amplifier. Data was collected by

ADC and computer, which used variable averaging in accordance with the detector signal level.

The detector was placed on a heavy-duty rotation table capable of 0.01 -degree steps and ±55 degrees of travel. The detector was encased in a special assembly designed to reduce the scattered light reaching the detector, consisting of a narrow-bore tube, specially lined to prevent reflections. This ensures only light coming directly from

the fiber end gets to the detector, but careful attention must be paid to the internal surface in order not to artificially increase the light collection angle by virtue of the tube acting as a "light pipe".

The test fiber was placed in a fiber clip and the fiber cleaved using a specially adapted cleaver, whilst still held in the clip. The clip was then transferred to the instrument so that the protruding cleaved end fitted into in a long Vgroove. The V-groove is pre-aligned to the detector in X- and Y-axis directions to allow precise and repeatable

fiber location with very low tilt angles. Although the fiber clip itself is located against an end stop, this is not

31
sufficient to ensure the fiber end is always in the correct Z-axis position, (i.e. directly over the centre of rotation). Instead, the entire V-groove assembly is mounted on a slide driven by stepper motor. A miniature video camera is positioned below the fiber on the axis of rotation so as to display a side-view image of the fiber on a PC monitor. The provision of digital cross hairs on the monitor then allows the fiber end to be precisely aligned over the centre of rotation using the Z-axis stepper motor. The image allows the fiber location and end cleave angle to be

monitored. Figure 5a) shows the overall schematic of the detector area of the instrument with video image. Figure

5b) shows a typical result, obtained on the same fiber that was measured in Figure 2b), but this time with <0.5 degree collection angle, showing excellent agreement with the NPL value (Table 1). In this case, at each step of the

table, both 1310nm (red line) and 1550nm (blue line) sources were selected in turn, using an ultra-fast solid state monochromator, so both wavelengths could be measured in almost the same total measurement time as for one

wavelength. This yields still more improvement in overall speed for production applications.

Fiber

|.;v-.*.>0-.sv: Clip

Stepper motor

V-groove and clip mount assembly

Slide

Lens

JNarrow tube

~j Detector

Rotation table

Camera

Axis of rotation

Figure 5. a) Overall schematic of detector assembly

b) dual wavelength far-field scan taken on instrument,

0.5 degree collection angle

1310 nm = red line, 1550 nm = blue line.

POWER vs. ANGLE

-20 0 20 Angle (degrees)

b)

Wavelength 1 31 O.Onm

MFD : 9.1 35 urn

Aeff : 65.399 um2

NA : O.I 40

Wavelength 1 550. Onm

MFD : 1 0.334 um

Aeff : 01 .1 75 um2

NA : 0.1 A7

Conclusion

We have described the development of a fast and accurate tunable wavelength MFD and Aeff measurement system

(PerkinElmer MA400). It was found that the detector collection angle was a substantial source of error, and must be

limited to less than 0.5 degrees to maintain <1% error. By careful optical design, with fiber location by a V-groove,

and with a video camera to monitor the fiber position, it has been possible to design a production-compatible

instrument which has an overall specified ~+2% accuracy on MFD and ~±4% accuracy on Aeff, with a typical measurement time below 1 minute. Moreover the unit has tunable light source wavelength and dynamic range ~65dB. Scattered light was held to a negligible level by using a narrow entrance tube for the detector. We have shown for the first time that it is possible to implement the RTM (Far-Field Scanning) for MFD and Aeff with variable wavelength and high dynamic range in a production environment.

References

1 . Roger Bighouse, Corning Inc., Private Communication.

2. M. Young., " Mode Field Diameter of Single Mode fiber by Far field scanning", Jnl. Appl. Optics-LP, vol.37,

no..24, 1998,pp5605-5619.

3. TIA FOTP-191 "Measurement of Mode Field Diameter of Single-Mode Optical Fiber"

4. TIA FOTP-132 "Measurement of Effective Area of Single-Mode Optical Fiber"

5. W. T. Anderson at al, "Mode Field Diameter Measurements for Single Mode fibers with Non-Gaussian Field

Profiles" Jnl. Lightwave Technology, LT-5, 1987, pp.21 1-217.

6. The authors are grateful to NPL for providing raw far-field scan data.

32
Mode-Field Diameter and "Spot Size" Measurements of Lensed

and Tapered Specialty Fibers

Jeffrey L. Guttman

PHOTON, inc., 6860 Santa Teresa Blvd., San Jose, CA 95119

Phone: 408-226-1000, FAX: 408-226-1025, e-mail: jguttman@photon-inc.com

Abstract: The Mode-Field Diameter (MFD) and "spot size" of an assortment of lensed and tapered specialty fibers were determined from far-field and near-field measurements. In the far field, measurements were made using a 3Dscanning goniometric radiometer that provides a complete hemispherical profile. Indirect measures of the near field derived from these data are reported, including the Petermann II MFD, the 1/e

2 spot size using the far-field Gaussian

approximation, and a measure obtained from 2D Fourier transform inversion of the far field using phase retrieval techniques. In the near field, direct profile measurements were made using an IR Vidicon camera and magnifying

objective lenses, with the spot size reported as the 1/e

2 diameter of the imaged profile.

1. Introduction

Lensed and Tapered specially fibers are designed to optimize coupling between the fiber and various

optical components such as edge-emitting laser diodes and AWGs. The light from these fibers forms a focus at some

finite distance away from the fiber end. The MFD and corresponding spot size of these fibers is typically in the range of 5 microns or less. These small spot sizes and corresponding high divergence present challenges to near field and far field measurements. Typically the near-field measurements are limited by the optical performance, and the

far-field measures must extend to very large angles. Results of measurements of 6 commercially available fibers are presented, including different type lensed/tapered fibers (4 axially symmetric and 1 elliptical) and a standard singlemode fiber for reference. Also, since the focused beams are in free space, there are some fundamental questions as

to the applicability of the MFD, a measure originally formulated to describe the field distribution within a fiber.

2. Measurement Technique

The fibers were coupled to a stable narrow-linewidth diode laser source operating at a nominal wavelength

of 1 550 nm and output power of approximately 7dBm.

Far-field profiles were obtained using a 3D scanning goniometric radiometer, with optical dynamic range

greater than 60 dB. This instrument provides NIST-traceable measures of MFD to the 0.5% level for single-mode

fiber. The angular measurement range for each scan is ±90°, with sampling every 0.055°. By rotating the source about the scan plane, a full hemispherical measure of the far-field profile is obtained. The 3D profiles for each fiber

in this study consist of 50 azimuthal scans at increments of 3.6° about the fiber axis. Near-field profile measurements were made using an IR Vidicon camera and 2 different magnifying

objective lenses: a 100X NA 0.9 microscope objective intended for use in the visible and a 40X NA 0.48 aspheric

lens designed for the IR. The point-spread function of this lens at 1550 nm is approximately 2.6 urn. The

characteristics of the 100X lens at 1550nm are not known. The fibers were positioned using a high precision 3-axis

translation stage. Absorbing glass filters were used for optical attenuation. The RS-170 camera video images were

acquired using a framegrabber with 8-bit resolution, i.e., 256 levels. Measurement accuracy depends on the camera

noise, sensor response uniformity, the digitization, the number of pixels in the image, and on the optical properties

of the lens used. With adequate pixel count and lens quality, the signal noise and sensor response provide accuracy

to the ±3% level. Accuracy is also strongly dependent on the lens position because of the short depth of focus of

both the lens and the fibers being measured.

3. Measurement Results

Complete hemispherical far-field profiles of the 6 fibers, (designated fibers # 1-6), and the corresponding

ID cross-sectional profiles through the principal axes of the distribution, are shown in figure 1. The background

33
level of the measurements, seen in figure la for the profile of the standard single-mode fiber, is at the -60dB level

relative to the peak. The profiles of the lensed/tapered fibers extend in all cases to ±90°. The profiles for fibers #1-5

have the appearance of a superposition of a main beam and a scatter background, probably due to surface modifications and defects introduced in the fabrication process. The angular extent of the main beam for these

profiles ranges from approximately ±30° for the standard single-mode fiber to greater than ±70° for fiber #5. The

profile for fiber #6, the elliptical fiber, consists of a main beam with a prominent diffraction structure. (Although not shown here, the scatter and diffraction structure extend to angles greater than ±90°, in the backward direction.)

Example images obtained in the near field for fiber #6, the elliptical fiber with the smallest spot size of all the fibers measured here, are shown in figure 2. The profile in figure 2a obtained with the 40X lens is clearly seen to be broadened by the spread function of the lens, and is also near the limit of adequate pixel count.

a.)40X b.)100X

Figure 2. Near field profiles of fiber #6, the elliptical lensed/tapered fiber, obtained with a.) 40X lens and b.) 100X lens. The

horizontal scale in the profile cross sections is 1 um/division.

34
4. Analysis and Discussion

The far field data were analyzed to provide the Petermann II MFD [1], the 1/e

2 diameter from a diffraction- limited Gaussian approximation using the IS07DIS 13694 laser standard fit [2], and the 1/e

2 diameter of the near

field obtained from 2D Fourier analysis with phase retrieval [3-5]. The near field profile data were analyzed to provide the 1/e

2 diameter, using the equivalent scanning slit method. The profile diameters obtained with the 40X

lens were corrected for the spread function width. The MFD for the lensed/tapered fibers depends significantly on the angular integration limit of the Petermann II integral, due to the wide angular extent of the far field. This is shown in the graph of MFD versus the Petermann II integral limit shown in figure 3. The MFD stabilizes for most of the fibers in the range from 40° to 60°. For the elliptical fiber #6 the integration needs to extend beyond 70°. However, the Petermann II formulation has

radial symmetry as an underlying assumption. Therefore, strictly speaking, it is inappropriate to use this MFD

measure for elliptical fibers. Table 1 summarizes the MFD results over the integral limit ranging from 40° to 60°. The fractional percent variation from the average value for fibers #1-5 is well within acceptable limits, and errors associated with the elliptical fiber are quite significant.

MFD vs. Petermann II Integral Angle

—X— #1 Major —X—#1 Minor —a—#2 Major —*—#2 Minor —«— #3 Major —•—#3 Minor —•— #4 Major

« #4 Minor —•—#5 Major

#5 Minor —a—#6 Major

—•—#6 Minor

Petermann II Integral Angle (degrees)

Figure 3. MFD vs. Petermann II integration limit for fibers #1-6.

Table 1. Mode-Field Diameter for Various Angular Limits of the Petermann II Integral

Fiber

Mode-Field Diameter (|j.m)

1 2 3 4 5 6

Integral Limit Major and Minor Axes

40 10.406 10.375 5.069 5.118 4.141 4.154 3.851 3.742 3.478 3.506 2.668 1.920 45 10.395 10.361 5.054 5.104 4.113 4.128 3.842 3.734 3.442 3.476 2.593 1.902 50 10.382 10.345 5.043 5.095 4.100 4.110 3.832 3.725 3.420 3.457 2.391 1.887 55 10.367 10.328 5.034 5.087 4.091 4.100 3.823 3.715 3.405 3.443 2.221 1.873 60 10.352 10.311 5.026 5.081 4.084 4.094 3.814 3.705 3.395 3.434 2.139 1.851 Average 10.380 10.344 5.045 5.097 4.106 4.117 3.832 3.724 3.428 3.463 2.402 1.887 Difference from Average MFD

40 0.2% 0.3% 0.5% 0.4% 0.9% 0.9% 0.5% 0.5% 1.5% 1.2% 11.1% 1 .8%

45 0.1% 0.2% 0.2% 0.1% 0.2% 0.3% 0.3% 0.3% 0.4% 0.4% 7.9% 0.8%

50 0.0% 0.0% 0.0% 0.0% -0.1% -0.2% 0.0% 0.0% -0.2% -0.2% -0.5% 0.0%

55 -0.1% -0.2% -0.2% -0.2% -0.4% -0.4% -0.2% -0.2% -0.7% -0.6% -7.6% -0.7%

60 -0.3% -0.3% -0.4% -0.3% -0.5% -0.6% -0.5% -0.5% -1 .0% -0.8% -1 1 .0% -1.9%

35
The 1/e

2 diameter spot sizes obtained from the far and near field analyses are summarized in Table 2. For any fiber, the diameter reported using the different methods varies significantly, on the order of ±15-20%. This

result is not surprising for these sources. The extremely non-Gaussian shape of the far field makes the Gaussian

approximation highly questionable. Similarly, the very small spot size of the lensed/tapered fibers is at or beyond the performance limits of the optical near-field imaging techniques, and the measured values must undergo significant corrections that increase uncertainty and error. The most accurate method here may be that of the 2D Fourier transform with phase retrieval. It is also observed that these values are overall the most consistent with the MFD

values.

Table 2. Near Field 1/e

2 Diameter Spot Size from Near Field and Far Field Data

Fiber

1/e

2 Diameter (urn)

1 2 3 4 5 6 Method of Analysis Major Axis x Minor Axis

1/e

2 FF Gaussian 11.77x11.77 6.20x6.16 5.07x5.11 3.64x3.51 4.23x4.25 3.62x2.07

1/e

2 NF Profile 100X 10.29x9.71 4.67x4.67 4.37x4.29 4.23x4.09 3.50x3.36 3.58x2.34

1/e

2 NF Profile 40X 9.24x9.03 4.85x4.73 4.24 X4.15 3.79x3.55 4.03x3.79 3.55x2.77 2D FF Fourier Transform 9.94x9.93 5.04x5.03 4.02x4.07 3.60x3.55 3.71x3.30 2.96x1.94

5. Conclusion

Lensed and tapered specialty fibers exhibit wide angular divergence and corresponding small spot sizes. These characteristics pose significant challenges to measurement of MFD and spot size. The results presented

highlight the limitations of standard near-field optical techniques, and the necessity for far-field measurements to include very wide angles. Specifically, for some of the fibers measured here, far-field measurement instruments must acquire data at angles extending to ±60° or greater for accurate determination of the MFD. For near-field measurements using conventional optical techniques, the small spot sizes of these fibers push the limits of resolution and can lead to significant errors. Also, the typically non-Gaussian profiles of lensed and tapered fibers also lend doubts as to the accuracy of Gaussian approximations used to determine spot size. Estimation of spot size using

these methods shows considerable variation. Due to this, and also to ease of measurement, far-field transform

techniques are the preferred method of characterization. For radially symmetric fibers, specification of the Petermann II MFD to characterize the focused beam

yields consistent results and appears to be fine, but due to variation in the integral with angular limit and to avoid

ambiguity, the actual limit used in the calculation should be specified as well as the MFD value. For non-radially

symmetric fibers, use of the Petermann II MFD, although it does provide a measure, is problematic and highly

questionable based on the underlying assumptions of radial symmetry in the Petermann II integral. For such nonradially symmetric fibers, the development of new metrics using 2D Fourier transform methods may provide more

accurate and consistent specifications.

6. Acknowledgements

The author is grateful to David Pikey for his efforts in the implementation of the algorithm for the 2D Fourier transform with phase retrieval.

7. References

1. "Measurement of Mode-Field Diameter of Single-Mode Optical Fiber", Fiberoptic Test Procedure FOTP-191,

Telecommunications Industry Association, Standards and Technology Department, 2500 Wilson Blvd., Suite 300, Arlington,

VA, 22201 (1998).

2. ISO/DIS Standard 13694, "Test methods for laser beam power (energy) density distribution", International Organization for Standardization, September 1998. 3J.R.Fienup, "Reconstruction of an Object from the modulus of its Fourier transform", Optics Letters, Vol. 3, No. 1, pp 27-29,

July 1978.

4. J.R.Fienup, "Phase retrieval algorithms: a comparison", Applied Optics, Vol. 21, No. 15, pp. 2758-2769, August 1982.

5. J.R.Fienup and C.C.Wackermann, "Phase retrieval stagnation problems and solutions", J. Opt. Soc. Am. A, Vol. 3, No.l 1, pp. 1897-1907, November 1986.

36
Anomalies in Online Fibre Measurements and Their Implications

for Fibre Array Manufacture

Law, S. H., Phan, T. N., Barton, G. W. 1

, Barton, M. J. and Elsey, J. Australian Photonics CRC

Optical Fibre Technology Centre, University ofSydney, NSW 2006, Australia 'Department of Chemical Engineering, University of Sydney, NSW 2006, Australia ABSTRACT

V-groove fibre arrays are commonly used in the packaging of high port number devices. As alignment

tolerances must be in the order of 0. 1 micron for single-mode devices to ensure a consistent low insertion

loss across all ports, any misalignments in the array can impact on device yields after packaging. In this paper the variation in cladding diameter along a single fibre is measured using both a laser shadowgraph

technique and video greyscale analysis. It is found that there is significant variation over short length scales within a single fibre sample. This variation also has implications for the filtering of feedback control measurements of fibre diameter in the drawing process.

Keywords: photonics packaging, optical fibre manufacture, optical fibre arrays, optical fibre measurement. INTRODUCTION

Fibre metrology and consistency is becoming an area of increasing concern in photonic packaging. In

particular, the packaging of high port number devices is dependent on the passive alignment of many fibres

in large arrays. Although anomalies in fibre geometry can have a detrimental impact on device yields, this area has received little attention in the literature.

The mnst obvious time to measure fibre diameter variations is during the drawing process before the coating is applied. At this point, physical contact measurements are not possible, so optical techniques are

typically used. Laser shadowgraphs are the most commonly used technique, whereby a laser beam is scanned over the moving fibre. The fibre edges are located as a function of the scanning position allowing

the fibre diameter to be calculated. Unfortunately there is usually a significant amount of noise in these measurements.

Measurements are typically available from a shadowgraph at a rate of up to 1000 Hz, which is faster than can be utilised by the fibre draw tower's control system. Conventionally, the signal is averaged to smooth

out any noise variations and give a stable indication of the mean fibre diameter. Therefore, although the control system only sees the filtered fibre measurements, the question arises as to what the true fibre diameter variation is.

The purpose of the present investigation is to study the accuracy of a laser shadowgraph and to compare its predictions with measurements obtained using the more accurate video greyscale analysis. By

understanding the nature of the true fibre diameter variation, one can then be in a position to select the most

appropriate filtering technique to remove noise while preserving the integrity of the true diameter measurement. ANALYSIS OF NOISE ON THE LASER GAUGE

Static Fibre Measurements

The nature of the noise on the shadowgraph laser gauge was studied using a static length of stripped fibre mounted in the gauge's measurement area. The noise was measured over a range of different positions in the measurement area, and also using a variety of different data acquisition rates. A plot showing the signal as a function of time when the fibre is positioned at the centre of the measurement area is shown in Figure

1. The power spectrum, shown in Figure 3, is reasonably flat over the measured frequency range, indicating

white noise, with a small peak at 50Hz corresponding to the mains power supply. Plotting the data against a normal .r-axis results in a straight line, indicating that the noise is Gaussian with a correlation coefficient of

37
0. 99. The standard deviation of the measurement is 0.1 3um (Figure 2), and there are no outliers so that the

entire signal lies within two standard deviations from the mean.

On-line Fibre Measurements

Figure 4 shows data collected from a fibre draw tower running at 20 m/min using a laser shadowgraph

gauge. The dashed line shows the data collected at 62 Hz. It can be seen that there is rapid variation in the

signal indicating measurement noise. The solid line shows the result of applying an advanced filter of

window size 30 to the signal offline. A simple averaging filter is used online to massage the signal for the control system. Qualitatively, it can be seen that there are a larger number of outliers in the data compared

to the static fibre measurements. This suggests that there might be additional noise introduced due to the movement of the fibre through the shadowgraph gauge (perhaps as a result of vibrations), or that there may

be some significant variation in the fibre diameter over a short length scale. Video Greyscale Analysis

Video greyscale analysis (VGA) is a destructive measurement technique that uses a magnified video image

of the fibre end to measure the cladding diameter, core diameter, core eccentricity and ellipticity. The

precision of the VGA equipment is 0.05um, therefore it was used to ascertain the true variation in fibre diameter over short length scales. One end of a length of fibre to be measured was stripped, cleaved and

placed into the source port of the VGA. The other end was prepared similarly and placed into the measurement port and the cladding diameter of this end was measured. This procedure was repeated by

cutting back approximately 4 cm of the fibre each time. The results from these measurements are shown in Figure 5. It can be seen that there is appreciable variation in the fibre diameter even over these short

lengths. While it is felt that procedural differences may account for some variation in the measurements,

these results indicate that there is a real variation in fibre diameter over short length scales of sufficient magnitude to result in significant core offsets when the fibres are used for making V-groove arrays. IMPLICATIONS FOR V-GROOVE ARRAY MANUFACTURE

Fibre arrays have become a key component in the manufacture of high-channel-count devices. In most

cases they are manufactured by passively aligning fibres from a single roll in undersized V-groove blocks.

In most cases a lid of some sort (V-grooved or flat) is used to try and ensure that the fibres are sitting firmly

in the bottom of the V-grooves. A simple study of the geometry will show that if one of the fibres is anomalously large (by as little as 0.2-0.3 um) it will provide a pivot point for the lidding block (Figure6),

and prevent many of the other fibres from being truly located. This will add significantly both to the average coupling between device and fibres, but also to the channel-to-channel variation [2].

An estimation of the increase in positional error of the end fibre can be obtained by simple triangulation. For an 8-fibre, 250 mm spaced array (as shown in Figure6), if we assume that the upper (clamping) block is resting on the first (normal) and fifth (anomalously large) fibre and that the large fibre is 0.2 um larger than

the normal, then the clamping block will be 1 .75 x 0.2 = 0.35 um above the top of the eighth fibre, and the

potential error in the core position is correspondingly increased. CONCLUSIONS

In this preliminary study the question of fibre diameter measurement and consistency has been raised and

investigated through experiments using a shadowgraph laser gauge and video greyscale analysis. Measurements using the shadowgraph appear to be laced with Gaussian white noise, and significant

outliers. The observed rapid variation in fibre diameter over short lengths may at first glance be attributed

to instrument noise or measurement errors. However, similar diameter variations are also observed when

using the more accurate video greyscale analysis. While procedural errors may contribute to the observed

fibre diameter variations, it appears that there is a significant variation in fibre diameters over short length

scales. Such variations can have a significant impact on array precision for device assembly.

REFERENCES

1 . Anritsu Corporation, SLB DIA Measuring System Instruction Manual, 1988

2. Law, S. H. & Poladian, L., Effect of Waveguide Optical Parameters on Alignment Tolerancesfor Fibre

Attachment, Session 38, Paper 2, 52nd Electronic Components and Technology Conference, San Diego

(2002)

38
12SJr

125.4

124.8 -

124.7 -

124.6

124jl 1 1 . . 1 1 1 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Time (s)

Figure 1: Static fibre readings from the laser gauge.

9000r

8000-

7000

6000

& 5000

S 4000

3000

2000

1000

oL

-0.6 -0.4 -0-2 0 0.2 0.4 0.6 0.8 1 Delation [microns]

Figure 2: Distribution of diameter deviation

readings for a stationary fibre.

5

0

-5 m

io1 -10

-15

-20

) 50 100 150

Frequency [Hz] 200 250

Figure 3: Power Spectral Density of the static readings.

39

Performance characterization of components

with group delay fluctuations

Michael Eiselt, Carl Balslev Clausen, and Robert W. Tkach,

Celion Networks, Inc. One Sheila Drive, Ste 2. Tinton Falls, NJ 07724, USA

Abstract—A variety of components in optical communication systems exhibit group delay fluctuations,

which degrade the quality of transmitted signals. In this paper, we present a method to derive two

independent figure-of-merits, based on the measured group delay, which accurately determines the system performance degradation caused by any type of group delay fluctuations in a component.

I. Introduction

Components in optical communication systems that are of a resonant or reflective nature, will often

exhibit a transfer function with non-negligible ripples or fluctuations in both amplitude and phase. Some

examples are fiber Bragg gratings, ring resonators, and etalons [1-5] which have found use as building

blocks in dispersion compensation modules and add-drop modules, as circulators and interleavers, and

more. It is evidently of interest to be able to determine, from a characterization of the component, the negative impact that the fluctuations have on system performance. Here, we will constrain ourselves to

fluctuatior'S in phase response (for amplitude fluctuations see e.g. [3]). The severity of phase fluctuations

induced by a component is usually specified in terms of the group delay ripple, e.g. as a peak-to-peak

value. However, the system performance degradation from a group delay ripple depends strongly on the period of the ripple [3,4]. A characteristic period may not exist or may not easily be identified from a measured group delay response. Indeed, it was shown in Ref. [5] that performance degradations caused

by measured ripples of four particular fiber Bragg gratings were uncorrelated with the magnitude of

single-period group delay ripples. Therefore, the peak-to-peak group delay ripple is not the most

appropriate parameter to use when specifying component performance.

In this paper, we show with numerical simulations that performance degradations correlate with two

independent parameters that are easily extracted from the measured group delay. The parameters may

thus serve as figure-of-merits in specifications of the phase response of a component.

It is reasonable to expect that group delay fluctuations should have two separate and independent effects. Part of the fluctuations that are at the order of the signal bandwidth will affect the signal spectrum by

imposing an average chromatic dispersion, whereas the remaining fluctuations, which contain higher

order frequency variations, will distort the signal electrical field in a similar way as spectral phase noise

does. The induced average dispersion is unsurprisingly found as a linear fit to the group delay within the

signal bandwidth. A less trivial finding is that the remaining fluctuations cause a system penalty, which is proportional to the variance of the residual phase fluctuation within the signal bandwidth. We will show

the validity of this statement later in the paper. First, we will describe how the figure-of-merits are extracted from an arbitrary group delay spectrum of a given component.

II. CHARACTERIZATION RECIPE

We take as example a dispersion compensating module (DCM). We will assume that the group delay

values, Texp j, have been measured in wavelength steps of AX, e.g., by the modulation phase shift method.

The first step is to obtain the actual, undesired fluctuations, Tfluct,i, that are to be analyzed. This is found

by subtracting the ideal group delay, TideaU, for which the DCM was designed, from the measured group

delay:

41
T — T — T fluct exp (cfeo/ The constant T0 defines an arbitrary fixed group delay. The ideal group delay of the DCM is calculated as

where D(Aq) is the target dispersion at a reference wavelength, Aot and S is the (constant) target dispersion

slope (dD/dA) of the DCM. For this particular example, we have generated , from a numerical model

of a DCM with random group delay fluctuations added to the desired design target. The target dispersion

at 1550 nm was -400 ps/nm, and the target dispersion slope was -8 ps/nm2

. A fixed group delay of -1250

ps and a random group delay of up to ±10 ps was added to the target group delay. Figure 1 (left) shows

both and tfluct over a band of 1 nm. A sliding window, shown as an inset in Figure l(left), centered at wavelength Xc and with the width

^w of the signal bandwidth, is applied to the group delay

fluctuations, Tf\uct. Here we choose a bandwidth of 0.2 nm, which is relevant for, e.g., a 12.5 Gbit/s RZ

signal. At each position, the group delay fluctuations within this window are considered and we extract two numbers: the residual dispersion and the standard deviation of the residual phase.

First, the residual dispersion. A linear function is fit to Tflucl. The coefficients of the linear function

represent a fixed group delay and the residual dispersion at Ac. The dotted line in the inset of Figure

1 (left) depicts the curve fit. If the curve fit can be written as Tf„= cti(ArAo)+a0, then the residual dispersion

at the considered wavelength is the linear fit parameter: Dres =ai. In the example, the fit parameter ai yields a residual dispersion of 55.6 ps/nm.

" 1(?544 1546 1548 1550 1552 1554 1556 1558 1560

wavelength [nm]

1546.2 1546.4 1546.6 wavelength (nm)

1546.8 1547

0.1

0.08

0.06

L0.04

0.02

0

(b>

1544 1546 1548 1550 1552 1554 1556 1558 1560

wavelength [nm]

Figure 1: Left figure: Measured (xexp) group delay versus wavelength and the fluctuating part

Camlet)- Inset: Group delays in window of 0.2 nm. Dashed line is residual phase fluctuation. Right

figure: (a) Residual dispersion in sliding window, and (b) standard deviation of residual phase

fluctuation in sliding window over the full bandwidth of the DCM.

Secondly, the standard deviation of the residual phase. The dashed line in the inset of Figure l(left) is the residual group delay ripple, Tres , after the linear fit (the dispersion offset and the fixed group delay)

has been subtracted. It represents the high frequency part of the DCM induced group delay fluctuations

as opposed to the average dispersion. The phase fluctuation in the window is derived from the measured

group delay by integrating within the window, the residual group delay over frequency,

"XI A/=Ac-Aivindow/2 The term (KqIc) equals 8 ps-nm around 1550 nm. A linear curve fit to the residual phase, representing

a phase and delay offset, is then subtracted from the residual phase.

Ores (4 ) = <Pres Ui ) " <P\ U: " K ) " %> yielding the pure, residual phase fluctuation, 6res . The constants, <p0 and q>i are the linear fit parameters to

42
(Pres within the window. Finally, we can then calculate the standard deviation, cfo of 6res . In the example

of the window inset in Figure 1 we find <7e to be 28 mrad.

The procedure described above yields the two numbers Dres and oe for a given position of the window.

These are the figure-of-merits that determine the impact on system performance resulting from group

delay fluctuations. Figure 1 (right) shows the values of Dres and oe as the window is moved across the usable bandwidth of the DCM. The maximum values of Dres and o$ are seen to be about ±60 ps/nm and

about 60 mrad, respectively. In order to obtain a statistical measure of Dres and ag we can calculate their average v;.lue and standard deviation. For the example, we find the average residual dispersion to be

0.1 ps/nm and the standard deviation of the residual dispersion to be 23 ps/nm. Likewise, the average

value and the standard deviation of cr^is 34 mrad and 8 mrad, respectively.

The figure-of-merits for the residual dispersion and the residual phase fluctuations in the DCM are based on their impact on the system performance.

When a component with residual dispersion is located inline it will disturb the dispersion map of the system. The performance penalty for disturbing the dispersion map is inherently system dependent. If the system is very nonlinear, the signals may be more tolerant to a residual dispersion, due to nonlinear self- trapping, than if the system is linear. On the other hand, if the system is linear, the accumulated residual

dispersion can be compensated at the receiver. However, since each channel experiences a random

residual dispersion offset, this requires per-channel dispersion compensation. In a specification of the

residual dispersion it is reasonable to specify a maximum value just as a DCM is specified with a tolerance for an offset relative to the target dispersion. Therefore, we propose that the figure-of-merit

characterizing the residual dispersion in the component should be based on the maximum value of the

residual dispersion within the bandwidth of the component.

The impact of the residual phase fluctuation does not depend on the dispersion map or nonlinear

propagation effects. We have performed numerical simulations of a system composed of 100 spans of

NZDSF. A single RZ channel was propagated at a bitrate of 12.5 GHz. After each span a DCM provided

chromatic dispersion compensation with 12 ps/nm under-compensation, and an erbium doped fiber amplifier compensated the fiber loss. The channel power was 1 dBm, which makes nonlinear propagation

effects very visible after 100 spans. We added 100 phase fluctuations either inline at every DCM, or concatenated at the receiver. The phase fluctuations in the y'th DCM were based on the following group

delay ripple:

where App

is the peak to peak group delay amplitude ripple, AX is the offset from some center wavelength, Xp is the period of the ripple, and ^ is the phase of the ripple. In simulations we kept the amplitude and period the same in all 100 ripples, whereas the phases, z^, were random. Also, an amount

of dispersion was added to each fluctuation such that the residual dispersion was zero. The simulation

results are shown in Figure 2(a). The dashed line shows the penalty versus group delay ripple period for the case when all ripples are concatenated at the receiver. The solid line shows the performance penalty

when the group delay ripples are added inline at every DCM. Since they are approximately equal, the impact of residual phase fluctuations can be investigated by simulating a single instance of fluctuations at the receiver. The phase fluctuation distorts the signal electrical field and therefore depends on the

particular shape of the pulses and the signal quality. We have found that it is generally valid that the impact is proportional to ai. In Figure 2(b) we show the performance penalty for various ripple periods

together with the function: Penalty=48(j/. The proportionality constant of 48 is specific to the particular

pulse shapes and other signal distortions that have occurred in the particular system we simulated.

III. System penalty

43
Figure 2: Q-penalty for a system with perfectly periodic group delay fluctuations. Period of ripple

is Xp. Magnitude of group delay ripple, App, is 42ps for all ripple periods. Solid line: Fluctuations

added at every span. Dashed line: Fluctuations are added at the receiver. Dotted line: Estimate of

penalty from the scaling: AQ = -48<r/.

Most group delay fluctuations are not perfectly periodic. We have therefore made simulations with group

delay fluctuations that are generated from random numbers. Figure 3(a) shows the results from

simulations of the 100-span system. The random fluctuations are added at the receiver. The impact is seen to follow a scaling of AQ = -48cr<?

2

, which is indicated by the dashed curve. Figure 3(b) shows the induced dispersion (calculated as a change in optimum post-dispersion) versus the residual dispersion as calculated from the group delay fluctuations.

Figure 3: Random group delay fluctuations, (a) Q-penalty versus standard deviation of residual

phase fluctuation, (b) Change in optimum post-dispersion versus residual dispersion.

When many instances of fluctuations are concatenated, they will accumulate in a random, linear way. We

therefore propose that the figure -of-merit for the high-frequency phase fluctuations be based on the mean

value of <7#. In summary, we have proposed a method to characterize components with group delay

fluctuations. We have shown that two numbers, the residual dispersion, Dres , and the standard deviation

of the residual phase ripple, cr& determines the system impact.

References

[1] C. K. Madsen, G. Lenz, A.J. Bruce, M.A. Capuzzo, L.T. Gomez, and R.E. Scotti, IEEE Photon.

Techn. Lett., vol. 11, pp. 1623-1625, 1999.

[2] F. Oullette, Opt. Lett., vol. 12, pp. 847-849, 1987.

[3] K. Ennser, M. Ibsen, M. Durkin, and M.N. Zervas, IEEE Photon. Techn. Lett., vol. 10, pp. 1476-

1478, 1998.

[4] B.J. Eggleton, A. Ahuja, P.S. Westbrook, J.A. Rogers, P. Kuo, T.N. Nielsen, and B. Mikkelsen, vol. 18, pp. 1418-1432, 2000.

[5] S. Jamal and J. C. Cartledge, J. Lightwave Technol, vol. 20, pp. 28-35 (2002).

44
High-resolution group delay measurements

of a hydrogen cyanide gas cell using low-coherence interferometry

Shellee D. Dyer, R. Joseph Espejo, and Paul A. Williams

National Institute ofStandards and Technology

Optoelectronics Division

325 Broadway, Boulder, CO 80305 USA

sdyer@boulder. nist.gov

Abstract: We demonstrate interferometric measurements of the relative group delay of a hydrogen cyanide gas cell with group-delay resolution of 0.3 ps at a wavelength resolution of 6

pm. We use simulations and measured data to illustrate the tradeoffs between group-delay

resolution and wavelength resolution.

1. Introduction

Low-coherence interferometry is a fast and accurate method to measure the relative group delay

(RGD) and spectral reflectance or transmittance of optical components. We have previously

demonstrated repeatability better than 1 ps, and agreement with an independent measurement

better than 1.5 ps [1].

In this paper we present high-resolution interferometric measurements of the RGD of a gas cell containing hydrogen cyanide (H 13 C

14N) at a pressure of 13 kPa (100 Torr). Hydrogen cyanide

has more than 50 strong absorption lines in the optical-communications C-band, making it very

useful as a wavelength-reference artifact [2]. We chose to measure the relative group delay of a hydrogen cyanide cell for several reasons.

First, the RGD of the cell can be predicted from a measurement of the cell's transmittance profile

using the Kramers-Kronig relationship [3,4]. This predicted RGD is a valuable reference for

estimating the uncertainty of our measurement. Also, the absorption lines of our hydrogen

cyanide cell are very narrow (<1 00 pm), and therefore the group delay features are very narrow

as well (<50 pm). The RGD of our hydrogen cyanide cell also includes weak hot-band lines,

which are less than 2 ps deep. Therefore, an accurate measurement of the cell's RGD including

the hot-band lines can be achieved only with a measurement system that has sub-picosecond

RGD resolution and a wavelength resolution on the order of picometers. Thus, our hydrogen

cyanide cell measurements will demonstrate the high-resolution capabilities of our

interferometric measurement system. Additionally, the peak absorption wavelengths of the cell are well characterized; therefore, we can determine the absolute wavelength accuracy of our measurement system through a comparison with the NIST-certified absorption wavelengths of

the cell. The final reason for measuring the cell's RGD is that the hydrogen cyanide cell might

be applied in the future as an artifact for calibrating RGD measurement systems.

We have also created a simulation program to model the tradeoffs between wavelength

resolution and RGD resolution. These tradeoffs are an important issue, regardless of the RGD

measurement technique used, and wavelength and RGD resolution should always be specified

together. Specifying an RGD resolution is meaningless unless the corresponding wavelength

resolution of the measurement system is also specified.

45
2. Experiment

Our RGD measurement system is shown in Fig. 1. An erbium fiber superfluorescent source (BBS) provides our low-coherence signal. Our system consists of a fiber-optic Mach-Zehnder

interferometer with the hydrogen cyanide cell (DUT) placed in one arm of the interferometer.

We include a variable-length air path in the other arm of the interferometer, so that the total optical path difference (OPD) of the interferometer can be adjusted. At the output of the

interferometer, two detectors (Dl and D2) receive two 1550 nm fringe signals that are 180° out

of phase but have similar noise characteristics. By directing these two signals to a difference

amplifier, we are able to reduce significantly the noise on our interference signal. We use a 1300

nm Nd:YAG laser (RL) to monitor the OPD as the translation stage moves. The interference

signal created by the 1300 nm laser light is separated from the 1550 nm signal using a wavelength-division multiplexer, and the 1300 nm signal is sent to a zero-crossing detector

circuit. This circuit triggers the A/D card sampling of the difference amplifier's output at every

zero crossing of the 1300 nm interference signal. This gives a sampling rate of approximately

2.4 samples per 1550 nm fringe. This system is a significant improvement over our previous

low-coherence interferometric system. The reference laser signal now travels in the same fiber as the broadband signal, virtually eliminating the large wavelength uncertainty that occurs when

the two signals do not travel exactly the same path. Through improved electronics, we have also

significantly increased the signal-to-noise ratio (SNR) of our system compared with our previous

system (42.2 dB compared to 32 dB).

A/D -- Computer

TRIG

Figure 1. Diagram of the low-coherence interferometer used to measure the RGD of optical components. A/D:

analog-to-digital board, AR: antireflection endface, BBS: broadband source, D1,D2: 1550 nm signal detectors,

DUT: device under test, L: lens, M: mirror, PC: polarization controller, RD: detectorfor 1300 nm reference signal, RL: 1300 nm reference laser, TS: translation stage, WDM: 1300/1550 nm wavelength-division multiplexer, WFC:

wavelength-flattened coupler, ZCC: zero-crossing detector circuit, A: difference amplifier.

To determine the RGD of our hydrogen cyanide cell, we first measure the 1550 nm interference

signal as a function of OPD. We then calculate the Fourier transform of the interference signal,

and separate the result into magnitude and phase. To calculate the RGD, we differentiate the

phase of the Fourier transform with respect to wavenumber [1]. We determined the RGD of our hydrogen cyanide cell from the average of five independent

measurements of the interferogram. Each measurement consists of 600,000 data points. The

result is shown in Fig. 2, along with the RGD calculated directly from a measurement of the

transmission of the gas cell using the Kramers-Kronig relations [4]. The standard deviation of

46
the difference between our measured data and the Kramers-Kronig result is less than 0.3 ps, and

the wavelength resolution is approximately 6 pm, as determined from the following formula:

NXr where AX is the wavelength resolution, N is the total number of data points that are included in

the interferogram, Xr is the reference laser wavelength, and Xs is the wavelength of the lowcoherence signal. This formula is derived from the fact that the resolution of a discrete Fourier

transform is inversely proportional to the product of the number of data points and the sampling

interval [5].

3. Wavelength resolution and RGD resolution

We analyze the

tradeoffs between

wavelength and RGD

resolution using a simulation program.

Our simulation program

starts from a measurement of the

transmission of just one

absorption line (PI 6) as

a function of

wavelength. Using the

Kramers-Kronig

relation, we calculate

the complex refractive

index of the gas cell [4]. Combining the complex

refractive index with a

i T" r

LCI KK

1554.4 1554.6 Wavelength (nm)1554.8 1555

Figure 2. Plot ofrelative group-delay results as afunction ofwavelength.

LCI=Low-coherence interferometric measurement results (average offive measurements); KK=Kramers-Kronig calculation.

measurement of our low-coherence source spectrum, we perform a Fourier transform to create a simulated interferogram. We add Gaussian random noise to the simulated interferogram to model the effects of noise in our experiment. The standard deviation of the Gaussian random

noise was determined from the desired SNR. We quantize the result to simulate the discrete

effects of our analog-to-digital (A/D) board, and truncate the interferogram to model the effects

of interferogram length. We then calculate the group delay by taking a Fourier transform of our

simulated, truncated interferogram and differentiating the phase. Comparing our simulation

RGD results to the RGD predicted directly from the Kramers-Kronig calculation, we calculate

the standard deviation of the difference between the two signals over a portion of the spectrum

where the RGD is expected to be flat. The results are shown in Fig. 3, where the standard

deviation between the two RGD results is shown as a function of wavelength resolution for three

different values of SNR.

In Fig. 3, we also show our results for the standard deviation between measured RGD data and

the Kramers-Kronig RGD for several different SNRs. We varied our experimental SNR by

adjusting the polarization controller shown in Fig. 1 to reduce the total fringe visibility. We

could not directly determine the time-domain SNR of our measured data because the interference

47
signal created by a narrow absorption line extends to very large OPD. Therefore, we determined

the frequency-domain SNR of our measured data from a Fourier transform of the interferogram

[6]. Using our simulations, we derived a linear relationship between time-domain SNR and

frequency-domain SNR, and we used that linear relationship to convert the frequency-domain

SNRs of our measured data to equivalent time-domain SNRs.

The wavelength

resolution of our measurement is inversely

proportional to the total length of the truncated

interferogram. Thus,

longer interferograms

give finer wavelength

resolution, but they also

include more noise, and

that noise degrades the

group-delay resolution.

The limiting factor is the

experimental SNR; with

higher SNR, both the

wavelength resolution

and RGD resolution can be improved.

4. Conclusions

We have demonstrated high-resolution interferometric measurements of the RGD of a hydrogen

cyanide gas cell. When compared to a Kramers-Kronig prediction of RGD, our results have a

0.3 ps resolution at a wavelength resolution of 6 pm. We used simulations and measured data to

illustrate the tradeoffs between group delay resolution and wavelength resolution.

Acknowledgements: The authors thank Tasshi Dennis of NIST for supplying the measured

absorptioj data and Kramers-Kronig calculation routine.

References

[1] S.D. Dyer, and K.B. Rochford, "Low-coherence interferometric measurements of the dispersion of multiple fiber Bragg gratings," IEEE Photon. Technol. Lett., vol. 13, pp. 230-232, 2001.

[2] S.L. Gilbert, W.C. Swann, and CM. Wang, "Hydrogen cyanide H

13 C

14N absorption reference for 1530-1560 nm

wavelength calibration - SRM 2519," Natl. Inst. Stnd. Technol. Spec. Publ. 260-137, 1998.

[3] A. Motamedi, B. Szafraniec, P. Robrish, and D. M. Baney, "Group delay reference artifact based on molecular

gas absorption," in Optical Fiber Communications Conference Technical Digest, ThC8-l, 2001.

[4] T. Dennis and P.A. Williams, "Relative group delay measurements with 0.3 ps resolution: toward 40 Gbit/s

component metrology," in Optical Fiber Communications Conference Technical Digest, pp. 255-256, 2002.

[5] E. O. Brigham, The fast Fourier transform and its applications, (Prentice Hall, Upper Saddle River, NJ, 1988),

pp. 170-172.

[6] R.J. Bell, Introduction to Fourier transform spectroscopy, (Academic Press, Inc., San Diego, CA, 1972) pp. 7-9.

Wavelength Resolution (pm)

Figure 3. Plot ofgroup delay resolution as afunction ofwavelength resolution

for three different SNRs with no averaging. The solid lines are simulation

results, and the data points are experimental results. Averaging multiple measurements will improve the group delay resolution by approximately -Jm , where m is the number ofmeasurements.

48
Group delay and spectral response of free space optics

Mux/Demux measurement using OLCR

X. Chapeleau^1 ' 2

), D. Leduc^, C. Lupi^, R. Le NyW and C. BoisrobertW

(^L.P.I.O., Universite de Nantes, 2 rue de la Houssiniere, 44300 Nantes, France.

( 2)NetTest, 45 avenue Jean Jaures, 78433 Les Clayes, France.

xavier.chapeleau@physique.univ-nantes.fr

ABSTRACT

A complete characterization of the spectral response and group delay of a free space optics

Mux/Demux is performed using Optical Low Coherence Refiectometry. OLCR allows for fast and accurate measurements and shows the similarity of the responses of the different channels.

1 INTRODUCTION

Recent advances in DWDM system designs have led to a significant increase of the number of

wavelengths in a single fiber. As network architects start to apply DWDM to regional and metro

networks, high performance characteristics for mux/demux (weak insertion and polarizationdependent loss, low group delay responses,. .

. ) are needed. Accurate measurements of these

characteristics become also necessary [1,2]. In this paper, we focus on the determination of

the passband and group delay of a free space optic Mux/Demux and show that the optical lowcoherence refiectometry is an efficient method for this kind of measurements.

2 EXPERIMENTAL SETUP

The optical system is a Michelson single mode fiber-interferometer lined up around a two by

two coupler (fig. 1). The broadband infrared light source is 1.5 fim amplified spontaneous

emission fiber source. The sample under test is connected to the test arm fiber. The wave

propagating along the reference arm is collimated at the output of reference arm fiber on a

parabolic gold mirror, reflected and folded on an airborne sliding corner cube and reflected on

a fixed plane mirror back to the coupler. The optical path length is known with a high accuracy

using a frequency stabilized HeNe fringe counter. When the comer-cube carriage slides along the rail, the infrared interferogrammes are detected

by the InGaAs-PIN photoreceiver and sampled by the red fringe counter signal trigger. It can

be shown [3] that they are the inverse Fourier transform of a function 1(a) :

7^)=r(a) 5(a) exp[t 0(a)] (1)

where r(a) is the reflection coefficient of the propagation defect, 5(a) is the source optical

49
Figure 1 : Experimental device

spectrum filtered by the system optical elements and (f>(a) is the phase difference between

the two waves interfering on the photodetector. These quantities can be easily obtained from

the interferogramme Fourier transforms. The phase <E>(cr) of this transform can then be used

to calculate the group delay rg and the chromatic dispersion Da of the component from the

following relations :

A

2 d&{&)

4ttc' d\

and D<A

> = §

1

4-kc

2X

Tx

+x lv (2)

Thus, a single measurement gives the reflection coefficient and the group delay of the component vs wavelength inside the source bandwidth.

3 CHARACTERIZATION OF A FREE SPACE OPTICS MUX/DEMUX

The devices under test are NetTest commercial products using bulk gratings in a free space

optics configuration to separate wavelengths [4]. The first sample is a 16 channels mux/demux.

Figure 2a shows the measured normalized spectral responses of the first height channels. The

peaks seem to be regularly spaced. This is confirmed by the "+" curve of the figure 2b, which

represents the central wavelengths versus the channel number. The crosses are perfectly aligned

and the linear fit gives a spacing equal to 800 pm between adjacent peaks. The difference

between the measured central wavelengths and the constructor values is smaller than 1 0 pm for

all channels except for 3 ones and remains always below 25 pm.

The similarity of the peaks shape can be observed on figure 2a. This appears clearly on figure

3a where the spectral responses of all the channels are plotted versus the wavelength detuning

(ie the difference, for each channel, between the wavelength and the central wavelength of the

channel). The different curves are hardly dinstinguishable and a non linear fit shows that all

50
the peaks have the same gaussian shape. Their -1 dB bandwidths are almost the same (see the

squares on figure 2b) and are close to 230 pm.

Figure 3b shows the relative group delays of all the channels versus wavelength detuning. The

curves have almost the same shape. They are slightly decreasing inside the bandwidth, but the

relative group delay variations remain small and lower than 0.2 ps.

1.00

-0.4

0.15

-0.2 0.0 0.2 Detuning (nm)

0.4 0.20

-0.05 0.00 0.05 Detuning (nm)

0.10

(a) (b)

Figure 3: Normalized responses and group delays of all the channels.

We also present on figure 4 the special cases of channels Jjl, JJ5, ftlO and JJ15. The dotted curves correspond to the chromatic dispersion. As for spectral response and group delay, this

characteristic is almost the same for all the channels. Its absolute value is less than 2 ps/nm

inside the -1 dB bandwidth. This result remains valid for the other channels.

51
-0.15 1548.480 1548.520 1548.560 1548.600

Wavelength (nm)

(a)

-2.1 w -o.i i ' 1 1 ' ' -2.2 1551.680 1551.720 1551.760 1551.800 1551.840 Wavelength (nm)

(b)

1555.680 1555.720 1555.760 Wavelength (nm)

(C)

2.2 U

1555.800 1555.840 1559.760 1559.800 1559.840 1559.880 1559.920

Wavelength (nm)

(d)

Figure 4: Group delay (straight lines) and chromatic dispersion (dotted lines) in the -1 dB bandwidth of

(a) channel tfl (b) channel Jj5, (c) channel (J 10 and (d) channel (J15.

4 CONCLUSION

OLCR is a very useful and fast method for characterizing optical Mux/Demux : one single

measurement gives both spectral response and relative group delay of the component with

high accuracy. In this paper we reported on the full characterization in terms of spectral re- sponse, group delay and chromatic dispersion of a 1 6 channels free space optics Mux/Demux

and showed its homogeneity.

References

[1] G.D. Maxwell M.E. Vieira Segatto and R. Kashyap. Optics Communications 195, pages

151-157, Aug. 2001.

[2] A.H. Rose, C. M. Wang, and S. D. Dyer. J. Res.Natl. Inst. Stand. Technol., 105:839-866,

2000.

[3] C. Lupi. PhD thesis, University of Nantes, Sept 2001.

[4] B. Chassagne, K. Aubry, A. Rocher, B. Herbette, V. Dentan, S. Bourzeix, and R Martin.

ECOC'01, 2001.

52
High accuracy relative group delay measurements of a

chirped grating (NIST Telecom Round Robin)

X. Chapeleau(1 \ D. Leduc^, M. Wicks^, R. Le NyW and C. Boisrobert (1 >

(l)LPIO University of Nantes

2 rue de la Houssiniere 44300 Nantes

Xavier.Chapeleau@physique.univ-nantes.fr

Tel: (33) 02 51 12 55 46 Fax: (33) 02 40 14 09 87

(2) National Physical Laboratory (NPL), UK

Abstract

In this paper, we bring more results obtained on a chirped grating submitted to Round Robin tests. We

confirm that the relative group delay can be accurately measured with optical low coherence reflectometry.

Introduction

WDM telecommunications systems require more and more high-performance components like fiber gratings and mux/demux. The relative group delay (RGD) must be known with high accuracy. In June 1999,

NIST launched the first round robin measurements of optical fiber Bragg gratings, called "telecom round

robin". Its purpose was to compare different measurements methods of RGD. The NIST members A.H.

Rose, CM. Wang and S.D. Dyer analysed the results obtained by all participants and synthetized them

in a report entitled "Round Robin for Optical Fiber Bragg Grating metrology" [1]. They considered

optical low coherence reflectometry (OLCR) as one of the RGD measurements technique and showed

results obtained by this method. In order to bring more results, we have analysed the chirped grating of NIST telecom round robin using our OLCR experimental set-up. In this paper, we present our results outline their precision.

Experimental set-up

The experimental set-up [2] is a Michelson interferometer assembled around a "2x2" single mode fiber coupler and a broad spectrum C-band light source. The device under test (DUT) is connected to the

test arm. In the reference arm, a moving reflector vary the optical path. The photodetector detects interferogramms which are representative of the DUT. These signals are sampled using a frequency

stabilized laser He-Ne fringe counter to ensure accurate sample spacing.

We can demonstrate that the intensity received by the detector is a function of Ax the distance

of the reflector to the optical path balance and can be written as [3] [4] : /+oo

r{a)S{<T)j*^ e-"*±*n~r» da (1)

-oo

where S(a) is the power spectral density of the source, r(a) is the amplitude reflection coefficient of the

sample under test and $(<r) is the phase shift that it causes. This last relation means that the phase

shift can ba computed from the inverse Fourier transform of the interferogram. We can then calculate the group delay rg of the component with the help of the following relation :

A

2 d*{a)

T

° = -^-c-d)T (2)

The reflection coefficient and the group delay of the component vs wavelength can therefore be derived

from a single measurement into the source spectrum.

53
Characterization of a chirped grating

Relative reflectance

The comp( nent under test has two ports, labelled #1 and #2, connected to either end of the grating. The

figures 1(a) and 1(b) show the relative reflectance vs wavelength for the ports #1 and #2 respectively.

Ten successive results have been plotted on the same graph. We can see a spectral "window" with a

width of about 16 nm. The top of these two curves presents some ripples feature of a chirped grating.

The figures 2(a) and 2(b) show the relative reflectance vs wavelength into the -20 db bandwidth

respectively for the ports #1 and #2. We clearly observe that the spectrum is different in accordance

with the direction of the measurement. This demonstrates that a chirped grating is a non-reciprocal

component.

1535 1540 1545 1550 1555 1560 1565 1535 1540 1545 1550 1555 1560 1565 Wavelength (nm) Wavelength (nm)

(a) Port #1 (b) Port #2

Figure 1: Relative reflectance of the chirped grating

i

i i i i i i [ i 1540 1542 1544 1546 1548 1550 1552 1554 1556 1558 1560 156 Wavelength (nm)

1540 1542 1544 1546 1548 1550 1552 1554 1556 1558 1560 156: Wavelength (nm)

(a) Port #1 (b) Port #2

Figure 2: Relative reflectance of the chirped grating into the -20 dB bandwidth

Relative group delay

The figures 3(a) and 3(b) show ten plots corresponding to successive measurements of the RGD respectively for the ports #1 and #2. We can see that the group delay varies linearly vs wavelength of about

100 ps between 1554 and 1558 nm. Moreover, ripples appear on the group delay curves. These results are in good agreement with those reported by NIST [1] [5]. We can also see on the figures 4(a) and 4(b),

54
that the ten RGD measurements are very well superimposed on one another for the two ports. This

demonstrates the high-precision of our measurements.

1540 1542 1544 1546 1548 1550 1552 1554 1556 1558 1560 156 Wavelength (nm) Wavelength (nm)

(a) Port #1 (b) Port #2

Figure 3: Relative groupe delay of the chirped grating into the -20 dB bandwidth

S

"32

- fr\

\ : / \

/'

1551.4 1551.6 Wavelength (nm)

1S51.4 1551.6 Wavelength (nm)

(a) Port #1 (b) Port #2

Figure 4: Relative groupe delay of the chirped grating between 1551 and 1552 nm

Precision of the relative group delay

We have calculated the group delay deviation from the mean value for each measurement in order to estimate the precision of our results. The figures 5(a) and 6(a) show this deviation vs wavelength for the

ports #1 and #2 respectively and the figures 5(b) and 6(b) their distribution. We can see on these last figures that the distribution follows the normal law and the precision of our measurements is about 0.5 ps for the two ports.

(a) Deviation from the mean relative group delay (b) Distribution of the deviation from the mean rela- tive group delay

Figure 5: Precision of relative group delay for the port # 2 into the -5 dB bandwidth

55
(a) Deviation from the mean relative group delay (b) Distribution of the deviation from the mean rela- tive group delay

Figure 6: Precision of relative group delay for the port # 2 into the -5 dB bandwidth

Residual RGD linear fit

The significant parameters of the RGD are the linear slope across the operating bandwidth of the grating

and the ripple magnitude. We have used a linear fit and found a mean slope of -6.63 ± 0.14 ps/nm (k=2)

for the ten measurements. For each one, we have superimposed the residual RGD linear fit on the figure

7.

1550 1552 1554 Wavelength (nm)

1550 1552 1554 Wavelength (nm)

Conclusion

(a) Port #1 (b) Port #2

Figure 7: Residual RGD linear fit of the chirped grating

In this paper, we have presented the relative reflectance and the relative group delay measurements for the ports #1 and #2. The results we obtained with our experimental system are reproducible and in good agreement with those reported by NIST. This study has been realized within the framework of the

COST 265 action. References

[1] A.H. Rose, C. M. Wang, and S. D. Dyer. Round robin for optical fiber bragg grating metrology. J. Res. Natl. Inst. Stand. Technol, 105:839-866, 2000.

[2] C. Lupi, D. Leduc, X. Chapeleau, R. Le Ny, J. L. Goudard, and C. Boisrobert. Measurements of resonant dispersion in short length er3+ doped fibers. ECOC'01, Amsterdam, 2001.

[3] C. Lupi. Realisation et mise au point d'un banc de reflectometrie optique a faible coherence: etude de

fiabilite et caracterisation de fibres optiques passives et actives et de divers composants. PhD thesis,

University of Nantes, Sept 2001.

[4] S. Dyer and B. Rochford. A fast and accurate measurement of both transmission and reflection group

delay in fiber bragg gratings. Optical Fiber Communication Conf. (OFC'01), pages 169-172, Mar.

2001.

[5] M. Wicks, T. Niemi, M. Wegmuller, H. de Riedmatten, and N. Gisin. Preliminary results of a european

intercomparaison of group delay measurements of fibre bragg gratings. OFMC'01, Cambridge, 2001.

56
Direct Dispersion Slope Measurement by Mach-Zehnder

Interferometer on Short Length Optical Fibre

Y. C. Zhao, S. Fleming

Australian Photonics CRC, Optical Fibre Technology Centre

University of Sydney, NSW, Australia

Tel: +61 02 9351 1939, Fax: +61 02 9351 1911

y.zhao@oftc.usyd.edu.au

Abstract: We propose and demonstrate a new direct method of second order dispersion

measurement by determining the second symmetric interferometric fringe pattern. This

measurement was performed with a Mach-Zehnder interferometer, a broadband LED and

an optical spectrum analyser. We experimentally measured the dispersion and dispersion

slope directly over an ultra-broad wavelength range of a short length of dispersion shifted

fibre. Experimental results show close agreement with theoretical results.

1. Introduction

Application of new functional optical waveguide devices requires accurate knowledge of chromatic

dispersion slope as well as dispersion. Many techniques have been developed for dispersion measurement.

Conventional optical fibre dispersion measurements include the time of flight method and the phase shift method [1,2]. The time of flight technique injects different wavelengths into the test fibre where time delays

through the test fibre are compared with a reference fibre. The phase shift technique measures phase delay as

a function of wavelength. Both methods calculate chromatic dispersion curves from the derivative of the

fitted polynomial time delay curves. Despite the importance of dispersion slope, it cannot be measured

directly from these two techniques. It can only be derived by successive derivatives of the group delay

spectrum. Shang first proposed the elegant white light interferometric method to measure optical fibre dispersion [3]. Stone and Marcuse first proposed a method based on white light interferometry to directly measure the dispersion coefficients by solving three simultaneous equations obtained from interferometric

fringes [4]. Based on a Mach-Zehnder interferometer, we propose a new method to directly measure second

order dispersion by determining the second symmetric interferometric fringe pattern position.

2. Theory

Based on a Mach-Zehnder interferometric scheme, the electric field of the two beams will superpose at the output point. Interference, which depends on the amplitude components and on the phase difference, will take place and maximize when the optical path lengths are equal. Due to chromatic dispersion, different wavelength components of the broadband light will propagate through the fibre with different time delay.

The reference path time delay is varied to match the time delay of each wavelength of interest so that interference fringes can be observed in the optical spectrum. The output interference fringe pattern of the combined beams can be expressed following the general approach of Tateda [5] and Shang [3]

* A- A, ^ /(A)^2V/1 (A)-/2 (A)[7 cos(fi)]cosL0 -^jr(A) - ncLD(XT (1)

-^M'(Ar )-4D(Ar )] r

where ! l (X),f2 (X) are the intensities of the two arms; J is visibility, Q is the angle between the polarization

directions of the two arms, L is the test fibre length, Z)(AT

) and D'{Xr ) are dispersion and dispersion slope at

'Our analysis agrees with Shang to equation (3) in Ref. 3 for I(co) , however it diverges for /(A) where we believe that the correct form is as above which differs in a sign and a factor of 2.

57
Xz Respectively. In the hypothetical case of constant dispersion, there will only be one wavelength at which

the path lengths are matched. However, in the real case where dispersion itself is a function of wavelength,

the path lengths may match at two (or more) wavelengths. Thus, typically over a broad enough observation

wavelength range, two (or more) symmetric fringe patterns can be seen in the optical spectrum. As the air path is changed the positions of both these sets of fringes shift. The first order dispersion can be obtained by

determining the shift of the first symmetric fringe pattern. The second order dispersion can be obtained by

determining the second symmetric fringe pattern shift. As can be seen from Eq.l, the higher order terms have no influence on first symmetric fringe centre wavelength, but have some influence on symmetry. Both

first and second order dispersion have influence on the position of the secondary symmetric fringes. Using

the first order dispersion derived from the first symmetric fringe, the second order dispersion can be derived

by determining the secondary symmetric fringe centre wavelength. Fig. 1 shows a simulation result in which

second symmetric fringe appears on the left of the first symmetric fringe due to the influence of dispersion

slope. In the calculation, the primary symmetric centre wavelength is A, = 1665.2nm , dispersion

D = 8.4/?s I'nm-km , dispersion slope D' = 0.072ps/nm 2 km , and the secondary symmetric centre wavelength is A2 = 143

1

.5nm

.

v v v v y v

1300 1400 1500 1600

W avelength (nm

)

1700 1800

Fig. 1 Theoretical analysis of dispersion slope influence on interference fringe

3. Experiment

The experimental configuration based on a Mach-Zehnder interferometer (MZI) is schematically shown in Fig. 2. Light from the broadband LED is divided into two arms by a 3dB coupler, the test fibre is inserted

into one arm and the other arm is built with a variable air path of negligible dispersion by attaching one lens

Variable Air Path

0 0

o — 0

Test Fibre

Fig. 2 Experimental setup for first and second order dispersion measurement

58
to a translation stage. The test fibre is a short length of Corning SMF/DS CPC6 dispersion shifted fibre and

its zero dispersion wavelength is near 1550nm. The test fibre length is 90cm. The two arms are combined

through another 3dB coupler. The output of the interferometer is connected to an optical spectrum analyser.

The length of the variable air path changes the relative time delay, t

g (A) , between the MZI arms. When the

optical path length of the reference air path is equal to the optical path length of the test fibre at a certain wavelength, the first symmetric fringe pattern will be easily observed in the optical domain. When the broadband source and observing wavelength range is broad enough, a second symmetric fringe can be

observed either on the left or the right of the first symmetric fringe, depending on the relative sign of the first order dispersion to the second order dispersion. In this experiment, the first order and second order

dispersion of test fibre are both positive in the observation wavelength range. The second symmetric fringe

will be on the left of the first fringe. Fig. 3 shows two interferometer spectra corresponding to two different reference path lengths, showing the first symmetric fringes centred at wavelength AT] = 1656.64 nm (top

right arrow) and Ar2 = 1634.81 nm (bottom right arrow), and their corresponding second symmetric fringe

centres are ATl = 1435.53 nm (top left arrow) and Ar2 = 1464.06 nm (bottom left arrow), respectively. The

smaller the dispersion slope, the further apart the two symmetric fringes. Therefore, to measure small second

order dispersion, a broader wavelength range light source is needed.

Fig. 3 Interferometer spectra obtained for ATl = 1656.64 nm (top trace)

and At2 = 1634.81 nm (bottom trace)

4. Results and discussion

The first order dispersion can be obtained by the measured time delay curve of the first symmetric fringe

shift. In the experiment, the first order term in Eq. 1 will be adjusted to be zero by the experimenter. The

second order dispersion can be obtained by trial and error fitting Eq. 1 . Starting with an initial guess of the second order dispersion D\XX )

, the calculated second symmetric centre wavelength is compared with the

test results to determine the second order dispersion. Measured first order and second order dispersion curves are shown in Fig. 4. The solid line is the measured dispersion (left axis), the filled squares are the measured dispersion slope (right axis). The calculated dispersion (diamond) and dispersion slope (cross) are shown in Fig.4. A comparison of our results with calculated results show close agreement. Because the spectrum of LED source is not flat, the interference visibility varies across the test wavelength range. The

interaction of dispersion and dispersion slope and the visibility variation makes the interference fringes

59
asymmetric. The asymmetric interference fringe patterns affect the determination of the symmetric centre wavelength. In this work, we did not take the visibility influence into consideration in fitting the second

order dispersion. These factors all lead to the discrepancy between the calculated results and experimental

results. The maximum deviation between theory and experiment of the first order dispersion is less than 0.3 ps/nm.km, and of the dispersion slope is less than 0.01 ps/nm2 .km.

Fig.4. Measured first and second order dispersion

5. Conclusion

We have proposed and demonstrated a new direct method of dispersion and dispersion slope measurement

based on an interferometric method. This method involves the observation of shifts in two sets of symmetric

fringes. The first order dispersion was determined by calculating the first symmetric fringe position. The

second order dispersion was determined by the shift of second symmetric fringe. Experimental results show

close agreement with theoretical analysis.

Acknowledgment: We would like to thank Dr. Martijn van Eijkelenborg for helpful discussion.

References

1. Cohen, Leonard G., 'Comparison of single-mode fiber dispersion measurement techniques' J. of

Lightwave Technol. 1985, 3, pp.958-966

2. Chae Jung-Hye, Lee Yong-Tak, 'A novel chromatic dispersion measurement method in frequency

domain using a multi-wavelength optical pulse train generated by Fabry-Perot laser diode', Optics

Comm. 2002, 206, pp. 1-6

3. Shang Hen-Tai, 'Chromatic dispersion measurement by white-light interferometry on metre-length

single-mode optical fibres', Electron. Lett. 1981, 17, pp.603-605

4. Stone, J., and Marcuse, D., 'Direct measurement of second-order dispersion in short optical fibres using

white-light interferometry', Electron. Lett., 1984, 20 pp.75 1-752

5. Tateda, Mitsuhiro, Shibata Nori, Seikai Shigeyuki, Tnterferometric method for chromatic dispersion

measurement in a single mode optical fibre', IEEE J. Quantum. Electron. 1981, 17, pp. 404-407

60
Dispersion measurements on multiple kilometer-length few-mode fibers with

an RF spectrum analyzer

J.W. Nicholson, S. Ramachandran, S. Ghalmi, and M.F. Yan

OFS Laboratories

600-700 Mountain Avenue, Murray Hill, NJ 07974

Abstract: We present a novel technique for measuring the chromatic dispersion of the higher order mode of an

opticalfiber. The measurement technique is simple, accurate, and capable ofmeasuring the dispersion ofkilometer

lengths offiber without the needfor mode converters. The dispersion of the LP02 mode is measuredfor 2, 5 and 10

km lengths offiber, and accuracies ofbetter than 4% are achieved.

Recently, dispersion compensation using the LP02 mode of few-moded fibers has gained a lot of attention because of

the feasibility of achieving a variety of dispersion and dispersion slope values

1,2

. Higher-order-mode (HOM)

dispersion-compensating modules (DCM) can achieve large dispersion and dispersion slope values while

maintaining a large effective area for light propagation. This makes the device resistant to nonlinear distortions even

at high input power levels, which can result in higher optical signal-to-noise ratios and thus longer transmission

distances in optical communication systems

3

. A HOM-DCM typically comprises a few-moded fiber that is designed to provide the desired dispersion and

dispersion-slope, and two mode-converters (such as long-period fiber-gratings

4

) at the input and output of the HOM

fiber

2

. The mode-converters transform the incoming LP0 i mode into the dispersive LP02 mode and vice-versa, at the input and output of the device respectively. The assembly of this device requires fabrication of the mode-converters

and care in achieving adiabatic mode-transitions between the mode-converters and the HOM fibers. In order to effectively design new HOM fibers, one must be able to quickly and accurately characterize the dispersion of the higher order modes. Thus, ideally one would like to measure the dispersion on HOM fibers without using mode

converters.

Typically, dispersion measurements of long (kilometer) lengths of fiber are done using the modulation phase-shift

technique. A tunable laser is modulated at GHz frequencies and launched into the fiber under test. At the output

end of the fiber, the RF phase is measured as a function of laser wavelength, giving the group delay, and ultimately

the dispersion, of the fiber under test. While this technique works well for single mode fibers, the presence of

multiple modes propagating in the fiber at once will cause the measurement to fail, unless strong mode-converters

are employed at the input and output of the HOM fiber.

Recently, the group delay and dispersion of higher order modes in a HOM fiber was obtained by measuring the wavelength dependent spectral fringe spacings of a fiber-interferometer. The two arms of the interferometer were

the distinct paths for light propagating in the LP0 i and the LP02 modes of a HOM fiber, respectively

5

. This technique

is attractive for quick measurements of the dispersion in higher-order-modes, because no mode-converters are needed. However, it is limited to measuring dispersion of a few meters of fiber because the fringe spacing of the interferometer must have a spacing larger than the wavelength resolution of the tunable laser. We present here an alternate technique, based on RF measurements of an interferometer for obtaining the dispersion

of higher order modes. This technique does not require the use of mode converters and works on kilometer lengths

of fiber. Phase noise in coherent sources can be coupled to intensity noise in an interferometer. A photodetector

placed at the output of the interferometer will have a photocurrent whose electrical spectrum shows a dependence on

the relative delay, t, between the two arms of the interferometer. If the interferometer is in quadrature (i.e. the

relative delay between the two arms is a multiple of ft), the electrical spectrum will have the form6

P(f)

A/

.{l + e-**V* -2e-lK6f* cos(2^)},

61
where Af L the source linewidth. In the case of a HOM fiber, the two arms of the interferometer are the two

orthogonal co-propagating modes. Excitation of co-propagating modes in a HOM fiber can be easily achieved by

butt-coupling (or splicing) a single-mode fiber to the HOM fiber, obviating the need for high quality mode

converters since an interferometer with power ratios as small as 10% can yield sufficiently large modulation depths.

The electrical spectrum of a coherent source at the output of the HOM fiber will show a cosine modulation whose

frequency is the inverse of the relative group delay between the two co-propagating modes. Because of the high

resolution of electrical spectrum analyzers, relative group delays from hundreds of picoseconds to hundreds of

nanoseconds can easily be measured. To measure such long group delays with techniques based on the optical

spectrum would require a wavelength resolution on the order of 100 femtometers. By measuring the beat frequency

of the electrical spectrum as a function of source wavelength, the relative group delay as a function of wavelength

can be obtained, and therefore the dispersion difference between the two modes can be calculated.

DFB lasersIN

K 11

polarization

controller

isolator

HOM fiber

Er amp

ESA

air gap

Figure 1 Experimental setup for higher order mode dispersion measurement.

The experimental setup for the dispersion measurement is shown in Figure 1 . A bank of multiplexed DFB lasers was used as a signal source. DFB lasers were chosen for their relatively broad (few MHz) linewidth, making

measuring the beat note in the wings of the spectrum easier. An isolator was used to prevent feedback to the lasers, and a polarization controller was used to ensure parallel polarization at the detector by optimizing the beat note. The

HOM fiber consisted of three lengths of 2.3 km, 5.25 km, and 10.32 km. This fiber had cutoff wavelengths greater than 2000 nm for the LP02 and the LPn mode. An erbium amplifier was used to boost the signal after the HOM fiber and an electrical spectrum analyzer (ESA) was used to measure the RF power spectrum.

In order to ensure a simultaneous launch into the desired modes (in this case, the LP0 i and LP02 modes), the SMF

and HOM pigtails were cleaved and aligned with a small air-gap on the order of 100 um between them at the input

and output of the spools. The free spectral range of these air gaps was about 1.5 THz; therefore, any etalon effects from these gaps were well outside of the range of detection.

E

CD2,

>—<Do

CL

-24-

i

1 i —• - -10-

-26- -20-

-28- -30-

-30-

1531 nm

c

-40-

-32- i/VyYAAnj. 1541 nm

" ay (

-50-

-34- <D "D -60-

-36- " WVVU* . 1547 nm- CL

-38- o -70-

O) -80-

-40- ^n/W\%A/^Vuww

1561 nm^

-42- (a) -90-

0.2 0.4 0.6

freq (GHz)

0.8 1.0 -100

2000

1530 1540 1550 1560 wavelength (nm)

Figure 2: (a) Electrical power spectrum as a function of signal wavelength for the 10.32 km spool. The traces have been

for clarity, (b) Measured relative group delay and calculated LP02 dispersion for 10.32 km spool.

offset

Although an interferometer in quadrature generates a strong cosine modulation, the electrical power spectrum from

an out-of-quadrature interferometer is relatively smooth. Experimentally, we observed the power spectrum to

62
oscillate between strong modulation and no modulation on a time scale of a second, meaning the interferometer was moving in and out of quadrature, and the polarization state of the interferometer was changing. The beat note could be optimized to a certain extent with the use of the input polarization controller; however, nothing could be done

about the movement in and out of quadrature. We found that averaging the traces reduced the maximum observed

amplitude of the beat note, but meant that the shift in quadrature was not a significant issue.

The electrical power spectrum for four different wavelengths for the 10.32 km spool is shown in Figure 2a. As the wavelength of the DFB laser increases, the frequency of the modulation increases, meaning the relative group delay

between the LP0 i and LP02 mode increases. The electrical power spectrum at each wavelength was Fourier transformed to obtain the peak of the modulation frequency, and therefore the relative group delay. The group

delay, obtained from Figure 2a is shown in Figure 2b. This data was fit to a second order polynomial and the

derivative taken to give the dispersion difference between LP01 and LP02- The LP0 i dispersion was measured with

the modulation phase-shift technique (an Agilent 86037C Chromatic Dispersion Test Solution), and added to the dispersion difference measurement from the RF MPI technique to obtain the LP02 dispersion, also plotted in Figure

2b.

freq (GHz)

Figure 3: Electrical power spectrum as a function of signal wavelength for the 5.25 km spool. The low frequency of the beat note at 1536 nm indicates the spool has a turn-around point in this region, where the group delay of the LP0 i and LP02 modes are equal.

It is worth noting that because the modulation frequency is obtained through the use of a Fourier transform, the presence of small amounts of unwanted higher order modes, such as the LPU , do not show up as noise in the data. The LPoi and LPn will have a different relative group delay, and thus a different beat frequency than the LP0 i and

the LP02- Fourier filtering during the data analysis will therefore effectively remove the LP n mode.

One potential difficulty in this measurement technique occurs at the wavelength where the group delays of the two modes are identical (this wavelength has also been called the turn-around point wavelength due to its significance

for fabricating broadband long-period fiber-gratings

4

). At exactly this wavelength the frequency of the cosine modulation goes to infinity. This situation occurred in the 5.25 km spool around 1536 nm, and is illustrated in Figure 3. At 1536 nm the cosine modulation becomes very long, whereas at 1533 nm and 1541 nm, the modulation

has nearly the same frequency, meaning the relative group delay has equal value but acquires a change in sign as the wavelength is swept through the turn-around point. Typically, we acquired the electrical spectrum out to frequencies

of 3 GHz for the 2 and 10 km spools. However, we found that for the 5 km spool, where the turn-around point was

within the measurement range, we had to increase the frequency range to 5 GHz to obtain repeatable results.

In order to test the accuracy of this measurement technique, complete HOM-DCMs were constructed (with mode

converters at the input and output of the test fibers), and the LP02 dispersion was measured directly with the modulation phase-shift technique. The results of the modulation phase-shift measurements and the RF MPI

63
measurements are compared for the three different spools in figure 4a. The results of all three spools match very

well for the two techniques. The percent deviation between the two measurements for the three different spools is plotted in figure 4b. Even for the 5.25 km spool, which was the most problematic due to the presence of the turn- around point within the measurement range, the maximum deviation is less than 4%. For the other two spools, the deviations are typically less than 1%. The oscillations in the percent deviation curves come from the modulation

phase-shift measurement of the LP0 i mode, which showed increased noise due to small amounts of residual higher

order modes.

Figure 4: (a) Comparison between the modulation phase-shift measurement of the LP02 dispersion and the RF MPI measurement

for the three different spools, (b) Percent deviation between the two measurements for the three different of spools.

In conclusion, we have presented a simple measurement technique for obtaining the dispersion of higher order modes in an optical fiber. This measurement has the advantage, as compared to previous techniques, of not

requiring the use of mode converters and being applicable to long lengths of fibers. The measurement is simple,

accurate, and easy to implement.

References

1 A.H. Gnauck et. al, Proc. Opt. Fiber Comm., PD-8, 2000.

2 S. Ramachandran el. al, IEEE Photon. Tech. Lett., vol. 1 3, pp. 632-634, 2001.

3 S. Ramachandran et al, Electron. Lett., vol.37, p 1352, October 2001.

4

S. Ramachandran et al, Optics Lett., vol. 27, p 698 (2002).

5 D. Menashe eta\, Electron. Lett., vol. 37, p 1439 (2001).

6 R. W. Tkach et al, J. Lightwave Tech., LT-4, p 171 1 (1986).

64
Group-Delay Measurements with RF optical frequency scanning

Maria C. Santos, Josep Prat and Marcal Soler

Universitat Politecnica de Catalunya, Signal Theory and Communications Dept.

Abstract: We derive the analytical basis of a new group-delay measurement method at optical frequencies.

By using a similar experimental setup to that required for the standard Modulating Phase Shift Method

(MPSM) and computation of amplitude and phase measures, we show that it is possible to scan the optical

frequency by frequency sweep of the rf modulating signal.

1. Introduction

Increasingly, the optical communications industry is demanding the characterization of optical components

with respect to chromatic dispersion more accurately and more simply [1]-[4]. Standard to the matter is the modulation phase shift method (MPSM) [5], whose wavelength resolution is determined by the tunability of the laser which provides the optical signal to which sidebands are attached by external RF modulation prior to injection into the DUT. Group delay data are then obtained from determination of the phase difference acquired between sidebands [5]. We have shown recently that wavelength stability of the tunable laser employed constitutes a critical point determining to a great extent the accuracy of the measures [6]. Several modifications to the phase shift method have been proposed to ease the requirements of frequency

stability of the laser source and improving its accuracy [1-4]. Some are based on the use of single sideband

modulation [1] and other clever ways of combining the sidebands [2]-[4], the interest often being laid on

benefiti.ig from better frequency stability and resolution provided by radiofrequency signals. Here we will outline the principles of a technique which by properly combining phase and amplitude

measurements of all frequencies generated as a result of the modulation and optical detection process, namely, continuous wave, fundamental (modulating frequency) and its second harmonic, should allow for optical frequency scanning, and hence wavelength resolution control, in the electrical rather than the optical

domain, through minimal modifications to the basic standard setup.

2. Measurement Technique

Figure 1 shows the experimental setup required. The use of phase instead of amplitude modulation of the

optical carrier as usually encountered with MPSM, is not fundamental to the method that we derive here,

because group delay data could in principle be extracted as well, but as it will be seen, the use of narrow band phase modulation helps to improve accuracy. Assuming a very small index of modulation, m « 1, the signal at the output of the phase modulator is given by

SM = A0 cos(oy + eo )- [sin {(co0 + (om >

60 + 6m )+ sin ((a)0 -com

)t + d0 -dJ (1)

with the Ao ,Am

,0)o , COm ,d0 ,dm , respectively, the amplitudes, frequencies and phases of the optical and

microwave (modulating) signals.

On reflecting from the DUT, each frequency component gets phase and amplitude variations here denoted

7° ,y

+ ,y~ ,(p + respectively, for the DUT's amplitude and phase response at the carrier frequency,

the upper and lower sidebands. According to that, the signal reflected from the DUT is expressed

SG = Ao7o cos(coo

t + 60 +(p

0 )-

mA„A„ y+sin(((o0 +(om )t+do +em +<p

+ )+

+ y-sin(((00 -com

)t + d0 -em +(l)-)_

(2)

The detected signal includes terms at the modulating frequency as well as at its second harmonic provided

they fall within the detector bandwidth, and a continuous power level. The power functions at each of these frequency components are given by

65
PD

{<o = (oJ = -^=Zl

J(r J + (y

- J

- lrr cos(25 )

sin

( (

1 a - 5 + tg

/>D

(fl> = 2©J =

m(28)

1 + 7 /y

+ cos(2<5)

(3)

(4)

(5)

where a = Q)J + 6m + and 5=0°-

2 2

When using the standard MPSM, the group delay, T

g

is obtained from the phase difference between

sidebands as

d(p A(j) T„ =

dco co.

(6)

where the A<p = is the semi-difference between the phase acquired by each of the sidebands.

The modulating frequency thus determines the frequency resolution when using the standard MPSM and

therefore, it is usually set to be very small. That allows assumption of no significant fluctuations of the amplitude response that thus can be considered approximately constant over the bandwidth of interest. When an rf scanning is pursued, that could no longer be the case, and then the amplitude variations ought

to be considered in the analysis.

In what follows we will outline the procedures which allow to perform optical frequency scanning through rf modulating frequency sweep using the setup in Figure 1, both for the simpler case when the DUT's

amplitude response in reflection can be assumed constant over the range of frequencies of interest, and for the case when the amplitude reflections from the DUT are significantly different at each incident frequency.

3. Equal amplitudes

In the case when the amplitude response of the DUT can be assumed constant for all the frequency

components contained in the incident signal, SM , i. e. y~ ~ y° ~ y

+ = y , from (3)-(5), the expressions

for the power at the three detected frequency components reduce to

|2„,2 /

PD

(co = 0) = i+

2 ;2 \ m A„

V PD

{co = com ) = -mA 20 Am y

2 sin(<5)sin

r-<i>

PD

(co = 2com ) = M^ZLcos(2av + 26m +<t>

+ -0-)

(7)

(8)

(9)

We use the measured phases (PH) and amplitude levels (L) at the three detected frequencies to obtain the

o and the A(p = values for each modulating frequency in the sweep. Directly, as with MPSM,

A0 = PH +mn , me Z (10)

66
Calculate the auxiliary value

2„,2 LC0 =L0 -L2(0 = (11)

or alternatively, get it as the continuous power level measured when only the unmodulated carrier is launched into the system. And then get

( \

8 = sin' (12)

A COS instead of sin function is obtained for the calculation of o when amplitude instead of phase

modulation is used for the optical carrier and therefore narrow band phase modulation is preferred to improve resolution. From the values of <5

( and A0(

. obtained for each modulating frequency C0mi in the sweep, we get the phase differences at each side of the optical carrier, which is kept fixed (rf optical

frequency scanning), as follows. First get the difference functions AS. and AD(

.

AS, =8M

-8i =V+K-^-^

AD, =A0,+1 -A0(

. = 0m -0w -0/ +rV

(13)

From those, addition and substraction gives the phase differences between the two lower and respectively, the two upper frequency sidebands (see Figure 2) A0-=0r-0~+ i=AZ).+AS, A0,

+ =0;+1 -0;=AZ),-A5(

. (14)

and thus, the frequency resolution for group delay calculation is determined by the frequency difference between modulating frequencies in the rf scan

A0,

+

8i Aft)

(15)

FIXED FREQ. LASER

A0 cos(w„t)

Am cos(wmt+9m)

CW-METER NETWORK

ANALYZER T5ET~hFigure 1. Experimental setup

4. Different amplitudes

LOWER

SIDEBANDS

CARRIER A0+

UPPER

SIDEBANDS

0" A0, j: c

Aft+1

Figure 2. Schematic of phase differences between frequency components

When the amplitude differences among the reflected waves at each of the three detected frequencies need

to be taken into account, one has to deal with the complete (3)-(5) expressions. It is important to note that even when using MPSM, a significant difference in the reflected amplitudes introduces an error in the detected phase difference, A0 , between upper and lower sidebands. In such case the use of a Microwave

Transition Analyser to measure the relative phase at the second harmonic frequency is advised, for direct obtaining of A0 . On the other side, the auxiliary value LCo has to come necessarily from the cw power

level detected when only the unmodulated carrier is launched into the system.

67
Using the definitions: T

+ = A0 Am my+

, F = A0 Am my , the measured power levels at the three detected frequencies are respectively,

LC„ +

La = fiLC~J{T+

)

2 + (r-

)

2 - 2rT" cos(25)

L2w =T+ T-/4

also, we measure the phase at the detected modulating frequency, and get

( sin(28) A

(16)

(17)

(18)

PHC0 =2PH2(0 -8 + tg

i + r-/r+ cos(2(5)

(19)

The above four equations (15)-(19) provide the means to determine the <5,A0,r+ r~, and

r

+ /revalues. The 8 and A0 will be used to determine the group delay response following the

procedure outlined in the previous section, while the other two, if one takes good care to keep the Ao Am m

value unchanged through the sweep, will serve to characterize the amplitude response in reflection of the DUT at each side of the optical carrier, in a procedure that is explained next. For each modulating frequency in the sweep, (Dmi , let

Ay. (dB)

i o iog(r; / 17 ) = r,

+ (dB) - y; (dB)

I,yi (dB) = l0\og(r;r-)=y;(dB) + y-(dB)+20\og(Ao Am m)

Get the difference functions as follows

AS, = *YM ~ s7, = 7m + 7m - 7i ~ 7i = ArI+, - Ay,. = y

+

+1 - yM - y] + y;

and from here, the amplitude difference in dB at each side of the carrier follows

(20)

(21)

Ay," =7; -7M =

5. Conclusion

AD, -AS.

2

Ay,

+ =y,+

+1 -y,

+ =

AD, +AS; (22)

We have established the theoretical basis of a new group delay measurement method that should provide,

by appropriate combination of both phase and amplitude measurements, over the MPSM standard setup,

frequency scanning in the electrical domain, enhancing wavelength resolution to the levels that can be

accomplished in the RF part of the spectrum. Both the cases when the frequency amplitude response of the DUT can and cannot be considered constant have been analysed, providing in the latter a procedure to characterize the amplitude response of the DUT.

6. References

[1] J. E. Roman et al., Optics Letters, vol. 23, pp. 939-941, 1998

[2] R. Fontenberry, Technical Digest OFC '98, pp. 363-364, 1 998.

[3] C. K. Madsen. Technical Digest OFC'01, pp. M06-1/-3, 2001.

[4] B. Christensen, J. Mark, G. Jacobsen and E. Bodtker, Electron. Lett., vol. 29, pp. 132-134, 1993.

[5] Chapter 12, Fiber Optic Test and Measurement, Dennis Derickson, editor, Prentice Hall PTR, 1998.

[6] M. Soler, J. Prat, M. C. Santos, IEEE Workshop on Fibre and Optical Passive Components, Glasgow, June 2002.

68
Optical waveform and Q-factor measurement using optical sampling

for ultra-high speed TDM systems

Hidehiko Takara, Ippei Shake, and Satoki Kawanishi

NTT Network Innovation Laboratories, NTT Corporation

1-1 Hikari-no-oka, Yokosuka, Kanagawa, 239-0847 Japan

Abstract

We report recent progress in optical sampling techniques for measuring optical signal waveforms. The

principle of sum-frequency-generation optical sampling is explained, and our experimental results are presented. We also describe how it offers transparent and flexible monitoring of optical signal quality.

1. Introduction

With the development of ultrahigh-speed TDM systems (over 40 Gbit/s) [1], the need has arisen for a technique to measure optical waveforms with extremely high time resolution. The conventional approach is to combine a photodetector with electrical sampling. However, this combination limits the temporal resolution to 10 ps due to the bandwidth (up to 50 GHz) of the photodetector and the electrical sampling circuit. This is insufficient to measure optical signals at over 40-Gbit/s, where a timeslot is less than 25 ps. In contrast, optical

sampling based on optical nonlinear effects is attractive because of the ultrashort response times possible. So

far, several optical sampling methods have been demonstrated based on sum-frequency-generation (SFG) [2,3], cross-phase-modulation [4], and four-wave mixing [5]. We investigated an SFG optical sampling method in order to realize over 100 Gbit/s bandwidth optical

waveform measurements [6,7]. We also recently assessed averaged Q-factor measurement based on optical

sampling for optical signal quality monitoring in transparent optical networks. This paper describes the principle and features of this optical sampling method and demonstrates the waveform/Q-factor measurement

of ultrahigh-speed TDM signals.

2. Principle of SFG optical sampling

The configuration of SFG optical sampling is shown in Fig. 1. Optical signal pulses and optical sampling

pulses are combined and injected into a nonlinear optical material in order to generate the cross-correlation

signals (sum-frequency light). The repetition rate of the sampling pulses is set to f0 /N minus offset Afwhere f0

is the repetition rate of the signal pulses. The sampled waveform is an expanded version of the signal pulse

waveform and is displayed on a monitor.

sampled waveform

optical signal {frep =fQ

) (frep -40

optical sampling

pulse source —

Photooptical

material

detector

optical sampling pulses ( / =f0 /N - Af

)

Fig. 1 Fundamental configuration of optical sampling

69
This optical sampling technique realizes waveform sampling all-optically by utilizing the ultrafast optical

nonlinear effect and ultrashort sampling pulses. Therefore, it has high temporal resolution, subpicosecond

order, and can be used to measure optical signals at over 100-Gbit/s.

3. Subpicosecond resolution waveform measurement

The temporal resolution of optical sampling depends on the optical sampling pulse duration, jitter, and SFG

response time. A low jitter oscillator can hold the jitter under 0.3 ps, and the SFG response time is less than 0.1

ps. The main factor limiting the temporal resolution is the optical sampling pulse duration. We generate

subpicosecond sampling pulses by utilizing a mode-locked Er-doped fiber laser and the supercontinuum (SC)

technique [8]. Figures 2 (a) and (b) show the SC pulse generator and an autocorrelation trace of output pulses, respectively.

The 3.0 ps optical pulses from the mode-locked Er-doped fiber ring laser (ML-FRL) are converted into SC

pulses in an SC fiber. Subpicosecond sampling pulses are obtained by compensating the chirping and then

filtering the pulses with an optical bandpass filter (OBF). The calibrated pulse duration of the SC pulse was 0.4

ps. These ultrashort pulses realize optical waveform measurements with subpicosecond resolution.

Fig. 3 Measured waveform of 400 Gbit/s data pattern

Figure 3 shows the measured waveform of a 400 Gbit/s optical signal. The data pattern "0100101 101 101 10" with pulse duration of 1.5 ps was successfully measured. The temporal resolution of the measurement system

is given by this equation

tres ~ifmeas " tsig -UzT 0),

70
where tmeas is the signal pulse duration as measured by optical sampling, tsig is the signal pulse duration as measured by an autocorrelator and

y

s;g

is the timing jitter of the signal pulses. From measured values (tmeas =1.5

ps, tSig =1.4 ps,jSIg =0.3 ps), the temporal resolution tres of this system is estimated to be 0.4 ps.

4. Eye-diagram measurement

Eye-diagrams that measure the waveforms of randomly-modulated optical short pulse signals are needed to evaluate the characteristics of ultra-high speed TDM systems. In order to measure the eye-diagram, each

sampled signal must have a high signal-to-noise-ratio (SNR). We improved the SNR of the measured

waveform by employing type II phase-matching SFG and an organic crystal (AANP) with high optical

nonlinearity [9], and by amplifying sampling pulse peak power to 200 W.

The type II phase-matching condition is satisfied when the polarization states of the two input lights are orthogonal to each other, as shown in Figure 4. Therefore, this configuration is effective in eliminating the DC

background light, the second harmonic light of the sampling or signal light, because each input light has only one polarization component [3,6]. Type II SFG

Crystal

Fig. 4 Type II phase-matched SFG

The AANP crystal has femtosecond response time and high nonlinearity ( d3i= 80 pm/V). Figure 5 shows

the wavelength dependency of SFG efficiency for both the AANP crystal and a KTP crystal, which is the conventional choice. The AANP crystal offers SFG efficiencies that are at least 10 times those of the KTP

crystal for the wavelength range from 1535 nm to 1570 nm. The maximum efficiency value obtained is 3 x 10"4 W . Broader wavelength range, 1530-1600 nm, was recently reported in ref. [10].

c

g>o

C

g

'too

0

1CH r

10-5 r

1530 1540 1550 1560 1570 1580

Signal wavelength (nm)

Fig. 5 SFG efficiencies of AANP crystal and KTP crystal

71
With these improvements, SNR values greater than 20 dB can be obtained, and the optical sampling system

can produce high-speed TDM signal eye-diagrams.

Figures 6 (a)-(c) show the waveforms of the 100-Gbit/s optical signal as measured with electrical sampling

(a 50-GHz bandwidth pin-photodiode + a 50-GHz bandwidth sampling oscilloscope), a streak camera, and

optical sampling, respectively. With the electrical sampling method, the pulses of the 100-Gbit/s optical signal

could not be resolved due to the system's limited temporal resolution (Fig. 6(a)). The streak camera could measure only averaged wavefoims at 1.5 um (Fig. 6(b)). In contrast, our optical sampling method accurately

captured the 100-Gbit/s optical signal's eye-diagram (Fig. 6(c)).

—i r 10 ps/div

Fig. 6 Measured 100 Gbit/s optical signal eye-diagram

(a) pin-photodiode + sampling oscilloscope

(b) streak camera

(c) optical sampling

5. Averaged Q-factor monitoring

The proposed optical sampling technique can also be used to monitor the optical signal quality in optical

networks. We have investigated a simple, asynchronous sampling technique for averaged Q-factor

measurement [11-13]. Its bit rate range is up to 160 Gbit/s, and asynchronous sampling allows bit-rate independent Q-factor monitoring [11, 14, 15]. A block diagram of the averaged Q-factor (Qavg) measurement circuit using optical sampling is shown in Figure 7. The optical signal is received at the O/E converter after being sampled using a locally-configured

short pulse generator. It is then launched into a signal processing circuit. The insets in Fig. 7 show a typical

asynchronous eye-diagram and its amplitude histogram obtained by asynchronous optical sampling, which

illustrates the principle of our method. Among the sampling points that constitute the histogram, we determined

that the set of points whose level is higher than a predetermined threshold level, //,/,/ belongs to level "MARK"

(i.e., "1"), while the set of points whose level is lower than a predetermined threshold level, fi,ho, belongs to level "SPACE" (i.e., "0"). We define Qavg by

Qavg =

| Lf-l.avg ' Mo.avg \ ' (<?l.avg f^O.avg) (2)

where ju ,, avg and aiavg are the mean and standard deviations of the MARK and SPACE levels distributions,

respectively. The data obtained by asynchronous sampling includes unwanted cross-point data in the eye72
diagram, which decreases the measured value of the averaged Q-factor. Thus, it is necessary to remove the cross point data. In this way, we set two threshold levels, //,/,/ = jui-a/u and ntho = Mo+aju; coefficient a is defined to lie between 0 and 0.5.

I Repeater

OBPF

Amplitude

Hi.

i

Ho..

Transmission r Averaged Q-factor measurement circuit line Receiver (O/E converter)

Sampling module

Signal

processing

circuit

Short pulse gen.

Amplitude

°l*,g ti

j«H~ ft &*s £ .

Mark

\

|

O0.«vg Space

Number of tunes Time

Fig. 7 Block diagram of averaged Q-factor measurement circuit, using optical sampling

aaAa

O 13

12

1

1

1 0

9

6

76

5

-HfcsK —Pf——

).39

i i Number of times Time

10 12 14 16 1 (g)

-H

; slo| ie~ J. 40

10 12 14 16 18 (f)

-SlO 031

Q, dB

10 12 14 16 u

(h)

Fig. 8 Amplitude histograms (left), asynchronously measured eye-diagrams (middle)

and synchronously measured eye-diagrams (right) ((a) 10-Gbit/s, (b) 40-Gbit/s,

(c) 100-Gbit/s,(d) 160-Gbit/s RZ signal), Relationship between Qavg and Q for

(e) 10-Gbit/s, (£) 40-Gbit/s, (g) 100-Gbit/s, (h) 160-Gbit/s RZ signal.

Figures 8(a)-(d) show the eye-diagrams and amplitude histograms of the RZ optical signals where the BER

equals 1x10"'°, as measured by optical sampling. The figures on the left show the amplitude histograms

obtained from the asynchronous eye-diagrams. These eye-diagrams from (a) 10 Gbit/s to (d) 160 Gbit/s were

measured by using the same averaged Q-factor monitoring circuit. The amplitude histograms show that high

73
bit-rate signals, over 40 Gbit/s, can be easily processed by our method. Eye-diagrams recorded using

conventional synchronous measurement are shown on the right for comparison. Figures 8(e)-(h) show the relationship between Qavg and Q for the 10, 40, 100, and 160-Gbit/s RZ optical signals, respectively, when the

signal SNR was changed. Coefficient a was set to 0.3. The figures show that the averaged Q-factor changes

with Q in each case. The maximum value of Q in this experiment is 17.3 dB; therefore, we expect this method

can be used for BERs better than 10" 13

. Qavg is strongly correlated to Q at each bit rate, which shows that bit- rate flexible monitoring of the optical signal quality is achieved by this method. We can also obtain the BER by

measuring the averaged Q-factor and by referring to Figs. 8(e)-(h). The reason why the slopes of the 40, 100,

and 160 Gbit/s plots are lower than that of the 10 Gbit/s plot is probably due to the bit-by-bit pulse peak power

fluctuation and to the differences in the bit-to-bit interference caused by waveform differences.

6. Summary

We have described an optical sampling technique for measuring optical waveforms with subpicosecond

resolution. With this method, over 100 Gbit/s optical signals were successfully measured with 0.4 ps temporal

resolution and more than 20 dB signal-to-noise ratio. We also introduced an optical signal quality monitoring

method that uses asynchronous sampling. Bit-rate flexibility with 10 to 160 Gbit/s optical RZ signals was also demonstrated. This method is intrinsically flexible with respect to the signal format and modulation format. It

is expected that this optical sampling technique will prove essential for future high-speed TDM systems.

References

[I] S. Kawanishi et al., Tech. Dig. OFC'96, PD-24, 1996.

[2] T. Kanada et al., Opt. Lett., 1 1, pp. 4-6, 1986.

[3] H. Takara et al., Transactions of IEICE (B-l), J75-B-1, pp. 372-380 (in Japanese), 1992.

[4] B. P. Nelson et al., Electron. Lett., 27, pp. 204-205, 1991.

[5] P. A. Andrekson et al., Electron. Lett., 27, pp. 1440-1441, 1991.

[6] H. Takara et al., Electron. Lett., 30, pp. 1152-1153, 1994.

[7] H. Takara et al., Electron. Lett., 32, pp. 1399-1400, 1996.

[8] K. Mori et al., J. Opt. Soc. Am. B, 18, pp. 1780-1792, 2001.

[9] A. Yokoo et al, Journal of Crystal Growth, 156, pp. 279-284, 1995.

[10] A. Otani et al, OFC2001, WDD65, 2001.

[II] I. Shake et al., Electron. Lett., 22, pp. 2152-2154, 1998.

[12] I. Shake et al., Electron. Lett., 25, pp. 2087-2088, 2000.

[13] I. Shake et al., IEEE Photonics Tech. Lett., Vol. 13, No. 4, 2001.

[14] G. Bendelli, et al., ECOC2000, Vol. 4, pp. 1 13-116, 2000.

[15] C. M. Weinert, ECOC2000, Vol. 4, pp. 121-122.

74
Frequency-controlled supercontinuum lightwave source applied

to optical measurements with high frequency accuracy

Kunihiko Mori, Toshio Morioka, Atsushi Takada and Etsushi Yamazaki

NTT Network Innovation Laboratories, NTT Corporation

1-1 Hikari-no-oka, Yokosuka, Kanagawa, 239-0847 Japan

Phone: +81-468-59-4664, Fax: +81-468-59-3396, e-mail: morikuni@exa.onlab.ntt.co.jp

Abstract

A frequency-controlled supercontinuum light- wave source with high frequency accuracy and

stability is applied to optical measurements at a frequency spacing of 25 GHz, such as multicarrier optical frequency sweep and calibra- tion of linearity in optical spectrum analyzers.

1. Introduction

The recent progress of optical amplifiers such

as S-band amplifiers [1] or fiber Raman amplifiers [2] has expanded the fronteer of optical

transmission. Also, the progress of optical fil- tering devices such as arrayed-waveguide gratings has allowed dense WDM (wavelengthdivision-multiplexing) signals to be easily manipulated. For measurements and testing

of these optical devices under development,

multi-carrier optical sources with high accu- racy and high stability are in increasing de- mand [3, 4, 5] which cover a wide range of

wavelength and whose optical frequencies axe

well-aligned on the standardized optical fre- quency grid [6]. Using such multi-carrier optical sources, optical devices and equipments

can easily be calibrated to be aligned to the

optical frequency grid as a secondary optical

multi-carrier standard.

Supercontinuum (SC) lightwave source is one of the promising solutions for such multicarrier optical sources for measurements and

testing which can emit a well-aligned optical frequency grid and can compactly be re- alized as is shown in Figure 1. The SC light- wave source has already been used to measure chromatic dispersions in optical fibers

[10, 11]. For the demonstrations of high ca- pacity dense WDM communication, the SC

lightwave sources have been used to generate

the well-aligned optical frequency grids with

frequency spacings of 12.5 GHz [7], 25 GHz

[8] and 50 GHz [9] by employing a modelocked laser diode as a seed optical pulse

source. These SC lightwave sources can also be used for optical frequency measurements by

controlling wavelengths of their longitudinal

modes. In this report, we present optical fre-

'•a- £. EL

!

Figure 1 : The prototype of SC lightwave source with an optical frequency spacing of 25 GHz. Dimension: W43 x H13 x D48 (in centimeter)

quency domain measurements employing the

SC lightwave source. Optical frequencies of

longitudinal modes are manipulated by ther- mally controlling the optical frequency of the

seed optical source. Two applications demonstrated are a multi-carrier optical frequency

sweeper and calibration of linearity in optical

spectrum analyzers.

2. Optical-frequency control of SC

lightwave

A 25-GHz SC lightwave source consists of the

following components: A mode-locked laser diode (ML-LD) with an average wavelength

75
of 1538 nm (optical frequency: 194.9 THz)

driven at frequency of 25 GHz was employed

as a seed optical pulse source. A decreasing

dispersion fiber with convex dispersion profile

[12, 1?] was employed as a SC generating fiber into which the amplified output of the ML-LD.

An optical amplifier was employed for boosting the output of the ML-LD before the SC

generating fiber. Figure 2 shows the output

spectrum of the 25-GHz SC lightwave source. Optical signal-to-noise ratio defined as the visibility of longitudinal modes lay from 10 dB to 25 dB over the spectral range from 189 THz

(1586 nm) to 199 THz (1507 nm).

Longitudinal modes

of SC lightwave

190 192 194 196 198

Optical frequency [THz] Figure 2: The spectrum of SC lightwave with an optical frequency spacing of 25 GHz. Frequency resolution

is 2 GHz.

Figure 3 schematically illustrates the de- tection of frequency deviation of the SC fre- quency grid from the optical frequency stan- dard. A beat signal is detected between the

optical frequency standard uq and the nearest

longitudinal mode in the SC lightwave. By

controlling the beat frequency fs, the whole

longitudinal modes of the SC lightwave can be tuned that is realized by tuning optical

frequencies of the longitudinal modes of the

ML-LD output with its operation temperature. The frequency spacing of longitudinal

modes can also be tuned within a detuning

range of up to 100 MHz. As an anchor of optical frequency, an optical frequency standard

source was employed which generates the optical frequency fixed at uQ = 193.1000 THz

(1552.524 nm) and guarantees a frequency ac- curacy of ±10 MHz and a frequency stability withii. 0.4 MHz. When optical frequency

control was active, the temperature of MLN = -2 N = -1

Optical frequency standard

N = 0 N = 1 N = 2 6 U H

Optical frequency

Beat signal

RF frequency

Figure 3: Schematic illustration of anchoring of lon- gitudinal modes of SC lightwave, o: optical spectrum,

b: RF spectrum, ^o: optical frequency standard, /mlfrequency spacing of SC lightwave, fs'- beat frequency.

LD was adjusted so that the beat frequency

Jb matched the target frequency. Figure 4

shows the stabilization of optical frequency of the SC lightwave by thermal control of the

ML-LD. With the optical frequency control,

the fluctuation of the beat frequency /b was

suppressed with a standard deviation of 5.0 MHz for 2 hours. Without optical frequency

control, the beat frequency drifted more than

100 MHz away from the target frequency of

1 GHz. The relative frequency accuracy of longitudinal modes with respected to the optical frequency standard in the SC grid de- pends on that of the beat frequency /# and

degrades proportional to the absolute value of

mode number N.

X

«5

a> 1

CT

O) M—

•£ 0.9

CO

CD CO

I

1 1 1

' I

Without X control

With X control

0 1000 2000 3000 4000 5000 6000 7000 Time[sec] Figure 4: Frequency stabilization of SC lightwave.

76
o- 198.150 -

_ 194.975

-5 0 5 Beat freq.[GHz] Figure 5: Measured optical frequencies in the SC

lightwave when varing the beat frequency /a- Mode

numbers: a: N = 202, 6: N = 74, c: N = -199.

3. Multi-carrier optical frequency

sweep

There can be two modes of manipulating optical frequencies of SC lightwave: (1) by shift- ing optical frequencies via changing operation

temperature of ML-LD or (2) by expanding or shrinking frequency spacing via changing driving frequency of the ML-LD. Figure 5 shows

the measured optical frequencies when varing

beat frequency Figure 6 shows the measured optical freqencies when varing the driv- ing frequency /ml of ML-LD. The longitudi- nal mode nearest to uq was adjusted to be

fixed at uq + fg as a mode number N = 0. The mode number of SC lightwave can be obtained by calculating the slope of the graph.

the SC grid were measured over the spectral

range from 186 THz (1611 nm) to 203 THz

(1476 nm). Model a shows a uniform deviation within 5 GHz over the entire range measured, while model b shows a large deviation

at optical frequencies of more than 198.8 THz

(1508 nm).

q. 188.10 o

24.95 2 5 25.05 25.1 25.15 ML freq.[GHz] Figure 6: Measured optical frequencies in the SC

lightwave when varing the driving frequency of MLLD. Mode numbers: a: N = 202, b: N = 74, c: N =

-199

4. Conclusion

Frequency-controlled supercontinuum light- wave source for optical measurements with

high frequency accuracy and stability was pre- sented. Stability of optical frequency of ther- mally stabilized SC lightwave with a frequency

spacing of 25 GHz was achieved to be 5.0 MHz. Applications were demonstrated as

multi-carrier optical frequency sweep and cal- ibration of optical spectrum analyzers.

3. Frequency calibration of optical

spectrum analysers

Using the optical frequency grid generated

from the SC lightwave source, optical spec- trum analyzer can easily be calibrated. Figure

7 shows characterization of optical frequency

accuracy for two models of optical spectrum

analyzers. Optical frequency deviations from

77
186 1 88 190 192 1 94 1 96 1 98 200 202

Grid freq[THz]

Figure 7: Characterization of linearity in optical fre- quency for two models of optical spectrum analyzers.

References

[1] S. Aozasa, H. Masuda, H. Ono, T. Sakamoto,

T. Kanamori, Y. Ohishi and M. Shimizu, "1480- 1510 nm-band Tm doped fiber amplifier (TDFA)

with a high power conversion efficiency of 42Proc OFC2001, PD1 (2001).

[2] M. Nissov, C. R. Davidson, K. Rottwitt, R. Menges, P. C. Corbett, D. Innis and M. S. Bergano, "100 Gb/s (10 x lOGb/s) WDM trans- mission over 7200 km using distributed Raman

amplification," Proc. ECOC'97, vol. 5, pp.74-76

(1997).

[3] L. Hollberg, C. W. Oates, E. A. Curtis, E. N. Ivanov, S. A. Diddams, Th. Udem, H. G. Robinson, J. C. Bergquist, R. J. Rafac, W. M.

Itano, R. E. Drullinger and D. J. wineland, "Optical frequency standards and measurements,"

IEEE J. Quantum Electron., vol.37, pp.1502-1513

(2001).

[4] R. Holzwarth, Th. Udem, T. W. Hansen, J. C. Knight, W. J. Wadsworth and P. St. J. Russel, "Optical frequency synthesizer for precision spectroscopy," Phys. Rev. Lett, vol.85, pp. 2264-2267

(2000).

[5] S L. Gilbert, S. M. Etzel and W. C. Swann,

"Wavelength accuracy in WDM: Techniques

and standards for component characterization," Proc. OFC2002, THC2, pp.391-393 (2002).

[6] ITU-T Recommendation G. 694.1, "Spectral

grids for WDM application 1: DWDM frequency

grid," Geneva, May, 2002.

[7] H. Takara, T. Ohara, K. Mori, K. Sato, E. Yamada, K. Jinguji, Y. Inoue, T. Shibata, T. Morioka and K-I. Sato, "More than 1000 channel

optical frequency chain generation from a single

supercontinuum source with 12.5 GHz channel

spacing," Electron. Lett., vol.36, pp. 2089-2090

(2000).

[8] E. Yamada, H. Takara, T. Ohara, K. Sato, T. Morioka, K. Jinguji, M. Itoh and M. Ishii, "150 channel supercontinuum CW optical source with

high SNR and precise 25 GHz spacing for 10 Gbit/s DWDM systems," Electron. Lett., vol.37, pp. 304-306, (2001).

[9] H. Takara, H. Masuda, K. Mori, K. Sato, Y.

Inoue, T. Ohara, A. Mori, M. Kohtoku, Y. Miyamoto, T. Morioka and S. Kawanishi, "Ultra- wideband tellurite/silica fiber Raman amplifier

and supercontinuum lightwave source for 124- nm seamless bandwidth DWDM transmission," Proc. OFC 2002, FBI (2002).

[10] K. Mori, T. Morioka and M. Saruwatari, "Group

velocity dispersion measurement using supercon- tinuum picosecond pulses generated in an optical

fibre," Electron. Lett., vol.29, pp.987-988 (1993).

[11] K. Mori, T. Morioka and M. Saruwatari, "Ul- trawide spectral range group-velocity dispersion measurement utilizing supercontinuum in an optical fiber pumped by a 1.5 fxm compact laser source," IEEE Trans. Instrumentation and Measurement, vol.44, no.3, pp.712-715 (1995).

[12] K. Mori, H. Takara, S. Kawanishi, M. Saruwatari and T. Morioka, "Flatly broadened supercontin- uum spectrum generated in a dispersion decreasing fibre with convex dispersion profile," Electron. Lett., vol.33, pp. 1806-1808 (1997).

[13] K. Mori, H. Takara and S. Kawanishi, "Analysis

and design of supercontinuum pulse generation

in a singlemode optical fiber," J. Opt. Soc. Am.

B, vol.18, pp.1780-1792 (2001).

78
Recent developments of excited-state optical frequency

standards for telecommunications

D A Humphreys, C Campbell, F Bernard and P Patel: National Physical Laboratory, Queens Road,

Teddington, Middlesex, TW11 OLW, UK.

Abstract

Optogalvanic transitions in metal vapour falling close to the ITU grid in L-band are reported and a portable

saturated optogalvanic reference standard based on the Krypton transition at 1582.441 nm is described. This work is part of the Certified Reference materials for wavelength standards (CREW) European

Community project.

Introduction

High accuracy optical frequency references are required to support the continuing development of dense

wavelength division multiplex (DWDM) systems. For operation at spacings of 50 GHz or less, some form

of active reference is essential. Local references such as etalons and filters are commonly used. However, in some designs it is possible to lock to an adjacent channel in error. Molecular absorptions or excited-state optogalvanic transitions can be used to provide a local absolute reference. Many of the available lines will be inconveniently placed for the ITU grid. It is possible to synthesise lines close to the ITU grid by four- wave mixing 1 but this adds additional complexity. If the reference material is correctly chosen, it should

also be possible operate within the transmission system tolerances. DWDM component manufacture also requires high measurement accuracy. This is often achieved using

wavelength meters. Although these instruments are predominantly based on the Michelson Interferometer,

and contain an internal reference, they still require calibration to correct for systematic errors, such as optical alignment and reference stability.

Molecular absorptions and excited-state transitions are being studied for this application as part of the Certified Reference materials for wavelength standards (CREW) project

2

.

Metal vapour lines

Noble gasses are normally used for excited-state transitions. These can be operated at low currents, extending the cell life to several years, and the transitions can be saturated at modest optical powers. However, by operating the cell at high currents, (5-15) mA, it should also be possible to access metal vapour lines by sputtering material from the electrodes. This approach increases the number of lines available but at the expense of the cell lifetime.

Table 1 L-Band metal-vapour excited-state optogalvanic transitions

Element Wavelength, nm Frequency, GHz Difference from ITU 50 GHz grid, GHz

Cd 1571.6128 (2) 190754.636 (24) 4.636 (24)

Mg 1577.0147(2) 190101.217(21) 1.217(21)

Mg 1575.3294(2) 190304.597 (24) 4.597 (24)

In a previous paper

3

, a number of possible elements were proposed, based on their emission spectra. Experimental results using cells with magnesium and cadmium electrodes have shown encouraging results. Measurements have been made using a wavelength meter to measure the optogalvanic transitions and

l3 C2H2 lines as a reference. The results are given in Table 1

.

79
Portable Kr saturated reference

Saturated optogalvanic transitions have been reported by a number of authors4, 5

. At NPL, we have

achieved saturation of a number of L-band and C-band transitions

6

, at powers of < 10 mW, which is within

the powers achievable from a DFB laser. In these experiments the laser was frequency modulated (123 Hz)

and a chopper (1.5 kHz) was used to distinguish between the unsaturated and saturated signals. The signal

processing required two cascaded

lock-in amplifiers and this placed

restrictions on the laser modulation

rate and the chopper speed so that the filtering of the first instrument's output stage had sufficient bandwidth to accommodate the

optical signals. A new approach,

using a complex interrogation

waveform, has been adopted as it gives considerable design flexibility. The principle of operation is shown

in Figure 1. The laser modulation

frequency was 5 kHz, with a chopper

frequency of 330 Hz.

Original Scheme: Error signal = < (OG X f1) X f2)

OG

signal

Filter

Chopper

Frequency f1

Filter Error Signal

Laser modulation Frequency f2

New scheme : Error signal = < OG X (f1 X f2) >

Chopper

Frequency f1

Filter Error Signal

Laser modulation Frequency f2

Figure 1 Signal processing to recover the saturated signal

A DFB laser can be tuned over (1-2) nm and modulated at much higher speeds, offering considerable design flexibility. The DFB lasers used in the experimental work can be tuned at approximately 10 GHz/C.

However, this gives a separate problem because temperature stabilities in the milli-kelvin range are required to achieve accuracies of a few MHz. The width of the saturated dip at the turning points is about 220 MHz. Within this region the loop is stable and will close on the centre of the dip. However, outside this region, the error signal has the opposite slope and gives positive feedback, driving the system out of lock. Additional heat or cold input can throw the control loop out of lock and so to reduce the temperature

sensitivity, the laser is thermally insulated and mounted on a metal block to increase the thermal mass.

TE ci oler

Laser Thermistor A/D

OG Cell

Chopper

Filter

1f Unsaturated

Filter

A/D

Composite Saturated

*—

Filter A/D

o

o

coO

2f Lock Quality

Figure 2 Block diagram of portable optogalvanic reference

The instrument is controlled by

a microcomputer that stabilises the laser temperature and

searches for the transition. Once the lock has been

acquired under unsaturated

conditions, the control loop is switched to the saturated path.

If lock is lost, the control program reverts to the unsaturated lock as this has a wider capture range. If the lock has been lost irrecoverably, then the software will scan the

laser across a range of

wavelengths to reacquire the

signal.

80
The saturated signal and locking process can be seen in Figure 3. At the start of the trace, the laser wavelength oscillates through the transition and the slope of the Doppler broadened transition can be seen. As the loop closes, the oscillations fall within the Doppler free region and the slope of the error signal is opposite.

The electronics and optics have been designed so that the completed system can be housed in a compact

unit (283 x 380 x 104) mm that is easily portable. By using the controller to search for and lock to the

transition, the source is simple to use.

Figure 4 Portable locked saturated optogalvanic source and OSA

Measurements of the source wavelength have been made using two wavelength meters and an external cavity laser locked to

l3 C2H2 gas absorption lines as the reference. Eight acetylene lines were measured and

the results give the frequency of the source as 189449.319 (26) GHz, this falls within the uncertainty

81
bounds of the previous measurement. The dominant contribution to the uncertainty was the difference in the me :n results for the two wavelength meters. Summary

A compact portable saturated optogalvanic source has been described. This system uses a novel signal

processing approach to simplify the design. Preliminary measurement results for exited-state-metal vapour

optogalvanic lines have also been presented.

40

U

20 X X

l,

MHz *x * * X

X

X

ion

from

meai 0

20

:'viu( -U Q

"40

6U

1520 1525 1530 1535 1540 1545 1550 1555

Acetylene reference, nm

XXX

Wavelength meter 1 Wavelength meter 2

Acknowledgements

The work is funded by the European Community within the 5

th Framework GROWTH, generic activity "Measurement and Testing", dedicated call "Certified Reference Materials", under contract no. G6RD-CT2001-00425 and by the UK Department of Trade and Industry National Measurements Programme.

References

1 D A Humphreys: 'Synthesis of optical frequencies by four-wave mixing in optical fibre', pp. 69-72,

OFMC 2001, Cambridge, UK, September 2001.

2 E.G. Grosche et al.: 'Certified Reference Materials for Optical Telecommunication Wavelengths', OFMC

2001.

3 David A Humphreys, Colin Campbell: 'Preliminary results of L-band exited-state optical frequency

reference survey', pp. 179-182, OFMC 2001, Cambridge, UK, September 2001.

4 A. J. Lucero, Y. C. Chung, S. Reilly, and R. W. Tkach: 'Saturation measurements of excited-state

transitions in noble gases using the optogalvanic effect', Optics Lett., vol. 16, no. 1 1, pp. 849-852, 1991.

5 U. H. P. Fischer and C. V. Helmolt: 'Saturation and Isotopic Shift of the Kr84 Excited-State Transition at 1547.825 nm'JEEE Photonics Technology Letters, Vol. 7,No. 1, January 1995, p. 65.

6 D A Humphreys :'Saturated Optogalvanic transition in Krypton at 1564 nm', pp. 25-28, SOFM 2000,

Boulder, CO, USA, September 2000.

82
FIBER BRAGG GRATINGS AS WAVELENGTH REFERENCES - DEVELOPMENT AND CHARACTERIZATION x

E.G. Grosche1 and J. Meissner2

1 Physikalisch-Technische Bundesanstalt, Bundesallee 100, D-38116 Braunschweig, Germany

(gesine.grosche@ptb. de)

2 Advanced Optics Solutions, AOS GmbH, Ammonstrafie 35, D-01067 Dresden, Germany

(meissner@aos-fiber. com)

ABSTRACT

Wavelength references for current and future DWDM systems require intermediate accuracy (AAA ~ 10"6

), wide wavelength coverage, flexibility, easy handling and strong contrast. We report on special fiber Bragg

Gratings (FBGs), which show great potential as they can fulfill these requirements, and achieve adequate

wavelength stability to complement fundamental references - especially outside the C-band. We present measurements of such FBGs, giving examples of Si-traceable characterization of both fundamental and

artifact-based wavelength references, by using a custom-built large vacuum Fourier transform

spectrometer.

1 INTRODUCTION

Fiber Bragg gratings have found wide-spread application in optical telecommunications. Due to the well- developed technology, their narrow spectral width, fiber compatibility and comparatively low cost, FBGs

also show potential as cost-effective reference materials for optical wavelengths.

To increase the capacity of DWDM systems, in recent years the channel spacing has been decreased, and in addition the usable wavelength range is being extended from the C-band to other communication bands.

Therefore, more stringent demands are now made on the wavelength accuracy of system components and measurement instrumentation, thus requiring accurate wavelength references, which also have to cover a

larger wavelength interval. For the C-band, well-established standardized reference materials based on molecular absorption are commercially available with wavelength uncertainty quoted to better than 10"6 [1]. Developments are underway to extend this to the L-band. Molecular references of similar accuracy are more difficult to realize for the L-band due to the small absorption strength of suitable molecules, such as carbon monoxide

[2,3], and alternative fundamental references are also investigated [4]. Self-contained references e.g. for the calibration of optical spectrum analyzers should be compact, easy to handle (fiber-compatible) and feature a simple spectrum with good contrast, ideally displaying lines at ITU-T grid frequencies. For the 10"5 -10"6 accuracy class, FBGs may fulfill most of these requirements

comparatively easily and allow reference wavelengths to be generated on the ITU-T grid, or indeed

anywhere in any communication band, without reduced contrast.

2 FIBER BRAGG GRATING DESIGN

In their simplest form, the refractive index is modulated with period A along the core of the fiber, resulting

in a band stop in the spectrum, i.e. light around the wavelength ABragg = 2 n A, is reflected. Several FBGs

with different Bragg wavelengths can be combined to produce a multi -wavelength reference. The main

challenges for the use of FBGs as wavelength references are a) their sensitivity to environmental effects, such as mechanical strain and temperature and b) their comparatively large line-width. However, with

special design and suitable packaging, one can overcome these difficulties.

This work is funded by the European Community as part of the project "CREW" (Certified Reference

Materials for Optical Telecommunication Wavelengths) under contract no. G6RD-CT-200 1-00425 within

the 5

th Framework GROWTH, generic activity "Measurement and Testing", dedicated call "Certified Reference Materials".

83
2.1 Environmental effects An unpackaged FBG typically shows a wavelength shift with ambient temperature of about 10 pm/K. We

have achieved passive stabilization by mounting the FBG on a material of a suitable negative thermal expansion coefficient, so that the resulting stresses counteract the normal wavelength shift observed with temperature for a bare FBG. It was possible to reduce the net wavelength shift with temperature by one order of

magnitude, from + 9pm/K to less than (-)lpm/K. Active stabilization on its own using a thermoelectric cooler

(operative between about 5 and 50°C) has been found to achieve 0.1 K or better long-term stability. A

combination of both techniques can thus be expected to keep wavelength drifts due to temperature changes

below 0.1 pm long-term. This corresponds to a relative long-term stability of better than 7 x 10"8

.

2.2 Narrow line-width structures The accuracy with which an FBG can represent a wavelength depends on the line-width or the filter slope of the

spectral features generated by the Bragg grating structure. In contrast to molecular absorption lines with

Doppler widths of only a few hundred MHz, commercial FBGs display typical line-widths larger 400 pm

(50 GHz). For use as wavelength references we have obtained FBGs with a line-width of 200 pm (or 25 GH7

., FWHM) and about 30% maximum reflectivity. Even narrower spectral features can be obtained by introducing a phase shift of n into the FBG-structure. The

resulting narrow transmission peak within the stop band can be extremely sharp: line-widths of less than 1pm

(about 100 MHz) have been reported [5]. We believe that such FBGs have great potential as accurate wavelength references, and have produced narrow line-width FBGs in standard fiber featuring a narrow

transmission peak within a wider stop-band by using the phase-shifting technique. Structure and theoretical spectrum are shown in figure 1

.

"Reflection planes"

of the grating

IIHIIIIIII11IIIIIIIII

/

7i phase shift

Fig. la) Schematic ofrefractive index profile along 10

' thefiber core and lb) Resulting transmission profile 1549.5 isso.o 1550.5 (simulation) for slight variation ofthe phase shift. wavelength [nm]

3 CHARACTERIZATION AND TRACEABILITY

High-precision instrumentation providing traceability to the Si-unit of length is required to guarantee the wavelength accuracy of newly developed references. Active wavelength references, i.e. frequency stabilized

lasers, are often characterized by performing beat measurements with established frequency standards. For

visible wavelengths, where excellent frequency standards are available, such equipment can reach an accuracy better 10"9

. With frequency doubling and the development of frequency combs, a wider

wavelength range has also become accessible in the near-infrared. To date, however, mainly passive wavelength references, in particular molecular absorption cells, have

found widespread acceptance in the telecommunication community. In combination with broad band

sources they allow simple multi-wavelength calibration of measuring equipment. Two possibilities for determining e.g. the transmission spectra of such wavelength references are a) using a tunable laser, detection system and high accuracy wavelength meter and b) an optical spectrum analyzers used with a broad band source. We employ a custom-built vacuum wavelength meter based on a Michelson interferometer with maximum

1.8 m mirror movement and incorporating an iodine-referenced, stabilized HeNe laser as reference [6]. The

instrument can give wavelength readings that are traceable to the Si-unit meter and for its operation as a wavelength meter we estimate an absolute accuracy of about 10~9

, which is supported by measurements in

84
the near infrared [7]. This instrumentation has recently been adapted to operate as a Fourier transform

spectrometer. Thus directly Si-traceable measurements of new wavelength reference materials become

possible across a wide wavelength range.

3.1 Spectral characterization of narrow line-width FBG

The FBG reflects light only in the narrow spectral region of interest. By using a broad-band source and

measuring the reflected intensity of the FBG, we obtain an almost background free signal. From this, the transmission spectrum is calculated. Fig. 2 shows measurements of a FBG with phase-shift structure, obtained with a) a commercial tunable laser and wavelength meter and b) our system, consisting of a broadband ASE-source, optical isolator, fiber optic couplers, the device under test (FBG) and our Fourier transform spectrometer. We note the narrow transmission peak as predicted by theory and the excellent agreement of the spectral shape between the two measurements. We also point out the significant frequency

off-set of about 7 GHz between the two results: this is attributed predominately to the device-under-test

itself, being a bare FBG which was measured at ambient temperatures of 25°C and 20°C respectively.

193100

frequency (HP81680A) - 193200 193300 GHz

co

'(/) w

'E

(/) c

CD

h- T3

CDW

roEi—o

c

1,0-

0,8-

Q.

ii 0,4-

0,2-

0,0-

1

1 1

1

1

1

tunable laser, HP81680

° ASE with FT-Spectrometeri Jj

193100 193200

i.i.

193300 GHz 193400

frequency (FT-spectrometer)

Fig. 2. Transmission spectra obtainedfrom measured reflectance pfor a bare FBG incorporating a phaseshift to generate a narrow transmission peak (line-width < 10 GHz) within the band-stop. Measurements

taken by a) commercial system with tunable laser (resolution 2 pm, FBG at a temperature of25°C) and b) custom-built high resolution FT-spectrometer, using ASE broadband source (FBG at approx. 20°C).

3.2 Absorption spectrum of acetylene

To verify our instrumentation we have tested it using the currently best-characterized multi-line reference

available around 1.54 am: we have measured absorption spectra arising from the rotational-vibrational combination transitions in

13 C2H2 (acetylene). A large number of lines for the V!+v3 band have been

analyzed by laser spectroscopy in the low pressure limit and are tabulated in [8] with an accuracy of 10"9. One limiting factor for absolute frequency references based on molecular absorbers is the pressure dependence, as collisional frequency shifts and broadening of absorption lines occur. We have used cells containing 13 C2H2 at a pressure of 50 Torr (66mbar) and 200 Torr (266 mbar) respectively, so we also obtain information about these pressure effects. A typical spectrum covering some 30 nm and obtained at a resolution of 300 MHz is shown in figure 3a. We note the overlapping bands. Figure 3b illustrates the effect of pressure broadening: We have obtained

line center frequencies for a set of lines in the Vi+v3 band of 13 C2H2 at both 50 Torr and 200 Torr. Comparison to the published values in [8] gives very good agreement, indicating that our measurement

uncertainty is better than 10'7 for the center wavelength, and is dominated by influences due to interfering

nearby lines. We also deduce a significant dependence of the pressure shift on the rotational quantum

number of the initial state, similar to findings by [2,3] and [9].

85
-— wavelength (nm) 1550 1545 1540 1535 1530 1525

4 r-. 1——i 1

1 1

1

1

1 11 1

frequency (GHz) - 1 94 000 GHz frequency (GHz)

Figure 3a, 3b: Absorption spectrum of

l3 C2H2 near l,54\im obtained by Fourier transform spectroscopy:

overview spectrum showing overlapping bands (V1+V3 and V1+V2+V4+V5), and b) effect of pressure

broadening, exemplifiedfor line P(20) ofthe V1+V3 band.

4 CONCLUSIONS

We have described the requirements, development and characterization of wavelength references for modern Dense Wavelength Division Multiplexing (DWDM) systems. Man-made artifacts, such as fiber Bragg gratings (FBGs) can be cost-effective, robust and easy to handle, while offering wide wavelength

coverage and strong contrast. Special fiber grating structures make devices with a relative wavelength

uncertainty in the part per million range feasible. For the development, characterization and eventual

certification of narrow spectral filters we employ a self-built large vacuum Michelson interferometer,

originally designed as a wavelength meter. This instrument has been adapted to also operate as a Fourier transform spectrometer and allows Si-traceable high resolution measurements of new wavelength reference

prototypes.

5 ACKNOWLEDGEMENT

We thank Uwe Sterr and Peter WeBelhoft for generous technical support.

6 REFERENCES

1. S. L. Gilbert and W. C. Swann: "Acetylene 12C2H2 Absorption Reference for 1510-1540 nm

Wavelength Calibration - SRM 2517", NIST Spec. Publ. 260-133 (1997); S. L. Gilbert, W. C. Swann

and C.-M. Wang: "Hydrogen Cyanide H

13 C'^f Absorption Reference for 1530-1560 nm Wavelength

Calibration - SRM 2519", NIST Spec. Publ. 260-137 (1998)

2. W.C. Swann and S.L.Gilbert: "Wavelength Calibration Standards for the WDM L-Band" Conference

Digest of 6

,h Optical Fibre Measurement Conference, 26-28.09.2001 Cambridge (UK), 175-178.

3. J. Henningsen, H. Simonsen, T. Mogelberg and E. Trudso: "The 0->3 Overtone Band of CO: Precise Linestrengths and Broadening Parameters", J. of Mol. Spectr. 193, 354-362 (1999)

4. E.G. Grosche et al.: "Certified Reference Materials for Optical Telecomm. Wavelengths", Conference

Digest of6

th Optical Fibre Measurement Conference, 26-28.09.2001 Cambridge (UK), 289-192.

5. J. Canning and M.G. Sceats: "rc-phase-shifted periodic distributed structures in optical fibres by UV

post-processing", Electr. Lett. 30 (16), 1344-1345, (1994).

6. U. Sterr et al.: "A high accuracy Fourier transform wavelengthmeter", in preparation.

7. J. Stenger, C. Tamm, N. Haverkamp, S. Weyers and H.R. Telle: "Absolute frequency measurement of

the 435.5 nm

171 Yb+-clock transition with a Kerr-lens mode-locked femtosecond laser", Opt. Lett. 26

(20), 1589 (2001)

8. K. Nakagawa, M. deLabachelerie, Y Awaji, M. Kourogi: "Accurate optical frequency atlas of the

1.5 urn bands of acetylene", J. Opt. Soc. Am. B 13 (12), 2708-2714, (1996)

9. M. Kusaba and J.Henningsen: "The V1+V3 and the V1+V2+V4+V5 combination bands of 13 C2H2

. Line

strengths, broadening parameters and pressure shifts", J. Mol. Spec, (in press)

86
SIMULTANEOUS MEASUREMENT OF TRANSVERSE STRAIN AND

TEMPERATURE USING FBG WRITTEN IN HIBI FIBER

I. Abe*-', M. W. Schiller

c

, R. Nogueira8*, P. Lopes

a

, 0. Frazao

d

, J. L. Santos

d

,

J. L. Pinto^ and H. J. Kalinowskf

aDepartamento de Fisica, Universidade de Aveiro and

b Instituto de Telecomunicagoes - Polo de Aveiro, 3810-193 Aveiro, Portugal

c Centro Federal de Educacao Tecnologica do Parana, 80230-901 Curitiba, Brasil.

dINESC Porto, Rua Campo Alegre, 687, 41 69-007 Porto, Portugal

e-mail: ilda;«;fis.ua.Dt

Abstract

Fiber Bragg grating (FBG) written in high-birefringence H'Bi) fibers for the simultaneously

determination of transversal strain and temperature have been studied. The sensor is based on the monitoring of a complex spectrum resulting from the transversal load applied to the fiber. This work

describes the characterization of the sensor with the variation of the applied load and temperature. The

results obtained enable the simultaneous characterization of these two variables.

Introduction

Fiber Bragg grating sensors are generally based on a unique grating written in a standard fiber optic.

The wavelength shift in the reflection spectrum peak of these sensors may be used to measure a single

component of strain or temperature variation, but not both simultaneously [1].

Various sensors have been demonstrated for the simultaneous measure of longitudinal strain and

temperature: by using two overlaid gratings in different wavelengths [2], with two different types of

sensors (Bragg gratings and polarization-rocking filters) [3], using gratings written in fibers with different diameters [4] or using a Bragg grating based Fabry-Perot cavity [5],

FBGs written in high birefringence (HiBi) fibers are being studied as a means to determine strain along different axis, and temperature simultaneously [6,7]. In this work we analyze the complex spectral response of FBG written in HiBi fiber for determination of transversal strain and temperature. Many

applications based on embedded sensors may benefit from a sensor capable of measuring temperature and

transversal load components simultaneously.

Sensor description

In HiBi fibers, regions with high thermal expansion coefficients induce mechanical stress in the

core. Due to the birefringence induced by the intrinsic stress, the X and Y polarizations of the LPoi mode

are now split and have each one different effective index. These linear polarizations are the slow (axis Y)

and fast (axis X) modes associated to the main axes of the fiber (Fig.l). The reflection spectrum of FBG

written in HiBi fibers, with non-polarized light injected into the fiber, has a two-peak structure corresponding to the two orthogonal polarization modes of the fiber. Fig.l shows a diagram of a FBG

written in a HiBi fiber with Internal Elliptical Cladding (IEC). The axis X, Y and Z are the coordinate system of the fiber.

One of the characteristics of the fibers written in HiBi fibers is their spectral response to an applied

transversal load. Due to the non-homogeneous structure of the fiber, the internal stress variations and,

consequently, the deformation to each one of the main axes of the fiber will be different [8].

If a load is applied to one of the main axes X or Y, it should lead to a variation in the respective

band in the reflection spectrum of the grating. However, the band associated to the other axis will have a lower variation [8]. With a transverse load, the peak separation will increase.

87
Figure 1 - FBG written in IEC HiBi fiber

The stress-strain relationship, for completely diametric load (applied force F during the length L of

the grating) over a fiber with circular profile and considering a plane-stress, may be written as [9,10]

ev =-2-

YrcrL

(1)

where r is the core radius (125 um), and Y the Young's modulus (for glass Y= 69x10s1 N/m2

).

The wavelength change, in the reflection spectrum of the sensor, due to a temperature variation AT

and a strain Aey, is, for each axis,

AX,

dX^3T -AT + -dX±

3e -AEx

AXY =——AT + ——AEa 3T Be

(2)

(3)

where dXy/dT and dXx/dT are the temperature variation coefficients and dXy/de and dXx/de are the deformation coefficients. The expressions (2) and (3) can be rearranged and written in matrix form in order

to calculate the transverse strain and temperature, given the measured wavelength shifts: AT

" "A\x~ = K"J AeY _AXy_

where K is a non-singular matrix given by,

K

dXx dXx "3T~'~ar

.IF'IT.

(4)

(5)

Simultaneous measurement of transverse strain and temperature

The FBGs have been written in HiBi fibers using a phase mask illuminated by UV light (248 nm)

[1 1]. The FBG has a length L=10 mm and a period of 535 nm. Fig. 2(a) presents the reflection spectrum of a FBG written in an IEC fiber. The figure also displays the simulation spectrum based on the values of L and

period [12]. The birefringence value obtained by simulation has been 6.7 x

10"4

.

The transversal load used for the sensor characterization has been performed by a micro-scratch

mechanical system. The system uses an arm to apply a load with a precision of 0.1 N. The grating written

in HiBi fiber has been placed between two plates having a length of 13mm. Two other fibers have been

placed in parallel with the FBG to serve as a guide and then, the load has been applied by the arm to the upper plate.

The FBG has been previously characterized with several applied loads over different fiber angles (p. Fig. 2(b) shows the reflection spectrum obtained with the pressure over the Y axis (cp = 90°).

88
WAVELENGTH (nm) 1546.0 1546.5 1547.0 1547.5 1548.0

WAVELENGHT (nm)

(a) (b)

Figure 2 - (a) Reflection spectrum of a FBG written in IEC fiber (solid line) and theoretical fitted bands (dotted lines) (b) Spectral changes of the reflection spectrum for several applied loads. Applied angle (p = 90°

The first band (ky) has a strong spectral variation as the applied load increases, while the second

band (kx) has only a slight change. This is due to the phase shift induced by the applied load. The phase

shift effects are known to lead to spectral changes due to the corresponding change in the core refractive index [9]. The change occurs in the same spatial region where the grating is located (due to the position of

the applied load), causing a phase shifting region superimposed to the Bragg gratings. The resulting

complex structure is known to be responsible for spectral changes of Bragg gratings subject to mechanical

stress.

The strain calibration line for the X.Y band has been obtained by identifying and measuring the several peaks (to a certain extent, then followed by depressions - Fig.2(b)) as a function of the applied load. Peaks have been observed from 0 to 3.9 N/mm, the turning point at 5.3 N/mm and depressions from 6.6 to 13.3 N/mm. Data has been acquired at a constant temperature of 21°C. The strain calibration lines are shown in Fig. 3(a). The slopes for those lines have been evaluated as being equal to -0.00146 nm/\ie and

-0.00021 nm/u£.

The cooling/heating system has been placed outside the holding plate of the fibers in order to avoid any influence from the applied strain. That system is composed of two thermoelectric coolers (TEC)

controlled by a dedicated electronic circuit. The calibration lines for the temperature variation are shown in Fig. 3(b). The obtained slopes have been 0.00676 nm/ °C and 0.00671 nm/°C.

1547,4

1547,2

1547,0

I j ) 4 j 4 (..

j ' ^ -o-q-O" e(-- o- a-dro- q.

: 1 4— ( i 4 \.

i i i i i i

! ! ! —i

l—

i

i i iJrrofew-.

_i_ J_

-120 -100 -80 -60 -40 STRAIN hie)

_ 1547.4 E

cX

1547.2 H

o

Z 1547.0

UJ

_l

UJ> 1546.8 s

1546,6

1546.4

i 1 i h 1 (- _-! .-

i i i 1..Q--*'"" i t—irjyfrTf -j—r—

:

.4-...,r-««-Jt'.!.f_ 4 —! j~ «•!••*(

i i i i i

i "i *

j i _ i i _ i_ i ,

! ! !"' r ~j:^.-T' "! ~

- -i i — ^.-.a -'-^ i i 1

i i i i i i

10 20 30 40 50 TEMPERATURE (°C)

60 70

(a) (b)

Figure 3 - Variation of band peak with (a) strain and (b) temperature.

Measurements have been made with simultaneous variation of strain and temperature. The results have been obtained by spectral analysis and using the two slopes got from the separate experimental

evaluation of peak wavelength dependence on strain and temperature. On Table 1, some of those measurements are shown.

i

89
Table 1 - Obtained results with simultaneous variation of strain and temperature

T

6 Y 12°C 23°C 31 °C 46 °C

-61 jie 11.8°C 24.6 °C 31.6°G 45.5 °C

-65 ue -71 ue -70 ue -75 |Lie

-76 fie 12.0°C 25.4 °C 32.6 °C 46.3°C

-69 He -79 ue -73 ue -81 ue

-91 jie 12.7 °C 26.8 °C 34.0 °C 48.0 °C

-76 ue -83 ue -78 |ie -79 ue

The strain values have been evaluated with an error of ± 15 ue for the interval between -61 and -91

ue, while the temperature error has been estimated to be ± 4 °C for values from 12 to 46 "C.

Conclusion

Simultaneous measurements of strain and temperature have been made possible and actually

obtained in HiBi IEC fibers, by knowing in advance the calibration lines for the peak wavelength shift of

the reflection spectrum, for strain and temperature, separately. The associated errors have been found to be

±\5 \xe and ± 4 ° C, respectively.

Acknowledgments

This work has been supported by CNPq, Fundacao Araucaria, CAPES (Brasil) and ICCTI (Portugal).

References

[I] R. Kashyap, "Fiber Bragg Grating", San Diego, Academic Press, 1999.

[2] M. G. Xu, et. al., "Discrimination between strain and temperature effects using dual-wavelength fiber grating sensors", Electronics Letters, vol. 30, p. 1085, 1994.

[3] S. E. Kanellopoulos, et. al., "Simultaneous strain and temperature sensing with photogenerated in- fiber gratings", Optics Letters, vol. 20, n°.3, pp. 333-335, 1995.

[4] S. W. James, M. L. Dockney and R. P. Tatam, "Simultaneous independent temperature na strain measurement using in-fibre Bragg grating sensors", Elec. Letters, vol. 32, n°. 12, pp.1 133-1 134, 1996.

[5] W. C. Du, X. M. Tao and H. Y. Tarn, "Fiber Bragg grating cavity sensor for simultaneous measurement of strain and temperature", IEEE Photonics Technology Letters, vol. 1 1, n°. 1, pp. 105- 107,1999.

[6] M. Sudo, et. al., "Simultaneous Measurement of Temperature and Strain using PANDA Fiber

Grating", 12th Int. Conf. on Optical Fiber Sensors, Technical Digest Series, v. 16, pp. 170-173, 1997.

[7] C. M. Lawrence, D. V. Nelson and E. Udd, "Measurements of transverse strain with fiber Bragg

gratings". Proc. SPIE 3042, pp. 218-228, 1997.

[8] I. Abe, R. Nogueira, B. W. Diesel, A. S. Ehlke, J. Tosin, P. S. Andre, J. L. Pinto and Hypolito J. Kalinowski, "Analysis of Bragg grating written in high birefringence fibre optics", Proc. 4th

International Conference on Photonics, Devices and Systems, Prague, 2002.

[9] P.I. Torres, "Analise Teorica e Experimental de Aplicacoes de Redes de Bragg em Fibra Optica",

Ph.D. Thesis, Physics Department, Pontifical Catholic University of Rio de Janeiro, Brasil, 2002.

[10] R. GafsiandM. A. El-Sherif, "Analysis of Induced-Birefringence Effects on Fiber Bragg Gratings".

Optical Fiber Technology 6, pp. 299-323, 2000.

[I I] F. M. M. Araujo, "Redes de Bragg em Fibra Optica", Ph.D. Thesis, Department of Physics, University

of Porto, Portugal, 1999.

[12] I. Abe, M. C. Fugihara, B. W. Diesel, R. C. Kamikawachi, J. L. Fabris, H. J. Kalinowski, C. L. Barbosa. "Modeling and Production of High Birefringence FOBG Sensors", Proc. SPIE, v.4419. pp.371-374, 2001.

90
A Simple and Direct Method to Estimate Long Period Grating Parameters

K. Thyagarajan*, Mini Das andM. N. Satyanarayan

Department of Physics, Indian Institute of Technology, New Delhi- 1 10016, India.

Abstract

We demonstrate a novel and simple technique to estimate the parameters of long

period gratings (LPGs). It is shown that by measuring the diffraction pattern obtained by

the side illumination of the fiber grating, we can estimate the grating period as well as

the duty cycle. This technique can be used to characterize the LPGs fabricated by any

method.

1. Introduction

Long period fiber gratings (LPG) which have periodicity typically above lOOum

find applications as wavelength filters, gain flattening components and sensors [1-3].

While the grating parameters of a fiber Bragg grating can be estimated from the

reflectivity profile [4], the estimation of grating parameters from transmission spectra of

LPG is not straight forward. Moreover the measurement of reflection or transmission

spectra of these gratings requires sophisticated and expensive equipments. Estimation of

Bragg grating parameters with sinusoidal refractive index modulation was done by Krug

et.al,[5] where Bragg reflection of the probe beam at a suitable incidence angle was used

to study the grating properties. In this paper we extend the method of Ref. [5] for the

evaluation of the parameters of a long period grating.

2. Theory

Since fiber gratings are periodic modulations of refractive index along the length

of the fiber, they behave as phase gratings when side illuminated by a light beam. Since

LPGs have periods of 100 um or above they behave as thin phase gratings. The refractive

index modulation of the grating induces a transverse phase modulation on an incident

light wave which then undergoes diffraction after emerging from the fiber. The Fourier

Transform of the phase modulated wave emerging from the LPG gives an estimation of

the diffraction pattern of the LPG.

As a specific example we consider a rectangular modulation of the refractive

index such that each period A comprises of two regions l\ and h = A-l\. Thus the

refractive index modulation may be described by:

n(z) = n0 +An 0<z</,

= n0

/, < z < A

where An is the peak change in refractive index and n(z+AJ =n(z).ln order to obtain the

diffraction pattern we first make a Fourier expansion of Eq.l and obtain

oo Sn(z) = An [(/, / A) + (]T (2 An I nit) (sin(2>?;r /, / 2 A) cos(2«;r z I A))] (2)

n=\

The phase of the plane wave incident normally on the

fiber, Ein (x = 0) = E0 exp(/<y t) gets periodically modulated and the wave emerging is given by

Eout (x = d) = E0 expDXfi* - k0 n(z)d)] = E0 exp[i(cot - k0 n0 d - ko Sn(z) d)] (3)

where d is the fiber diameter and 8n(z) is given by Eq. 2. The Discrete Fourier Transform (DFT) of Eq. 3 is found using the Fast Fourier

Transform (FFT) algorithm to estimate the diffraction pattern.

91
Fig. 1(a)

100r

90

70

S 50

Fig. 1(b)

100

90

£ 50

J

r

40 60 Sample Number

^yvvvv 40 60 80 Sample Number

Figure 1(a) shows the numerically evaluated intensity distribution in the

diffraction pattern of a grating with a rectangular refractive index modulation

with A=50um, li=10um and i2=40um, and Fig. 1(b) corresponds to that for /i=5um,

/2=45um, again with A=50um. It can be seen that the fringe width (P) depends on A,

while the position of the first zero of the envelope depends on the smaller of l\ and h. The

number of fringes separating the principle maxima and the first zero of the envelope is just the ratio of the grating period A to the length of the shorter region of the grating.

Thus from measurement of the diffraction pattern, we can estimate the period A as well

as the duty cycle (I\/A) of the index modulation.

3. Experiment

LPGs were fabricated by arcing an optical fiber (Corning SMF-28) periodically

along its length using a commercially available splice machine. The electric arcing results

in a perturbed region whose width would depend on the spatial extent of the electric arc between the electrodes of the splice machine. This results in a refractive index

modulation. For any period of the fabricated grating the width of this region would

remain almost the same if the same arc current and exposure time has been used on the same fiber type for grating fabrication. Upon viewing the fabricated grating under highresolution microscope, it was seen that no physical deformation of the fiber had resulted

by arcing which was expected since there was no tension applied on the fiber. A laser beam (the probe beam used in our experiment was He-Ne laser beam of

wavelength 0.633um) illuminated normal to the fiber axis containing the grating resulted

in a clear diffraction pattern. Figure 2 shows the experimental setup used showing the

axes. y

Fig. 2

Incident laser

beam

LPG Screen

92
Figure 3(a) shows the diffraction pattern on the screen as produced by a fiber region

without the grating and Fig. 3(b) shows the corresponding pattern produced by the fiber

portion containing a typical LPG with a period of 450um. These patterns were obtained

using a high resolution CCD camera.

Fig. 3(b)

Fig. 3(a)

t

1

1

«

The presence of LPG clearly produces a diffraction pattern parallel to the fiber

axis. The other artifacts are due to the cylindrical nature of the optical fiber. The inset of

Fig. 4(b) shows the intensity distribution obtained at a selected plane.

Gratings used in the experiment had different periods and were fabricated on

Corning SMF-28 with the same arc current and exposure time to ensure uniform

refractive index modulation and dopant diffusion width. By scanning a photodetector

along the diffraction pattern of the LPG the intensity pattern at any plane can be

measured. We can measure the average distance P between the diffraction peaks, from

which the grating periodicity A=AX)/p can be estimated assuming normal incidence of

light on the grating. The average distance between the central maximum and the first principal minima, y is measured experimentally. From this we could find l\=XD/y. The

same experiment was repeated for gratings with periodicity 450 um, 680|im and 830fim.

Table 1 gives the grating parameters as estimated from the diffraction pattern.

Table I Comparison of the estimated grating period with the fabricated values.

Fabricated Period of Estimated grating li h

the grating period from the (smaller width in the (larger width in the

diffraction pattern. rectangular grating) rectangular grating)

450u,m 458|am 152um 3 06am

680um 685um 314um 364um

830um 832um 316um 516um

It can be seen from Table I that the grating period estimated from the diffraction

pattern match very well with the values used for fabrication. In all these gratings, we find

regions of widths 306fj.m, 314um and 316um which are very close to each other in spite

of the very different periodicities in the grating. We saw earlier in Sec.2 that the first principal minimum of the diffraction envelope is determined by the smaller of the widths

93
//and h. From this we can conclude that the width of the region that gets modified due to the arc must be about 312um. Hence apart from the grating period, the proposed

technique clearly gives us the width of the modified region as well in the LPG. This is not

easy to estimate from the transmission spectrum.

It is estimated from experiment that the width of the perturbation due to arcing is 312 micrometers. A very interesting observation during the grating fabrication is that the

grating formation almost vanished when the period of grating was brought as low as 3 1

5

micrometers point out that the perturbation due to arcing was about that width.

4. Conclusion

In conclusion we have proposed and demonstrated a simple and direct

experimental technique to estimate the period and the duty cycle of a long period grating

by measurements on the diffraction pattern obtained by a transverse illumination. Apart

from the grating period, the method also gives us an estimate of the width of the

perturbed region. The experimental results have been shown to match fairly well with

actual parameters. The proposed method does not require any sophisticated equipments

and can be used to estimate the parameters of long period fiber gratings fabricated using

different techniques.

Acknowledgements

The authors thank Dr. Joby Joseph (Physics Dept., IIT Delhi) for help in imaging

the fringe pattern and for fruitful discussions. One of the authors (Mini Das) would like to thank G. Unnikrishnan (Physics Dept., IIT Delhi) for technical discussions and the

Council of Scientific and Industrial Research, Govt, of India for providing with a Senior

Research Fellowship. This work was partially supported by a research project sponsered

by the Department of Electronics, Govt, of India.

References

1 . A. M. Vengsarkar, P. J. Lamaire, J. B. Judkins, V. Bhatia, T. Erdogan, J. E. Sipe,

J. Lightwave. Technol. 14, 58 (1996).

2. A. M. Vengsarkar, J. B. Judkins, P. J. Lamaire, Opt. Lett. 21, 336 (1996).

3. V. Bhatia and A. M. Vengsarkar, Opt. Lett. 21, 692 (1996).

4. E. Brinkmeyer, Opt. Lett. 20, 810 (1995).

5. P. A. Krug, R. Stolte and R. Ulrich, Optics Lett. 20,1767 (1995)

94
A Simplified Model of Modal Dispersion in Multimode Fiber

(Invited)

A. John Ritger

OFS Fiber Optics Division 2000 Northeast Expressway

Norcross GA 30044

ritger@ofsoptics. com

Steven E. Golowich

Bell Laboratories, Lucent Technologies

700 Mountain Avenue

Murray Hill, NJ 07974

golowich@research.bell-labs.com

Abstract

We develop a simplified model ofmodal dispersion, where the fiber is described by the delay properties of

the principal mode groups. We demonstrate how this model explains the modal structure seen in Differential Mode Delay measurements. We compare model predictions to correlations observed between

850 and 1300 nm overfilled launch bandwidth for collections ofmultimodefiber. We use the model to show

how one can calculate overfilled launch bandwidth from DMD data.

Introduction The growth of data network applications and data rates has led to increased interest in the use of multimode fiber over the last several years. While the data rates that can be realized over multimode fiber are much lower than those

that can be realized over single mode fiber, multimode fiber lends itself well to the use of low cost laser devices, such as 850 nm VCSEL's, which would be unsuitable for use over single mode fiber. Also, the large core of a multimode fiber allows use of reduced tolerance in aligning the laser source to the fiber, again reducing the cost of a

practical laser transmitter. Applications of interest require transmission of up to 10 Gbs, and include local and

storage area networks, as well as equipment interconnects.

The primary limitation of multimode fiber is its modal dispersion, which is caused by the various modes having

different group velocities. It is possible to solve for the modal dispersion directly from Maxwell's equations with

knowledge of the physical characteristics of the fiber, primarily the refractive index profile. However, much greater

insight can be gained from the use of an approximate model that holds in the situations of interest. We are concerned with propagation over distances of <~1000 m, at wavelengths near 850 and 1300 nm, in Germanosilicate glass fibers with nearly

parabolic index profiles with index

contrasts A of 1 or 2%. Such fibers support hundreds of guided modes, but

the modes divide naturally into principal

mode groups, indexed by an integer

M=l,2,..., where the modes within a group have approximately equal wavenumber. The importance of principal

mode groups is that the modes within such a group freely share power with one another over length scales of tens of

meters, while modes in different mode

groups remain almost completely

uncoupled out to distances well over a

kilometer. The effect of intra -group coupling is that when the constituent modes of a mode group are excited, the pulses in the various modes of the group

coalesce into a single pulse, the width of

which grows as the square root of the length of the fiberfl ,2]. Each of these mode group pulses travels at its own

group velocity, so the separation between the pulses associated with different mode groups grows linearly in the length of the fiber. Since we are interested in short length applications, we can ignore mixing among the mode

d

o

d

o 850-optimized • 1300-optimized

Ew in — d

>>

1 to

a o o o—o—o—oooo—o—oo o o o—

o

5 10 15

Principle Mode Number

Figure 1 : Relative modal delays

95
groups. We also assume that the index profile of the fiber, and therefore its modal structure, does not vary with

position. Currently, the fiber design of most interest has core diameter of 50 |im and A = 1%. At 850 nm, such

fibers support about 19 mode groups, M=l to 19, each with M modes (2 M including polarization). So, such a fiber can be represented as a set of 19 mode group delays, conventionally as delays relative to the delay of the fundamental mode.

Figure 1 shows the representation of 2 such fibers, one optimized at 850 nm, and one optimized at 1300 nm. The

linear change of delay with mode number for a fiber optimized at one wavelength when excited at a different wavelength will be discussed below. A convenient feature of this model is that if the mode group delays and the mode power distribution are known, it is straightforward to calculate the shape of the temporal impulse response. This allows detailed modeling of laser/fiber links, both from the standpoint of bandwidth and of inter-symbol

interference. [3, 4]

Differential Mode Delay

The modal structure of a multimode fiber can be directly probed using Differential Mode Delay (DMD). [5, 6, 7]. A probe fiber, single mode at the measurement wavelength, is scanned radially across the face of the multimode

fiber under test. At each radial offset position, a short -duration, spectrally -narrow pulse is injected into the multimode fiber and the output pulse is recorded.

Figure 2 shows 850-nm DMD data obtained from 0.75-km, 50-|^m, 1%-A fiber that exhibits near-optimum

performance at 1300 nm (OFL Bandwidth > 5 GHz-km), and compares it to simulated DMD data calculated using

the delays from Figure 1 . The data were obtained by exciting the SM probe fiber with pulses from a mode locked Titanium-Sapphire laser which produces pulses of FWHM ~ 4 ps. Injecting the probe pulse directly into our

detector results in near Gaussian waveforms with FWHM ~ 45 ps.

Measured DMD Simulated DMD

03C

D)

</) T3

<DN

CDEo

c —rrrrrv/^O-

. -~7\^r=0 A

0.0 0.5 1.0 1.5 2.0

delay - ns/km

0.0 0.5 1.0 1.5

delay - ns/km

2.0

Figure 2: 850 nm DMD data for a fiber nearly optimized at 1300 nm,

for SM probe fiber offsets from 0 urn to 25 um.

To calculate simulated DMD data from a known set of delays, we need to know how much light from the probe SM

fiber is coupled into each of the mode groups of the multimode fiber. Here we must make use of a full modal

treatment, calculating the overlap integrals between the electric field of the output beam from the SM probe fiber and each of the mode fields of the multimode fiber. The energy coupled into each of the modes in a mode group is summed, resulting in a set of 19 coupling coefficients for each offset position. Each trace in the simulated DMD is

96
the sum of 19 Gaussians, each with FWHM 45 ps, with temporal spacing given by the delays and fiber length, and

with amplitudes given by the coupling coefficients for that offset.

Comparing the data and the simulation, we can see several interesting features. Except for several mode groups

excited for offsets near 18 urn, we can see relative arrival times of the individual mode groups. Those mode groups

that are well separated show the same temporal width, and are not appreciably broadened by intra-mode group

dispersion. We can see that the magnitude of the M=l mode, i.e. the fundamental mode, drops off radially as expected from the simulation. The M=2 mode is not seen for on-axis excitation, but increases and then decreases in magnitude, starting at r ~ 2 urn. The M=3 mode is present for on axis excitation, but then drops off before rising

again. All these features are well captured by the calculated coupling coefficients. Finally, we note that the highest

order modes are much smaller than expected from the attenuation free calculation. The highest order mode group, presumably M=T9, is only weakly seen, even for excitation at the core-clad boundary. We know that the mode

fields of M=19, and to a lesser extent M=18, extend well into the cladding, and that energy coupled into these modes

is quickly attenuated, even over distances as short as a few 100 m.

Spectral dependence of modal delays

We will now discuss the linear change of delay with mode number for a fiber optimized at one wavelength when

excited at a different wavelength. All communications grade multimode fibers are manufactured using GeQ doped

SK>2 to achieve a nearly parabolic index profile. A 50-um, 0.20-NA fiber has a maximum index difference A =

1 .0%, while a 62.5-um 0.265-NA fiber has A = 2%. Since the index changes linearly with GeQ concentration over

the range of interest, the GeC>2 concentration profile is also nearly parabolic, rising to about 10% for a 1%-A fiber. From the individual mode fields of a 50-um, 1%-A fiber we first calculated the Near Field Intensity (i.e. /E/

2

) for an

incoherent superposition of the modes within each mode group. Using the resulting NFImW we find the effective Ge02 concentration of the mode group M as:

Eff.Conc.(M) = 2n~jNFIM (r)C(r) rdr

o C(r)=C0 (l-(r/a) 2

) for r<a, C(r) = 0 for r>a,

where the maximum concentration C0is just 10A for Ge02 doped fibers.

The results of this calculation are shown

in Figure 3 (a). The effective GeQ>

concentration of each mode group

changes nearly linearly with mode

number, except for the M=19 mode

group. This shows markedly lower

effective concentration, reflecting the

fact that modes in this group extend

deeply into the undoped (and lossy)

cladding.

Several studies have been published [8, 9] on the variation of chromatic

dispersion with Ge02 concentration. The spectral dependance of delay times was measured for graded index fibers with a wide range of A, and the studies showed consistent behavior. Using the values from [8], and using 10% Ge02

concentration for A = 1% we find values of zero dispersion wavelength, ^o(M) _ and dispersion slope, So(M), to calculate the delay as a function of wavelength for the effective GeC>2 concentration of each mode group,

delay M a) = (S0 (M)/%)k 2 {l+a0 (M)/X)4

).

97
The result of this calculation is shown in Figure 3(b) for the M=l mode and for the M=18 mode. The M=l mode

sees a higher GeC>2 concentration, and so has larger %o(M) than do the M=18 modes. (Some fibers are co-doped

with small admixture of P2O5. The impact of this on chromatic dispersion can be neglected in the current

discussion. T8])

Now we consider the response of a 1300 nm optimized fiber when excited at 850 nm. The index profile of such a fiber has been adjusted to achieve the same delay for each mode group at 1300 nm. At 850 nm, the shifts with

effective concentration of ^o(M) and So(M) result in a chromatic delay that changes linearly with mode number (at least up to M=18). The difference in chromatic delay increases linearly with M, and between M=l and M=18 we

find a maximum chromatic delay difference of -1.31 ns/km going from 1300 to 850 nm. This is in good agreement

with the observed delay difference in Figure 2, and is the value used to generate the delays in Figure 1. The value of

maximum chromatic delay difference scales linearly with GeO? concentration, so a 2%-A fiber will be characterized by a value of about -2.6 ns/km.

While the number of mode groups for a given fiber varies with wavelength, at any given wavelength, the effective GeC>2 concentration varies linearly over the same range as in Figure 3(a). Mode groups at the same value of

M/Mmax see the same effective Ge02 concetration. The value of maximum chromatic delay difference varies approximately linearly with the difference between excitation and optimization wavelengths for fiber optimized at

0

&"3-

e" ^0N Q. I O 1"

la_i ° 0

£<=> 0°O

CO S'•• /' : :^v''!:

!vJ.^.<r^; : :—-______

CD1 0 500 1000 1500

850 nm OFL BW (MHz-km)

Figure 4: OFL BW for 1 000 1 .25% Delta, 50 urn core fibers

any wavelength in the 800 to 1500 nm

range. Figure 4 shows OFL bandwidth values obtained at 850 and 1300 nm for a random sample of 1000 50- um, 1.25%- A fibers. (The values of

850 nm bandwidth were limited to less than about 1500 MHz-km by the chromatic dispersion associated with

the laser used to make the measurements.) The solid line was calculated using a maximum chromatic delay

difference of -1.65 ns/km, scaled for the non-standard A value. Each point on the line represents a fiber optimized at some wavelength but measured at either 850 nm or 1300 nm. At either wavelength, the delays vary linearly with mode group number. The overfilled launch is designed to put equal power into each

of the modes of the fiber, so the power in each mode group also increases linearly with the mode group number.

Pulses were calculated as a superposition of Gaussians, leading to approximately triangular pulse shapes. The

distribution of 850 vs. 1300 nm bandwidth values is quite typical for large collections of multimode fiber, and is associated with typical (in the mid 1980's) manufacturing variations on the index profiles. The solid line shows the behavior of a collection of "perfect" fibers, and maps out the boundary for what is allowed by chromatic dispersion

for real fibers. Similar plots can be made for 1%- A fibers using -1.3 ns/km, or 2%- A fibers using -2.6 ns/km. In

all cases the limiting behavior of real fibers is accurately shown by the idealized calculation.

Calculating OFL Bandwidth from DMD data Given the modal delay values and the mode power weights, it is straightforward to calculate the temporal impulse

response of a fiber. While it is possible to extract the actual modal delay values from a complete set of DMD data, it

is much more convenient to work directly with the DMD data. It is particularly convenient to consider the case of

the OFL measurement since in this case the mode power weight of each mode group is proportional to the mode

group number. An excellent approximation for the mode power weight can be obtained by using the fact that an SM

probe beam at radius r launches a mode power distribution in a relatively narrow range of mode groups centered on mode number Mmax (r/a)

2

, where Mmax is the maximum principle mode number for that fiber. So, to obtain the OFL

98
impulse response, we weight the DMD trace at radius r by the factor Mm DMD traces.

t (r/a)

2 and compute a weighted sum of

Calculated OFL from DMD

Measured OFL pulse

time ns/km

The results are illustrated in Figure 5. This was a 9 km, 2%-A, 62.5 um fiber with OFL

bandwidth 450 MHz-km. The data in this figure were obtained using a probe pulse from a diode laser, which had 1.8 ns FWMH when

connected directly to the detector. The DMD

data shows the low order modes arriving much

later than the high order modes, but

contributing little to the overall OFL output

because in an overfilled launch most power is coupled into high order modes. The multi-peak

character of the OFL pulse is typical of nonoptimized fiber. The impulse response constructed from the DMD data shows is in excellent agreement with the pulse shape

actually measured with OFL excitation.

Discussion:

Representing the modal dispersion of a multimode fiber by the delay values associated with the principle mode

groups results in considerable simplification and insight into its behavior. We can explain the variation of modal

structure with wavelength. In the special case of the known OFL distribution, we can explain observed limits on the bandwidth correlation between 850 nm and 1300 nm values. A straightforward approximation to the discrete mode

delay picture allows us to predict the observed OFL temporal response of a fiber from DMD data.

References

[1] D. Marcuse, Theory ofDielectric Waveguides, Academic Press, New York, 1974

[2] S. Kawakami and H. Tanji, Electron. Lett., Vol. 19, no 3, pp 100-102

[3] S. E. Golowich, P. F. Kolesar, A. J. Ritger, and P. Pepeljugoski, "Modeling and Simulations for 10 Gb

Multimode Optical Fiber Link Component Specifications", OFC 2001, paper WDD57

[4] P. Pepeljugoski, S. E. Golowich, "Measurements and simulations of intersymbol interference penalty in new

high speed 50 (am multimode fiber links operating at 10 Gb/s", OFC 2001, paper WDD40

[5] D. Marc lse, Optica! Fiber Measurements, Academic Press, New York, 1981, p288.

[6] C.M.Miller, S.C.Mettler, and I.A.White, Optical Fiber Splices and Connectors, Marcel Dekker, New York,

1986, pl77.

[7] FOTP-220 (TIA-455-220), "Differential Mode Delay Measurement of Multimode Fiber in the Time Domain "

[8] J.J.Refi and H.T.Shang, "Determining the Zero Dispersion Wavelength and Dispersion Slope of Fibers used for

the Fiber Distributed Data Interface", SPIE Vol. 841, p66 (1987)

[9] M.J.Hackert, "The impact of multimode fiber chromatic dispersion on data communications", SPIE Vol. 1 178, pi 88 (1989)

99

DMD Measurement and Simulation on Short-Length, 850-nm Laser-Optimised,

50 jim Core Diameter, GIMM Optical Fibres

F.J. Achten1

, M. Bingle23, B.P. de Hon2

, M.J.N, van Stralen

1

'Draka Fibre Technology, P.O. Box 1442, 5602 BK Eindhoven, The Netherlands

2 Eindhoven University of Technology, Faculty of Electrical Engineering,

P.O. Box 513, 5600 MB Eindhoven, The Netherlands

presently at EM Software & Systems, P.O. Box 1354, Stellenbosch 7599, South Africa

Abstract

A new Differential Mode Delay (DMD) measurement set-up has been developed as standardised by the IEC [1]. This

set-up will be used in an optical glass fibre production environment for characterising 850-nm laser-optimised, 50

um core diameter, graded-index multimode (GIMM) optical fibres for 10 Gb/s applications. Additionally, the set-up has been used together with a new, full-wave numerical model for multimode fibres, to investigate the effect of

profile deviations.

Introduction

The demand for high bandwidth in data- and telecommunication systems has led to the development of 10 Gb/s

Ethernet networks. The laser and detector characteristics, as well as the fibre characteristics determine the system

bandwidth. In the IEEE standard for 10 Gb/s Ethernet networks, a new GIMM fibre with a 50 um core diameter is considered as a feasible solution at 850 nm for fibre lengths up to 300 metres. The bandwidth of a multimode fibre is predominantly determined by intermodal dispersion. The observed intermodal dispersion depends on the specific source conditions. Therefore, in addition to the traditional bandwidth measurement (for an overfilled launch), the

quality of the multimode fibre is tested by performing a differential mode delay (DMD) measurement, according to the IEC standard [1]. A DMD measurement provides a means to characterise the modal structure of a multimode fibre in detail. The

multimode fibre is connected to a short, 850nm single-mode fibre probe. This single-mode probe is excited by a pulsed 850nm laser with a very narrow spectral width. The probe is moved gradually from the centre of the core towards the cladding of the multimode fibre and the output pulses are detected after propagating through a specified

fibre length. The output pulses form the DMD pattern of the fibre. It exhibits the travel-time drift between the

different mode ensembles excited for different probe positions, and the pulse broadening due to intermodal

dispersion between mode groups. The DMD pattern provides a means to assess the quality of the fibre.

At Draka Fibre Technology, a DMD measurement set-up is developed to conform with the EEC 60793-1-49 standard

[1], yet with the specific objective to perform DMD measurements in a PCVD (Plasma-activated Chemical Vapour

Deposition) fibre production setting as a means of quality control. A commercial set-up to perform a standardised DMD measurement on short length fibres (hundreds of metres, up to two kilometres) does not yet exist to our knowledge. In order to support the DMD characterisation of multimode fibres, a full-wave numerical model was

developed at the Eindhoven University of Technology. In this paper, we present the DMD results for a graded-index

multimode fibre, with a typical deviation from the graded-index profile in the region around the fibre axis.

The DMD measurement standard

The DMD measurement standard, as defined by [1] specifies the optical source, launch system and detection system.

The end face of the fibre under test is irradiated by pulsed laser tight at a specified wavelength (850 ± 5 nm). One

option is to image the output spot of the probe fibre with a modefield diameter (MFD) of 5 ± 0.5 um onto the end

face of the fibre under test. The beam is moved across the end face of the fibre from the optical centre of the core towards the cladding. The spectral width of the laser and the duration of the pulses are specified, and dependent on

the length of the fibre to be measured.

101
The propagating pulses are detected to form a DMD pattern from which the DMD values are calculated. The pattern

is considered within two masks: an inner mask, including the pulses from radius 5 to 18 (j.m, and an outer mask

including all pulses from the core centre to a 23 um radial offset. The DMD value is the time difference (at 25% of

the maximum) between the leading edge of the fastest pulse and the trailing edge of the slowest pulse within the mask [1, 2, 5]. A set of standardised templates determines the quality of the fibre.

The DMD measurement set-up

The objective was to develop a DMD set-up for production environment while it still complies with the DMD

measurement standard [1]. The main challenge was to develop a low power laser, instead of the commonly used high power, mode-locked Titanium Sapphire laser. The safety regulations are less stringent for the pertaining low power

laser. This laser generates pulses with a full width, half maximum (FWHM) duration of 90 ps, a centre wavelength of

849.9 nm and a line width smaller than 0.2 mn. The small line width is necessary to prevent the effect of chromatic

dispersion in the fibre from influencing the DMD [1] [4]. The pulse is coupled into a single-mode probe fibre (launch

fibre) with a core size of 5 um. The other end of the probe fibre is scanned across the core of the multimodc fibre, with the aid of a closed-loop piezo-electric system with nanometre resolution. The end face of the probe fibre is positioned at a distance closer than 10 |j.m from the cleaved multimode fibre end, as prescribed by the standard. The

pulses are detected by an optical-to-electrical converter with a bandwidth of 8 GHz. The DMD value is calculated,

and compared with the specifications of the two masks. These values are two of the parameters which determine

acceptance of the 850 mn laser-optimised multimode fibre according to [5].

The full-wave numerical model for DMD computations

The multimode fibres under consideration are assumed circularly symmetric, isotropic and translationally invariant along the longitudinal direction. A fibre consists of a radially inhomogeneous core, and a homogeneous cladding of

infinite radial extent. The permittivity of the fibre material is characterised by the Sellmeier coefficients for a three- term harmonic oscillator model of doped, bulk, fibre glass [7]. In the relevant wavelength band, the losses are

negligible. We employ a vectorial field model to compute the properties of the HEW« and EHm« modes, where m and

n are the azimuthal and radial modal indices, respectively. In particular, we consider a vectorial transverse resonance method in the radial directions, involving numerical integration of a system of ordinary differential equations [3] [7].

The determination of the modal field distribution excited in the multimode fibre at the splice with the single-mode

fibre probe comprises a scattering problem. However, the actual splice is not specified, other than that the distance between the fibres should not exceed 10 um. Further, the permittivity contrast between the fibres is small. Hence, it suffices to project the probe field onto the modal fields in the multimode fibre with the aid of overlap integrals [8]. The modal power distribution will also be affected by the differential mode attenuation, primarily due to bending

losses. Differential mode attenuation has not been incorporated in the model. At the receiver end of the fibre, the transmitted signals are detected by a power sensor, which measures the moving time average of the total instantaneous power flowing through a cross-section. The instantaneous power corresponds to a convolution in the frequency domain. In general, modes at different frequencies cease to be orthogonal, inducing instantaneous-power

coupling between modes. Further, for off-centred excitation the rotational symmetry with respect to the probe

polarisation is broken. However, for the multimode fibre setting under consideration, these effects on the DMD are

insignificant [3].

For DMD experiments conducted according to the DMD standard with a laser source that generates a single lasing

mode, the pulse-width and the fibre length are such that the chromatic dispersion may safely be neglected. The modal

group delays are of importance. Assuming an optimal resolution of the time window of observation of a few

picoseconds, the group delays must be computed to within six significant digits. For the accurate computation of a group delay, we evaluate the total derivative of the characteristic equation and invoke the implicit function theorem

[7]. Regarding the sum of the modal amplitudes, two significant digits suffice.

Example: A graded-index fibre with a distortion near the centre

The DMD pattern for a good fibre in terms of 10 Gb/s standards shows minimal travel-time drift between the various

offset pulses (i.e. they are aligned in time) and the pulse distortion is similar for all the pulses. It is well-known that there exists an optimal alpha-parameter in a graded-index profile for which the bandwidth of the fibre will be

optimised at a specific wavelength. This is supported by numerical experiments, some of them reported in [3]. We

102
found that the numerical optimal alpha-parameter (relating to the fibre refractive index profile) is slightly higher than

the one used in practice (relating to the preform refractive index profile). This is mainly due to a change in the

effective profile of the drawn fibre.

Figure 1 : Refractive index profile of the preform from which the fibre under investigation is drawn. The right figure is an enlargement to show the "bump". The dots are the measured values; the solid curve is an alpha-profile.

z p i —t

t i 1 —1—

-0.8 -0.6 -0.4 -0.2 0 0.2 Relate time normalised to fibre length [ps/m]

Figure 2: Measured (dotted line) and computed (solid line) DMD pattern of the fibre under

consideration.

The inset shows a "bump" deviation from the graded index profile fit which results in pulse distortion in the DMD

pattern for probe positions close to the centre. The measured and computed DMD patterns are shown in Figure 2. The result saows the combined effect of a non-optimal alpha-parameter and a deviation from the ideal graded-index

profile. The appearance of a second peak in the DMD pulses is an indication of the non-ideal refractive index profile close to the fibre axis. It is important to recognise that the profile model for the computation is based on preform data and therefore it does not include the effect of the drawing process on the specific sample under test. A better agreement with the measured DMD pattern is obtained for a numerical profile model with a slightly higher value for

103
the alpha-parameter. This supports the idea that the drawing process influences the refractive index. Further

differences between the numerical model and practice might be a non-ideal intensity distribution for the light

emanating from the probe (non-ideal cleaving) and the small offset between the probe and the fibre under test, in

addition, differential mode attenuation is not included in the model. Nevertheless, computation and measurement show similar trends in the DMD patterns. A fibre with a DMD pattern shown in Figure 2 will be rejected according

to the fibre specifications indicated in [5].

Conclusions and future work

A new Differential Mode Delay (DMD) measurement set-up has been developed according to EC [1] for short- length, 850-nm laser-optimised, 50 urn core diameter, GIMM optical fibres. The set-up is employed to investigate the influence of profile deviations on the fibre performance. The latter is supported by computations with a full-wave numerical model. Deviations in the refractive index profile of the preform are reflected in the measured and

computed DMD patterns.

More measurements and computations will be performed in the future to obtain a better understanding of the

relationship between DMD and the related refractive index profile, as well as the mapping from the preform to the drawn fibre profile.

References

[1] 1EC 60793-1-49 Ed. 1 - Optical fibre - Part 1-49: Measurement methods and test procedures - Differential Mode Delay.

[2] TIA, FOTP-220 Differential mode delay measurement of multimode fiber in the time domain, TIA-455-220,

PN3-0008, 2001.

[3] M. Bingle, B.P. de Hon, "Differential mode delay - Full wave modeling and various levels of

approximations' ', paper 2060, URSI General Assembly, Maastricht, The Netherlands, 2002.

[4] M.J.N, van Stralen, B.P. de Hon, M. Bingle, F.J. Achten, "Short pulse, small spot size, central launch in multimode fibres: comparison between measurement and computation ", SOFM 2000.

[5] TIA Standard, TIA-492AAAC, Detail Specification for 850-nm Laser-Optimized, 50-jum Core Diameter/125

fm Cladding Diameter Class ofGraded-Index Multimode Optical Fibres.

[6] W. Hermann and D. U. Wiechert, "Refractive index ofdoped and undoped PCVD bulk silica, "Mat. Res. Bull,

vol. 24, p. 1083, 1989.

[7] M. Bingle, B. P. de Hon, and M. J. N. van Stralen, "Electromagnetic modelling and optimisation for the design ofsingle mode optical fibres", Proc. 2001 URSI Int. Symposium on Electromagnetic Theory, Victoria, Canada, pp. 515-517, 2001.

[8] E.-G. Neumann. Single-Mode Fibers, Fundamentals. Berlin: Springer, 1988.

104
Determination of Skew in Multimode Ribbon Fibers

Arthur J Barlow, PerkinElmer Optoelectronics, Wokingham RG41 2GY UK

E-mail: arthur.barlowfolperkinelmer.com

Michael J Hackert, Corning Inc, Corning NY USA

Email: mHackert@stny.rr.com

Abstract:

This paper discusses issues of how multimode (MM) fiber ribbon skew at 850 nm may be estimated from

1310 nm measurement with high accuracy using single-mode fiber test sets. Modern high-speed

applications such as the 10 Gigabit Ethernet standard and high-speed parallel interconnects are driving

measurement requirements. It is shown that less than 5 ps/m fiber-to-fiber skew should be achievable

with careful fiber selection and cable design.

Introduction

Modern multimode fibers have been developed to operate at 1 Gb/s, using the Gigabit Ethernet (GbE) standard. Considerable effort has been expended to ensure these fibers have sufficient modal bandwidth. This is typically

achieved by careful differential mode delay (DMD) control via special attention to the index profile. In addition, by

limiting the number of modes and/or mode groups that are launched, the required bandwidth for data transmission can be achieved. For the new 50 (im fiber designed for 10 GbE, such as Corning® InfiniCor® SX+ fiber, the fiber DMD characteristics are measured using the pulse delay method [1], and the results compared to a DMD mask.

In this paper, we discuss the prediction and measurement of skew in GbE optimized fiber ribbon cables, designed to operate at 850 nm. However, everything we present applies equally well to all types of MM fiber, including both 50

|im and 62.5 |am core diameter types. The key focus is on the fiber properties rather than cabling factors.

Background

In digital parallel transmission, the term "skew" is used to denote the time difference between the different parallel- transmitted bits of data. In high-speed operation, there are strict standards for the permissible amount of skew [2]. Typical criteria range from £17-23 ps/m to £5 ps/m at typical lengths of a few hundred meters. The former is relatively easily achievable with careful cable construction; the latter challenges the intrinsic limits on the fiber properties and current measurement technology. Within such a system, the fiber transmission medium (most

frequently in ribbon fiber form) is a strong potential contributor to the data skew.

Skew in a ribbon fiber is the relative delay time across the ribbon, so one fiber (typically one of the fibers at the edge, e.g., fiber #1), is chosen as the reference delay time for the other fibers [3]. The different relative delays Xj - Xi = Axj are the individual differential times of flight. The ribbon fiber skew is defined as the magnitude of the difference of the maximum relative time delay and the minimum relative time delay:

SKEW= | max(AxO - min (At0 | -( 1

)

Optical time delay differences will result from variation of group index N, called AN, across the different fibers within the ribbon. This variation originates from the effect induced by cabling, from the fiber itself, or the transmitter interacting with the fiber through its wavelength or launch. Once formed into a cable, changes will be

photoelastically induced in N by stresses "frozen-in" to the ribbon package incorporated during the ribbonizing

processes. The set of fibers used in the ribbon will have a range of indices due to the natural production tolerances on the group index. This range can be characterized by a skew measurement, time of flight or OTDR measurement,

or measurement of chromatic dispersion if the intrinsic delay is captured. Delay differences also originate from the

differential modal delay difference as measured by the DMD. Since restricted launch sources typical of lasers for high-speed application can selectively excite different modes, different launches can create skew in fibers that otherwise have no other source of skew. Likewise, the set of transmitters used with the ribbon may have a range of

105
wavelengths. Skew can also be created since the index is wavelength dependent.

This work has two prime motivations - 1) to determine if a fiber can be adequately characterized for skew using a single-mode launch, and 2) to determine if measurements at 1310 nm can adequately characterize skew at 850 nm,

which is the wavelength of most typical GbE short-length applications. This motivation arises from a practical consideration that single-mode fiber based strain/skew measurement equipment using 1310 nm sources is currently

commonly available within a cable factory [4].

Skew Contributions

CABLING INDUCED DIFFERENCE: We consider first the cable fiber contributions to skew in turn. From the known theory of strain [5, equation 8] in fibers, the AN at the frozen-in stress within a ribbon is proportional to:

AN= (-N2

. { Pl2-o-(p„+p12) } ) -(2) 2 where p the strain tensor components and a is the Poisson's ratio. For fused silica, the values are pn=0.121,

Pi 2=0.27, a=0.17, and N= 1.468. Examination of equation (2) shows that the variation in skew across wavelength is due entirely to the dispersion of N. Since the variation of N from 1310 nm to 850 nm is less than 1% [6], we can make the assumption that the stress within a ribbon induces a similar "stress" skew value at 1310 nm as it does at 850 nm - in each case proportional to the stress differences across the fibers. Extending this argument further, we

can expect the contribution to total skew due to stresses to be wavelength independent.

FIBER INDEX DIFFERENCE: Next, we consider the skew contribution due to the fibers having differing N

values across the ribbon. Conceivably, the cabler could deliberately tension each fiber to counteract the natural index difference. Unfortunately, keeping track of specific fibers and adjusting the stresses is hardly a practical

proposition for a modern cable factory. Realistically, the cabler can only reduce this source of skew by selecting

closely matching fibers, such as using fibers drawn from the same preform.

FIBER CHROMATIC DISPERSION DIFFERENCE: In order to evaluate the variation in skew with wavelength

starting with a comparison between 1310 nm to 850 nm, we consider the impact of the variation in chromatic

dispersion between each fiber [7]. The chromatic dispersion is effectively a measure of the index as a function of

wavelength. We expect the dispersion of each fiber to fall within a tolerance band defined by the fiber specification.

From this allowed range, we can estimate the delay difference. In a standard unshifted fiber, the group delay curve

follows a Sellmeier equation:

where

A

So

A + -S0 *kj ps/m -(3)

a constant corresponding to the time of flight for a given length of fiber the zero dispersion wavelength

slope at the zero-dispersion wavelength

wavelength at which the delay is being calculated

To evaluate this dispersive skew, we take the edge fiber in the ribbon as a reference for the other fibers. Because we

have different fibers, the S0 and X0 become unique to each fiber - S0 i and Xoi for fiber 1 and S0j and ^.oi for fiber i. By

defining a reference wavelength X u we can evaluate the skew at another wavelength X2

. The dispersive skew at wavelength X2 is given by:

AtiK =\ [(x , (A., ) -x f ))- (x , (A.,

)

-t ! (A.

2 ))] ps/m -(4)

Substituting equation (3) in equation (4), we get:

106
1 +

A,oi

2« 2

1 . SOi 1 +

A, Of

A/2 A/i

> + A-A ps/m -(5)

Equation (5) allows the dispersive skew term to be evaluated across a ribbon fiber. Since we are focusing on the

issue of skew difference across wavelength, we take 1310 nm as our reference wavelength (where the dispersion term in (5) reduces to a constant {A; - AJ ). In fact, at this wavelength, a skew measurement would give the sum of

the stress skew, the intrinsic fiber index difference (i.e., range of A,), and the dispersive skew. If we now evaluate

the dispersion skew difference between 850 nm and 1310 nm, this would be the only major difference in the total skew between 1310 nm and 850 nm. Evaluating equation (5) at 850 nm ignoring the constant {Aj -A]}, the typical

fiber "box spec" values for 50 um fiber (S0 i=0.093 ps/nm2-km, Xqi =1305 nm, and S0j=0.095 ps/nm2-km, Xoi =1315

nm) results in 1.69 ps/m of skew. For 62.5 um fiber (S0) =0.090 ps/nm2-km, Xq\ =1335 nm, and S0i=0.093 ps/nm2

- km, Xoi =1345 nm), the result is 2.19 ps/m of skew. Therefore, over the ribbon, at 850 nm, we would expect a maximum skew difference of less than 2 ps/m due to this dispersive skew. TRANSMITTER WAVELENGTH IMPACT: An additional concern with chromatic dispersion mismatch is that over the typical ±10 nm width of the 850 nm waveband there will be a finite difference in chromatic delay.

Equation (5) reduces to equation (6) if the chromatic dispersion is assumed to be the same for all fibers. The half wavelength tolerance (e.g., ±x nm) is plotted for typical characteristics at 850 nm in Figure 1.

8

A2 + - 2 A2 J

A/l + « 2 A»i _

> + A,-Al ps/m -(6)

10 15 20

Half Wavelength Tolerance (nm)

Figure 1 - Interaction of Wavelength and Fiber Index at 850 nm (Xo = 1310 nm, S0 = 0.101 ps/nmA2-km)

Thus, even the simple wavelength tolerances across the parallel laser transmitters will invoke a "wavelength skew" term as well, amounting to approximately 3 ps/m of ribbon for the typical 10 nm wavelength variation. Moreover, this is outside the control of a ribbon cable or fiber manufacturer. We can evaluate the dispersive skew if the dispersion characteristics of each fiber in the ribbon were known. Fortunately, test equipment

typically used for skew testing in ribbons can also perform chromatic dispersion measurements at the same time [8]. These measurements enable the

possibility of using a "correction factor" for skew

at 850 nm versus 1310 nm. This is especially useful in the case where a multimode fiber might

be used at either wavelength.

DMD DELAY RANGE: So far we have neglected the modal delay differences within the MM fiber. The fiber DMD can give rise to apparent skew [3]. The case of the most recently developed fiber, a 50 um fiber designed for 10 GbE application, is the easiest to handle. This fiber, Corning® InfiniCor® SX+ fiber, is specified to have a

restricted range of DMD. The maximum allowable delay difference is 0.7 ps/m. This results in 1.4 ps/m of skew

between two fibers. This is well below the 5 ps/m typical tighter skew requirement. All other fiber types require

approximation since it is only this new 50 um fiber for which there is a DMD range requirement. During the course of 1 GbE development, 62.5 um fiber was shown to have up to 2 ps/m delay difference [9]. The maximum DMD

range can be approximated using simple Gaussian assumptions. In this case, the DMD range can be estimated by

the following formula [10]:

107
/ \ 44U DMD range [in ps/m)= 7 \ -(7) 5 v ; Bandwidth (in MHz -km)

In the case of 500 MHz-km fiber, the DMD range is 0.88 ps/m, resulting in a potential 1.76 ps/m skew between two

fibers. Although this approximation provides an estimation of the skew resulting from DMD, there can be a large difference between this prediction and the actual performance on fiber specified in terms of the standard overfilled bandwidth. This is evident by the difference between the 0.88 ps/m predicted and 2 ps/m previously shown. Thus,

since the maximum fiber-to-fiber estimated DMD-induced skew is 4 ps/m, it is possible to use skew tests on only

the lowest order mode, using single-mode optics to reveal the cable-related skew effects.

Conclusion

This paper has focused on the issue of skew testing in multimode fibers, in particular fibers designed for high-speed

applications operating at 850 nm operation. We have shown that: • Better than 5 ps/m skew performance should be deliverable on new 50 urn fiber designed for high-speed

application at 850 nm (i.e., meeting a DMD requirement) by testing at 1310 nm using a single-mode launch

to confirm that the cable induced skew is negligible.

• The difference in skew resulting in measuring at 1310 nm to determine 850 nm performance and the mismatch in index between two fibers is estimated to be less than 2 ps/m for typical 50 um and 62.5 urn

fibers. This can be quantified from the measured chromatic dispersion.

• The ribbon fiber skew due purely to the wavelength tolerance of the set of transmitters used on a link can be significant compared to a 5 ps/m allowance. The effect using 850 nm sources with a 20 nm range is estimated to be less than 2 ps/m for typical 50 um and 62.5 um fiber. • The impact of intermodal dispersion on skew should be less than 1 .4 ps/m on new 50 um fiber designed for 10 GbE application. It could be as high as 4 ps/m on installed base fiber. • A few ps/m is close to the state-of-the-art skew accuracy that may be obtained for ribbon fibers. This

makes delivery to a £5 ps/m requirement problematic, but a 15-20 ps/m specification more realistic.

Utilizing this understanding of the various factors affecting multimode fiber skew, delivery of ribbon cable meeting

5 ps/m skew should be achievable. Current measurement equipment can be utilized to improve the estimation of

skew. For example, equipment designed for testing of single-mode fiber at 1310 nm can provide insight into the most significant factors affecting skew, specifically cabling induced stress. Therefore, the difficulty of obtaining

costly single-mode optics at 850 nm, or indeed using 850 nm multimode optics with the corresponding requirements on launch control within the test instrument, can be avoided. Careful selection of the fiber, such as selection of fiber from the same preform, or by utilizing the measurement equipment to estimate any index differences should control

the fiber related skew. By utilization of this measurement equipment in conjunction with careful selection of the

fiber, this requirement should be achievable.

Acknowledgement

The authors are grateful to Chris DiMinico of CDT Corporation for detailed and helpful discussions.

References

1 . TIA FOTP-220 "Differential Mode Delay Measurement of Multimode Fiber in the Time Domain".

2. IEEE HPPI-640-OPT standard in draft, Project number 1 249-D.

3. A .Barlow et al, "Measurement of Ultra-low Skew in Ribbon Fibers". OFMC, 1997, London.

4. G. Brown, "Chromatic Dispersion Measurement in Graded-Index Multimode Optical Fibers", Jnl. Lightwave Technology. 12, 1 1, pp. 1907- 1909, 1994

5. M. Brininstool, Optical Engineering, 26, 1987, pp. 1 1 12-1 1 19.

6. M.J. Adams, "An Introduction to Optical Waveguides", Wiley, p. 246

7. M. Hackert, "The Importance and Application of Dispersion of Multimode Fiber in LANs and Its Relation

to NA", International Wire and Cable Symposium, 1988, pp.237-242.

8. PerkinElmer CD400 Series Measurement Systems.

9. M. Hackert, "Characterizing Multimode Fiber Bandwidth for Gigabit Ethernet Applications", SOFM 98.

10. Corning Cable Systems Application Note 20, "Bandwidth / Dispersion Equation Derivation".

108
Phase imaging methods for optical fiber characterization

A. Roberts*, G. Baxter1

, N. Dragomir*, S.T. Huntington^,

E. Ampem-Lassen , M.L. Michna* and K.A. Nugent*

'School of Physics, University of Melbourne, Victoria, 3010, Australia

+ School of Communications and Informatics, Victoria University, PO Box 14428, Melbourne, Victoria,

8001, Australia

^Particulate Fluids Processing Centre, School of Chemistry, University of Melbourne, Victoria, 3010,

Australia

Abstract

In this paper we demonstrate the application of two phase imaging techniques, Differential Interference Contrast (DIC) and Quantitative Phase Microscopy (QPM), to the determination of the microscopic

physical structure of optical fibers and fiber gratings. We also show that birefringence images can also be

obtained using QPM with polarized light. As well as being able to image fibers, these methods can

provide quantitative information on refractive index and axial stress profiles within axially symmetric

fibers.

Introduction

The development of a wide range of optical fibers with complex structures means that the ability to accurately determine the physical properties of the fiber is essential. Two quantities of central importance

are knowledge of the refractive index profile of a fiber and stress introduced into the fiber during the

fabrication process or through bending. In this paper we demonstrate the application of two phase

imaging methods, DIC and QPM, to the determination of the physical structure of the fiber. In addition to enabling the determination of the physical properties of the fiber, we also present images of an in-fiber Bragg grating which display the artifacts introduced into the fiber by the grating writing process. A knowledge of the refractive index profile is invaluable since from it fiber properties such as the mode

profile, dispersion and cutoff wavelength can be calculated. The commonly used industry standard

method, the Refracted Near Field (RNF) technique, cannot be used to study fibers where the refractive index varies along the axis of the fiber, has difficulty analyzing fibers with complex structure and it is destructive since the fiber must be cleaved. The calibration of any instrument based on the refracted near

field technique is also critical if precise numerical values for the index change An are required.[l] A range

of other methods have also been considered and are summarized in Reference 2. Here we present two

phase imaging methods, DIC and QPM, that can be used to quantitatively determine the phase shift in

light as it traverses an optical fiber and from this information determine the refractive index profile.

There is also a great deal of interest at present in further understanding stress within fibers and its role in the index change of fibers on irradiation with ultraviolet light [3]. An understanding of the role that changes in stress play in the change in refractive index of a fiber on thermal annealing is also important if index change mechanisms are to properly understood. Commonly used methods for determining stress within fibers generally involve variations on polarimetry [3, 4] and tend to suffer from poor signal-tonoise and/or spatial resolution. Here we also demonstrate that QPM can be used to accurately measure

birefringence and we are currently in the process of extending this research into the determination of

intrinsic stress within fibers.

The optical microscopic methods discussed here are simple to implement, accurate, relatively inexpensive

and non-destructive. Their spatial resolution is diffraction-limited. They can be used to study fibers where

the refractive index profile and stress vary along the axis of the fiber (for example tapered fiber sensors

109
and fibers containing gratings), and can be extended to the study of non-axi symmetric fibers by

employing tomographic techniques.

Phase Imaging

Differential Interference Contrast (DIC) microscopy [5] has achieved widespread popularity amonst the biological community for its ability to very simply elucidate the structure of transparent specimens. DIC

involves the inclusion of a Wollaston prism into the microscope beam path which splits the incoming

light into two spatially separated, orthogonally polarized beams of light. These two beams are recombined

after they have traversed the specimen and their interference provides information about phase gradients

within the object. Using certain a-priori assumptions, this method can also be used to determine the

refractive index profile of an axially symmetric fiber.

Quantitative Phase Microscopy (QPM) [6] is a new noninterferometric technique that can be used to quantitatively determine

the phase of a transparent specimen. QPM is based on the transport of

intensity equation where variations within the phase introduced into the lightfield by a specimen are manifested as variations in the transmitted intensity as the distance is varied. A recently developed

algorithm [7] can be used to retrieve the phase of the field from three

(or in the case of uniform intensity, two) intensity images. Two key

advantages of this technique is that the phase determined in this manner does not been to be 'unwrapped' and the method can be used

with partially coherent light. This algorithm has also been shown to Figure 1: Typical DIC image of be robust and has been applied to phase imaging with light, x-rays, an optical fiber. electrons, atoms and neutrons. [8] We present below the application

of this method to the determination of the refractive index profiles of

axially symmetric optical fibers. In the case of non-axially symmetric fibers, a series of phase images can be obtained as the specimen is rotated about its axis and tomographic methods used to determine the index profile. [9] In addition, QPM can be used with polarized light to quantitatively determine the birefringence of a specimen and we have applied this to the determination of the axial stress induced

when a fiber is bent through a known radius of curvature [10].

Differential interference contrast imaging

DIC images were obtained using an inverted

Olympus IX FL infinity corrected optical system

equipped with high resolution Nomarski optics. An

argon ion laser operating on a single line at a wavelength 488 nm was used as the light source. In

addition, the system used a computer to control the

fine focus of the microscope via a stepper motor,

translating the objective of the microscope in

0.1 p,m increments along the optical axis of the microscope. The laser beam was raster scanned over an area of the specimen using galvo mirrors. Fibers

under study had their plastic coating removed and

placed in a cell and surrounded by index matching

oil. A typical DIC image of a Er

3+-doped fiber is shown in Figure 1 . The core, along with the well-known

depression in index at its center, are clearly visible as is the boundary of the depressed cladding region. In order to demonstrate the high spatial resolution and the application of DIC to the study of fibers and

devices possessing variation along the axis of the fiber we investigated a Bragg grating. This grating was

Figure 2: DIC images of a Bragg grating. The

fiber was rotated about its axis by 90° to obtain

the second image. Image sizes 9.7 x 10.4 um.

110
fabricated at Victoria University using our own facilities by the familiar phase mask technique with

standard communications fiber. The samples were hydrogen loaded prior to being irradiated with an UV

laser source (244 nm CW). An interference pattern was formed at the core of the fiber using a 1.06 |im

pitch phase mask. The spectral response of the fiber was measured and a transmission minimum found at approximately 1534 nm. Two DIC images of the Bragg grating are shown in Figure 2. The second image was taken after the fibre was rotated about its axis by 90° with respect to its initial orientation. The

structure of the grating is apparent from these images. Particularly striking is the asymmetry of the grating

and the appearance of artifacts resulting from the grating fabrication process.

Quantitative Phase Microscopy

QPM was performed using transverse images obtained with a standard bright-field microscope (Olympus

BX-60 microscope, 0.95 40* UplanApo microscope objective). The condenser numerical aperture was set to 0.2 and a bandpass filter with a central wavelength of 521nm and a passband of lOnm was included in the light path. A dilute solution (~85%) was used as the index matching fluid. Fibers under investigation

have their plastic coating removed.

(a) (b) Figure 3: Refractive index of an optical fiber determined using QPM. (a) shows a surface plot of the index as a function of radial and axial position within the fiber and (b) shows the average radial profile (solid line) compared

with the topography measured with an AFM (dots) of the fiber after etching.

Three bright-field images of GF1 (Optical Fibre Technology Centre, Sydney, Australia) were obtained.

These consisted of an in-focus image and two defocused images at ± 2.6 um. The in-focus image

displayed virtually no structural information about the fiber. These three images were then processed

using an algorithm based on the transport of intensity equation [6] to produce a phase image of the fiber. The inverse Abel transform [11] was then applied to this phase image to determine the refractive index

profile shown in Figure 3(a). The average profile over the 100 Jim length of fiber displayed in Figure 3(a)

is shown in Figure 3(b). Note that the core and the various deposition layers are clearly resolved. The

maximum refractive index change measured using this technique was found to be 0.0064 ± 0.0003

(standard deviation), which is in good agreement with that found using a conventional profiling

instrument of 0.0056. It should be noted, however, that the profiler did not resolve the feature near the index maximum at a radius of ~ 3um and its resolution of the deposition rings in the depressed cladding was noticeably poorer than that obtained using QPM. In Figure 3(a) a shaded surface plot demonstrates

the ability of this method to determine axial variations in refractive index, while in Figure 3(b) the

refractive index determined using QPM is compared with the vertical structure of the endface of the fiber

after it has been cleaved and etched in a saturated solution of buffered hydrofluoric acid for 3 minutes.

Ill
The topography was measured with an Atomic Force Microscope (AFM) operated in contact mode. [12]

Given the complexity of the etch rate due to the presence of multiple dopants, the AFM profile is not expected to be proportional to the index profile, but structures seen in the topography measured in this way clearly match the features seen in the QPM profile.

Polarized light QPM

We have also demonstrated that QPM can be used with

polarised light [10] to determine the birefringence of

specimens. This is performed by acquiring a phase image of

the specimen when the light is polarised along one principal

axis of the specimen (for example, along the axis of an optical

fiber) and a second with the light polarized in the orthogonal

direction. Simply subtracting these two images produces a

quantitative birefringence image of the specimen. In particular, we obtained birefringence images of an optical fiber bent

through known radii of curvature ranging from 1cm to 8cm

and obtained excellent agreement between the birefringence

determined and that calculated using a simple model which

assumes that the fiber behaves as a homogeneous cylindrical

cylinder. Figure 4 shows the birefringence image obtained

when the fiber is bent through a radius of curvature of 1cm.

The center of curvature is to the left of the image and the regions of compressive (dark) and tensile (light) stress are clearly visible.

Conclusion

We have demonstrated the applicability of phase imaging methods to the characterization of the physical

properties of optical fiber and other photonic devices. In addition to the fact that these methods enable the visualization of the fiber or device structure with diffraction-limited resolution, they can also be used to determine the refractive index profiles of optical fibers. These techniques are straight-forward, relatively

inexpensive and accurate compared with other techniques.

Acknowledgements

The authors would like to acknowledge useful conversations with Peter Farrell and John Canning. The

authors would also like to thank Tom Ryan of the Optical Fiber Technology Centre (OFTC), Australia,

for obtaining independent refractive index profiles of samples, and the OFTC and the Laboratoire de

Physique de la Matiere Condensee, Universite de Nice for the provision of the fiber specimens.

Figure 4: Birefringence image of an

optical fiber bent through a radius of

curvature of 1cm. The center of

curvature is to the left. Image size 176 x 121 urn.

References

1 . D. Marcuse and H. M. Presby, Proc. IEEE, 68, 666-688, 1 980.

KW Raine, JGN Baines and DE Putland, J. Lightwave Tech., 1 162-1 169, 1989.

N.H. Ky, G.G. Limberger, R.P. Salathe, F. Cochet and L. Dong, Appl. Phys. Lett., 74, 516-518, 1999.

K.W. Raine, R. Feced, S.E. Kanellopoulos and V.A. Handerek, Appl. Opt., 38, 1086-1095, 1999. T.R. Corle and G.S. Kino, Confocal scanning microscopy and related imaging systems, (Academic

San Diego, California, 1996), p. 247. D. Paganin and K.A. Nugent, Phys. Rev. Lett. 80, 2586-2589, 1998. A. Barty, K.A. Nugent, D. Paganin, and A. Roberts, Opt. Lett. 23, 817-819, 1998

K.A. Nugent, D. Paganin and T.E. Gureyev, Physics Today, 54, 27-32, 2001.

A. Barty, K.A. Nugent, A. Roberts and D. Paganin, Opt. Comm., 17, pp. 329-336, 2000.

A. Roberts, K. Thorn, M.L. Michna, N. Dragomir, P. Farrell and G. Baxter, Opt. Lett., 27, 86-88,

2002.

M Kalal and KA Nugent, Appl. Opt., 27, 1956 - 1959, 1988.

S.T.Huntington, P.Mulvaney, A .Roberts and KA Nugent, J. Appl. Phys., 82, 2730, 1997.

10.

11.

12.

112
Measurement of fiber birefringence

using Lyot-Sagnac interferometer

Chang-Seok Kim, Young-Geun Han*, Raymond M. Sova and Jin U. Kang

Department ofElectrical and Computer Engineering,

Johns Hopkins University, Baltimore, MD 21218

Phone: 410-516-8186, Fax: 410-516-5566, E-mail: ikane(a,jhu.edu

Un-Chul Paek and Youngjoo Chung

Department ofInformation and Communications,

Kwangju Institute ofScience and Technology, Kwangju, Korea

* Permanent Address: Department ofInformation and Communications, K-JIST, Kwangju, Korea

Abstract: We propose and demonstrate a simple and accurate optical fiber modal birefringence measurement technique. The technique is based on discrete tuning of the periodic spectrum

produced by the dual-segmented Lyot-Sagnac fiber interferometer. The modal birefringence of optical fiber is an important parameter for both the polarization-dependent optical devices using high birefringence fibers [I] and the optical fiber telecommunication systems using low birefringence

fibers [2]. Various techniques have been proposed to measure the birefringence of optical fibers [2] [3] [4]. A

polarization-sensitive analysis of the backscattered signal was proposed for measurement of low-birefringence fibers

[3], which requires a length of fiber too long to be practical for some applications. For the measurement of fibers with less than one beat length, fiber twist adjustment in the fiber-optic loop mirror was suggested [2]. The fiber Sagnac loop interferometer can be also used to determine the birefringence of fiber, where the birefringence, or beat

length, of optical fiber could be determined from the periodic transmission spectrum of the standard fiber Sagnac

loop interferometer [4]. However, this measurement technique has not been practical for a short section of a low- • birefringence fiber because its periodic transmission function is very broad. In this paper, we suggest a novel

technique based on a Lyot-Sagnac fiber interferometer to measure a birefringence of low-birefringence fiber by

decreasing the width of the periodic transmission function without using a very long fiber length.

A conventional fiber Sagnac loop interferometer has been demonstrated for applications in wavelengthdivision multiplexing (WDM) filters and in sensors because of its several advantages, such as temperature

insensitivity, high extinction ratio, and independence of input polarization [4]. This device consists of a directional coupler with two output ports connected by a birefringence fiber loop. A phase difference between two counter- propagating beams results in transmission dependence on wavelength or fiber birefringence. The wavelength period,

AX, is a function of the AnL product value, which is the intrinsic properties of the fiber. This is shown in Eq. (1), where A is the operation wavelength, An is the fiber modal birefringence, L is the effective length of the fiber.

Since the wavelength period depends on the An L product of the fiber, AX is a large value for the short length of

a low-birefringence fiber. This requires an additional curve fitting process to deduce the value accurately. [4]. In order to reduce the width of the transmission function significantly, one can use a very long length of a lowbirefringence fiber, but a long fiber length is a cumbersome to deal with and there is an additional uncertainties due

to a possible tension and strain in the spool.

a

Reference

Fiber 1 b Measured

Fiber 2 c

Fig. 1. Fiber Lyot-Sagnac interferometer setup.

113
Recently, we demonstrated a novel Lyot-Sagnac filter capable of discretely tuning the wavelength period, AX, by

varying the effective value of the AnL product [5]. The fiber Lyot-Sagnac loop interferometer is composed with a 50:50 fiber coupler, two sections of fiber with a length LI and L2, and all-fiber polarization controllers acting as half-wave plates, 7J2. This is schematically shown in Fig. 1 . The arrows inside circle represent the relative angle

directions of the fast axis of high birefringence fiber and the plane of Sagnac loop. By changing the fast axis direction angles of two fiber, such as each fast axis is either +45 0 or -45 0 relative to the plane of Sagnac loop, we

can discretely vary the effective value of AnL and, thus, the wavelength period of the filter is discretely tuned. For

the fixed angle polarization angles, 45 °, 0 °, -45 0 at the position of a, b, and c in Fig. 1 , respectively, the effective value of AnL for the device becomes AnrLi+An2 L2

. In the other combination of relative angles, 9(a) = 45 °, 0(b) = - 90°, and 9(c) = 45 °, the effective value of An L product becomes An1 -L,-An2 L2 . Therefore, the distinct values of

An L product result in two different wavelength periods, AXS and AXL as shown in Eq (2), where S denotes the summing case and the L denotes the difference in that length;

AA =

An, L. ± An, Z,, (2)

In the fiber Lyot-Sagnac loop configuration of the Fig. 1, the section 1 is used as a reference section with a known high birefringence fiber and the section 2 becomes a measurement section having a low birefringence fiber to be measured. As compared with the conventional Sagnac loop, we could decrease the bandwidth of periodic

transmission function of low-birefringence fiber easily and precisely since the denominator of Eq. (2) is increased as

the larger value of Ani-Lj is applied. Here, the small value of An2 -L2 controls the discretely tuned two bandwidths of

periodic transmission spectrum, AXS and AXL, as represented in the Eq. (2). Therefore, from measuring the two

distinct wavelength periods AX$ and AXL , and the length of L2 , we could precisely determine the birefringence, An2, of optical fiber. From the Eq (2), the equation for the birefringence value of fiber 2 can be shown in Eq. (3);

A 4-4-1 (3) {AXS AXL ) Note that the values of An/ and Lt of the reference fiber 1 are not required in calculating the birefringence value of fiber 2. For the experimental demonstration of measuring the small value of the An2 L2 in the fiber Lyot-Sagnac

loop configuration, we used a commercial high-birefringence fiber 1 (FS-PM-78 11) with 4«; of 7.47X10"4 and a low-birefringence fiber 2 with An2, of 2.6xl0"5

. The birefringence value of fiber 2, which is 30 times smaller than

that of fiber 1, was designed to set up the fiber Lyot-Sagnac loop with a similar length for each fiber section. Fig 2 shows the calculated transmission spectrum of the conventional fiber Sagnac loop interferometer having the fiber 2 with the length, L2, of 1.8m. It is impossible to measure the wavelength period value, AX, of 51.3 nm using the conventional C-band light source of 1530-T565 nm wavelength range because the wavelength period value is larger than wavelength width of light source. Though we could measure the wavelength period value using a broadband

white light source, it is hard to couple into a single mode fiber for the measurement and is a low power per bandwidth. This also requires a following curve fitting process to estimate the birefringence of fiber from the measured value of AX and the Eq. (1) as explained earlier.

Fig. 2. Typical calculated transmission spectra of the conventional fiber Sagnac loop interferometer with low

birefringence fiber 2 only.

114
Wavelength [nm] Fig. 3. Experimental measurement of two distinct bandwidths of periodic transmission of the fiber Lyot-Sagnac

loop interferometer.

In the proposed fiber Lyot-Sagnac interferometer configuration, we could decrease the width of periodic transmission function using the reference section with 1.02 m of the fiber 1 (FS-PM-781 1), which has a shorter length and a significantly higher birefringence than fiber 2. Fig. 3 (a) and (b) show the corresponding experimental

result, respectively. The measured two different wavelength period values, AXs of 2.97 nm and AXL of 3.36 nm, can

be directly obtained from the graph and the Eq. (3) can be used to determine the birefringence value as 2.61xl0"5

. This method does not require the curve fitting because the wavelength period only vary insignificant amount within

the spectral range needed to extract the period values. In general, An; Lh of a reference fiber should be between 10

to 50 times the An2 L2, of a low birefringence fiber in question. In this experiment, the transmission spectra are measured using an Erbium-doped fiber laser source at the center wavelength of 1550 nm and an optical spectrum

analyzer (Ando, AQ-6315) with a resolution of 0.05 nm.

In conclusion, we have proposed and demonstrated a simple and precise low-birefringence measurement

technique for based on a Lyot-Sagnac interferometer configuration. Using the novel scheme, we discretely tuned the bandwidths of periodic transmission spectrum to induce the value of the An L product.

References

[1] Raymond M. Sova, Chang-Seok Kim, and Jin U. Kang, "Tunable dual wavelength All-PM fiber ring laser" IEEE Photon. Tech. Lett., 14, 287 (2002)

[2] E.A.Kuzin, J.M. Estudillo Ayala, and B. Ibarra Escamilla, "Measurements of beat length in short lowbirefringence fibers", Opt. Lett. 26, 1134 (2001)

[3] A. Galtarossa, L. Palmery, M. Schiano, and T. Tambosso, "Measurements of beat length and perturbation

length in long single-mode fiber", Opt. Lett. 25, 384 (2000)

[4] Xiaojun Fang and Richard O. Claus, "Polarization-independent all-fiber wavelength-division multiplexer

based on a 3agnac interferometer", Opt. Lett., 20, 2146 (1995)

[5] Chang-Seok Kim, Raymond M. Sova, Jin U. Kang, and Jacob B. Khurgin, "Novel multi-wavelength

cascaded-Raman source based on tunable fiber Sagnac loop filter", in the Technical Digest of Optical Fiber Communication Conference 2002, WJ1, Anaheim, CA (2002).

i

115

Determination of the degree of polarization based on a coherent

quantum measurement

Matthieu Legre, Mark Wegmuller, Nicolas Gisin

Group ofApplied Physics, University of Geneva,

20 rue de l'Ecole-de- Medecine, CH-1205 Geneve, Switzerland.

Abstract: A novel method for the measurement of the degree of polarization is described. It is one of the first practical implementations of a coherent quantum

measurement, the projection on the singlet state. Our first results demonstrate the

successful operation of the method. However, due to the nonlinear crystals used

presently, its application is limited to light beams with spectral widths larger than

~8nm.

I. INTRODUCTION

PMD (polarization mode dispersion) is one of the limiting factors in optical fiber data

transmission. The degree of polarization (DOP) is routinely used in PMD compensators as a feed-back parameter to control the dynamic adjustment of the compensator [1,2]. For such

applications, it is interesting to have a compact, fast, and cheap measurement apparatus to determine the DOP.

n. BASIC IDEA AND PRINCIPLE OF OPERATION

The DOP of photons propagating at the same time, in the same spatial mode, and at the same wavelength equals 1 . Depolarization appears when at least one of these conditions is no

longer satisfied. A D0P<1 consequently means that there are temporal fluctuations of the

polarization, or that the beam is composed by several spatial modes, or that the light is not

monochromatic (or a combination of the above). In our case, we are interested in the

depolarisation due to the action of the PMD on a telecom laser with a spectral bandwidth of

~0.3nm.

For this case, one of the authors has demonstrated in [3] the possibility to do a direct

determination of the DOP with a coherent quantum measurement, the projection on the singlet

state = ^Hx ,V1 )-\Vx ,H2 ))/42 . \|/ is one of the four Bell states (which are the standard

base of two photon polarization states). A fundamental property of the singlet state, exploited

in your experiment, is its rotational invariance. This means that the result of the projection on

is independent of the arbitrary frame chosen (or in other words, that only the relative, but

not the absolute, polarization of the two photons determines the result). In [3], it is demonstrated that the result of the projection is proportional to (1-DOP2

).

Bell states are very common in quantum optics, so projection on the singlet state has

already been done [4], however only for photons with a large wavelength difference (85nm).

This value is very far from the <0.3nm desired here. \|/

(_) is antisymmetric and photons are bosons, which makes it harder to realize the projection on the singlet state for photons with

similar wavelengths.

117
The principle of the projection is described in figure 1. We use two identical crystal for SFG (Sum Frequency Generation, (A,i,A,2)—>A<3) of type II (polarizations of X\ and of Xi are orthogonal). The second crystal is orthogonal to the first one (i.e. rotated by 90° around the

light path). Using H for horizontal and V for vertical polarizations, we have, for exemple, in

the first crystal (Hi,V2)->V3 and (Vi,H2)—>H3 in the second one. The phase difference

between the SFG waves created in the first and second crystal is adjusted to n by tilting a birefringent plate. The two waves are then projected on a 45° polarizer. The intensity of the

interference signal correspond to the (non-normalized) projection on the singlet state of the

two input photons.

Type II crystals

turned by 90°

Polarizer

at 45°

•

• t ®

Figure 1 : Schematic of the principle of the projection on the singlet state of a photon pair

III. EXPERIMENTAL SET-UP AND RESULTS

We chose KTP type II crystals (XZ plane) as they promise for a good SFG efficiency and

are readily available. To avoid any problem with the spatial walk-off (3°) we opted for a short

crystal. This however implies a low wavelength selectivity: for a KTP crystal of 3mm length,

the phase-matching bandwidth equals 18nm -this means that for | X\-X2 1 <18nm, both

((Hi,V2)->V3 and (Vi,H2 )—>V3 ) SFG processes start to be phase-matched, perturbing the

singlet projection as we will see later. The set-up used for the singlet projection

OKI'KITUK

Figure 2: Diagram of the experimental setup.

118
is shown in figure 2. The source is composed of two tunable lasers around 1550nm, combined

by a fiber coupler. Each polarization can be controlled independently. The total power after amplification is about 70mW. Before being projected on the singlet state, the

light is collimated with a fiber GRIN lens. Further, to analyse the correct operation of the

DOP meter, a polarization analyzer could be inserted in front of the crystals (dashed elements

in Figure2). For simplicity of notation, we allow for linear polarizations only, and define the

two polarizations with two angles 0 and cp in the plane (x,y), with x parallel to the X axis of

the first crystal (figure 3). ). 6 is the angle between the x axis and the polarization ofX\, and (p the angular difference between the two polarizations (i.e. X2 is polarized along 9+(p). Note that for the elliptical polarizations we can use the same notation but cp becomes the difference

between %i and %2 (tan%=Ey/Ex) and 0 equals %\. The DOP of a source composed of two lasers

with wavelengths X\ and Xi is ^{lx +I2 f ~4I} I2 sin

2 q> j{lx +

1

2 ).

Figure 3 : Definition of the angles 9 and (p. The

directions x and y are parallel to the optical

axis of the first and second crystal,

respectively.

The projection on the singlet state has been tested for several wavelength differences. For

Xi=1542nm and ^2= 1560nm (see figure 4), one sees that the closer (p gets to 0, the smaller the

number of counts. This is the expected behavior where the number of counts is proportional to (1-DOP2

). However, the (theoretically absent) G dependence of the result reduces the accuracy

of a single measurement, and one should therefore rather use the mean value from several

measurements with different 9s. As the figure demonstrates, this mean values follow the

theoretical behavior very well.

1.0 -

0.8 -

Model: a. sin (<p)+b a 0.86029 ±0.00308

b 0.0336 ±0.00205

Figure4: Measured intensity of the

singlet-state as a function of the relative

polarization angle (p for ^i=1542nm and

^2=1560nm. Square data points: results for different 9s, crosses: mean values,

solid line: fit with the function

asin 2 ((p) + b

.

-100 -50

I 50 100 angle (p(°)

The results become qualitatively different for a wavelength separation as small as 4 nm

(Figure 5). The noise 'fluctuations' are very large now, covering almost completely the

119
dependence on (p, i.e. the DOP. Nevertheless, the experimental data are still found to be very

reproducible. The mean values are not constant as one might expect at first view, but are found to vary as a +bsin 2 ((p) + csin 2 (<p + 2d)

.

Figure 5: Measured intensity of the

singlet-state as a function of the

relative polarization angle (p for

A,i=1542nm and A.2=4546nm.

Square and bar data points: two

different sets of measurements,

solid line: fit with the function a + bsin 2 ((p) + csin 2 ((p + 2d).

Angle <p (°)

This is due to the earlier-mentioned co-existence of the two SFG processes for small

wavelength separations. The relative weight of the second perturbing SFG interaction

increases when the two wavelengths become closer. If we consider a signal to noise ratio

(signal: contribution from first process, noise: from second process) of 1 as the limiting

criteria for a proper singler projection, a minimal wavelength difference of ~5.5nm is find,

this is in fairly good agreement with our experimental results.

IV. CONCLUSION

A direct measurement of the DOP is possible with a coherent quantum measurement, the

projection on the singlet state. This projection can be realized with nonlinear interactions. The

minimal spectral bandwidth of the source we can measure is determined by the phasematching bandwidth of the crystals. With crystals of GaSe or HgS of 1cm length, it should be

possible to measure the DOP of a telecom laser working at 40Gbits.

Acknowledgements: Financial support from the Swiss OFES in the frame of the COST 265 project

and EXFO Inc (Vanier, Canada) are acknowledged.

References

1- "A simple dynamic polarization mode dispersion compensator", F. Roy, C.Francia, F. Bruyere, D. Penninckx, Tech. Dig. OFC'99, San Diego (1999)

2- "Higher order polarization mode dispersion compensator with three degrees of freedom", M.

Karlsson, C. Xie, H. Sunnerud, P.A. Andrekson, Tech. Dig. OFC'01, Anaheim (2001)

3- "Coherent quantum measurement for the direct determination of the degree of polarization and

polarization mode dispersion compensation", N. Gisin, Journal of Modem Optics 48, 1397(2001)

4- "Quantum teleportation of polarization state with a complete Bell state measurement", Y. Kim, S. P. Kulik, Y. Shih, Physical Review Letters 86, 1370(2001)

5- "Experimental investigations of coherent quantum measurement of the degree of

polarization of a single mode light beam", submitted to Journal of Modern Optics

120
Visualizing the Limitations of Four-State Measurement of PDL

and Results of a Six-State Alternative

R. M. Craig

Optoelectronics Division

Electronics and Electrical Engineering Laboratory

National Institute of Standards and Technology

Boulder, CO 80305

Abstract

I present a method of visualizing polarization-dependent loss in single-mode optical fiber and

components. This method uses generalized Poincare spheroids wherein the power (though polarized) is no longer normalized to unity. The resulting graphical development permits a better understanding of the

limitations of the four-state Mueller-Stokes measurement of this parameter in the presence of combined

parasitic birefringence and external polarization-dependent losses. A six-state alternative that improves

accuracy and repeatability is shown along with the results of preliminary comparative measurements.

The alternative is also found to be more tolerant of non-orthogonal states while maintaining short measurement times.

Introduction

The widespread use of wavelength multiplexing necessitates the rapid measurement of polarizationdependent loss (PDL) over wavelength, which I refer to as PDL^. Currently, PDL^ is typically measured

with either a random all-states (A/S) technique [1] or the four-state technique of Nyman, et al.[2,3] which

I refer to as Mueller-Stokes (M/S). The all-states technique is precise and simple to apply, but typically

slow for wavelength-dependent measurements. However, the A/S method is only as accurate as the

statistical sum of all internal system PDL's [4]. By contrast, the four-state M/S method is typically very

fast and capable of subtracting the effect of internal system PDL, which makes it potentially much more

accurate in a laboratory setting. However, in field or production situations, conditions can be far from

ideal, with large parasitic birefringence and PDL sources in the optical circuit. In addition, the M/S

technique assumes strict orthogonality of the polarized states wherein the four states are separated by

equal quadrants on the Poincare sphere [5]. When this condition is not met, the M/S method can show

dramatic uncertainties that serve to negate much of the perceived benefits. Long, coiled and unrestrained

patch cords can lead to large values of static and dynamic strain birefringence [6]. Poor connectors and

open beams can lead to large parasitic PDL in the circuit, while misalignment or wavelength dependence

in the polarization controller can lead to non-orthogonality of input states. Though not always present,

the combination of these effects can be devastating to the accuracy of the M/S method. My goal has been

to understand the nature of this limitation and to devise a suitable alternative that retains the speed benefit

while reducing the impact of parasitic effects.

Visualizing PDL

To visualize PDL and its interactions, it is useful to consider Poincare spheroids: a unit intensity

(radius) sphere representing the input polarization state, and an output spheroid of polarization-dependent

intensity. A computer model produces the viewpoint seen in Fig. 1 for the example of a 3 dB PDL, where

the distorted output spheroid (PDL) is coincident within the unit input sphere. Relative to the input

reference frame, the output spheroid can appear "rotated" if the PDL is seen through a retarder (middle

image). Adding two orthogonal 3 dB PDL's is equivalent to multiplying the equivalent spheroids, which

overlap along the "PDL axis", to generate a half-unit Poincare sphere, i.e., a 3 dB attenuator (right image).

With the aid of this device, it is now possible to better understand the limitations of the M/S method by

allowing us to see the newly obvious symmetries or lack thereof.

121
A 3dB PDL following A 3dB PDL as seen Result of crossing an unpolarized source through a retarder orthogonal 3dB PDL's

Figure 1 : Visualizing a 3 dB PDL and certain interactions with the aid of Poincare

spheroids (inside the unit sphere) that depict the actual Stokes intensity.

The Four-State Problem Viewed Geometrically

The ideal four states of the M/S method can be represented by partial, orthogonal great-circle

trajectories, as in Fig. 2. In actual measurements, however, the relative positions of the four states may

vary somewhat, particularly with wavelength X. This variation will lead to non-orthogonal states and a

further loss of symmetry. For the purposes of this example, we may take the unit sphere as representing

the light as launched from the measurement system and the internal prolate spheroid as representing the

light as it exits the device-under-test (DUT). Note that, as long as the axis of any retardance is coincident

d

No Parasitic Birefringence Lead Retardance Axis Lead Retardance Axis Not

Coincident with PDL Axis Coincident with PDL Axis

Figure 2: 4-State M/S trajectories superimposed on the input (system) and output (DUT) spheroids.

with the PDL axis, symmetry is maintained and ratios of relative radii between corresponding system and

DUT trajectories (a - 1, b - 2, c - 3, d - 4) are maintained. Conversely, when the parasitic retardance

axis is not coincident with the PDL axis, symmetry is broken and the 4-state approach loses information.

A simplified M/S measurement system described by this and a later model is shown in Fig. 3.

The Six-State Generalization

Significant improvement is offered by the six-state approach of Fig. 3, which is characterized by the incorporation of additional geometrical information afforded by the greater symmetry available in Poincare space. The fundamental idea is to require that 4-state measurements about the 1-2-3 plane must

be equivalent, i.e., measurements at states 1,2,3,4 or 5,2,3,6. This equivalence is used to generate six equations in six unknown Mueller matrix elements. However four unknowns can be combined into two

matrix elements (m^ and m^) by taking an average based on symmetry. The result is the comparison

table shown below in Table 1, where mii(^)...mi 4 (A.) are the Mueller matrix elements relevant to PDL.

122
No PDL,

No Birefringence

No PDL,

Birefringence Present PDL Present, Birefringence Present Figure 3: Simplified representation of the polarization state trajectories associated with the 6-

state generalization of the MVS technique for both the measurement system and DUT.

The IJX). . .If(X) are measurement system baseline intensities at each input polarization state, while the

I\(k)...I6(X) are the corresponding intensities when the DUT is in series with parasitic retardances.

Table 1 4-State Matrix Elements

mu (X) m[2 (A)

/,(A)/t (A) + /2 (A)/.(A)

/,(A)/t (A)-/2 (A)/.(A)

iM , aW

aW A (4

, a W

iM) AW

.AW

AW

i AW

AW

/'DL^/3Z)Z,(/l) = 101og

6-State Matrix Elements

mn (X) mn

{X) mn (X)

AWAW

/,(2)/t (A)-/2 (A)/a (A)

AWAW

^WAW'AWAW'

AWAW

A W/, (A)

i W+ >/w»

(A)

2 + w,3 (A)2 + w,4 (A)2

, ( A) - i//wI2 (^)

2 + w13 (A)2 + w14 (A)2 (dB)

Results and Conclusion

From the figure and table above, it is clear that for the small additional "expense" of two additional

measurements we are gaining considerable symmetrical information that will help to offset the

uncertainties associated with parasitic birefringence and other PDL's in the system. The system of Fig. 4 was used to test this approach, and the results of a comparison measurement of a 0.395 dB PDL is presented in Fig. 5. A 0.1 dB PDL artifact was placed in series with the state randomizer (a separate

polarization controller) that was stepped through 100 various states following the initial baseline

measurement. The 0. 1 dB artifact acted as a parasitic PDL in the optical circuit, and the polarization state 4

J Remove for Baseline 0 X/4 . CCD,

Polarization

State Generator

Source

Ratio

DUT

State Randomizer

Optical Power

Meter

Figure 4: A typical configuration for 4 and 6-state PDL measurements. The randomizer allows

for testing system repeatability under various conditions of parasitic birefringence.

123
randomizer allowed the method to be tested under various polarization conditions, simulating different orientations of parasitic birefringence within the measurement system. The result of these 100

10 30 50 70 90

Arbitrary Polarization State

Figure 5: Comparison measurement of a 0.395 dB PDL at 1550 nm using the 4-state and 6-state M/S methods with the apparatus of Fig. 4. Standard deviations are shown at right.

measurements was a clear improvement in both mean and standard deviation for the 6-state method over

the 4-state method. The 6-state result was 0.396 ± 0.009 dB while the 4-state result was 0.398 ± 0.021

dB. Though numerical models show that the 6-state method is essentially exact for perfectly orthogonal

states, even under parasitic influence, the inclusion of slight non-orthogonality produces some

uncertainty. However, for an equivalent deviation from orthogonality in both the 4-state and 6-state methods, the models readily reproduce the approximate factor of two improvement in standard deviation.

This method and further generalizations are now being implemented at NIST with the goal of qualifying

PDL artifacts to higher accuracy than before. Bibliography

[1] Derickson, D., Fiber Optic Test and Measurement Upper Saddle River, NJ: Prentice Hall PTR,

1998.

[2] Craig, R. M, Gilbert, S. L., and Hale, P. D., "High-resolution, nonmechanical approach to polarization-dependent transmission measurements," Journal ofLightwave Technology, vol. 16, no. 7, pp. 1285-1294, Julyl998.

[3] Nyman, B. M. and Wolter, G., "High-Resolution Measurement of Polarization-Dependent Loss," Ieee Photonics Technology Letters, vol. 5, no. 7, pp. 817-818, Julyl993.

[4] Gisin, N., "Statistics of Polarization-Dependent Losses," Optics Communications, vol. 1 14, no. 5-

6, pp. 399-405, Feb. 1995.

[5] Collett, E., Polarized Light, Fundamentals and Applications New York, NY: Marcel Dekker,

Inc., 1993.

[6] R.Ulrich, S.C.Rasleigh, and W.Eickoff, "Bending induced birefringence in single mode fibers,"

Optics Letters, vol. 5 pp. 273-275, 1980.

124
Four-state measurement method for polarization dependent wavelength shift

W.C. Swann, S.D. Dyer and R.M. Craig

National Institute of Standards and Technology

325 Broadway, Boulder, CO 80305

swann@boulder.nist. gov

ABSTRACT

We present a novel four-state method for measuring the polarization dependent wavelength shift (PDW)

of a fiber Bragg grating. We show that measurement of the grating's wavelength for only four different polarization states is sufficient to completely determine the grating's PDW, and we show favorable

comparison of four-states PDW measurement results with results obtained using the conventional "all states" technique.

1. Introduction

Use of Bragg gratings in wavelength division multiplexed (WDM) systems with ever decreasing channel

spacing and in sensor systems with ever increasing accuracy requirements has placed stringent demands

on the absolute accuracy and stability of a grating's wavelength. The two largest effects on a grating's

wavelength: temperature and strain, are well understood and are often compensated by using active

stabilization or athermal packaging. It is more difficult to control the grating's response to polarization,

where the center wavelength of a grating can shift due to birefringence. In systems using unpolarized

light, or where polarization is maintained using polarization maintaining (PM) fiber, this is not an issue. However, where polarized lasers are used or PM fiber is impractical, the grating's wavelength can wander

with polarization. It is therefore important to know a grating's PDW if it is to be used in a system where

wavelengta accuracy is important. In this paper we define PDW as the maximum wavelength shift of the

grating's spectrum that is induced by changes in polarization.

The most straightforward means of determining a grating's PDW is to monitor the wavelength shift of the

grating's reflection (or transmission) spectrum while randomly varying the polarization of the light at the grating until the polarization state space has been reasonably well covered. A similar approach uses a

large number of well-defined states uniformly distributed over the state space. Unfortunately, the large

number of individual measurements these "all states" techniques require make them time consuming, and

therefore impractical in a manufacturing environment. Furthermore these techniques can underestimate a

grating's PDW; they will more closely represent the true PDW as the state space is more completely

covered. The four-states technique described here allows a grating's PDW to be completely determined

with only four measurements, and does not underestimate the PDW. This measurement

technique can also be applied to the measurement

of PDW for other types of wavelength-selective

Fast filters. axis

Figure 1: Birefringent fiber core in the region of

the gratirg. A is the physical pitch of the grating.

2. Theory

The four-states technique assumes that PDW is caused by linear birefringence within the section of

fiber containing the grating (Fig. 1). This

birefringence may be caused by any combination of

several mechanisms, most notable being fiber core

125
geometry or strain asymmetry, asymmetry inherent in grating side writing techniques [1], or asymmetry

due to the polarization of the writing light [2]. This birefringence results in polarization dependence of

the Bragg grating's optical pitch, and thus the grating's center wavelength. Light polarized along the grating's fast axis sees a shorter optical pitch, and thus a shorter Bragg wavelength, than light polarized

along the slow axis. For the purposes of this paper we define the fast and slow axes as the eigenaxes of

the grating, and polarization states that lie on these axes as the grating's eigenstates. The difference

between the grating's wavelengths for the two polarization eigenstates is the PDW of the grating.

Arbitrarily polarized light has components along both the fast and slow axes, resulting in two spectral

profiles shifted in wavelength with respect to each other. If the PDW is less than the grating's spectral

width these two profiles overlap, resulting in a combined spectrum with a center wavelength somewhere

between the fast axis and slow axis extremes. To determine the combined spectrum's wavelength shift verses polarization state, we modeled the grating's spectrum as a combination of two spectra shifted with

respect to ?ach other by the PDW shift, and weighed these spectra in proportion to the E field strength on

the grating's eigenaxes for a given polarization state. We then observed the combined spectrum's

wavelength shift as the model's polarization state was varied, and found that the shift varied sinusoidally

Figure 2A: Modified Poincare sphere at the

grating. The sphere is rotated with respect to conventional notation. The grating's mean

wavelength is on the sphere's equator.

bX

I _ 6X= AX cos <5

B

Figure 2B: Variation of wavelength shift dX with

angle <I>. AX is the maximum shift and occurs when

the polarization is on either the grating's eigenaxes.

The PDW for the grating is 2AX.

as the polarization evolved from the grating's slow axis to its fast axis eigenstate [Fig. 2]. In theory a

grating's PDW can be determined by finding the shift in the grating's center wavelength for the two

polarization eigenstates. In practice determining the grating's eigenaxes is difficult, and furthermore any

polarization state launched into the fiber may transform into some other, arbitrary state at the grating.

With a suitable choice of four input polarization states, however, and assuming the unitary transformation

between these input states and the states at the grating (i.e. the angular relationship between the states is preserved), in the absence of PDL and depolarization in the grating, we can determine the grating's PDW

as follows.

To discuss the theory behind the four-states technique we enlist the following conventions [Figs. 2 and 3]. We use modified Poincare spheres S and S', respectively to describe the polarization states Sj and s' at the input end of the fiber and at the grating. Our modified Poincare sphere notation maps center wavelength

rather than power onto the sphere's surface. 27 is an axis running through the grating's eigenstates on the sphere S', and Osi ' is the angle between If and polarization state Sj' on S'. For the four input states we

126
choose two orthogonal states (for example S\ = linear horizontal and s2 = linear vertical) and two states displaced by 90° on S from the first two states and from each other (for example s3 = +45° linear and s4 =

right circular). An example showing this choice of four input states is shown in Fig. 3. Notice that the four states laid out on the sphere resemble three mutually perpendicular unit basis vectors together with a fourth vector directed opposite to one of the other three. These four input states Sj will evolve to four

other states s{ at the grating.

For each state Sj launched into the fiber we measure the center wavelength Xs\ of the grating's reflection peak. From the average of wavelengths Xs]

' and Xs2

' given by the two orthogonal polarization states, we

determine a mean wavelength ?imean =

(Xs \

/ +Xs2 y2. From this we determine 8XS

' = ^si'-^mean, where 8Xsi ' is the shift from the mean wavelength for polarization state S;'. Now, from Fig. 2 we see that SXsi^AXcosOsi', where AX is the difference

between the maximum wavelength and

?imCan . Disregarding one of the two

orthogonal states, and taking cos<J>si

- as direction cosines [3] between If and Sj', we

use the relationship cos

2 Os2 + cos2 Os3 +

cos

2 Os4 = 1 [4] to get [(5X's2 ? + (6?i's3 )2 +

(bX's4)

2

] m = AX. (We could just as easily use cosOsl instead of cosOs2 , and 5XS] instead of 8Xs2 .) The PDW for the grating

is 2AX.

Figure 3: Poincare spheres S at the input end of the fiber and S'

at the grating, showing evolution of input states Sj to states s

'.

3. Experimental Results

We measured three gratings with different amounts of PDW using the four-states technique, and

compared the results to "all states" measurements of the same gratings. For the all states measurement we chose 26 states uniformly distributed about the sphere. Each state's measurement entailed setting a tunable diode laser's polarization to the desired state using a pair of waveplates and scanning the laser's wavelength across the grating's reflection spectrum while monitoring the wavelength with a wavelength

meter. For each polarization state, we fitted the resulting plot of reflectance versus wavelength over the wavelength values ranging between the reflection spectrum's FWHM points using a fourth order

polynomial fit. We found that the grating profiles were slightly asymmetric, leading to a slight difference

between the profile's center and extremum wavelengths. Because the profile's extremum is better defined than its center, we used the shift in the extremum of the fit vs. polarization state to determine the grating's PDW.

For the all-states technique we took the difference between the maximum and minimum wavelength

returned by the 26 scans as the PDW. This technique has the potential of under-determining the PDW by

up to about 1 0 %, as dictated by how closely the launched states approach the fast and slow axes at the

grating. In addition to this there is an uncertainty in the all-states PDW of V2a, where a is the standard

uncertainty in the extremum wavelength given by the polynomial fit. For the four-states technique we

determined the PDW as described in the previous section, and we calculate the PDW uncertainty to be

about 2.5a. Both of these uncertainties are given using standard propagation of errors formalism.

127
The results for the three gratings are shown in Table 1 . We ran two trials on gratings 1 and 2, and four

trials on grating 3 for both the four-states and all-states technique. Gratings 1 and 2 have a standard

uncertainty c in their extrema of about 0.25 pm, leading

to an uncertainty of about ± 0.6 pm for the four-states PDW, and about 0.4 pm for the all-states PDW. Grating

3 has a standard uncertainty a of about 0.14 pm, leading

to a predicted uncertainty in the four-states PDW of

about 0.4 pm and in the all-states PDW of about 0.3 pm.

For gratings 1 and 2 the 26-states results are lower than

the four-states results by up to 8%, as expected for reasons stated above, and the four-states and all-states results agree for grating 3. Also, the results for the two

trials agree to within the expected uncertainties,

indicating repeatability of the measurements.

5. Conclusion

We have presented a four-states technique for measuring the polarization dependent wavelength shift of a

fiber Bragg grating. Although we describe measurement of a relatively narrow grating, this technique

should be applicable to measuring shifts in the band-edge of WDM channel filter or similar widebandwidth gratings. Furthermore, with suitable reference detectors, it could be generalized to include

simultaneous measurement of polarization dependence in the reflectance, transmittance, or loss of the

grating.

References:

1. A.M. Vengsarker, Q. Zhong, D. Inniss, W.A. Reed, P.J. Lemarie and S.G. Kosinski, "Birefringence

reduction in side-written photoinduced fiber devices by a dual-exposure method," Opt. Lett. 19, pp. 1260-1262 (1994).

2. T. Ergodan and V. Mizrahi, "Characterization of UV-induced birefringence in photosensitive Gedoped silica optical fibers," J. Opt. Soc. Am. B 11, pp. 2100-2105 (1994).

3. G. Arfkin, Mathematical Methodsfor Physicists, third edition (Academic Press 1985), pp. 4, 191.

4. M.R. Spiegel, Mathematical Handbook, Shaum's Outline Series (McGraw-Hill 1968), pp. 46.

Table 1: Comparison of 4-state and 26-state PDW resuhs

Grating Trial 26-states PDW 4-states PDW

(pm) (pm)

1 1 30.7(4) 32.3(6)

2 29.8(4) 31.6(6)

2 1 8.1(4) 8.8(6) 2 7.9(4) 8.5(6)

3 1 1.0(3) 0.9(4) 2 1.1(3) 1.0(4) 3 1.1(3) 0.9(4) 4 1.1(3) 1-3(4)

128
Measurement of Dispersion in Photonic Bandgap

Fibers

J. Jasapara

OFS Laboratories, 600 Mountain Ave., Murray Hill, NJ 07974. Ph: 908-582-3234, email:jasapara@ofsoptics.com

Abstract: Phase dispersion of light propagating in the fundamental mode in multiple bandgaps

of a photonic bandgap fiber is measured using the technique of spectral interferometry. The

dispersion data show a strong influence of the Bragg scattering crystal structure surrounding

the core. A simple two dimensional model that includes the effects of a wavelength dependent

angle of propagation, where the angle is determined by the Bragg scattering condition, and the

effects of thin-film-like resonant scattering planes in the fiber is found to explain the observations

qualitatively.

1 Introduction

Photonic bandgap structures consist of a crystal like periodic arrangement of materials of different refractive

indices. Bragg reflections off structures having periodicity extending in greater than one dimension can result in the complete reflection of light at certain frequencies independent of the angle of incidence. The structure

is said to possess a bandgap at these frequencies. If there is a defect in the periodicity of the structure then light frequencies lying in the bandgap would be confined to the defect by Bragg reflection from the

surrounding crystal structure, thus making the defect a light guide. Photonic bandgap structures have been

studied extensively over the past decade because of both their unique science as well as their potential

applications in fields such as integrated light circuits, switches, etc.

Recently propagation of light in a hollow core fiber using photonic-bandgap-guidance (PBG) was demonstrated [1]. The PBG fiber consists of a periodic lattice of air holes embedded in a solid matrix that run

uniformly along the fiber length. A break in the periodicity ("defect") serves as the core. PBG fibers are a new class of fibers in which light is confined to the core by Bragg reflections instead of total internal

reflection (TIR) seen in standard fibers. They could prove to be disruptive to current technology trends since transmission down a hollow core would reduce pulse distortion due to effects such as nonlinearity, material

dispersion and material losses.

So far only the amplitude response of bandgap fibers has been studied experimentally [4, 5] while the phase

dispersion has only been modeled theoretically [5-8]. Since PBG fibers are resonant structures propagation is strongly wavelength dependent. For example, the dispersion of 1-D [2] and 2-D [3] photonic bandgap devices were measured to vary strongly across the bandgap. The waveguide dispersion of a PBG fiber carries the signature of the mechanism of propagation. Its measurement is crucial to gain a physical insight into their working which would enable better fiber design for future applications.

Measuring the dispersion of PBG fibers is tricky. They have high losses (~ 5 dB/m). There might be

variations along the fiber length arising due to imperfections during fiber draw. These factors make it desirable to use short fiber lengths of a few tens of centimeters for measurements. Hence conventional fiber dispersion measurement test beds cannot be used. In this paper we present the experimental measurement of chromatic dispersion of the fundamental mode across multiple bandgaps of a PBG fiber using the technique

of spectral interferometry with a supercontinuum as a coherent white light source.

2 Experiment

The PBG-fiber used in our experiment consists of a triangular lattice of air holes in silica. The diameter of the air holes is 2.4 /xm and their separation is 4.3 fim. The core is formed by removing the center most and

its first surrounding ring of air holes (see inset of Fig. 1(a)). Ten rings of air holes surround the core. The air

129
holes are filled with a high index liquid (index ranging from 1.8 at 600 nm to 1.76 at 850 nm) which raises the effective index of the cladding to above that of the silica core. This ensures that the bandgap effect is the only possible guidance mechanism. The unnormalized transmission spectrum of the fiber (cf. Fig. 1(a))

shows that light is guided only over discrete frequency bands.

«

a

700 750 800 wavelength (nm)

900

Mach-Zehnder

interferometer

microstructured

fiber

pinhole

polarizer i

(a)

a —, ioo fs T<; Ti:S pulse spectrometer

(b)

Fig. 1: (a) The unnormalized transmission spectrum of the PBG fiber over the wavelength range of interest. The inset is a cross section of the fiber - the dark regions are the liquid filled air holes, (b) Spectral

interferometry setup.

Spectral interferometry [10, 11] is an extremely sensitive technique to measure the phase response of optical

samples. In a spectral interferometry setup the sample to be characterized is placed in one arm of a Michelson

or a Mach Zhender interferometer. Coherent broadband light is sent into the interferometer. The output

from the interferometer is sent into a spectrometer. The dispersion of the sample gives rise to a wavelength

dependent path length and phase difference between the arms of the interferometer. This gives a beating in the spectral domain with maxima and minima occurring at frequencies where the phase difference between

the interferometer arms is an integral multiple of 2n and 2(m + l)-7r (m is an integer) respectively. By

analyzing the spectral beat pattern one can recover the phase dispersion of the sample.

Figure 1(b) is a schematic of our spectral interferometer. It consists of a Mach Zehnder interferometer with

the PBG fiber in one arm (referred to as the signal arm below). The other arm (called the reference arm) is left empty. In order to measure dispersion across multiple bandgaps of the fiber using spectral interferometry, we require a coherent broadband source of light that covers the spectral range. We used 100 fs pulses from a

Ti:sapphire laser to generate a supercontinuum in an air-silica microstructure fiber [12] that stretched from ~ 400 nm to ~ 1400 nm. The collimated continuum is sent into the interferometer. The spectral response of the optics in our interferometer restricts our measurements to bandgaps lying between 600 nm and 850 nm.

During the experiment the delay of the reference arm with respect to the signal arm is adjusted so that it is shorter than the signal arm at all wavelengths by > 0.8 ps. The recombined light is sent through a pinhole and a polarizer into a spectrometer (resolution = 0.2 nm)

with a CCD where interference is observed. The pinhole lets only the center-most part of the beam through

and thereby transmits mainly the fundamental mode and discriminates against higher order modes of the

PBG fiber. The polarizer defines the polarization of the detected light which increases the fringe contrast. The air-silica microstructured fiber used for continuum generation is birefringent. If the signal arm is blocked,

then light from just the reference arm itself gives rise to a beat pattern in the spectral domain due to the

different propagation times along the two polarization axes of the fiber. Therefore the input polarization to

130
the continuum generating fiber is matched with a A/2 waveplate to the birefringence axis of the fiber which

then defines the input polarization to our interferometer.

Similarly, the output from only the signal arm containing the PBG fiber, with the reference arm blocked,

gives fringes in the spectral domain (see Fig. 2(a)). The fringe spacing increases linearly with a decrease

in fiber length from which we conclude that the fringes arise due to multi-path interference (MPI) in the PBG fiber. From the contrast of the fringes the energy in the second mode is found to be about 2% of the fundamental mode. This MPI contributes to the noise in the spectral interference pattern between the

reference and signal arms.

In order to obtain spectral fringes of good contrast it is essential that the wavefronts from both arms have

the same curvature. To ensure this the recollimation of the light from the PBG-fiber is adjusted so that the spatial interference fringes between the reference and signal arms observed at zero delay with a slightly

misaligned interferometer have no curvature. The interferometer is then realigned for optimal contrast. In

addition, for good fringe contrast the intensity from the two arms are equalized using neutral density filters.

Besides the sample the interferometer is unbalanced by elements such as the focusing and recollimating

lenses. Therefore the dispersion measurements are made at two different fiber lengths of 263 mm and 130

mm and the difference is taken to subtract out the dispersion of the unbalancing elements.

3 Analysis and results

Fig. 2: (a) signal, (b) reference, (c) interference, (d) retrieved cosine modulation, (e) retrieved group delay,

and (f) retrieved phase dispersion, over a small wavelength range.

of light in vacuum) dependent intensity of the interference pattern I(u>), the reference arm Ir {u), and the

signal arms Ia (u), are recorded sequentially (Fig. 2(a-c)). The beating due to MPI is seen in the spectrum

of the signal arm. The spectrum of the reference arm is noisy around the Ti:sapphire pump wavelength of ~ 795 nm, probably due to modulational instability effects in the continuum generating fiber. The spectral

131
intensity of the interference pattern is given by,

I{u) = Ir (u) +Is (oj) + 2 v

//rH/s (w)cos(*(w)), (1)

where <£>(cj) is the phase difference between the reference arm and the signal arm. From the recorded data the

cosine modulation can be retrieved by inverting Eq. (1) and is shown in Fig. 2(d). Ideally the cosine should

vary smoothly between ±1. However fluctuations in the continuum over the time taken to record all the

data adds noise and misalignment of the interferometer reduces the fringe contrast. The cosine modulation can be smoothed to some extent to get rid of the noise so that the fringe peaks are sufficiently well defined. The peaks in the modulation occur at frequencies at which there is constructive interference between the

reference and signal arms. The phase of the signal arm at frequencies at two consecutive peaks differs by 2ir. We find that the modulationis slower near the center compared to the edge. To retrieve the fiber dispersion,

the group delay as a function of frequency is calculated as,

tV)

6u

2tt du (2)

where is the frequency of the i th peak in the cosine modulation and u>' — (u^ + Wj+i)/2. The retrieved group delay is shown in Fig. 2(e). As the wavelength increases the group delay goes through a minimum

before it increases sharply near the long wavelength edge. This curve is to be compared against the linear group delay curve expected from a standard TIR guiding fiber. The delay is fitted with a polynomial curve. The derivative of the fit yields the dispersion dr/dX (Fig. 2(f)).

Figure 3 shows the dispersion from cutback measurements over three different bandgaps of the fiber overlaid with their transmission curves represented by Is (u>)/Ir (uj). The dispersion across all three bandgaps exhibit the same qualitative behavior: (i) dr/dX is strongly wavelength dependent, (ii) dr/dX has an inflection point

as it goes from negative values at shorter wavelengths to positive values at longer wavelengths, (iii) the

zero dispersion wavelength is shifted towards the shorter wavelength side of the transmission curve, and (iv) dr/dX increases very rapidly to greater than 5000 ps/nm-km near the peak of the transmission which is orders of magnitude greater than that of a standard fiber. The qualitative shape of the curve is in agreement

-1000

-2000

wavelength (nm) elength (nm)

770 780 790 800 810 820 830 wavelength (nm)

Fig. 3: Dots: Dispersion measured over three different bandgaps of the fiber. Solid curve: Is (u)/Ir (uj). with the theoretical calculations by West et. al. and Johnson et. ai. [5,8] These dispersion curves are unique

and unlike those of any known fiber. The large group delay near the long wavelength edge of the bandgap

suggests that the light propagates very slowly over that wavelength range. The quantity Is (u>)/Ir (u) (cf. Fig. 3), measured through the pinhole, represents the transmission spectrum

of the fundamental mode of the PBG fiber convolved with effects such as the spectral response of the optics

in the two arms of the interferometer, the efficiency of coupling into and the recollimation out of the fiber, etc. Is (u>)/Ir (u) show a sharp cutoff at the long wavelength edge of the bandgaps. This cutoff arises due to the cutoff of the fundamental mode [3] and has been confirmed in another experiment where the spectrum of only the fundamental mode was measured. The short wavelength cutoff is governed by the loss characteristics of the bandgap structure.

132
4 Model

The PBG fiber dispersion curves are similar to the dispersion across the resonance peak of a resonant

structure such as a Fabry-Perot cavity or a thin film. However the dispersion of such resonant structures is symmetrical about the peak of the resonance with the zero crossing occurring at the peak. To qualitatively

explain the observed dispersion we propose a simple model of Bragg scattering from multiple planes of resonant structures. Consider the 2-D waveguide shown in Fig. 4(a) in which light propagates in the z

direction. The walls of the waveguide consist of Bragg scattering planes. These Bragg planes are depicted as thin films in order to represent the resonant nature of the actual crystal planes which contain liquid filled holes. They behave like resonant structures with internal multiple scattering determining the phase response. The phase change seen by the ray per reflection is given by,

Fig. 4: (a) Geometry of propagation in a waveguide surrounded with a thin film Bragg crystal, (b) Dispersion

under the condition that the transverse wave vector is a constant (equal to the total wave vector at 808 nm)

for all wavelengths. The dashed line shows the reflectivity; R: dispersion on reflection off the film stack; L: dispersion of the longitudinal component; T: total dispersion. = ksm[6(uj)}L + k cos[9(lu)]D + cf) r (u), (3)

where 9(u) is the angle of incidence on the Bragg crystal as a function of frequency, D is the width of the

guide, L is the length of propagation per bounce along the z direction, and <fi r (u) is the phase change on

reflection. Constructive interference between Bragg scattering from multiple crystal planes are a requirement

for a defect mode to exist and is crucial for the high reflectivity needed for propagation over long fiber lengths. Hence the angle of propagation for wavelengths in the bandgap is defined by the Bragg condition

Ak cos[#(u>)] = m7r, where A is the spacing between the crystal planes, and m is an integer. This implies that

the transverse component of the wave vector, kx = kcos9 = rmr/A, is a constant across the bandgap and

therefore its contribution to the phase dispersion is zero. The Bragg scattering condition also implies that the

angle of propagation decreases with increase in wavelength resulting in a decrease in the forward propagating

component of the wavevector kz = ksin9. Based on the long delays and sharp transmission cutoffs seen for the fundamental mode, we postulate that at the long wavelength edge of the bandgaps (frequency = tue dge), 9 tends to the smallest angle 9mi n that can support the fundamental mode. For our qualitative understanding we will assume that at the long wavelength edge of the band 6mi n = 0 and k = rmr/A so that no energy propagates in the z direction. The propagation angle as a function of frequency in the band can now be

133
defined as 6(u) = cos

1 (u>edge /u). The phase dispersion of the fiber is hence given by,

d

2 ^{u) _ d2 dw2 dw2 [k sm(9(u))] +

d

2

<pr (u)

dlO 2 (4)

The dispersion of the waveguide in Fig. 4(a) is calculated assuming ten thin films of thickness d = 2.4 /im and

index 1.78, separated by silica regions of thickness 4.3 /zm and index 1.45. The amplitude and phase change

due to reflection {(f>r ) is calculated for p-polarized light using the stack- matrix formalism. [14] The transverse component of the wave vector is set equal to the wave vector at a point on the long wavelength edge of the resonance of the structure (chosen randomly here to illustrate the concept), which then defines the long

wavelength edge of the bandgap and the wavelength dependent angle of propagation. Figure 4(b) shows the

contribution to dispersion of each term from Eq. (4) as well as the total dispersion across a resonance. The

dispersion due to reflection off the Bragg crystal (curve R) causes the inflection in the total dispersion curve. The dispersion of kz due to the wavelength dependent angle of propagation (curve L) gives rise to a rapid

increase of dispersion at the long wavelength edge and also shifts the zero crossing of dispersion to the short wavelength side of the resonance peak. The three orders of magnitude difference between the observations

and the calculations is due to the choice of setting dmin to zero. Hence this simple model qualitatively

explains the main features of our observed dispersion.

5 Summary

Spectral interferometry using a supercontinuum as a broadband light source was used to measure the phase

dispersion of a photonic bandgap fiber across multiple bandgaps. Our experiments show that wave vector matching requirements between the propagating light and the surrounding Bragg crystal strongly influence propagation in PBG fibers resulting in a strong waveguide contribution to the dispersion. The wavelength de- pendent angle of propagation results in large positive dispersion at the long wavelength edge of the bandgap,

while the reflections off the surrounding resonant structure results in an inflection point in the dispersion curve which resembles that of a Fabry-Perot structure. The former effect would be detrimental to the the

use of PBG fibers for communication purposes. These studies provide a physical insight into the propagation

mechanisms under PBG conditions and should aid in the design of new PBG fibers with desirable properties.

1. R. F. Cregan, B. J. Mangan, J. Knight, T. A. Birks, P. S. J. Russell, P. J. Roberts, and D. C. Allan, "Single-Mode Photonic Band Gap Guidance of Light in Air," Science 285, 1537-1539 (1999).

2. J. Tirapu, T. Lopetegi, M. A. G. Laso, M. J. Erro, F. Falcone, and M. Sorolla, "Study of the Delay Characteristics of 1-D

Photonic Bandgap Microstrip Structures," Microwave and Optical Technology Letters 23, 346-349 (1999).

3. M. Notomi, K. Yamata, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, "Extremely large group-velocity disper- sion of line-defect waveguides in photonic crystal slabs," Physical Review Letters 87, 253902(4) (2001).

4. J. A. West, J. C. Fajardo, M. T. Gallagher, K. W. Koch, N. F. Borrelli, and D. C. Allan, European Conference on Optical

Communication (Munich, Germany, 2000), pp. 41-42.

5. J. A. West, N. Venkataraman, C. M. Smith, and M. T. Gallagher, European Conference on Optical Communication

(Amsterdam, 2001), pp. 582-585.

6. S. E. Barkou, J. Broeng, and A. Bjarklev, Optical Fiber Communication (San Diego, CA., 1999), p. FG5.

7. J. Broeng, T. Sondergaard, S. E. Barkou, P. M. Barbeito, and A. Bjarklev, "Waveguidance by the Photonic Bandgap

Effect in Optical Fibers," J. Opt. A: Pure Appl. Opt. 1, 477-482 (1999).

8. S. G. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weisberg, T. Engeness, M. Soljacic, S. Jacobs, J. D. Joannopoulos, and

Y. Fink, "Low-loss asymptotically single-mode propagation in large-core OmniGuide fibers," Optics Express 9, 748-779

(2001).

9. J. C. Knight, J. Broeng, T. A. Birks, and P. S. J. Russell, "Photonic Bandgap Guidance in Optical Fibers," Science 282, 1476-1478 (1998).

10. C. Froehly, A. Lacourt, and J. C. Vienot, "Time Impulse Response and Time Frequency Response of Optical Pupils: Experimental Confirmations and Applications.," J. Opt. (Paris) 4, 183-196 (1973).

11. J. Piasecki, B. Colombeau, M. Vampouille, C. Froehly,and J. Arnaud, Appl. Opt. 19, 3749 (1980).

12. J. K. Ranka, R. S. Windeler, and A. J. Stentz, "Visible Continuum Generation in Air-Silica Microstructure Optical Fibers with Anomalous Dispersion at 800 nm," Optics Letters 25, 25-27 (2000).

13. R. T. Bise, R. S. Windeler, K. S. Kranz, C. Kerbage, B. J. Eggleton, and D. J. Trevor, Optical Fiber Communication

(Anaheim, CA, 2002), pp. 466-468.

14. M. V. Klein and T. E. Furtak, Optics, 2nd ed. (Wiley, New York, 1986).

References

134
Counting Modes in Optical Fibres with Leaky Modes

Alexander Argyros and Ian M. Bassett

Australian Photonics Cooperative Research Centre, Optical Fibre Technology Centre, University of

Sydney, 206 National Innovation Centre, Australian Technology Park, Eveleigh, NSW 1430, Australia, and

School ofPhysics, University ofSydney, NSW2006, Australia.

Abstract: The number of guided modes in optical fibres is an important aspect of their design

and characterisation. Some optical fibres, such as microstructured fibres and Bragg fibres, have no strictly bound modes in the same sense as in conventional step and graded index fibres. All modes in these fibres are leaky so what exactly becomes regarded as a mode becomes important..

We propose a method for counting the number of modes in fibres that takes into account the leaky nature of some modes. The method is based on the loss of each mode and the length of the

fibre. This leads to a definition of singlemodedness for fibres with no bound modes.

1. Introduction: The definition of singlemodedness, and indeed what constitutes a mode is fundamental to optical fibres and almost all aspects of their characterisation. In conventional step

and graded index fibres there are strict definitions for bound and leaky modes: bound modes are

radially evanescent in the depressed cladding layer whilst leaky modes have oscillatory fields in the cladding, allowing power to leak out of the fibre [1]. Equivalently, bound modes are described by real mode effective indices and leaky modes are described by complex mode

effective indices, where the loss is proportional to the imaginary part of the effective index [1]. In the case of step and graded index fibres the number of modes unambiguously refers to the number of bound modes, and when this equals one, the fibre is unambiguously single-moded.

For other types of optical fibres such as W-fibres, holey fibres [2] - microstructured optical fibres (MOFs) or photonic crystal fibres (PCFs)), band-gap fibres [3] - and Bragg fibres [4] there are no bound modes in this strict sense. In holey fibres the guiding mechanism is effective index

guidance [5]; the core is surrounded by an arrangement of air holes that effectively produce a depressed index annulus around the core. In band gap fibres and Bragg fibres guidance is achieved by surrounding the core with a 2- or 1 -dimensional photonic crystal. In both cases the

structure around the core that provides the guiding mechanism is finite in extent and therefore the

fibre only supports leaky modes. Since all modes in these fibres are leaky, quoting the number of

modes guided by each fibre design becomes ambiguous. Many such fibres have been claimed to be single-moded but no convention exists to clarify the statement. We propose a method for counting the number of modes in these fibres that takes into account the loss of each leaky mode

and the length of fibre in question. This method also sets out the conditions required for singlemodedness and outlines the requirements through which some fibres may be effectively

single-moded though some or all modes are leaky.

2. Characterisation and Effective Singlemodedness: We outline below a method for characterising and counting modes and for characterising fibres. Using this, we set out criteria by

which fibres can be effectively single moded whilst having no bound modes.

2.1 Characterising Modes: If the power in a mode is attenuated to less than 1% of its original

value (i.e. by more than 20 dB) the mode is no longer deemed useful. If the power in a mode is attenuated to less than 0.01% of its original value (i.e. by more than 40 dB) the mode is considered to not exist. Modes attenuated between 20 and 40 dB can be considered to display

135
low guidance. Using this, we can characterise each mode with two length values: Li% represents

the length required for that mode to be attenuated by 20 dB and L0.oi% = 2LWo represents the length required for that mode to be attenuated by 40 dB.

The values of 20 and 40 dB have been chosen somewhat arbitrarily, with the justification that amplifiers are capable of recovering signals attenuated by 30 dB. Thus, an attenuation of 20 dB

represents a useful signal, in that it can be recovered easily, and an attenuation of 40 dB

represents a signal that cannot be recovered, is effectively lost, and may be treated as non-existent.

2.2 Counting Modes in Fibres: Any given fibre will have a set of leaky modes and may have some bound modes. For a fibre of a given length, the guided modes will be those whose L0.oi% value is greater than the length of fibre. A useful amount of power will be transmitted in those

modes that have Li»/o greater than the length of the fibre (useful guidance). The modes whose L[%

is less than the length of the fibre but their L0.oi% is greater than the length of the fibre cannot be

said to be either extinct nor useful with certainty and so are said to exhibit low guidance but not

useful guidance. We believe that this transition stage between "useful" and "non-existent" needs

to be present to strengthen the definition of effective singlemodedness below. For example, a 3 m

long fibre with three leaky modes characterised by (L\%, L0 .oi%) = (4, 8), (2, 4) and (1, 2) m will have two guided modes (the third mode will be lost) and will only have a useful amount of power

in one mode (the first mode). The counting method is illustrated further in Fig. 1

.

2.3 Characterising Fibres and Effective Singlemodedness: We can use the counting method

outlined above to characterise a fibre as a whole using two length values, in a similar way to that of characterising the modes. The value Lmax denotes the maximum length of fibre over which a useful amount of power can be transmitted in any mode. The value Lmax is simply ~L\% of the least leaky mode of that fibre. If the difference in the losses is sufficiently large and L0.oi% of the second least leaky mode is less than Lmax then there will be a length of fibre over which only the

least leaky moded is guided and all other modes have been attenuated enough to deem them nonexistent. In this case the fibre only guides one mode and can be classified as effectively singlemoded (see Fig. 1). In the effectively single-moded regime we do not allow low guidance modes

to be present, as we cannot say with certainty that they will be sufficiently extinguished to eliminate modal dispersion. A second length Lsm denotes the length at which the fibre becomes

effectively single-moded, and is equal to the L0.oi% value of the second least leaky mode. For a

fibre to be effectively single-moded, the losses of the least and second least leaky modes must

differ by a factor greater than 2 (when measured in dB/m) otherwise the value Lsm will be greater

than the value Lmax and no length of fibre will be effectively single-moded.

Matching the terminology used for standard fibres, we can allow the term "effectively singlemoded" to include the case where there are actually two modes orthogonally polarised, with the same (or nearly the same) loss.

3. Theoretical Calculations and Experimental Results: We present below results from the

literature as examples and to illustrate the applicability of the method outlined above. The first set of results reported in [6] are for a microstructured polymer optical fibre (MPOF) in which the core was surrounded with four hexagonal rings of holes - the four rings form the lower index

region required for effective index guiding. The two least leaky modes of this structure as calculated in [6] are reproduced in Table 1(a). It can be seen that Lsm for this fibre is 0.2 m and

Lmax is 6.7xl0

6 m (material absorption was not accounted for in the modelling). Samples of this fibre of length 1 m were experimentally found to be single-moded [6], consistent with our

definitions.

136
Stage (a) Multimode

2 modes but 1 useful mode

Stage (b) Effectively

Single-mode

Stage (c)

1 mode but 0

useful modes

G

Useful Guidance Modes

X X u

(< 20 dB attenuation)

d Low Guidance Modes

X X

ed

(> 20 dB but < 40 dB

attenuation)

L

Negligible Guidance

XXX... XXX... XXX ... 0

s

t

Modes

(> 40 dB attenuation)

20 dB

i Attenuation

40 dB

Figure 1. The graph above shows how the power in a set of modes would be attenuated along the

fibre length. Three stages along the fibre are marked by the vertical lines and explained in the table to

illustrate the mode counting method discussed. An "X" in each square indicates the presence of a mode that falls in the attenuation range indicated on the right column. In stage (a) there are 2 guided

modes: 1 useful mode and 1 mode with low guidance. The number of lost modes is irrelevant. In stage (b) there is 1 useful mode and no low guidance modes so the number of guided modes is 1 and

the fibre is effectively single-moded. Stage (c) has only one low guidance mode and the fibre is not considered to guide a useful amount of power.

The second set of results reported in [7] are for another MPOF, this time with three circular rings

of holes surrounding the core. The calculations for the two least leaky modes are presented in Table 1(b). It can be seen that for this fibre Lsm = 28 m and Lmax = l.lxlO3 m, once again material

absorption was omitted. Experimentally, 20 cm lengths of this fibre were found to be singlemoded whilst 5 cm lengths were found to be multimoded [7]. An explanation for the apparent

inconsistency is given below.

These experimental results illustrate that our definitions, apart from forming a theoretical basis

for describing fibres, also apply to experimental observations. These results show that singlemodedness of fibres with no strictly bound modes, as treated in our definitions above, is a property that depends on the length of the fibre. The reason the experimental and theoretical

results do not agree quantitatively is because of simplifications in the modelling - as with the

137
Table 1(a) Mode Label Loss (dB/m) Li% (m) Lo.oi%

1 3xl0"6 6.7xl06 1.3xl07

2 200 0.1 0.2 Table 1(b)

Mode Label Loss (dB/m) Ux (m) Lo.oi% (m)

1 1.9xl0"

3 l.lxlO3 2.2x1

0

3

2 1.48 14 28

Table 1. (a) Calculations of the two least leaky modes of the fibre reported in [6]. (b) Calculations of the two least leaky modes of the fibre reported in [7]. The last two

columns contain the two lengths that characterise each mode. The two lengths that characterise the fibres as a whole are in bold-face, with the corresponding label at the

right of the table.

majority of fibre modelling, the fibre was assumed to be straight, with a perfect structure and a

lossless material. We believe that quantitative agreement between theory and experimental

observations can be reached with more accurate modelling, which includes material loss, scattering from hole surfaces, structural defects etc. Experimental observation of

singlemodedness is independent of launch conditions since one of the tests for singlemodedness

in [6,7] was to inspect the near field image of the mode and to observe that it remained

unchanged as the launching conditions were changed.

4. Conclusion: We have presented a method for characterising leaky modes in fibres in terms of

two lengths that represent the maximum length over which a mode is useful and the length

required to extinguish the mode completely. This characterisation allows for the number of leaky

modes guided in a fibre of given length to be counted unambiguously. This counting method in turn unambiguously defines effective singlemodedness for fibres with no bound modes. The fibre as a whole can be characterised in terms of a maximum useful length and, if applicable, a length

required to attain singlemodedness.

Acknowledgements

We wish to thank Maryanne Large, Simon Fleming and Martijn de Sterke for helpful discussions.

References

[1] A.W. Snyder, J.D. Love. Optical Waveguide Theory. Chapman & Hall, London, 1983.

[2] J.C. Knight, T.A. Birks, P.St.J. Russell, D.M. Atkin. Endlessly single-mode optical fibre with

photonic crystal cladding. Optics Letters 21,(19) p. 1547 (1996).

[3] R.F. Cregan, B.J. Mangan, J.C. Knight, T.A. Birks, P.St.J. Russell, P.J. Roberts, D.C. Allan,

Single-mode photonic band gap guidance of light in air. Science 285, p. 1537 (1999).

[4] P. Yeh, A. Yariv, E. Marom. Theory of Bragg fibre. Journal of the Optical Society of America

68(9), p. 1196(1978).

[5] T.A. Birks, J.C. Knight, P.St.J. Russell. Endlessly single-mode photonic crystal fibre. Optics

Letters 22(13), p. 961 (1997).

[6] M.A. van Eijkelenborg, M.C.J. Large, A. Argyros, J. Zagari, S. Manos, N.A. Issa, I. Bassett, S. Fleming, R.C. McPhedran, CM. de Sterke, N.A.P. Nicorovici. Microstructured Polymer Optical

Fibre. Optics Express 9(7), p.319 (2001).

[7] A. Argyros, I.M. Bassett, M.A. van Eijkelenborg, M.C.J. Large, J. Zagari, N.A.P. Nicorovici, R.C. McPhedran, CM. de Sterke. Ring structures in microstructured polymer optical fibres. Optics

Express, 9(13), p. 813 (2001).

138
Measurement of multipath interference and resulting optical

communication system penalty

D.L. Craig, M.G. Taylor, W. Zheng, J. Fowlkes, H. P. Sardesai CIENA Corporation, 920 Elkridge Landing Road, Linthicum MD 21090, USA

dcraig@ciena.com

Abstract: Derivation and method for measuring multipath interference 'MPI' in broadband passive fiber devices is presented. Presented is an example of how these measurements can be applied, to determine the impact of MPI

in an optical communication system

Introduction

Multipath interference 'MPI' from a discrete number of sources, e.g. dirty connectors, and from double

Rayleigh bac kscatter have been presented in the

literature. [1-3] A general measurement method for broadband optical devices and how the measured

value relates to optical communication system

performance has been lacking. MPI for these devices can be characterized as an amplitude noise from the generation of randomly polarized, delayed echoes of the signal. For optically amplified systems MPI can

be defined as: P

fs (L) ?A L )(1)

where Pfs

(L) is the forward scattered power

measured at a point L and P^L) is the signal power

measured at L. This definition is derived for an

opticaly amplified system, where double Rayleigh

backscatter is the dominant source of MPI. [4] Accurate MPI values depend upon knowledge of Rayleigh backscatter coefficients and attenuation. This knowledge is not necessary to measure MPI of passive fiber devices and more generally any passive

optical component. Derivation of a definition, description of the measurement system and an example of applying the measured results to predict the system penalty to a 10Gbps optical system is presented.

Derivation

Multipath Interference at the receiver can be defined

as

MPI=^—

Po

(2)

where Po is the optical power of the signal and Pi is the pow er of the ith multipath signal. The electric field

at the receiver is the sum of the signal and the delayed multipath components. The resulting electric

field at the receiver is expressed as E = E„eHPJ -ox) Sn + 5>'<A l-ot)

,

(3)

where E0

is the amplitude of the signal and Ej is the amplitude of the /th multipath component. pn is the propagation constant of the fiber, I is its length is

the effective propagation constant of the ith multipath

component and accounts for differences in path

length. The optical power seen at the receiver is N P=E E* =E0

2 +2j£OJE;.cos0(

. cos0, +0(Ei Ej

).

where, (4)

0i =s0 si O^E^istheremainingtermsof order Ei Ej For path length much greater than w avelength (e.g. X«l or equivalently 2x « <p) and the interfering light

is depolarized then cos (j>, 6=1/^/2" for time

averages much longer than the bit period. The

average power and standard deviation are Pav = Eo = Po and ^

2 = ^oS^

(5)

;=1 Plugging into equation (2) MPI can be defined as MPI=-^-r (6a) Pav2

or equivalently in decibels MPI =20\og(o/

pav ) (6b)

where 0 is the standard deviation of the insertion loss

ripple in transmitted power and Pav

is the average

transmitted power. Using the techique in the next

section, MPI can be determined by a simple insertion loss measurement No prior knowledge of the device

is needed, except for the shortest and longest path

length to be measured.

139
Measurement

A JDSU swept wavelength (i.e. SWS15100) with the PDL option w as used to make the insertion loss measurements. The system consists of a SOM

(Source Optics Module) a JDS tunable laser, a

receiver that has a control module and a detector,

Tunable

Laser

Polarization Controller

Computer

DUT

Receiver

Figure 2 Measurement Set-up

module. Features of the system are a 3pm step size and the ability of the tunable laser to sweep across

the wavelength range, increasing the speed of the measurement. Insertion loss can be measured every 3pm at a sweep speed of up to 20nm/sec. Sample

points in the measurement were every 3pm and the standard deviation was calculated on 1nm intervals. For fiber devices with multiple path lengths of 10cm to

MPI vs. wavelength, 330 points/nm (JDS swept laser 0.003nm step)

£45

0.5-50

-60

-•-Device 1 —-Device2

lum raicn uoro

1520 1530 1 540 1 550 1560 1570

Plot 1 MPI vs. w avelengthfor fiber devices

MPI Distribution Computation, 330 points/nm (JDS swept laser 0.003nm step)

£ 30%

Device !P-P MPI -O--0e«ce2PPMPI

10m Patch Cord •

jj,—

4 y

i

si

/

-—

V

•65 -60 -55 -50 -45 -40 -35 -30 -25 -20 -15

MPI (dB)

8km a scan speed of 8nm/sec works best. The laser coherence length, and the path length of the

interference must be taken into consideration when

determining optimal scan and sampling speed. [5]

Plots 1 and 2 show typical results from measurement

of some fiber- based devices. A 10 meter patch cord

is plotted as well to show where the noise floor occurs. In both cases data was taken every 3pm,

then 330 points (i.e. every 1 nm) bins w ere used to calculate the MPI as a function of wavelength. Notice

the wavelength dependence of the MPI in plot 1. Measuring a few discrete wavelengths using a RIN

based measurement would not uncover this wavelength dependence. Next is shown how these measurements can be used to determine OSNR

penalty for a 1 0 gigabit/second system.

Experiment

Multipath interference (MPI) is becoming a more

significant impairment in long haul fiber optic transmission systems. The system penalty from MPI

arising from multiple discrete reflections has been

calculated as a result of phase noise to amplitude

conversion [3]. The impact of distributed and discrete back reflections have been characterized as a power

penalty [6-8] and the expressions obtained, although

not explicitly stated in those papers, were equivalent

to an optical signal to noise ratio (OSNR) contribution. This paper will show that forward scattering MPI can be treated as an OSNR contribution.

To observe the effects of MPI in isolation from other impairments, a single channel was propagated

through three different system configurations, one of which was a special MPI loaded test bed. The three

configurations used the same transmitter and receiver subsystems. The transmitter generated a

conventional NRZ signal at 9.953Gb/s, and

comprised an external cavity laser at 1545nm

modulated by a lithium niobate Mach-Zehnder

modulator. Its output was combined with three other wavelengths from c.w. DFB lasers, the closest 14nm

aw ay, whose purpose was to keep the EDFAs at a known saturation point. The receiver employed an 8GHz bandwidth pin-preamp detector going into a

commercially available clock/data recovery unit. Prior

to the receiver were an EDFA and variable optical attenuator, which were used to add controlled amounts of ASE noise to the signal under

observation.

The three different system configurations were as

follows. Case 1 Six spans of standard non dispersion shifted

fiber (NDSF) of lengths 60, 40, 60, 60, 60 & 20km,

roughly with each span followed by dispersion

Plot 2 Distribution of MPI values per device

140
compensation modules (DCMs) having the same

magnitude of chromatic dispersbn as the NDSF

span. The DCMs were of a low dispersion slope type, available on the market for several years. The spans were each preceded by a two-stage gain flattened EDFA, with the DCMs located between stages. Case 2 Instead of the DCMs of case 1, high slope

DCMs were used which were of an old design known

to have high MPI. These DCMs had a higher loss, and were placed both between the EDFA stages and

following the NDSF spans. The end-to-end

dispersion was the same as case 1. Case 3 No transmission fiber, DCMs or line amps.

This configuration was used to make noise loaded measurements of the transmitter and receiver backto- back.

Note that because it is a single channel experiment

the difference in dispersion slopes of the two DCM

types does not afect the result, and the MPI of the DCMs is the relevant parameter. The output power of the EDFAs (main output and mid-stage output) was

-3dBm for the 1545nm channel. The experiment was

designed so that most impairments which usually have to be consider ed in a WDM transmission system

do not contribute to the Q factor: SPM, cross phase

modulation, four wave mixing, PMD, etc; only the MPI

and the OSNR were varied.

The multipath interference in the high slope DCMs is of the forward scatter type. It arises because some

light is scattered into transverse modes other than the one carrying the signal, and then scattered back into the same transverse mode as the signal. The MPI was determined from the measured ripple in insertion loss vs. wavelength via equation (6) where a is the standard deviation of the ripple in transmitted power

and Pav is the average transmitted power. This is the

correct equation assuming the multipath interfering

light ,s depolarised. The spacing between points in the measurement was 3pm and the standard

deviation was calculated on 1nm intervals. The time delay between the signal and the interfering light for

this type of DCM is thought to be of the order 500ns.

The 0 factor was repeatedly measured using the

decision threshold technique as a function of OSNR

for the three cases. The results are plotted in figures

1 & 2. Case 2, the high MPI case, shows a

substantial penalty in Q at high OSNRs. There is more scatter in the data points for the high MPI case

than the other two. This is probably because the

linewidth of the signal laser is less than the reciprocal

of the typical multipath delay, 500ns, and there is phase coherence in the multipath interference process, so it depends on the environmental

conditions which varied over the 24h period that the measurements were made.

Analysis of results The multipath interference is expected to appear as

an additional noise contribution, behaving like extra ASE. Because the MPI is the sum of replicas of the

signal after many random time delays, it has the same shape as the signal's optical spectrum, but the phase of each component is random. Thus it is similar to ASE, which has a flat optical spectrum and random phase. The equivalent OSNR of the mulfpath interference is

(7) OSNR" MPI.Bres where £^, g

is the signal's optical bandwidth and 4es is the resolution bandwidth associated with the OSNR.

The results of the experiment were used to test whether equation (7) applies. A curve, the solid line

in figure 1 , was drawn through the data points of case 3w ith the equation

Q = f(OSNR) (8> where

f (x) = 0.0130x 2 + 0.0395 x + 1.41 ( 9)

is simply a polynomial fit to the back-to-back (case 3) data points.

The two curves drawn on figure 4 (reproduced as the dashed curves on figure 3 so that all three cases can

be seen on the same graph) are mapped versions of the solid curve on figure 3 following the relationship

(r .-1 (5) Q = C.f

1 MPl.Br, OSNR Bsig The contents of the brackets is the sum of the MPI

equivalent OSNR from equation 7 and the actual OSNR. The multiplier C is there to account for the eye opening being slightly different in the three cases.

This was attributed to the end -to- end dispersion being

different, because of the granularity of the available DCMs. The values of C and MPI used are given in Table 1, and es)g=16GHz, Bres =12.5GHz.

C MPI (dB) case 1 case 2

1.02 0.98

-34.6

-25.4 Table 1 Values used in equation 5.

The MPI values are the sum of the measured MPIs of the individual fiber spans and DCMs at the signal wavelength. Factor C is fitted based on the Q values

at the low OSNR region.

Clearly, the two mapped curves do indeed fit their respective experimental data points. In particular the curve through the high MPI DCM points predicts the

deviation at high OSNRs correctly. We conclude that the multipath interference can be treated as a noise

141
If the variation of ocRS(r) is very small it may be excluded from the integration and the integrals left is the inverse of the effective area. Combining with (1) the following dependence ofK is obtained: a

K oc

RS,Si02 + KGe An + +KF An

X A

(6)

eff

Experimental setup:

Previous measurements of Rayleigh backscattering [6,7,8] are based on an OTDR but lack the availability

of scanning the signal wavelength. The setup presented here is based on a return loss module, a tuneable

laser and a powermeter (schematic in Fig. 1), all commercially available instruments. A measurement with

a reflection reference cable of known return loss is used to calibrate the return loss module and the recorded

return loss and power through the reference cable is used as a reference for all the measurements.

Tunable

laser

Point of reference measurement FUT -a

TUT

Splice point Mode filter

Power

Meter

Angled

cut 00000

5

Figure 1: Schematic of the experimental setup used for measuring Rayleigh backscattering

5x5 mm

on coils

The fiber under test (FUT) is spliced to a pigtail fiber and the splice is kept fixed for stability. To exclude multimode effects a higher order mode filter is applied to the FUT right after the splice by two coils of a

suitable diameter. One complete measurement consists of 4 cycles:

1 . The end of the FUT is terminated by 5 to 1 0 coils of a diameter less than 5 mm and an angular cut

to remove end reflections. The backreflected power of the FUT is recorded.

2. The end of the FUT is connected to the powermeter and the power throughput is recorded.

3. The FUT is cut approx. one meter after the splice and the mode filter and is again terminated by

small coils and an angular cut, and a reference return loss is recorded.

4. The fiber end is connected to the powermeter and the reference power is recorded.

According to (3) the power returning to the input end due to Rayleigh backscattering in the FUT of length

L is given by:

PRBS (0) = KPin (0)\e-2a*dz = Pm (0)^-(\-e-2aL

) (?)

o 2 «

where a and L is the spectral attenuation and the length of the FUT respectively. Defining

RFin^PRBsCOyPinCO) as the return power ratio due to the FUT we get for k: K = 7^% (8)

1 — e The total return power ratio Rtot seen by the return loss module is the sum of the return power ratio from the

pigtail + splice and the FUT:

P a

R -R 1 RBS pigtail+splice _ p p 2 (9)

"lot "-pigtail+splice p , "pigtail+splice

*r FUT pigtail+splice

in ^pigtail+splice where cXpigtai [ +Spi ice is the loss of the pigtail and the splice and is found from the calibration and reference measurements. This leads to

144
^ _

2a(Rtot Rpigtail+splice) ,, m

\-e-2aL

) m pigtail +splice V

c

/

The tunable laser makes it possible to measure K as a function of wavelength.

Results: A vast amount of different fibers have been measured. The fibertypes are Standard single mode fiber (SSMF), Non-zero dispersion fiber (NZDF), Super large effective area fiber (SLA), Inverse dispersion fiber (IDF), Raman gain fiber and different kinds of dispersion compensating fiber (DCF) with varying relative dispersion slope for dispersion slope compensation of different types of transmission fibers. All fibers have

been manufactured by OFS. The lengths of the fibers under test have varied from about 1 km up to 50 km

and cutback measurements have shown no indication of any length dependence in the measurement. The repeatability variation of the measurement is below 2% looking at actually measured values. Comparing results where a linear fit has been applied to the data the repeatability variation is below 1%.

In fig. 2 (to the right) measurements of the

different fiber types are shown. The variation with wavelength is seen to be almost linear and

linear fits have been applied to the measured K

values. It is seen that not only the magnitude of

k but also the slope of k changes for different

fiber types. From (6) it is seen that the slope of K

is proportional to 1/Aeff x A."

3

.

| 6.0E-07 oug 5.0E-07 IS 4.0E-07 u

tn% 3.0E-07

xDCF

DCF

x DCF —— Raman fiber

"* ' - ~X-X -

• DCF

• IDF

* NZDF SSMF

- z z z

1550 1570 Wavelength [nm]

Using measured values for K, Aeff, CR and fiber loss to predict [1] gain, noise figure and MPI of a Raman

amplifier gives good agreement with measured values. An example is shown in fig. 3: A measurement of a

dispersion compensating Raman amplifier consisting of 3.9 km Extra High Slope DCF (EHS DK)

compensating the dispersion and dispersion slope of 90 km Truewave®RS from 1528.8 nm to 1567.2 nm

[9]. The DCF has been backward pumped by pumps at three different wavelengths.

Fig. 4 shows K vs. spectral attenuation @1 550 nm. A linear dependence can be sensed but the large

spreading of the data indicates that the backscattering of a fiber cannot be predicted by just knowing the

spectral attenuation. That is due to other loss factors different from fiber to fiber (e.g. bending losses, anomalous losses etc.).

Fig. 5 shows the expected l/A^f dependence of k.

Fig. 6 shows the relation between k @1550 nm and the peak value of the Raman gain coefficient CR =

gR/Aeff measured with a pump wavelength of 1453 nm. A distinct linear correlation is seen. To a good

approximation gR can be written as [10,1 1] gR=CigS i02+ C2An" + C3 An

+ where gS i02 >s the Raman gain

coefficient of pure silica and Cu C2 and C3 depend on the overlap between the pump and the signal.

Comparing to (6) the observed linear correlation is expected.

Conclusion:

We have described a fast, simple and repeatable method to measure the Rayleigh backscattering coefficient of optical fibers as a function of wavelength, and measurement results from a broad range of fibertypes

have been presented. In combination with measurements of Aeff and CR we have shown that it is possible to calculate the behavior of the fiber in a Raman optical amplifier, especially predicting the MPI due to double

Rayleigh backscattering which is a limiting factor in Raman amplification.

145
References:

[1] P.B. Hansen, L. Eskildsen, A. J. Stentz, T. A. Strasser, J. Judkins, J. J. DeMarco, R. Pedrazzani and D. J. DiGiovanni, "Rayleigh scattering limitations in distributed Raman pre-amplifiers "

, IEEE Photonics Tech. Letters, vol.

10, No. l,pp. 159-161, 1998

[2] E. Brinkmeyer, "Analysis ofthe backscattering methodfor single-mode opticalfibers

"

, J. Opt. Soc. Am., Vol. 70, No. 8, pp. 1010-1012, 1980

[3] M. Nakazawa, "Rayleigh backscattering theoryfor single-mode opticalfibers" , J. Opt. Soc. Am., Vol. 73, No. 9, pp. 1175-1180, 1983

[4] I. Garret and C. J. Todd, "Components and systems for long-wavelength monomodefibre transmission ", Optical and Quantum Electronics, vol. 14, pp. 95-143, 1982

[5] A. Hartog and M. Gold, "On the Theory ofBackscattering in Single-Mode Optical Fibers "

, J. Lightwave Tech.,

vol. LT-2, No. 2, pp. 76-82, 1984

[6] A. Hartog and M. Gold, "Measurement ofbackscatterfactor in single-modefibers

"

, Electr. Lett., vol. 17, No. 25,

pp. 965-966, 1981

[7] A. F. Judy, "An OTDR based combined end-reflection and backscatter measurement" , SOFM, pp. 19-22, 1992

[8] M. E. Fermann, S. B. Poole, D. N. Payne and F Martinez, "Comparative measurements ofRayleigh scattering in single-mode opticalfibers based on OTDR technique", Journ. Ligthwave Tech., vol. 6, No. 4, pp. 545-551, 1988

[9] Y. Qian, C. G. Jorgensen, P. B. Gaarde, B. Palsdottir and B. Edvold, "C-band discrete Raman amplification with simultaneous dispersion and dispersion-slope compensation for NZDF" , Proceedings of OOA 2002

[10] Y. Qian, "Optically Pumped Waveguide Lasers and Amplifiers

"

, Ph.D. Thesis, 2000

[ 1 1 ] J. Bromage, K. Rottwitt and M.E. Lines, "A method to predict the Raman gain spectra of germanosilicatefibers with arbitrary index profiles ", IEEE, Phot. Tech. Lett., vol. 14, Issue 1, pp. 24-26, 2002

Meas. Gain Sm. Gain

1548

Wavelength (nm)

1.0 09 _ 0.8 TE 0.7 o

r 0.6

"i* 0.5 cS 0.4

in® 03

*

0.2

0.1

0.0

0.2 0.4 0.6 0.8 Spectral attenuation @ 1550 nm [dB/km]

Figure 3: Measured and calculated netgain, noise figure and MPI of a C-band dispersion

compensating Raman amplifier [9].

Figure 4: Measured Rayleigh backscattering

coeff. vs. the fiber spectral att. @ 1550 nm for various tvoes of fiber.

e o.7

E 0.5

<§) 0.3 02

0.1

Effective area @1 550 nm [\im2

]

1.0 2.0 3.0 4.0 5.0 Peak Raman gain cosff. CR [1/Wjkm], pump @ 1453 nm

Figure 5: Measured Rayleigh bsc. coeff. @ 1550 nm vs. the effective area @ 1550 nm for variour types of fiber.

Figure 6: Measured Rayleigh backscattering coeff. @ 1550 nm vs. peak Raman gain coeff. @ 1551 nm

(pump @ 1453 nm).

146
Measurement of Multimode Resonances in

Hexagonal Micro-Pillar Optical Cavities

Ma Ning and Andrew W. Poon

Department of Electrical and Electronic Engineering

Hong Kong University of Science and Technology, Hong Kong, China

I. Introduction

Optical micro-pillar ( u -pillar) resonators have attracted recent interests for potential

applications in integrated photonics due to their compact size (of 10 - 100 P m lateral dimensions and of ~ u m height) and high-Q resonances. Ring and disk u -pillar wavelengthdivision multiplexing (WDM) channel add/drop fdters have been demonstrated [1]. Very

large-scale integrated (VLSI) photonic chips using u -pillar cavities are feasible [2]. High-Q

optical resonances can be confined by nearly total internal reflection (TIR) at the u -pillar resonator sidewall. The U -pillar cavity can be evanescently side-coupled or vertically

coupled [3] to input and output waveguides. The main drawback of the conventional side- coupled circular ring and disk cavities is the short interaction length between the curved

cavity sidewall and the straight waveguide sidewall. Such short interaction length imposes a sub-micrometer gap distance for evanescent coupling.

Polygonal u -pillar resonators provide an alternative means of increasing the evanescent

side-coupled length for potential WDM add/drop filter applications [4]. The advantages of the polygonal cavities are twofold: (1) The entire flat polygonal sidewall allows a longer

interaction length, and therefore a wider gap distance for evanescent coupling between the cavity and the straight waveguides; and (2) the optical path length is identical for rays having

the same incident angle along the sidewall, and hence the same cavity mode can be coupled

anywhere along the flat sidewall. Fabrication of polygonal u -pillar cavities can be readily

achieved with established microelectronic fabrication processes. Recently, multimode

resonances in square-shaped u -pillar cavities were demonstrated [4], and hexagonal

microlasers have been reported [5]. In this paper, we report our recent measurement of multimode resonances in the elastic- scattering spectrum of hexagonal u -pillar optical cavities, using Gaussian beam coupled

along the cavity sidewall. The observed free spectral range (FSR) is consistent with the six- bounce closed-loop path length. By using the wavefront-matching concept [4], the observed

multimode resonances can be attributed to round-trip trajectories that need not be closed after each round trip.

II. Ray Optics in Hexagonal Cavities

Figure 1 (a) shows the six-bounce closed-loop trajectories with an incident angle 9 = 60°. All hexagonal orbits with 0 = 60° (such as the solid and dashed lines) have the same path

length of 3L (L is the distance between two parallel planes) and therefore have the same

cavity modes. Trajectories with 6 ^ 60° do not close upon themselves in each round trip. Figure 1 (b) shows the six-bounce open-loop trajectory with incident angle 0 i- 60°, and a complementary incident angle 120° - 0 at the adjacent sidewall. For the trajectory to be

confined by TIR, 0 needs to satisfy 0C < 0 < 120° - 0C , where the critical angle 0C = sin"

1 (1/n), and n is the refractive index of the dielectric cavity in air. In silica n -1.44 (X~ 1.5 u m), and

147
0C ~ 44°, 44 °< 9 < 76°. In the cavity, the incident wavefront and the wavefront of the openloop round trip ray can be spatially overlapped, as shown by the dashed line in Figure 1 (b). Following the discussion of multimode resonances in square u-pillar cavities in [4], we

believe such wavefront-matched open round trip can result in multimode resonances in hexagonal cavities.

Figure 1 (a) Six-bounce closed-loop trajectories with incident angle 8 = 60° . (b) Open-loop trajectory with incident angles 6 and 120° - 9 .

III. Experiment and Results

A commercially available hexagonal silica fiber was employed in the elastic-scattering

experiment. The fiber was side-couple perpendicular by a Gaussian beam, and thus acted as an optical u-pillar cavity. Two fiber sizes with L = 125 U m ± 2.5 u m and L = 200 u m ±

4 U m were used in the experiment. The fiber corners are slightly rounded. The fiber orientation was monitored with an uncertainty of +2° by a top-view microscope. A Gaussian

beam from a wavelength-tunable diode laser (1510 nm - 1580 nm-wavelength range) was

weakly focused (by a f /20 ~ f /33 cylindrical lens) to the fiber and tangentially onto the fiber

flat sidewall. The line beam was along the fiber axis. The estimated beam width was < 100 um. The incident polarization was parallel to the fiber axis (TM mode). We tuned the separation between the line beam and the fiber sidewall in order to excite the cavity modes.

The elastic-scattering spectrum was imaged (with an acceptance angle of 2.6°) from the fiber

flat sidewall onto an InGaAs photodiode. An analyzer was placed in front of the photodiode

to measure the TM spectrum. The laser linewidth is ~ 2 x 10"6 nm, and the spectral resolution was 0.003 nm. Figure 2 shows the schematic of the hexagonal fiber side-coupled with a Gaussian beam.

V

\ 120°

\

\ Gaussian beam

Figure 2 Schematic of the hexagonal fiber side-coupled with a Gaussian beam. The dashed

arrows indicate the scattering tangential to the cavity sidewalls.

Figure 3 shows the measured TM polarized elastic-scattering spectrum of a L = 200 um

hexagonal fiber imaged at 60° from the Gaussian beam direction. The highest measured Q

factor is > 2000. The spectrum is multimode. At least four orders of modes were observed

(labeled as A, B, C, D) with a FSR ~ 2.8 nm. The scattering spectra at other angles were also measured.

148
Assuming a six-bounce closed-loop trajectory, the FSR is calculated as follows: • I

2 FSR*— (1) 3nL

where 1 ~ 1550 nm, n = 1.44, L = 200 urn, and 3L is the closed-loop path length. The

calculated FSR ~ 2.78 nm is consistent with the measured FSR ~ 2.8 nm.

1540 !550 1560 Wavelength (nm)

Figure 3 Measured multimode resonances (at 60° scattering angle) in a TM-polarized elastic-scattering spectrum of a hexagonal optical fiber (L=200 U m). The FSR is ~ 2.8nm. The inset shows a schematic of the Gaussian beam (the thick arrow) grazing the hexagonal fiber sidewall and a six-bounce closed-loop

trajectory.

3

d

-4—

»

c

c

FSR * 4.4 run h \ / L = 125 urn

- 1 i f1 1' ft :

f \

|

1

; \ /

\ / \ 1

. v y u

1540 1550 Wavelength (nm)

1560

Figure 4 Measured multimode resonance in a TM-polarized elastic-scattering spectrum of a hexagonal optical fiber (L = 125 urn) at 60° scattering angle. The FSR is ~ 4.4 nm.

149
Figure 4 shows the measured TM polarized scattering spectrum at 60° in a 125 um

hexagonal fiber. The observed FSR ~ 4.4 nm is consistent with the calculated FSR ~ 4.45 nm

by means of equation (1). There are more than 4 orders of modes. By further reducing the cavity dimensions, larger FSR is expected, which is an essential requirement for WDM

add/drop filter applications. In order to obtain a FSR > 30nm, which spans the 1.55 Um

telecommunication window, a silica hexagonal u -cavity with L < 20 u m is needed. Such

small u -pillar cavities can be readily fabricated by microelectronic technologies.

In summary, the elastic-scattering spectra of hexagonal u -pillar resonators were

measured. The multimode resonances can be attributed to the wavefront-matched open-loop

trajectories. A smaller-sized hexagonal cavity coupled with waveguides has potential

applications in WDM add/drop filters. We gratefully acknowledge the support by the Hong Kong University Grant Council (HIA

01/02. EG05) and the Research Grant Council (DAG01/02. BG22). Andrew W. Poon's email

address is eeawpoon@ust.hk.

References

[1] B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Ippen,

L. C. Kimerling, and W. Greene, IEEE Photon. Technol. Lett. Vol. 10, no.4, pp.549-551,

(April, 1998).

[2] B. E. Little and S. T. Chu, Optics & Photonics News, pp. 25-29 (Nov. 2000).

[3] P. P. Absil, J. V. Hryniewicz, B. E. Little, F. G. Johnson, K. J. Ritter, P. T. Ho, IEEE

Photon. Tech. Lett. Vol. 13, no. 1, pp. 49-51 (Jan. 2001).

[4i A. W. Poon, F. Courvoisier, R. K. Chang, Optics Letters, vol. 26, no. 9, pp. 632-634

(May, 2001).

[5] S. Ando, N. Kobayshi and H. Ando, Jpn. J. Appl. Phys. Vol. 34(1995) pp. L4-L6.

150
MEASUREMENT REQUIREMENTS FOR OPTICAL AND OPTOELECTRONIC-MODEL

VERIFICATION, VALIDATION, AND CALIBRATION

(INVITED)

J. Morikuni, P. Mena, B. K. Whitlock, and R. Scarmozzino

RSoft Design Group, Inc. 200 Executive Blvd.

Ossining, NY 10562

INTRODUCTION

As optical communication systems become more and more complex, an accurate modeling and simulation

infrastructure becomes critical to their design. Even seemingly simple optical designs can become intractable when

attempted by hand; this is particularly evident in the physical design of fiber-optic communication systems.

Although any fiber-optic system can be described fundamentally as an optical source, a transmission medium, and a

detector, its design involves hundreds, if not thousands, of choices, decisions, and trade-offs. For example, what is the optimum type of laser to use? Will the targeted link require optical amplification? If so, should Raman amplifiers or EDFAs be used? What is the impact of additional DWDM channels? These questions can all be answered through

optical link simulation. Figure 1 depicts a typical simulation topology as seen from the graphical user interface of a physical-layer, link-level simulator [1].

Figure 1 : Topology of a link-level simulation as viewed from the graphical user interface.

In this figure, the simulation of a four-channel WDM system is depicted; each channel consists of a CW laser at a

different wavelength connected to an external modulator driven by a PRBS pattern generator and an electrical signal

generator. The four channels are combined with an optical multiplexer and transported through 40 km of singlemode fiber Finally, the four channels are separated with an optical demultiplexer and processed by individual photoreceivers. At any point along the link, the signal waveforms can be viewed in the time or frequency domain

using "virtual" measurement instruments such as oscilloscopes, spectrum analyzers, BER testers, and the like.

The square icons in the topology of Figure 1 represent models describing the performance of each device in the system. The device models that comprise a link simulator are arguably the most critical aspect of the tool. Each

model contains a very detailed physical description of the device's attributes using equations of quantum mechanics,

semiconductor physics, electromagnetics and the like. Because these models are physical and general, each one can

be used to simulate a wide range of device configurations. For example, the detector responsivity, the amplifier

bandwidth, and the filter type are three of the many photoreceiver model parameters that can be individually tailored. In order to construct real-world systems, each of the models in the link must be properly calibrated to the device that

it is intended to simulate. To this end, laboratory measurements are typically analyzed to extract all of the model

151
parameters that are relevant to the system under study. In this paper, we will describe representative measurements

required to validate and calibrate optical and optoelectronic models for the purposes of system simulation. We

review methods for three critical aspects of the link: the laser, the fiber, and the photoreceiver.

LASER DIODE

While there are many types of laser diodes, most of them can be described by the following rate equations [2]:

4M. = l-K-G(N-Nn)S — = Q— + GJN-Nn )S-— P = kS (1) dt q X„ dt X„ Xs

Here, Nand S are the total electron and photon populations, respectively, in the laser cavity; zn and T5 are the electron and photon lifetimes, respectively; G0

is the gain coefficient; N0is the electron population at optical transparency; /3

is the spontaneous emission coupling coefficient; / is the injected current; q is the electron charge; t is time, and k is the output power coupling coefficient. These parameters are clearly grounded very heavily in device physics. The

rate equation model describes the time varying interchange of energy between the electrons and photons in the laser cavity; using these equations, it is possible to predict the amount of optical output power P for a given amount of

input current /. Although this model does a very good job of qualitatively describing laser operation, laboratory measurements are necessary to calibrate the model to an actual device.

The six physical model parameters in (1) are unfortunately not directly observable nor measurable with typical

laboratory equipment. However, they can be determined through two commonly performed laboratory

measureme.its: the light-current characteristic and the time-domain step response. The first measurement

characterizes the amount of optical output power that results from a given amount of input current under steady-state conditions. The second measurement characterizes the transient response of the laser to a step current input of a fixed

level. From these two measurements, we can determine the following laser attributes: the threshold current I[h , the slope efficiency t]qe, the turn-on delay td, the frequency of the laser relaxation oscillations QR , and the decay rate of

the oscillations rR

(Figure 2). One additional parameter is the magnitude of the input current I0 used to produce the

transient step response. Analysis of the rate equations over different regimes of operation (e.g., well below threshold and well above threshold) [3] combined with numerical parameter optimization can be used to map these physically observable parameters to the theoretical rate-equation ones. If they are available, the S21 and Sn responses of the

laser can be used in place of the step response, though a different extraction procedure must be used.

For more complex device structures, the simple rate-equation description is insufficient. For example, the rate equations can be augmented by spatial and thermal ones to describe the attributes of a VCSEL (2)-(6):

Input Current (mA) Time (ns)

Figure 2: Representative laboratory measurements used to calibrate rate equation model. Data taken from the datasheet for a Rohm RLD-83MF short-wavelength 830 nm edge-emitting laser diode.

152
^0 = V NQ G(T){y00 [N0 -Nt (T)]-y0l N,}

s

I

leak (NQ ,T)

dt q X

n

\ +eS q

(2)

dN, N,

1 +eS

(3)

dS _ S

+ Wo + G(T){y0o[N0 -Nt (D]-yol Nl } ^

dt xpx

n 1+eS

T= T0 + (I

tot V-Pout)Rth -Xth ft (4)

heak = 7/o exP -aQ + a l N0 + a2 N0 T-

«4 + Ar

0

( ,^ a n + a ,T+a -iT "gO "g\ J u

g2 l (5)

GWD = G0 (T)[N-Nt (T)] = Ntr (cn0 + c

n J+ cn2 Tl) (6)

We do not attempt to describe the model [4] here; the point of this discussion is to illustrate the level of complexity of

a typical active device model. To properly calibrate the model to an actual device, the user can adjust over 40

parameters. While the first step in the analysis is to extract as many model parameters as possible from lab measurements (as in the previous example), the semi-empirical nature of this particular model necessitates a numerical optimization scheme such as least-squares fitting, the Levenberg-Marquardt method [5], or a genetic

algorithm [6]. This process is generally referred to as parameter extraction and is used very commonly in the

electronic design automation (EDA) industry. Figure 3 depicts the validated VCSEL model.

I—

a>

coc

O

Q.

COO

rrc

o3

12 S 1

1.6

1.4

T3 0 8

0.6

0.4

0.2

0.7 mA 4 Bias current

o/°o \ n 1.0 mA

of o\ er 0.5 mA 0/ \ 1.3 mA

37 0/°7vk/D/° /IX \\ 2.1 mA

—^ ' 1 +

1 0 5 10 15 20 25 30 3b 012345678910111213141516

Input Current (mA) Frequency (GHz)

Figure 3: Validated VCSEL model. Markers represent data, curves represent simulation results. Light-current-temperature data (left) are from [7], S21 data (right) are from [8].

OPTICAL FIBER

System-level link analysis tools must also be able to model the optical transmission medium. The link simulator of

[1] containr models for both single-mode and multimode fibers. One of the more interesting measurement-based

examples is the multimode fiber. There are several ways to model multimode fibers; the most fundamental method is to analyze the fiber's refractive index profile and to extract information about the fiber's spatial modes and

propagation constants [9]. This information can be used to predict fiber attributes such as modal dispersion, modal

noise, and the like. The fiber propagation constants are extremely sensitive to minor perturbations in the index profile

153
[10]; consequently, for high-speed applications, the degree of accuracy required in the refractive index measurement

often renders the index-based approach impractical. As a result, researchers have developed a measurement-based

approach for characterizing multimode fiber bandwidth [1 1], [12]. This method is referred to as differential mode

delay (DMD) [13] and involves injecting small, short spots of light at regularly spaced intervals of the multimode

fiber input face and measuring the resulting signal that emerges from the fiber output (Figure 4). Since these pulses

are scanned across the circularly symmetric fiber face, many of the fiber's relevant spatial properties can be captured.

By interpreting the optical inputs as spatio-temporal delta functions, the corresponding outputs can be used to calculate the fiber's spatio-temporal impulse response.

COc

o—o

E,

Q> o

-4-3-2-101234

Time (ps/m)

Figure 4: Refractive index profile of graded-index multimode fiber (upper left). Differential mode delay (DMD) measurement of multimode fiber (lower left). Simulated DMD impulse responses (right).

Multimode fiber performance can be estimated from the DMD measurements by combining them with encircled flux measurements. Encircled flux is a measure of the amount of optical power that is contained inside thefiber within a given radial distance from the fiber axis [14]:

2rc EF(r)

m - '< m i J J

I(r, Q)rdrdQ (7)

The encircled flux is clearly a function of the spatial attributes of the laser output, the laser/fiber positioning, and the

fiber's spatial mode distributions. Since the DMD data contains considerable spatial information, the response of the

fiber to an arbitrary optical input can be approximated as a weighted sum of these impulse responses. The weights

applied to each DMD profile are functions of the spatial relationship between the optical input and the pulses used to generate each DMD response.

The interesting aspect of this approach is that it is almost entirely empirical. While the previous examples depicted

models that were physical and semi-empirical in nature, the DMD approach to multimode fiber characterization relies almost completely on measured data. Consequently, the accurate measurement of these data is absolutely critical. The Telecommunications Industry Association has published several documents specifying the measurement

procedures for high-speed multimode fiber systems [13] - [16]. PHOTORECEIVERS

The photoreceiver is the final component in the optical link. As with the laser, a combination of optical and electrical measurements is necessary to accurately calibrate the photoreceiver. To facilitate use of a photoreceiver model, it should be designed with parameter extraction in mind. Using the system-level simulator of [1], the photoreceiver can be modeled a number of ways ranging from physical to semi-physical to empirical. To better illustrate the measurement-based aspects of the model, we focus here on the empirical approach. The photoreceiver's frequency

response H(j) and noise spectral density S$J) are represented as (8) and (9):

154
H(f) f

V

if+f

St (J) = a

Q + a2f + a^ + aef

H(f)dB = 20-log 10 |/7(/)| (8)

(9)

Here, Zris the DC transimpedance,/is the baseband frequency,^ is the zero frequency of the photoreceiver,^, is the pole frequency,y is the imaginary constant, and a0 -a6 are empirical fitting parameters.

Often, the only information available is a few parameters from commercial data sheets or simple lab meaurements

such as the 3-dB frequency and the receiver sensitivity at a given bit error rate. Using the above formulation, it is possible to calibrate the model with a few additional steps. Although most photoreceivers exhibit a single-pole response, (?>) allows for both a pole and a zero. The photoreceiver's frequency-domain response can be calibrated by

eliminating the zero frequency and setting the pole frequency to the measured 3-dB frequency.

The input-referred photoreceiver noise for a transimpedance-amplifier-based photoreceiver is defined to be [17]:

<e = r

W(f)\ 2

\H(0)\ 2 Siif)df (10)

If we assume the noise to be white, then a2 -a6 in (9) can be considered to be zero and (10) is easily determined from

(8) and (9). The bit-error rate (BER) of a receiver is expressed as [18]:

BER = -erfc

2

J Q_ Q (11)

Here, the complementary error function is represented as erfc; Ix and I0 are the photocurrents in the high and low

states, respectively; and the standard deviation terms represent the noise in the high and low states. Thus, for a given

BER, it is possible to determine what value of Q is required. Although this cannot be performed analytically, it can

be done either numerically or graphically. For example, from the BER vs. Q relationship plotted in Figure 5, it is clear that to achieve a BER of 10" 12 a Q of roughly 7 is needed.

If we make the simplifying assumptions that the power in the low state is zero and that the noise is independent of

signal level the average detected optical power T|P (which is proportional to the sensitivity) can be approximated by

(12) where h is Planck's constant, q is the electronic charge, and X is the wavelength. Thus, (9) - (12) can be used to calibrate the photoreceiver's noise attributes. nP-^QUD (12)

1E+0

1E-1 1E-2

1E-3

1E-4 1E-5 1E-6

(£ 1E-7

CO 1E-8

1E-9 1E-10

1E-11 1E-12

1E-13

1E-14 1E-1S 0123456789 10 Q

Figure 5: The relationship between BER and Q.

155
SUMMARY

In this paper, we have described the model development and measurement challenges associated with the calibration,

validation, and verification of optical and optoelectronic models for fiber-based communication system design.

Integral to this approach is the identification of the necessary measurements as well as the development of the model

with parameter extraction in mind from the start. We reviewed three basic examples (laser, fiber, receiver) that are key components of any optical communication system and demonstrated several methods for their verification.

This material is based upon work supported by the Naval Surface Warfare Center, Dahlgren Division under Contract No. N00178-01-C-3061. We would like to thank Gair Brown of the NSWC for his support.

REFERENCES

[I] Z. Huang, B. K. Whitlock, and R. Scarmozzino, "CAD optimizes component design at many levels," WDM

Solutions, pp. 41-48, August 2000.

[2] R. S. Tucker, "Large-signal circuit model for simulation of injection-laser modulation dynamics," TEE

Proceedings, vol. 128, pt. I, no. 5, pp. 180-184, 1981.

[3] G. P. Agrawal and N. K. Dutta, Long Wavelength Semiconductor Lasers. New York, NY: Van Nostrand

Reinhold, 1986.

[4] P. V. Mena, J. J. Morikuni, S.-M. Kang, A. V. Harton, and K. W. Wyatt, "A comprehensive circuit-level model of vertical-cavity surface-emitting lasers," Journal of Lightwave Technology, vol. 17, no. 12, pp. 2612-2632, 1999.

[5] W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C. Victoria, Australia: Cambridge University Press, 1992.

[6] D. E. Goldberg, Genetic Algorithms: In Search, Optimization and Machine Learning. Reading, MA:

Addison Wesley Longman, 1989.

[7] Y. Ohiso, K. Tateno, Y. Kohama, A. Wakatsuki, H. Tsunetsugu, and T. Kurokawa, "Flip-chip bonded 0.85- um bottom-emitting vertical-cavity laser array on an AlGaAs substrate," IEEE Photonics Technology

Letters, vol. 8, no. 9, pp. 1 1 15-1 1 17, 1996.

[8] B. J. Thibeault, K. Bertilsson, E. R. Hegblom, E. Strzelecka, P. D. Floyd, R. Naone, and L. A. Coldren,

"High-speed characteristics of low-optical loss oxide-apertured vertical-cavity lasers," IEEE Photonics

Technology Letters, vol. 9, no. 1, p. 11-13, 1997.

[9] R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, "Numerical techniques for modeling guided-wave

photonics devices," IEEE Journal of Selected Topics in Quantum Electronics, vol. 6, no. 1, pp. 150-162, 2000.

[10] M. J. Hackert, NIST Symposium on Optical Fiber Measurements, pp. 113-118, Sept. 1998.

[II] S. Golowich, P. Kolesar, J. Ritger, and P. Pepeljugoski, "Modeling and simulation for 10 Gb multimode

optical fiber link component specifications," Optical Fiber Communications Conference Technical Digest,

Paper #WDD57, 2001.

[12] J. E. George, S. Golowich, P. F. Kolesar, A. J. Ritger, and M. Yang, "Laser optimized multimode fibers for short reach 10 Gbps systems," National Fiber-Optic Engineers Conference Technical Proceedings, pp. 351- 361,2001.

[13] "FOTP-220: Differential Mode Delay Measurement of Multimode Fiber in the Time Domain," TIA/EIA

Standards Document, TIA/EIA 455-220, November 6, 2001

.

[14] "FOTP-203: Launched Power Distribution Measurement Procedure for Graded-Index Multimode Fiber

Transmitters," TIA/EIA Standards Document, TIA/EIA 455-203, March 2000.

[15] "FOTP-191: Measurement of Mode Field Diameter of Single-Mode Optical Fiber," TIA/EIA Standards

Document, TIA/EIA 455-191, September 1998.

[16] "FOTP-204: Measurement of Bandwidth on Multimode Fiber," TIA/EIA Standards Document, TIA/EIA

455-204, December 2000.

[17] R. G. Smith and S. D. Personick, "Receiver design for optical communication systems," in Semiconductor

Devicesfor Optical Communication. New York: Springer Verlag, 1980.

[18] T. V. Muoi, "Receiver design of optical-fiber systems," in Optical Fiber Transmission. Indianapolis, IN: Howard W. Sams & Co., 1987.

156
Photon-counting OTDR at telecom wavelength:

high-resolution and long-distance measurements

F. Scholder, A. Fougeres*, J.-D. Gautier, C. Barreiro, A. Haldimann, H. de Riedmatten,

M. Wegmiiller, and N. Gisin

GAP-Optique, University of Geneva, Rue de l'Ecole-de-Medecine 20, CH-1211 Geneve 4

(*) GAP-Optique S.A., Rue de l'Ecole-de-Medecine 20, CH-1205 Geneve

Abstract: Photon-counting OTDR has a big advantage over conventional OTDR because of its higher detection sensitivity. This technique leads either to an improved spatial resolution or to an enlarged dynamic range. In this paper we experimentally demonstrate both modes oj

operation: a two-point spatial resolution of better than 10 cm and a 44-dB (one-way) dynamic

range are obtained at a wavelength of1550 nm.

Introduction

Optical time-domain reflectometry (OTDR) is the most widely used fiber-test technique. It can measure either fibers of lengths over 1 00 km with kilometric spatial resolution or shorter fibers

with at best metric resolution. Further, state-of-the-art conventional OTDRs have a dynamic

range of up to ~40 dB with spatial resolutions in the kilometer range [1]. On the other hand, an OTDR based on photon counting (v-OTDR) has spatial resolutions that can be as small as a few

centimeters [2]. However, as for conventional OTDRs, the detection sensitivity is shown to depend on the spatial resolution [3]. Reducing this resolution from the centimeter range to the

hectometer range can drastically increase the v-OTDR detection sensitivity and dynamic range.

Photon counting and v-OTDR trace extraction

To detect single photons at a telecom wavelength of 1.55 |im, we are using an InGaAs avalanche

photodiode (APD), cooled by Peltier elements down to -57 °C. This APD is used in the so-called

"gated Geiger mode", with the detector being active only during a given time slot ("gate") [4,5].

During this period, a single photon falling on the APD can trigger an avalanche, which is then

detected by discriminator electronics. This process is then repeated many times, and from the

number of counts for a certain position (delay) of the gate, the reflectivity at the corresponding

location in the fiber is obtained. Obviously, in order to extract the real signal, the detector has to be operated below saturation. In the present experiments, the probability for a count within one

gate has to be smaller than 40% in order to remain in the linear regime. On the other hand, it has

to be large enough to be distinguishable from the noise. In order to go beyond these two

restrictions, one can use an appropriate data correction, which subtracts the noise and takes into

account the non-linear response when being close to saturation. If r| is the detection efficiency,

pn the noise count probability, and p the overall detection probability (signal + noise), the mean

number of photons per gate fl (i.e. the net signal) is given by the following equation, assuming a Poissonian photon distribution.

1 . u = — • In l-p

(1)

157
Hence—knowing the noise count probability pn—this equation will be used to obtain the net

signal power from the corresponding overall count probability p, and thus our v-OTDR trace. This correction is especially useful when p is either close to saturation or to the noise level.

High resolution v-OTDR measurement

Using the setup described in Fig. 1 we made a high-resolution measurement of an 11 -cm-long

standard singlemode optical patchcord connected with FC/PC connectors after a 2-km fiber. We

used 500-ps-long laser pulses, detection gates of x = 2 ns, and a detection efficiency T| = 10%.

We opened 100,000 detection gates for each of 200 different gate delays (by steps of 50 ps to have a 5-mm sampling resolution on a 1-m measurement range) at a repetition rate (gating

frequency) /= 50 kHz allowing for only one laser pulse in the fiber. Hence the whole

measurement took about 7 min. The corresponding v-OTDR trace is shown in Fig. 2. The two

reflection peaks are clearly distinguished and separated by slightly more than their FWHM

(~10 cm), thus demonstrating a 2-point spatial resolution of about 10 cm. Therefore v-OTDR is the reflectometry technique of choice if good spatial resolution at long distances is required. For

instance optical frequency-domain reflectometry (OFDR) can have a better spatial resolutions of

2 cm (or even ~1 mm), but only for measurement lengths <200 m (<10 m, respectively).

Dynamic range

To evaluate the dynamic range, we first calculate the noise equivalent power (NEP) of the

detector. After having used Eq. 1 to correct the signal, the mean noise level goes to zero and thus

towards minus infinity on the typically employed logarithmic dB-scale. Therefore we will use as NEP the noise mean fluctuation (i.e. the standard deviation of the noise). Due to the specifics of

the gated photon-counting technique the number of noise counts for a given measurement time

follows a binomial statistics. Hence the standard deviation of the noise goes as the square root of

the mean number of noise counts given by the noise probability pn times the number of gates N

(N=f- At, where At is the measurement time for a given gate delay). Therefore the NEP level is equivalent to a mean number of photons per gate

Note that theory and measurements both show that for small pn (i.e. pn < 10%) the noise

probability is proportional to the gate duration x (i.e. pn = nn

• x). The 7Cn factor was measured to be 30 kHz for the APD used in the present experiments. Thus, using Eq. 2, the NEP is given by

This simple model shows that the NEP is inversely proportional to the square root of the gate

duration x and the measurement time At for each gate delay. Therefore measuring for a longer

time or with larger gate duration (i.e. smaller spatial resolution) has the same effect on the

sensitivity of the v-OTDR. This behavior is illustrated in Fig. 3. The experimental data are seen

to be in good agreement with the theory. Consequently, for a given measurement time, the

v-OTDR can be operated either in high-resolution or in high-sensitivity mode, but not both at the same time.

^NEP "-'JpjN. (for small pn ) (2)

(3)

158
For classical OTDRs, the dynamic range is usually defined as the difference between the initial Rayleigh backscattering (i.e. at the beginning of the fiber)—for a laser source with a pulse length

of 10 |is—and the noise level after a 3-min measurement time [1]. Let us now apply the same

definition to our v-OTDR. Since we are using a laser source with a peak power of +8 dBm and

10-|j.s-long pulses, the Rayleigh backscattering power at the input is -31 dBm for the Rayleigh

backscattering coefficient of -72 dB/m of the fibers used in our experiment. From Eq. 3, a NEP

of -121 dBm is obtained for l-|a,s-long detection gates, a 3-min measurement time per gate delay, a detection efficiency of 10%, and a gating frequency of 400 Hz (allowing to measure distances

up to 250 km). Thus the (one-way) dynamic range that could be obtained using our v-OTDR can

be estimated to 45 dB, whereas for the same conditions, classical state-of-the-art OTDRs reach

40 dB [1]. Note that for a laser peak power of +13 dBm, we could even increase the dynamic

range up to 47.5 dB.

High dynamic range v-OTDR measurement

To illustrate the results found in the previous section, we performed a v-OTDR measurement of

three FC/PC-connected standard telecom fibers of 10.4-, 16.4-, and 25.3-km length, respectively.

This measurement was done with the same scheme as previously described (Fig. 1), except that

10-|is-long laser pulses, detection gates of x = 1 \is, and a gating frequency /= 1600 Hz were

used to reduce the measurement time. A 28-dB loss was added between the first two fibers using an optical attenuator (which simulates a ~140-km-long fiber). The v-OTDR trace we obtained is shown in Fig. 4. The vertical scale is defined as the one-way loss with the initial Rayleigh

backscattering level normalized to zero. Therefore the NEP level directly gives the dynamic

range. We measured 44 dB, which is in excellent agreement with the theoretical value of 45 dB

of above, even more so if considering that the extra 1 -dB loss due to the optical circulator was

neglected in the calculations. From the Rayleigh backscattering in Fig. 4, standard losses of 0.22,

0.30, and 0.25 dB/km are obtained for each fiber, respectively. Note that for the last fiber—for

which the backscattered signal is close to the noise level—the correct loss is only obtained when

the signal correction (Eq. 1) is applied. A loss of 0.047 dB/km is obtained otherwise. We also

note that there are hardly any fluctuations in the v-OTDR trace, except when we are close to the

NEP. Of course these fluctuations can be reduced when integrating over a longer period of time,

hence providing better statistics.

Conclusions

An investigation of the spatial resolution and dynamic range of a v-OTDR was presented.

Calculations and measurements showed that the NEP scales as the inverse square root of gate

duration and total measurement time. Therefore increasing the gate duration, and thus decreasing

the spatial resolution, enhances the dynamic range. Our v-OTDR can thus be operated in two

different modes: high spatial resolution or high dynamic range. In the high-resolution mode, we

reach a spatial resolution of 10 cm with ~30-dB dynamic range. On the other hand, setting the

spatial resolution to 1 km—as typically used for OTDR characterization—we obtain a 44-dB

dynamic range, which is better by 4 dB compared to state-of-the-art conventional OTDRs.

Acknowledgment

We would like to thank EXFO and the Swiss Commission for Technology and Innovation (CTI)

for financial support.

159
References

1. EXFO Reference Guide 2001: dynamic range of ~40 dB with 10-us pulses and a 3-min

average at SNR = 1

.

2. A. Lacaita, P. Francese, S. Cova, and G. Ripamonti, "Single-photon optical time-domain

refleciometer at 1.3 urn with 5 cm resolution and high sensitivity", Optics Lett., 18, pp. 1110-1112 (1993).

3. F. Scholder, M. Wegmiiller, and N. Gisin, "Long-distance OTDR using photon counting and

large detection gates", OFMC '01, pp. 169-172 (2001).

4. G. Ribordy, J.-D. Gautier, H. Zbinden, and N. Gisin, "Performance of InGaAs/InP avalanche

photodiodes as gated-mode photon counters", Appl. Optics, 37, pp. 2272-2277 (1998).

5. D. Stucki, G. Ribordy, A. Stefanov, H. Zbinden, J. Rarity, and T. Wall, "Photon counting for

quantum key distribution with Peltier cooled InGaAs/InP APDs", J. Mod. Opt., 48,

pp. 1967-1981 (2001).

Laser pulse (500 ps-lOus)

Peltier-cooled APD detector

J~

^Detection gate (2 ns-1 us) T

Fig. 1 v-OTDR experimental setup.

-110

spatial resolution [m] 10 100 1000

-115

E

CD

O.UJ

-125

-130

10

theoretical model

• experimental data \«

10 10

t [s] : detection gate length

10'

Fig. 3 Theoretical and experimental behavior of the detection sensitivity (i.e. the noise equivalent power).

Fig. 2 High-resolution v-OTDR trace of two FC/PC

connections separated by 1 1 cm and located after 2 km

of optical fiber.

20 30

Distance (km)

Fig. 4 v-OTDR trace of three FC/PC-connected

standard telecom fibers with a 28-dB loss between the

first two fibers. The bold line indicates the "NEP".

160
Coherent speckle in direct-detection OTDR

S.G.Murdoch

NetTest (UK) Ltd, York House, School Lane, Chandlers Ford, United Kingdom.

Strong coherent speckle is seen in direct-detection optical time domain reflectometers whenever the coherence length of the source is of the same order of magnitude as the pulse width. Starting from the previously derived statistics for Rayleigh backscattering in single-mode optical fibers [1,2], we

investigate the properties of coherent speckle in direct-detection OTDRs. We compare our predictions

with the measured behaviour of the coherence speckle seen in a wavelength tunable direct-detection OTDR, and show that such a system can achieve at least the same level of speckle suppression as its standard fixed wavelength counterpart.

1. Introduction

Optical time domain reflectometry is a well-established technique for the measurement of distributed loss of optical

fibers [3]. Though many variants of the technique exist [4], commercial long-haul OTDRs most commonly use a single pulse, direct-detection setup. Here the energy of the backscattered light of a single pulse travelling down the

fiber is measured as a function of time, giving direct access to the distributed loss of the fiber. It is well known that when the coherence length of the optical source approaches the pulse width in such systems, the resultant OTDR

signal takes on a jagged, noisy appearance [4]. This effect is called coherent speckle (or coherent fading) and is due

to the random distribution of scatterers along the length of the fiber. Light returning from these scatterers interferes coherently at the receiver resulting in large fluctuations in the received signal power. Most commercial long-haul

OTDRs use wide-band optical sources, with coherence lengths many orders of magnitude smaller than the pulse

width so as to operate in an incoherent regime, where this coherent interference is much reduced. For other OTDR

applications however, the use of wide-band optical sources is not possible, and these measurements often exhibit strong coherent speckle. For example, the distributed measurement of polarisation mode dispersion by polarisation

OTDR [5], requires the use of a narrow-band source to avoid depolarisation. Other OTDR applications such as

spectral modelling [6], distributed chromatic dispersion measurements [7], and the surveillance of passive optical

networks [8], can also benefit from the use of tunable optical sources, which are themselves commonly narrow-band.

In this paper we analyse the coherent speckle properties ofjust such a narrow-band tunable direct-detection OTDR.

Following die approach of references [1] and [2], we model the Rayleigh backscatter of a single-mode singlepolarisation fiber as a series of point scatterers randomly distributed along its length. Assuming that the probability

of multiple scattering is negligible, the backscatter signal seen at the receiver at time t=T from a quasimonochromatic pulse (pulse width W), is given by

where E^z,t) is the pulse's electric field, h,{z) is the backscatter response of the ith scatterer, and the sum over M is the sum over all scatterers lying between z=L-W/2 and z=L (L=vg

T/2). Further, assuming that the scatterer amplitudes and positions are statistically independent, and the scatterer positions are uniformly distributed along the length of the fiber, it can be shown that ER{T) is Rayleigh distributed. This in turn implies the receiver power, PR(T), has a negative exponential distribution (just as with spatial speckle and the intensity statistics of thermal light) [9]:

2. Theory

A/ ER (T) = EP (z,T)®^hi (z), (1)

exp ~P p>0

(2)

0 otherwise

161
The standard deviation of a negative exponential distribution is equal to its mean. Thus the contrast of P/?(7) (defined

as the standard deviation divided by the mean) is unity. This high contrast is what gives speckle patterns their pronounced granular appearance [10].

Equation (2) gives the probability distribution of the instantaneous receiver power at time t=T; however it makes no

predictions as to what timescale PR(T) fluctuates over. To evaluate this, we calculate the normalised correlation between PR(T) and PR(T+r):

\t\<W/ v

g

(3)

otherwise

By analogy with the theory of spatial speckle, we define the speckle size as the half-width of this correlation

function. This gives the timescale, //, over which PR(T) fluctuates as tf ~ 0.1W/vg

- a tenth of the pulse duration. In direct-detection OTDR the receiver integration time TR is usually much larger than this speckle size. In this limit, the

distribution of the measured receiver power tends towards a normal distribution, with mean <PR(T)> and contrast proportional to llsqrt^^ [9,11]. Also in this limit, we find that the measured speckle size is proportional to TR, rather than to the pulse width.

W lv„ — T CPr (T,T + t) = Wlvg

0

High speckle contrast makes it difficult to extract fiber parameters or identify events in an OTDR trace. In this sense, the small receiver bandwidth of a commercial long-haul OTDR is advantageous, as it results in a reduction of the speckle contrast. Another well known technique for reducing speckle contrast in OTDR is to use a source whose

coherence length is much smaller than the pulse width [2,9,12]. For a source consisting of N discrete wavelengths

(far enough apart in frequency that the speckle at each wavelength is uncorrelated), the contrast of the coherent

speckle varies as l/sqrt(N).

3. Results

Our experimental setup consists of a direct-detection OTDR (NetTest 8000) into which we have integrated a tunable

external cavity laser. Pulses are produced by electronically pulsing the external cavity laser just as one would a standard OTDR source. This gives us a narrow linewidth tunable OTDR which is ideal for the study of coherent

speckle.

Distance (km) Distance (km)

Figure 1

Figure 1 shows two typical traces measured using our tunable OTDR. The two traces were measured using different receiver bandwidths. In figure la the receiver bandwidth used was 1MHz, and in figure lb, 3MHz. The pulse width was 100m, the averaging time 30s, and the laser wavelength 1549.90nm. The fiber under test (used throughout this

162
paper) consists of two 25km lengths of standard single mode fiber. The speckle is clearly visible'on the two traces. If the fiber under test is left undisturbed the speckle pattern remains stationary over a period of 5 to 10 minutes, until small changes in the environmental conditions perturb it. Monitoring the correlation of this speckle has previously

been used to build distributed fiber sensors [13].

For a pulse width of 100m, tf is approximately 100ns - much smaller than the receiver integration time. Thus we

expect the speckle amplitude to vary as llsqrt(TR), and the speckle size to vary as TR. The measured RMS speckle

amplitudes of the two traces in figure 1 are 0.1 8dB, and 0.32dB respectively. The ratio of these two amplitudes is very close to l/sqrt(3) which is in good agreement with the theory. The speckle sizes of the two traces are 47m and

14m respectively. The ratio of these sizes is close to 3, also in good agreement with the theory.

Next we investigate the correlation of the coherent speckle as a function of source wavelength and input polarisation.

Figure 2a shows the correlation between the coherent speckle of an OTDR trace taken at 1549.90nm, and subsequent

traces detuned by multiples of 17pm. The OTDR setup is the same as that used in figure la. A 17pm change in source wavelength results in complete decorrelation between the speckle of the two traces. This result is in agreement with the theory of the previous section, which requires Ak WXo be of the order of 2k or less for two traces

to retain a degree of correlation. For 100m pulses this implies a decorrelation range of the order of several MHz.

Figure 2b shows the correlation of the coherent speckle as a function of input polarisation. The OTDR setup is again

the same that used in figure la. The correlation is calculated between a trace taken at a reference linear input

polarisation, and a trace taken with the input polarisation rotated by d9 degrees. A separate reference trace was taken

for each point to avoid any decorrelation of the trace speckle due to changes in the environmental conditions over the duration of the experiment. We see little decorrelation in the trace speckle as the input polarisation is rotated 90

degrees. With a more complete exploration of the Poincare sphere the lowest correlation we measure is 0.75. If the

fiber were isotropic (non-birefringent) then we would expect no decorrelation. In real fiber with a randomly varying

birefringence, the accumulated round-trip phase of the backscattered light from each scatterer becomes polarisation

dependent. This results in a dephasing of the backscattered light as the input polarisation is varied, and hence the decorrelation we observe. In principle this allows a measure of the distributed birefringence of the fiber; however in practice this measurement may be difficult to interpret quantitatively.

1«

c

o 0.8 a

a 0.6 oo

_a> 0.4

-co

© 0.2

a. w

0

-0.2 L0

(a)

• • •

50 100 6X (picometers)

Q.

CO

50

d9 (degrees)

100

Figure 2

Finally, we wish to examine the effect of source linewidth on the amplitude and size of the trace speckle. We have no

simple mechanism to change the linewidth of our source, but we can scan its wavelength during an acquisition

thereby increasing its effective linewidth [12]. In figure 3a we plot the RMS speckle amplitude (solid dots) and

speckle size (open squares) of an OTDR trace as a function of the number of discrete wavelengths stepped over

during the acquisition. The start wavelength is 1549.90nm, the step size 17pm, the pulse width 40m, the receiver bandwidth 1MHz, and the total acquisition time 120s. The dotted line is the coherent speckle amplitude of a standard 1550nm Fabry-Perot OTDR laser (3dB spectral width ~10nm), measured under identical conditions. This shows that by scanning the wavelength of our tunable OTDR, we considerably reduce the contrast of the coherent speckle.

Large enough scan ranges result in speckle contrasts below that of standard OTDR lasers. As expected we see no

change in the speckle size as a function of the number of wavelengths scanned.

163
In Figure 2a we saw a complete decorrelation between the coherent speckle of two OTDR traces taken at wavelengths separated by 17pm. This implies that the speckle contrast plotted in figure 3a should decrease as l/sqrt(N), where N is the number of wavelengths scanned. Figure 3b shows the same data as Figure 3a but plotted on

a log-log scale. The solid line is a fit to l/sqrt(N), showing that the coherent speckle does indeed obey this relationship.

0 500 1000 1500 2000

1(J

1Q

2 3 Number of wavelengths Num ber of wavelengths

Figure 3

4. Conclusion

In conclusion, the measured characteristics of coherent speckle seen in our direct-detection OTDR are in good

agreement with the theory presented. We find that coherent speckle may be suppressed by use of a small receiver bandwidth and a large effective source linewidth. Our results show that a narrow-band tunable direct-detection OTDR can achieve at least the same level of speckle suppression as its standard fixed wavelength counterpart.

5. References

[I] "Fading in heterodyne OTDR", P.Healey, Electron. Lett. 20 30-32 (1984)

[2] "Statistics of Rayleigh backscatter from a single-mode optical fibre", P.Healey, Electron. Lett. 21 226-228 (1985)

[3] "Fiber waveguides: a novel technique for investigating attenuation characteristics", M.K.Barnoski, S.M.Jensen,

Appl. Optics 15 21 12-2115 (1976)

[4] "Fiber optic test and measurement", D.Derickson, Prentice-Hall (1998)

[5] "Polarization optical time domain reflectometry", A.Rogers, Electron. Lett. 16 489-490 (1980)

[6] "Spectral attenuation modeling with matrix methods", T.A.Hanson, 8-1 1 Optical fiber measurement conference (1991)

[7] "Chromatic dispersion distribution measurement along a single-mode optical fiber", K.Nakashima, M.Ohashi,

M.Tateda, J. Lightwave Tech. 15 1095-1 101 (1997)

[8] "Field trial of optical maintenance of PONs using a tunable OTDR", K.Ozawa, M.Shigehara, J.Hanai, A.Ban,

T.Naitou, K.Shimoura, 65, ECOC (2000)

[9] "Statisti ;al optics", J.W.Goodman, Wiley (1985)

[10] "Some fundamental properties of speckle", J.W.Goodman, J. Opt. Soc. Am. 66 1 145-1 150 (1976)

[I I] "Measurement of Rayleigh backscattering at 1 .55um with 32um spatial resolution", W.Sorin, D.Baney, IEEE

Photon. Tech. Lett. 4 3 74-3 76 (1992)

[12] "Fading noise reduction in coherent OTDR", H.Izumita, S.Furukawa, Y.Koyamada, I.Sankawa, IEEE Photon. Tech. Lett. 4 201-203 (1992)

[13] "Distributed interferometric fiber sensor system", R.Juskaitis, A.M.Mamedov, V.T.Potapov, S.V.Shatalin, Opt.

Lett. 17 1623-1625 (1992)

164
Full Measurement of the Spatial Distribution of PMD Using

Backscatter

A. J. Rogers and S. V. Shatalin

Department of Electronic Engineering,

University of Surrey, Guildford, Surrey, GU2 7XH, UK.

a.rogers@surrey.ac.uk

Abstract

This paper describes a new technique for the determination of the full spatial distribution of

the polarisation mode dispersion (PMD) in a monomode optical fibre. It operates from one end of the fibre, via backscatter.

Background

The measurement of the spatial distribution of the polarisation properties of a monomode

optical fibre, from one end of the fibre, has important application to polarisation mode

dispersion (PMD) in high-bandwidth (>40 Gbs"1 ) optical-fibre communications [1]. There is a requirement to analyse and to understand the sources of PMD along the fibre installation, so that anomalous sections can be replaced and other appropriate alleviative action taken, if required. Knowledge of the spatial distribution of the polarisation properties also is of

considerable assistance in the design of PMD compensation schemes and in the fabrication of low-PMD fibre. This paper describes a method for the accurate determination of the distribution of the full polarisation properties of a monomode fibre, from one of its ends, with significant

implications for PMD diagnostics.

POTDR

The new method is based on Polarisation Optical Time Domain Reflectometry (POTDR) [2] in which a polarised optical pulse is launched into a monomode fibre, and the Rayleighbackscattered light is time-resolved and polarisation-analysed (via the Stokes parameters) as

it re-emerges from the launch end. This, however, provides only incomplete information on

the spatial distribution of the fibre's polarisation properties. To understand this, consider a section of fibre whose polarisation properties are reciprocal and uniform. These properties

can, in general, be characterized by a linear retardance, 8, and orientation, q, of that retardance's fast axis w. r. t. a reference direction Ox, and a circular retardance, 2p. The

polarisation transfer function can be represented by a Jones matrix, M. A go-and-return

passage of the section is represented by the matrix M multiplied by its transpose:

M' = M

T M

which takes the form of a pure retarder. This is easily appreciated when the element M is modelled as a linear-retarder/rotator pair, because the rotation (p) will be cancelled in goand-return passage, leaving only the retardation, 28e , at orientation qe . Hence the information

represented by pe is lost in backscatter, and only two independent pieces of information

(8e and qe) are available for calculation of three unknowns: 8, q, p. These latter, therefore, cannot be recovered.

(iii) CPOTDR

Computational POTDR (CPOTDR) [3] is a development which overcomes the POTDR

incompleteness problem.

165
In CPOTDR the polarisation element is divided into two equal halves, each half now

assumed to be described by M. Firstly, the front half is interrogated in backscatter (i.e. goand-return passage (J2 in fig. 1), followed by the two together (J3 in fig. 1). Each measurement

provides two pieces of information, i.e. the retardance, and the axis orientation of the two

equivalent retarders: M' = M

T M M" = MT M2 M" provides two more equations for 8, q, p. Hence, we now possess four independent

equations for these three unknowns, and the problem can be solved. This stratagem can now be applied to successive elements of polarisation-uniform fibre

(fig.l, upper diagram) in order to determine the complete spatial distribution of the fibre's polarisation properties.

However, in order to determine the relevant parameters for each element it is clearly necessary to know the input state and backscattered output state for a given element, and this requires an accurate knowledge of the properties of all elements which precede that element.

Hence there inevitably will be an accumulation of measurement error with distance along the

fibre, leading to a limitation on the total length of fibre which can be examined for any given

accuracy.

(iv) Avoidance of Error Accumulation

The error accumulation in CPOTDR can be avoided by using the averaged information in the length of fibre leading up to a given resolution element.

This 'lead' length again may be represented by a linear-retarder/rotator pair. Three

backscatter measurements can now be made (see fig.l), i. e. Jj, J2 , J3. The first of these determines 5e , qe , the second and the third together provide four equations for the four

unknowns pe , 8, q, p. However, the physical effect of the element depends only on the

relative orientation of the input polarisation state and the element's retardation axis, so that only (q-pe) can be recovered, not q, pe separately. Nevertheless, 5 and p can be measured

accurately throughout, without accumulation of error; q still suffers from some error accumulation in this case, but can be accurately determined (via CPOTDR) by using the backscatter information available at several wavelengths. This determination of q relies upon

the fact that pe is dependent upon wavelength (X), whilst q is not. The form of the dependence of pe is conditioned by the 1/ X dependence (to first order) of p and 8. This leads

to pe being expressible as a power series in 1 A,, thus allowing q to be determined by

extrapolation, to infinite wavelength, of the measurable quantity Q = (q-pe)- This process is illustrated in fig. 2. Hence this technique provides the spatial distribution of the linear retardance (8), the linear birefringence's axis orientation (q), and the circular birefringence (p), all without any

accumulation of error with distance along the fibre.

It, further, provides the wavelength dependence of these parameters. Consequently, all the information necessary for the derivation of the spatial distribution of PMD, of any order,

becomes available for any given fibre, with this technique.

(v) Results

Fig.2 shows the computed results for a sinusoidal variation of 8 along the fibre length. A

similar result is obtained for p: both are recovered with very good accuracy [4]. Fig.3 shows

the results for a sinusoidal variation of q, recovered via wavelength diversity. Again, the accuracy is very good, and there is no accumulation of error. Fig. 5 shows the cumulative PMD distribution calculated from the experimentally-derived

CPOTDR traces for a three-coil fibre arrangement.

(vi) Conclusions

A new technique for the determination of the spatial distribution of polarisation properties of

a monomode optical fibre has been developed. The method comprises a development of the

166
POTDR backscatter technique, and allows the determination of the spatial distribution of the

full polarisation properties of the fibre, from one end, without accumulation of error with

distance in two of the parameters.

This technique is applicable, with advantage, to PMD identification, analysis and

compensation in optical communications fibres.

(vii) References

(1) CD. Poole, 'Statistical Treatment of Polarisation Dispersion in single-mode Fibre',

Opt. Lett., Vol. 13, August 1988, pp 687-689.

(2) A. J. Rogers, 'Polarisation-Optical Time Domain Reflectometry : A Technique for Measurement of Field Distributions', Appl. Opt., Vol. 20, 1981, pp 1060-1074.

(3) Y. R. Zhou, V. A. Handerek and A. J. Rogers, 'CPOTDR for the Measurement of

the Spatial Distribution of PMD in an Optical Fibre', Proc. of OFMC '97, NPL,

Teddington, September 1997, pp 126-129.

(4) A. J Rogers, M. Wuilpart and M.Blondel, 'New Polarimetry for Fully-distributed Optical-fibre

Strain and Temperature Sensing', SPIE Conference on 'Smart Structures and Materials 2000',

Newport Beach, California, March 2000, paper 3986-42, pp 302-31 1.

0 M') M') )Mj.i) Mi. i ) M, )

M,j

)

(

) Sc, qc, L,

"j"

J3 <-

Fig. 1 Concatenation of Resolution Elements

Fig. 2 Determination of the Birefringence Distribution

167
0 1

-0.5 -1 - - Wavelength [1E-6 m]

Fig. 3 Extrapolation of Q

Computed q. when the parameters evolve as a cosine function of the length Error on the q parameter when the parameters evolve as a cosine function of the length

o too 20: O 100 200 300 400 500 60C Number of elements

700 800 900 1 000

Fig. 4 Determination of the Angle Distribution

Fig. 5 Experimental PMD Distribution for a Three-coil Arrangement

168
Polarisation Mode Dispersion in Restricted Optical Bandwidth: An

Evaluation of Measurement Techniques

Subrena Harris and David Ives National Physical Laboratory, Teddington, Middlesex, TW1 1 OLW, UK

Abstract

An evaluation is made of the suitability of four techniques to measure Polarisation Mode

Dispersion (PMD) in narrow optical bandwidth (a measurement condition that may arise when

looking at low PMD in Dense Wavelength Division Multiplexing components). A figure of merit

is assigned to the techniques, which reflect theoretical expectations. The interferometric

technique has a figure of merit of 1, fixed analyser 1, stokes parameter evaluation 200, and phase

shift 1800. The phase shift technique appears to be the most suitable for these measurements.

Further experimental work is to be carried out for the phase shift technique, using the Stokes

parameter evaluation technique for comparison.

Introduction

Polarisation Mode Dispersion (PMD) is the dispersion of a signal in a fibre optic system due to birefringence in the optical fibre or components in the system, and is a limiting factor preventing

higher rates of data transmission. As the PMD of single mode fibre has been reduced through

improved technology, this has led to a reduction in the overall level of PMD in fibre systems. In order to reduce the PMD levels further, systems designers/manufacturers are now requiring that

components have low values of PMD, so as not to add unnecessarily to the PMD budget of the

system.

If PMD in components is to be measured using the same techniques as for fibre PMD, the

suitability of the technique needs to be assessed. Components differ from fibre in that PMD can be low or high, depending on the device, and is likely to be deterministic due to fixed, low mode

coupling. There may be more than one birefringent element, and reflections from any optical

elements within the component (not necessarily PMD related). In addition, the level of PDL

varies between components, and if the level is too high it may cause problems in correctly

determining PMD. A component may also have a restricted operational bandwidth. [1]

This investigation is primarily concerned with the problem of measuring low PMD in restricted

optical bandwidth. Our requirement for a measurement technique is that it is able to accurately measure PMDs as low as 0.1 ps, in an optical bandwidth as narrow as 0.2 nm at 1550 nm, also

taking into consideration the other characteristics of components. A figure of merit (1) is defined

for each technique.

Figure of Merit = DGD [§] -

b

^dwidth [Hz] (1)

where, 'bandwidth' is the spectral range needed to measure the associated Differential Group

Delay, DGD.

169
An evaluation is made of the interferometric, fixed analyser, Stokes parameter evaluation and

phase shift techniques, and a figure of merit is assigned to each.

Evaluation of techniques

Interferometric technique

The interferometric technique is capable of measuring PMD of components, but relies on using a broadband source without ripples, which severely limits the techniques effectiveness in restricted

bandwidth. If a component has an operational bandwidth of just 0.2 nm then the coherence time

of the source Sourcetc , is such that the minimum PMD measurable is 40 ps (working under the

condition that sourcetc < PMD [2]). To reduce this PMD threshold the bandwidth would have to be

larger. It is therefore very difficult to improve the figure of merit of this technique above 1

.

An advantage of using the interferometric technique is that it clearly distinguishes between

birefringent elements and so the dependence upon prior knowledge of the internal structure of a device is reduced. An additional advantage is its tolerance to movement of the optical test path

during measurement.

Fixed Analyser technique

It is possible to measure the PMD of components using the fixed analyser, or wavelength

scanning technique. However, although able to operate in a limited spectral range, a large scan range is needed to measure small PMDs. For a bandwidth of 0.2 nm, the minimum PMD

detectable is 40 ps. The technique has a figure of merit of 1.

An advantage of this technique is that, during processing of the data, polarisation insensitive

contributions are removed or reduced from the device's PMD. Also, if processing is done using

Fourier Transforms then the distinction is made between different birefringent elements if more

than one is present

Stokes Parameter evaluation technique

This technique is capable of measuring PMD in components. The polarimetric measurement

system at NPL (figure 1 ) has been used to measure components such as chirped Bragg Gratings,

isolators and circulators, although in these instances a large wavelength range was used to make

the measurements [3]. However, measurements can be made in a restricted spectral range but at reduced accuracy. For a bandwidth of 0.2 nm, and using NPL's polarimeter that has a resolution

of 1.7 degrees, the lower limit for PMD is 191 fs. This gives a figure of merit of 200.

Optional

Wavelength

Meter DUT

Tunable Laser J OOP Polarisation

state selector

Polarisation state adjustor

Circulator

Polarisation state analyser

Figure 1: PMD measurement system for Stokes Parameter Evaluation.

(Set up shown for a reflective device.)

170
Stokes Parameter Evaluation methods determine DGD by measuring the polarisation state of

light at the output of a DUT, and PMD from the distribution of these DGD values. It is possible

to identify if there is more than one birefringent element in a device using this method, although

it is of limited use without prior knowledge of the device structure. Also, as normalised Stokes

Parameters are measured, the sensitivity to spectral shape is removed. A further advantage of this technique is its ability to remove erroneous contributions to the components PMD of

polarisation-insensitive and polarisation-sensitive origins.

Phase Shift technique

DUT

Wavelength meter

10%

Tunable )

Intensity Polarisation

laser 90% Modulator Scrambler

Synthesiser

100 MHz

750 MHz

1900 MHz

1

Circulator

Switch

Power meter

Switch

10%

J.

90%

Computer

Optical

• switch

PSD or Vector

voltmeter

PIN photodiode & FET Amplifier

Optical Receiver ±

Phase Measurement electronics Relays Filter AMP Filter

Figure 2: Phase Shift system (used to measure PMD and other parameters of components).

(Set up shown for a reflective device.)

The Phase shift method measures DGD by measuring the phase shift of light from one principal

state of polarisation to the other. One implementation is to find the PSPs by sampling over the

entire Poincare sphere [4]. An alternative is to launch states that form a Muller Set, which

eliminates the need to find the PSPs of the component to measure the DGD [5].

It is advantageous to use the Differential/Muller set method to measure the DGD of components

with restricted bandwidths as DGD is found at a single wavelength point without the need to

171
scan over a spectral range. A probable implementation will be to launch six polarisation states. NPL's Phase shift system (figure 2) has optional modulation frequencies of 1.9 GHz, 0.75 GHz

and 0.1 GHz, and uses a vector voltmeter with a phase angle resolution of at least 0.1 degrees.

This gives a theoretical lower limit of approximately 145 fs DGD and a figure of merit of 1800

(where the bandwidth is taken as twice the modulation frequency due to the sidebands that are created by modulation). The figure of merit is independent of modulation frequency.

Although the phase shift technique does not allow us to meet the target of measuring 100 fs PMD, it does offer detection of PMDs lower than the other 3 techniques discussed.

A further advantage of the phase shift technique is its removal of non-polarisation sensitive

reflections. A disadvantage is that it does not remove polarisation sensitive reflections.

Conclusions

The figure of merit of the interferometric technique is 1, fixed analyser is 1, Stokes parameter

evaluation is 200 and the phase shift technique is 1800. After assessment the phase shift technique was selected as the most appropriate to measure PMD in components for our purposes.

Further investigations will involve measurement of broadband and narrowband components

using the phase shift system, and the Stokes parameter evaluation technique for comparison.

Acknowledgement

The work reported here was funded by the National Measurement System Policy Unit of the

UK's Department of Trade and Industry.

References

[1] American Standard, TIA FOTP-196: to be published. Guideline for Polarization-Mode

Dispersion Measurement in Single-Mode Fiber Optic Components and Devices.

[2] GISIN, N. and PELLAUX, J.P. Polarization mode dispersion: time versus frequency

domains. Opt. Commun., 1992, 89, 316-323.

[3] IVES, D. Polarisation Mode Dispersion in Chirped Fibre Bragg Gratings. Proceedings of

the Symposium on Optical Fiber Measurements, NIST, Boulder, Colorado, 1998, edited by

G.W. Day, D.L. Franzen and P.A. Williams, Washington, DC, USA, U.S. Government

Printing Office, 1998, 15 - 18.

[4] WILLIAMS, P.A., BARLOW, A.J., MACKECHNIE, C. and SCHLAGER, J.B. Narrowband measurements of polarization-mode dispersion using the modulation phase

shift technique. Proceedings of the Symposium on Optical Fiber Measurements, NIST,

Boulder, Colorado, 1998, edited by G.W. Day, D.L. Franzen and P.A. Williams,

Washington, DC, USA, U.S. Government Printing Office, 1998, 23 - 26.

[5] WILLIAMS, P.A. Modulation phase-shift measurement of PMD using four launched

polarization states: a new algorithm. Electron. Lett., 1999, 35, 18,1578 - 1579.

172
Measurement and mitigation of multiple reflection effects on the Differential

Group Delay spectrum of optical components

P.A. Williams and J.D. Kofler

National Institute ofStandards and Technology - Boulder, Colorado, USA

Abstract: Ripple in the Differential Group Delay

(DGD) spectrum due to multiple reflections is described theoretically and demonstrated ex- perimentally. A technique of tilting the cavity

element to reduce these multiple reflection ef- fects is discussed and is demonstrated to remove

the ripples in the DGD spectrum.

I. Introduction

In the field of optical fiber metrology, it seems

that you can't measure anything without the result being affected by multiple reflections coming from a cavity somewhere in the optical path.

Polarization-Mode Dispersion (PMD) or, more

specifically, Differential Group Delay (DGD) is also affected by multiple reflections. The result

is a ripple in the DGD spectrum with a surprisingly large amplitude [1].

In this paper, we derive the spectral DGD behavior in the presence of multiple reflections, and

demonstrate how these effects can be significantly reduced by tilting the cavity component

with respect to the optical path.

Figure 1. Schematic of Fabry-Perot cavity with trans- mission and reflection coefficients t and r, containing

birefringent material with indices of refraction n„ and

II. Theory

We derive the DGD spectrum of a cavity composed of a simple birefringent material whose

eigenaxes are independent of wavelength ("nonmode-coupled"). The physical length of the cavity is L, and its birefringence is An=(n// - n±). For

simplicity, we assume the transmission and re- flection coefficients (t and r) at the input inter- face are equal to those at the output interface. Figure 1 illustrates the geometry. Note: this derivation assumes that the cavity is not tilted with respect to the light beam (ie. normal inci- dence). The tilted light beam in Figure 1 is only

shown to schematically to illustrate the features. We calculate the transmitted electric field for the two orthogonal polarization components aligned

with the birefringence axes of the cavity. The

electric field of the light that is transmitted

through the cavity without experiencing any re- flections ("single-pass") is given by

E\ij = E//0 e " t , El x =E10 e

iS-t2

.

E//o and E±0 are the input electric fields, and 8// and 8i are the phase delays accumulated by a

single pass through the cavity for light polarized

along each birefringent axis of the cavity. The

phase delays are given as Sa =a>na L/c, (2)

where co is the (radian) optical frequency, c is the speed of light, n is the index of refraction

with the subscript a denoting the corresponding

polarization state (// or J_).

Group delay is given by the radian-frequency

derivative of transmitted phase. So, we can find

the DGD of the single-pass transmission as the difference in group delay for the two orthogonal

components,

*.K !^

{!:I !*1\LJ"*\ (3)

dco v dco ) c c where An is the phase birefringence and

Ang = n//

>g - n_i_ig is the group birefringence, with

173
So we find that the DGD seen by the single-pass

light is Ar0 =—^- = («//>g -n1>g )-. (5)

This is the DGD that would be measured in this device if there were no reflections.

In order to find how the DGD is modified by

multiple reflections, we use a standard FabryPerot approach [2] to write the vector components of the total electric fields transmitted

through the cavity as

,2

1 r

2 e~

i2S» and

J L0

}

(6)

(7)

where a term containing the time dependence is common to both and omitted. The phases of Em

and E±t do not include the phase accumulated by

the first pass through the device. In other words,

the phase in Equations (6) and (7) is the perturbation to the transmitted phase caused by multiple reflections.

Writing the expressions for E//t and En in phasor

notation, we find the phases of each component:

(Pu - tan" R sin 28//

and

cpL

- tan

1 - R cos 28

- R sin 28i

(8)

(9)

1 - R cos 2S± j

where R, the intensity reflection coefficient, has

been substituted for r

2

. We find the perturbation to the DGD caused by

multiple reflections asd{<Pn ~<pj

or

Atfr ~ ,

, aco

- 2LR(cos 28u - R)n// g

(\ + R

2 -2Rcos28u )c

2LR(cos 28x - R)nl g

AtFR =

(10)

(11)

(\ + R

2 - 2Rcos28±

)c

Since the complicated nature of Equation (11)

clouds intuition about its behavior, we approximate Atfr as ArFR « 4Rt0 sin (2conL\ . ( coAnL^

sin

I c ) y c ) (12)

where

T0 =ng L/c (13)

is the group delay for a single-pass through the

cavity. Equation (12) requires the assumptions

RO.l, and At0/to<1.

The total DGD measured for transmission

through the Fabry-Perot cavity of Figure 1 is the sum of the single-pass DGD plus the perturbation DGD

At = Ar0 + AzFR . (14)

Equations (11) and (12) predict some important

features of the perturbation to the DGD spec- trum. Equation (11) has two obvious peri- odicities due to the cos(28//) and cos(25i) terms. Since 8// and 5<_ are functions of co, we expect the

first term of Equation (11) to repeat over a fre- quency spacing or Free Spectral Range (FSR) of

TCC Aav = - • (15)

Ln/Kg Likewise, the second term repeats over a FSR

7tc Acox (16)

Note that the refractive indices in Equations (15)

and ( 1 8) are group (rather than phase) due to the frequency dependence of n. When combined,

these two ripple "periods" will result in a fast ripple on AxFR that repeats over a frequency

spacing of

Aty0 =

1 1 2A(o,nc

,(17)

/// 2A(Ol

and in a "beat note" in the spectrum with a fre- quency spacing of

AcoB =

1 1

Aco,, Aco

nc LAnr (18)

This behavior is more obvious in Equation (12)

where the sine function at the left gives the fast ripples and the one at the right gives the envelope. Plots of the spectral behavior of Equation

174
(11) are shown Figures 2 and 3. The parameters

used to generate these plots were: L = 9.97 mm,

R = 0.001^ n = 1.532, An = 0.00847, ng = 1.554,

and Ang = 0.0094. These values were chosen to emulate the pigtailed quartz plate we measure in Section III.

0.65

0.00 1 ' 1 1 1 1

1190 1200 1210 1220 1230 1240 Radian Frequency, (THz) Figure 2. Simulated DGD spectrum showing Fre- quency beat notes due to multiple reflections in a bire- fringent cavity (from Equations (5), (11), and (14)).

0.65 r

0.60 -

U.1U

0.05 - 0.00 1 1 1 1 1 1

1233 1233.2 1233.4 1233.6 1233.8 1234 Radian Frequency, (THz)

Figure 3. Close-up of DGD spectrum in Figure 2. Equation (12) gives the amplitude of the ripple

envelope as 4Rx0

. This result is somewhat sur- prising in that the ripple amplitude depends on

the group delay of the cavity t0 and not the DGD

At0. Since typical sources of birefringence in components have To/At0»1, the amplitude of

the DGD spectral ripple can easily be larger than

the DGD itself.

III. Experimental Verification

These predictions are experimentally verified by

measuring the DGD spectrum of a pigtailed

quartz plate using a Modulation-Phase-Shift

(MPS) technique [3] with a spectral resolution of

Aco=4.92 GHz and a temporal resolution of 30 fs (yielding a bandwidth efficiency factor [4] of

over 6700,. The length and indices of refraction

of the quartz plate are expected to be equal to those used in the above simulation. Both faces of

the plate have a broadband anti-reflection coating expected to yield an R of 0.01-0.02, but this was not measured directly.

Figures 4 and 5 show the measured DGD spec- trum for this device. We see qualitative agree- ment with the theoretical predictions of Figures

2 and 3 when an R of 0.0014 is used. This unexpectedly low R value was estimated by using R

as a fitting parameter in Equation (12) to match

the size of the ripple envelope in Figure 4. We

attribute this low R value to a possible tilt of the waveplate, preventing some of the forward re- flected light from being captured.

1190 1200 1210 1220 1230 1240 Radian Frequency, (THz) Figure 4. Measured DGD spectrum for pigtailed quartz

plate with envelope portion of Equation (12) overlaid to estimate R.

0.65 I 1 0.60 - 0.55 -

0.05 - 0.00 1 1 1 1 1

1

1232 1232.2 1232.4 1232.6 1232.8 1233 Radian Frequency, (THz) Figure 5. Close-up of DGD spectrum in Figure 4.

By counting cycles in Figures 4 and 5, we measured the frequency spacings Aco0 and AcoB to be

6.16xl0 10s"' and l.OOxlo'Y 1

, respectively. In- serting A(o0 , AcoB and our estimate of the quartz

plate thickness Z=9.97 mm into Equations (17)

and (18) yields estimates for ne and A«g of 1.53 and 0.0094 respectively. These predicted values

are in good agreement (1.5 %) with the expected

values of 1.554 and 0.0094.

IV. Mitigation

An efficient means for reducing multiple reflec- tions in the backward direction (return loss) is to

175
tilt the cavity element so that the backwardreflected beam reflects at an angle and misses

the launch optics. However, in order to reduce

the multiple reflection effect on DGD, we must

suppress the multiple reflections that propagate

in the forv ard direction. In general, this requires a larger tilt angle, since the forward-reflected

beams experience only a transverse offset with

tilt. Figure 6 illustrates how tilting the cavity lets the single-pass beam enter the collection optics,

but causes a forward-reflected beam to miss.

Figure 6. Schematic of launching light into tilted cavity

element at angle 9 to prevent the reflected beams from

being captured.

From Figure 6, we see that the transverse offset p between the single-pass and the first forwardreflected beams will be

2L cos(0)sin(0)

(19)

sm

2 (0)

where L is the cavity thickness, 9 is the tilt angle

of the cavity, and n is the mean refractive index

in the cavity. With the collection lens and fiber arranged to efficiently collect the single-pass

light (intensity //), the fractional power in the

first reflected beam (intensity IFR! ) that will be

collected is given by (assuming Gaussian beam

profiles)

FR\ R

2 exp

2p2 A w

(20)

where R is the intensity reflection coefficient

and w is the beam radius (defined by the 1/e

2

point). Combining Equations (19) and (20) gives

the fractional power ratio between the first re- flected beam and the single-pass beam.

In order to minimize ripple in the DGD spec- trum, the ratio of Equation (20) should be minimized. To demonstrate the effectiveness of tilt- ing the cavity, we used the same pigtailed waveplate geometry measured in Figures 4 and 5 ex- cept with the quartz plate tilted by approximately 4-5° with respect to the incoming beam.

For our collimating lenses, w = 0.25 mm,

L = 9.97 mm, and n = 1.532, and we estimate

#«0.02. Equations (19) and (20) indicate that for the given parameters, the first reflected beam

will be severely attenuated (~150 dB) from the single-pass beam. Therefore, we expect to see no

spectral ripple on the DGD of this device. Figure

7 shows the measured spectrum for the tilted- plate device. Indeed, within the noise of the measurement, no spectral ripple can be seen.

1190 1195 1200 1205 1210 1215 Radian Frequency, (THz)

Figure 7. Measured DGD spectrum for pigtailed

quartz plate with 4-5° tilt of plate with respect to beam

path.

V. Conclusion

We have characterized the effects on the DGD

of a component with multiple reflections present. The resulting DGD spectral ripple has an

amplitude proportional to the product of the in- tensity reflection coefficient and the single-pass

group delay of the cavity. We have also shown

that tilting a reflective cavity can successfully

eliminate the multiple reflection effects on the measured DGD.

References:

[1] Normand Cyr, Michel Leclerc and Bernard

Ruchet, "PMD measurements in multipath components: The single waveplate example", Proceedings

ofPhotonics North, Quebec (2002).

[2] E. Hecht and A. Zajac, Optics, (Addison-Wesley,

1974), p. 305.

[3] P. A. Williams, "Modulation phase-shift measurement of PMD using only four launched polarization states: a new algorithm," Elecron. Lett. 35, 1578- 1579(1999).

[4] P. A. Williams, "PMD Measurement Techniques -

Avoiding Measurement Pitfalls," Presented at the Venice Summer School on PMD, Venice, (2002).

176
7C-shifted all-fibre Sagnac loop for characterization of

femtosecond Polarization Mode Dispersion

E. Simova and I. Golub,

Institutefor Microstructural Sciences. National Research Council Montreal Road, Build. M-23A, Ottawa. On. K1A 0R6

eli.simova(3>,nrc. ca ; ilya.golub(3),nrc.ca;

Abstract: A novel configuration for measuring PMD consisting of an all-fibre 7i-shifted Sagnac

interferometer is studied. Its advantages include insensitivity to the orientation of the device under

test. This allows an extension of the dynamic range to few femtosecond PMD measurements and

characterization of the device's principal states of polarization.

key words: Fiber optics and optical communications; Fiber characterization; Fiber measurements; Birefringence;

Polarization Mode Dispersion (PMD).

1. Introduction

Polarization Mode Dispersion (PMD) in fiber and fiber devices is caused by the wavelength dependent

birefringence and wavelength dependence of the birefringence axes orientation, or the associated principal

states of polarization (PSP). The use of a Sagnac interferometer for characterization of PMD was proposed

in [1] and it was compared to the fixed analyzer method [2], with the advantage of a better contrast between

minima and maxima in the transmission spectrum. Since these methods rely on counting fringes, in order to measure femtosecond PMD, they require several hundred nanometers tunable laser/broadband source while

measuring wavelength averaged PMD. Moreover, neither of these methods can determine PSP.

In this work, we present a novel ft-shifted configuration of the Sagnac loop for PMD characterization. The main advantage of this configuration is that the half-wave plate (HWP) inserted in the loop makes it insensitive to the orientation of the birefringence axes of the device under test (DUT). As a result, one can

characterize PMD values which correspond to a part of a fringe in the fixed analyzer method. This allows extending the dynamic range to femtosecond PMD values and measuring the wavelength dependence of

PMD. Furthermore, the orientation of the birefringence axes of the DUT can be determined.

2. Theory of the Sagnac loop

The Sagnac interferometer has been studied theoretically using Jones calculus [3-5]. We include the HWP

in the loop as shown in Fig.l (the polarization controller, PC, is used for canceling the loop's residual birefringence). Effectively, here the HWP introduces a 7i-shift between the clockwise and counterclockwise

propagating beams upon entry to the DUT. The polarization properties of the loop and the DUT can be

described by the electrical field vectors into and out of the fiber coupler, £,„ and Eoul , respectively, and the corresponding Jones matrix, j(co) . At the exit of the coupler, for arm 1 (the reflection arm), and for arm 2

(the transmission arm), the electric field vectors, £,"„" and E2n are:

k: =Ky{\-Kn rr{co)E[: +^-kj2 j°^ (1) E"2: =Kn r((oK+(l-Kn )j<(a))E*n

where the coefficient Kn

, represents the splitting ratio of the coupler with the index n referring to the x- or

y-component, J

c {co) and J"{co) are the clockwise and counterclockwise Jones matrices, respectively, for the propagation of the light through the loop.

177
Tunable laser

Power meter

Circulator

Power meter

50:50

fiber-optic coupler

HWP

DUT

PC

Fig. 1 . Configuration of the 7t-shifted Sagnac interferometer.

As can be seen from Eq. (1), an uneven splitting ratio, Kn

, of the fiber-optic coupler dependent on the wavelength results in a limited interference contrast, when the intensity distribution is recorded in the transmission arm 2, while for arm 1, Kn *0.5 does not limit the attainable contrast. Indeed, the fact that the

reflection arm 1 is more stable and gives better results was confirmed in the experiment. The following Jones matrices for the HWP and DUT were assumed in the calculations:

'icos2p /'sin2p

/' sin 2p - /' cos 2 p

f i'cos2p -;'sin 2p ^

-i'sin2p -i'cos2p

DVT

'7 2

2 • 2 e

1 cos a + e sin a

2; sin 2a sin —

2

2/ sin 2a sin —

2

.5 S J"

( s s e

2 cos a + e2 sin a

- 2i sin 2a sin —

2

(2)

-2/ sin 2a sin —

2

.5 s

where p and a are the orientation angles of the birefringence axes of the HWP and the DUT, respectively,

relative to the coordinate system defined by the plane of the loop and the coupler, and 5 is the birefringence

of the DUT. Assuming Kn = 0.5 the transmission in arm 2, for example, is:

r(A) = cos

2 Ssin2 2p (3)

T(X)=: -sin

1 2a (4)

Eq. (3) shows that the transmission response of the 7i-shifted Sagnac loop is independent of the orientation angle, a , of the DUT's birefringence axes and the polarization of the input light. It depends

only on the DUT's birefringence provided that the HWP's orientation angle, p , is optimized at 45° relative

to the coordinate system. The result in Eq. (3) is significant, because it allows us to recover the wavelength

dependent phase and the associated PMD through intensity measurement. The Differential Group Delay

(DGD or first order PMD) is calculated as DGD = dS/dco , where to is the optical frequency. For comparison, a similar equation for the conventional Sagnac loop with only DUT can be derived:

2 The drawbacks of the conventional Sagnac loop become apparent from Eq. (4), namely the dependence on

the DUT' s orientation angle, a . Since the fiberoptic DUT's axes cannot be rotated, there are two unknowns in the equation. This problem is bypassed through the fringe-counting technique [1], but then the

limiting factor towards measuring femtosecond PMD is the bandwidth of the source. Moreover, only the wavelength averaged PMD is measured.

In addition, using our scheme to determine the DUT's birefringence from Eq. (3), one can remove the HWP and determine the orientation of the birefringence axes of the DUT from Eq. (4).

3. Measurements

The measurements were carried out in the set-up according to Fig. 1. A tunable laser, a broadband 50:50

fiber-optic coupler and a broadband HWP were used to assure operation of the interferometer for a wide

range of wavelengths. In order to verify the possibility of measuring femtosecond PMD, another coupler

178
was tested as the DUT. The measurement system was calibrated to account for the losses 'in the loop, the HWP and in the DUT. The DGD calculated using Eq. (3) is presented in Fig. 2a for a wavelength step of

0.3 nm. For comparison, the DGD measured with the JME (Jones Matrix Eigenanalysis) based commercial

instrument is shown in Fig. 2b. It can be seen that there is a good agreement between the two methods. Fig. 3 presents the angle of the DUT's birefringence axes calculated from Eqs. (3) and (4).

1525 1540 1555 wavelength [nm]

Fig. 2a. DGD for the fiber-optic coupler calculated from the

it-shifted Sagnac loop.

Fig. 2b. DGD for the fiber-optic coupler calculated from the Jones Matrix Eigenanalysis.

Fig. 2. Orientation of the DUT s birefringence axes calculated using

the rc-shifted Sagnac loop in conjunction with a conventional one.

4. Conclusions

We have proposed and studied a novel rc-shifted configuration of the Sagnac loop for characterization of

PMD. The Tt-shift allows the recovery of the phase as a function of wavelength from the intensity scan. Thus the dynamic range is extended towards few femtosecond range without the need for a broadband

source while measuring wavelength dependent PMD. A comparison with the more complex JME method

showed a good agreement. Combining the proposed scheme with the conventional Sagnac loop allows determination of the DUT's birefringence axes.

5. References

1. B. Olson, M. Karlson and P. Andreson, Polarization mode dispersion measurement using a Sagnac interferometer and a comparison with the fixed analyzer method, "IEEE Photonics Tech. Lett., 10, 997-999 (1998).

2. CD. Poole and D. L. Favin, "Polarization mode dispersion measurements based on transmission spectra through a polarizer, "J. Lightw. Tech. 12, 917-934 (1994).

3. T. A. Birks and P. Morkel, 'Jones calculus analysis of single-mode Sagnac reflector V Appl. Opt. 27, 3107-31 13 (1988).

4. D. Mortimer, Tiber Loop Reflectors, "J. Lightw. Tech. 6, 1217-121224 (1989).

5. X. Fang and R. O. Claus, Polarization-independent all-fibre wavelength-division multiplexer based on a Sagnac

interferometer, "Opt. Lett., 20, 2146-2148 (1995).

Acknowledgments

The authors would like to express their gratitude to Prof. Xiaoyi Bao, Dr. Dongfeng Liu and David Waddy from the Physics Department of University of Ottawa, in Ottawa, Canada for their help with the JME measurements.

179

Using Importance Sampling to Assess the Effects

of PMD on System Performance

William L. Kath and Gino Biondini*

Department of Engineering Sciences and Applied Mathematics, Northwestern University

2145 Sheridan Road, Evanston, Illinois 60208; E-mail: kath@northwestern.edu

We describe the application of importance sampling to Monte-Carlo simulations of polarization-mode dispersion (PMD)

in optical fibers. The algorithm significantly increases the frequency of rare PMD events, while at the same time keeping

track of each event's original probability of occurrence, thus making it possible to assess the effect of PMD on power

penalties at realistic outage probabilities. The numerical application of the algorithm is straightforward; we also describe

its possible experimental implementation using a hardware-based PMD emulator.

1. Introduction

Polarization-mode dispersion (PMD) has been recognized

as a potentially major impairment in both terrestrial and

undersea transmission systems. To first order in fre- quency, PMD splits a pulse between the fast and slow axes of a fiber; at the same time, higher orders of PMD induce

depolarization and polarization-dependent chromatic dis- persion. At high bit rates, all of these effects lead to unacceptable transmission penalties.

A key difficulty with PMD is its stochastic nature. PMD is caused by random variations of an optical fiber's birefringence with distance. In addition, the penalties it produces change randomly over time as the ambient temperature and other environmental parameters vary. In sys- tem design, a maximum power penalty (typically 1 dB)

is usually assigned to PMD, and one demands that the outage probability (that is, the probability of the PMDinduced penalty exceeding this allowed value) is very

small (typically a minute per year, 10

-6

or less). Because

of this stringent requirement, it is very difficult to use ei- ther Monte Carlo simulations or laboratory experiments

to determine a system's outage probability, due to the ex- tremely large number of system configurations that must

be explored in order to obtain a reliable estimate. A measure of PMD is provided by the PMD vector T (also known as the polarization dispersion vector) [1-

3], the magnitude of which is the differential group delay (DGD). The rare events where the DGD is significantly larger than its mean are particularly important,

since they are the ones most likely to result in system outages. Of course, the PMD vector is frequency-dependent,

and therefore in general the DGD at any given frequency

is not the sole determiner of system outages. In particular, second-order PMD, which includes both depolarization

and polarization-dependent chromatic dispersion (PCD),

is known to produce additional system penalties [4, 5].

"Department of Mathematics, Ohio State University, 231 West 18th Avenue. Columbus, Ohio 43210; E-mail: biondini@math.ohio-state.edu

In the absence of effective tools for determining out- age probabilities, system designers must resort to stopgap

techniques. One such technique is to produce artificially large DGD values, determine the penalties at these large

DGDs, and then weight the results using the DGD's well- known Maxwellian probability distribution [1]. A funda- mental problem with this method, however, is that there is no direct relationship between the DGD (and/or secondorder PMD) and the power penalty. In addition, it is possible for different configurations to give both the same DGD and the same second-order PMD, but not contribute equally to the penalty (because of different higher-order

PMD), and therefore they should be weighted differently

in calculations of outage probability.

The technique of importance sampling (IS) [6-8], which is one member of a family of methods known as variance reduction techniques [9, 10], addresses these difficulties and provides a tool that can be used in numerical simulations — and, in principle, in experiments — to accurately estimate PMD-induced system penalties. The

technique allows low probability events to be efficiently

simulated by enabling one to concentrate Monte-Carlo

simulations in the most significant regions of interest in sample space. In this case, the regions of interest in the sample space are the configurations that lead to large val- ues of DGD and/or second-order PMD [11, 12]. This

method has also been applied to numerically calculate PMD-induced transmission penalties [13, 14]. Here we

give a description of the technique and its application.

2. The PMD concatenation equations

A standard technique for simulating PMD effects is the coarse-step method [15], which approximates the contin- uous birefringence variations present in real fibers by a concatenation of fixed length birefringent sections. Many

experimental PMD generation techniques also employ

a concatenation of birefringent elements, such as highbirefringence fibers [16] or birefringent waveplates [17],

181
connected by either polarization scramblers (e.g., polarization controllers [16]) or rotatable connectors [17]. We

will refer to the situation where there are no polarization

controllers as the case of rotatable waveplates.

In the case of discrete birefringent sections, the total PMD vector after the (n+l)-st fiber section can be obtained from the PMD concatenation equation [3],

T(«+ 1

) = Rn+1 xW+AT„+1 . (1)

Here X^ is the PMD vector after n sections and Ax„+i

is the differential contribution to the PMD vector of the (n+l)-st section. For fixed length sections, the magnitude of At„+i is fixed, and only its direction varies. For

linearly birefringent elements, Ax„+i lies on the equatorial plane of the Poincare sphere [18]. The Miiller matrix R„_j. i = exp [<p„+i (r„+i x)] represents a rotation through an angle <p„ + i about the axis r„+ i. This rota- tion is frequency dependent; for linearly birefringent ele- ments, f„+] = Ax„+i/|At„+ i| and(p„+i(co) = 2b'en+l (i) =

(pn+ i (coo) + 2b'£n+\ (co — (Do), where b' is the birefringence

strength of each element and £n+ \ is its length [3]. A similar concatenation equation holds for the frequency derivative of the PMD vector, Xu [3]: xir^R^+AT^xT^1 ). (2) When polarization controllers are present, an additional

rotation matrix Q„+ i appears between R„+ i and both T

n' and I© in Eqs. (1-2). The resulting equations are then formally equivalent to Eqs. (1-2) with a new rotation matrix R^+1 = R„+ iQ„+ i.

3. Importance sampling

In order to apply IS to the PMD concatenation Eqs. (1-

2), the rare events in which the DGD and/or second-order PMD assume values much larger than their means must

be targeted. We have found that to do so it is appropriate

to control the orientation of the differential PMD vector of each section, Ax„+i, relative to the total first- and secondorder PMD vectors up to that point, x^ and

Suppose the orientations of the differential PMD vectors depends upon the set of angles (61,62, . . . 0/v) = 8

where N is the total number of sections (note, of course,

there must be two angles for each differential PMD vector; we will see that the second angle does not need to be

controlled and can be left uniformly distributed). Suppose

further that we are interested in determining the probability P that a random variable which depends upon these angles falls in a given range. Note that any random variable can be considered, such as the amount of pulse broadening, the power penalty, or any combination thereof. The

probability P can be represented as the expectation value of an indicator function 7(0), where / = 1 if the random

variable of interest falls in the prescribed range and 7 = 0

otherwise. That is, P is represented by the N-dimensional

integral

P= Jl(B)p(B)dB, (3) 0

where the p(B) is the joint probability distribution function for the angles and 0 represents the configuration

space. Importance sampling is performed by first rewrit- ing the integrand in Eq. (3) as /(0)p(0) = /(8)L(8)p*(8),

where p*(B) is the biasing distribution, and where L(8) =

p(8)///(8) is the importance sampling likelihood ratio

[6-8]. We then estimate the integral through Monte Carlo

simulations; that is, we write an importance-sampled

Monte-Carlo estimate of the above probability P as [6-8]

1 M

P=TzJ,I(Qm )L(Bm ). (4) m=l

Here M is the total number of trials, and the samples Bm

are drawn according to the biased distribution p*{B). If p*{B) = p(B) (i.e., for unbiased Monte Carlo simulations),

Eq. (4) is simply the relative frequency of trials falling in the range of interest. A problem with this choice is that, when simulating low probability events, an exceedingly

large number of samples is necessary in order for the desired events to occur, and an even larger number is re- quired in order to obtain an accurate estimate. Using a bi- ased probability distribution causes the desired regions of sample space to be visited much more frequently, and the likelihood ratio L(8) automatically adjusts the results so

that all of the different realizations are correctly weighted,

thus contributing properly to the final probability.

4. IS for first- and second-order PMD

As mentioned previously, the appropriate variables to control when applying importance sampling are the orientations of the individual PMD vectors of each section,

At„+ i. IS works by biasing these random vectors to- ward specific deterministic directions bW which maximally increase the particular quantity of interest (e.g., the

total DGD or the second-order PMD). In the following, we will concentrate on the case of polarization scramblers and will characterize the vector b^"' relative to the orthonormal frame of reference 11 formed by the unit vectors {uj jUj ,113 where

u[

n) = u\

n) xu{2n)

. (5)

Here X^"\ is the component of perpendicular to X^

n \

as illustrated in Fig. 1. The magnitudes of Xu 11 (the component of Tfo' parallel to xW) and Xco x quantify the PCD

and the depolarization.

182
Figure 1: Diagram showing the preferential direction b for bias- ing the simulations in the plane identified by t'"' and tW x .

Biasing to increase the DGD is achieved by arrang- ing for AT„+i to be preferentially aligned with the total PMD vector up to that point, i.e., using b( ") = u^.

Specifically, we set the polarization scramblers so that 9„

(the angle between the PMD vector at the output of the n-th scrambler and the (n+l)-st differential PMD vector)

is biased towards zero. This choice does not uniquely de- termine the orientation of the PMD vector at the scrambler output, of course, because T„ can still be rotated by

an arbitrary amount about At„+ i while keeping Qn constant. We assume that this additional rotational angle is uniformly distributed. In the unbiased case, the angles 9„ are independent

random variables, with cos9„ uniformly distributed in [—1,1]. When applying importance sampling, we choose

cos0„ = 2jc'/a — 1, where x is a uniform random variable

in [0, 1] and a > 1 is a biasing parameter. Other choices

are possible for the biased distribution used for the 9„; the effectiveness of the method is not very sensitive to the particular distribution used. The above choice yields the likelihood ratio as

L(B)

jL pi(cos6„)

„=l pa (cosQn ) (6)

where />a (cos9) = (a/2)[(l + cos8)/2] a_1

[19]. The

value a = 1 reproduces the unbiased case (i.e., cos 9 is uniformly distributed), while increasing values of a bias the configurations towards increasingly larger values of DGD. Thus, each biasing distribution allows us to sample

a different range of DGDs, and simulations with different values of a can be combined in order to cover the whole

range of DGD values. This produces region 1 in Fig. 2. A technical detail is how to combine the results of the

different biasing strengths. The simultaneous use of several biasing probability distributions is called multiple im- portance sampling [20, 21], and the proper way to combine the different results is to apply separate weights to the samples from each different distribution. The weights al- low the biasing distributions that are expected to produce

the best results in each given region to be favored. A particularly useful choice of weights is know as the balance

heuristic [21]. We emphasize that different configurations with the same value of DGD (and/or second order PMD) can have

quite different likelihood ratios, and thus their relative contribution to the final result can vary substantially. As a consequence, different configurations producing the same DGD and/or second-order PMD are expected to give very

different contributions to the power penalty. First-order biasing yields the largest values of DGD.

It does not, however, produce very large values of Tm, be- cause when At„+ i is parallel to %„ the contribution from

that section to T^+ ^ is zero. Thus, if all the At„+ i were

parallel to T^, no second-order PMD would be produced.

Random fluctuations add second-order PMD, but large values are not specifically targeted. Over a single section, one can easily show that the choice that maximizes the contribution to T^"

1"

1

' is to align Axn+ \ with the direction of U3"'. The rate at which T^+1

' increases, however, also depends on t'"', and thus, when optimizing over many

sections, the growth of V>n

' must also be considered. When the number of sections in the emulator is large, we have found it useful to employ a continuum approximation to find the deterministic configuration that generates the maximum second-order PMD. Specifically, we

let lim^^o AT„+i/Az = b(z). The magnitude of b(z) describes the relative rate at which PMD is added by the birefringent sections. For simplicity, we concentrate upon

the case |b(z) | = b =const. In the continuum limit, for the case of polarization scramblers one obtains

dx

~dz dx„

dz

dz

b2

b3 T-b2

(7)

(8)

(9)

where {b\ ,^2,^3) are the components of b with respect

to 11. This system of equations can be solved exactly for any b(z) (although the solution is not displayed here). Note that d[|T(o| 2 ]/<iz = 2biXwlx. Thus, b2 does

not directly contribute toward increasing the magnitude

of second-order PMD; rather, it induces a rotation of

about 113, as seen from Eqs. (8,9). Since the maximum

xM j_ under such a rotation occurs when xw y = 0, we ex- pect the maximum second-order PMD to be generated for

Z?2 = 0, i.e., when b lies in the U1-U3 plane. Calculus of

variations can then be used to show that the maximum

growth of second-order PMD is obtained when

b(z) = b[u\ cos(3(z) +U3sin(3(; (10)

where (3(z) = (3 max z/zmax and (3max = rc/2. With multiple

biasing strengths, this generates region 3 in Fig. 2. We

183
180| 1 1 r

25

Figure 2: The regions of the |t|-|tm | plane targeted by the vari- ous biasing methods. Region 1 corresponds to first-order biasing

(P = 0), region 3 to pure second-order biasing (Pmax = n/2), and

regions 2, 4 and 5 to pmax = Jt/4, 3lt/4 and n, respectively. The

dashed line shows the much smaller region obtained with unbi- ased runs. 50 sections with 0.5 ps DGD each and polarization scramblers were used.

refer to this choice, which yields the largest values of |tw |, as optimal second-order biasing.

Of course, a more complete coverage of the

|T(o| plane is often needed. In this case, intermediate bias- ing choices must also be used in addition to optimal first- and second-order biasing. These intermediate choices can be obtained by using calculus of variations to maximize a

linear combination of |t| and |t<b|. The resulting form of

b(z) is the same as above, except that the value of the fi- nal angle pmax now varies between 0 and n, the particular value depending upon the specific linear combination of

first- and second-order PMD being maximized. A selection of angles, together with the resulting regions in the

|t|-|T(o| plane, is shown in Fig. 2. The advantage of us- ing multiple biasing -— as opposed to just pure first- or second-order biasing or no biasing at all — is evident. When a range of biasing strengths are used, each value of Pmax generates samples lying in a region that emanates in a roughly radial fashion from the location where the joint

pdf is maximum. Together, a selection of angles pmax and

biasing strengths a covers the entire |x|-|*C<0 1 plane.

When using rotatable waveplates, the relative ori- entations between birefringent sections are the primary

variables determining the total DGD, and each differential PMD vector must lie in the equatorial plane of the Poincare sphere. The biasing toward large DGD values

is then done by choosing the next differential PMD vector, At„+i, to be preferentially aligned with the projection of the total PMD vector obtained thus far, X„, onto the equatorial plane. Specifically, we choose AT„+ i so that the angle 6„ between it and the projection of X„ is biased

toward zero (mod 2k). This is done, for example, by tak- ing 0 = n [l +sgn(2x— 1)|2jc — l| 1//a], where x is again

uniformly distributed between 0 and 1 . Other choices for the probability distribution are possible, of course. Note

that if a = 1 (unbiased case), 8 is uniformly distributed between 0 and 2n, while for a > 1, 8 is concentrated near 0 and 271. Similarly, to increase the second-order PMD, or some combination of first- and second-order, the appropriate deterministic biasing directions are again obtained

merely by projecting onto the equatorial plane the vectors b found as described previously.

If frequency dependence is desired, or in the case of

rotatable waveplates, the differential phase retardations

<p„ + i(co) in the Muller matrix Rn+ i must also be specified. Recall that each beat length of a birefringent section generates a 2n retardation. In practice, sections with

significant DGDs will be many beat lengths long, and unless the section lengths are precise to within a small frac- tion of a beat length, these retardations will vary from

section to section. We therefore choose the retardation angles (p,!+ i(a>o) to be uniformly distributed between 0

and 2n. (Alternatively, one could assume a random dis- tribution of lengths £n +i; if the variance of the lengths

is large compared with the beat length, however, an ap- proximately uniform distribution of the angles <pn+ i((0o)

results. If, of course, the lengths are very precise, then

specific phase retardations should be used.) In the case of rotatable waveplates, different configurations are generated solely by rotating sections relative to one another. The results do not depend significantly upon the particular retardation angles used, except for certain clearly pathological cases such as identical angles with (p„ + i equal to 0

or n. When including the frequency dependence, a simple

strategy is to do the biasing at a single center frequency, but calculate the PMD vector over the required range of

frequencies. Furthermore, when considering pulse evolution, it is also necessary to calculate the Jones' form of the input-output transfer matrix [3].

5. Experimental implementation

Experimental PMD emulators employing a concatenation of birefringent elements have been built [16, 17], and it is possible that an emulator could be constructed to use the importance-sampled algorithm described above. Essentially, in order for it to be possible to use the algorithm,

it is necessary that the emulator be stable, repeatable and

predictable. The biggest difficulty associated with a possible experimental implementation of the algorithm is the requirement that the orientation of the PMD vector and

its frequency derivative be known after each birefringent

section. One possible way of doing this would be to monitor the PMD vector after each birefringent section; obviously, such an implementation would be prohibitively

cumbersome and expensive.

184
If the PMD vector is not monitored, then the next al- ternative is for each element of the emulator to be sufficiently well characterized that the PMD vector can be

calculated if the orientations of the different birefringent elements is specified. Here the problem is that the differ- ential phase retardations (p„ +i in the Muller matrix R„+ i must then be well characterized. If they are not known

relatively precisely, then the Muller matrix will rotate the PMD vector to an unknown location on the Poincare

sphere, and it will then be impossible to properly deter- mine the preferential orientation of the next differential PMD vector. As mentioned earlier, each beat length of a birefringent section generates a 2% retardation. Because

sections with significant DGDs will be many beat lengths

long, this means that the section lengths must precise to within a small fraction of a beat length, and that these

sections lengths must be stable with respect to temperature and other environmental fluctuations.

6. Examples

To demonstrate the ideas explained in the previous sections, we consider a concatenation of 50 birefringent sections with 0.5 ps of DGD per section (corresponding to a mean DGD of 3.26 ps), employing either polarization scramblers or rotatable waveplates. The average DGD is given by <x) = ^8(x2 )/(3n) , where (t

2 )=X?=i a2

„, the an are the individual DGDs of each section and N is the number of sections. Figure 3 shows the pdf of the DGD, obtained with optimal first-order biasing, while Fig. 4 shows

the pdf of second order PMD, obtained with the optimal second-order biasing technique. In both cases, the bias- ing parameters a = 1 , 2, . .

.

, 10 were used, with 200,000

realizations each. The individual samples are combined

by sorting the values of DGD and/or second-order PMD

obtained from all of the simulations into bins and adjusting the contribution ofeach individual sample for the bias using its likelihood ratio, as explained earlier. The solid

lines show the analytical pdfs for real fiber [22]. The emulator with rotatable sections yields better agreement with real fiber than the emulator with polarization scramblers. Note, however, that a concatenation of a small number of equal length, rotatable birefringent sections is not a good model for real fiber due to artificial periodicities of the PMD vector's autocorrelation function

in the frequency domain [16, 25]. For both scramblers and

waveplates, the pdfs deviate significantly from the real

fiber distributions in the tails, since here the PMD is generated by an emulator with finite number of birefringent

sections, which by necessity has finite maximums for both

|t| and |tu |. As a result, large values may be inaccessible

in the |x|-|lro | plane.

Figure 5 shows the joint pdf of the magnitudes of first- and second-order PMD (a two-dimensional reduction of

Ixl [ps]

Figure 3: Importance-sampled pdf of the DGD for 50 sec- tions with 0.5 ps DGD each and with polarization scramblers

(squares) or birefringent waveplates (circles). Solid curve: Maxwellian distribution with mean DGD of 3.26 ps; dashed

line: exact and asymptotic solutions from Ref. [23, 24]. Inset: the pdfs on a linear scale. A total of 2 x 106 Monte-Carlo

realizations were used.

0 40 80 , 120 160

It I [ps^]

Figure 4: The pdf of second-order PMD for a concatenation of 50 sections with 0.5 ps DGD each, using scramblers

(squares) or waveplates (circles). The solid lines show the pdf

for real fiber, from Ref. [22]. Inset: the pdf on a linear scale. As in Fig. 3, 2 x 106 Monte-Carlo realizations were used.

the full three-dimensional joint pdf of first- and secondorder PMD [1]) for an emulator with polarization scramblers, as calculated with the multiple biasing technique.

The results for the joint pdf confirm why the optimal first- and second-order biasing methods are the correct ones to use if one is only interested in first- or second-order PMD

statistics, respectively. As seen from Fig. 5, for any fixed value of DGD (a vertical slice in Fig. 5), the maximum of

the pdf occurs in a zone that falls within region 1 in Fig. 2. Similarly, for any given second-order PMD (a horizontal

slice in Fig. 5), the maximum of the pdf occurs in a zone

185
150

0 5 10 15 20 25

Ixl [ps]

Figure 5: Contour plots of the joint pdf for a concatenation of 50 sections with 0.5 ps DGD each and polarization scramblers. The contours are at 10~" with n = 30, 25, 20, 15, 10, 8, 6, 5, 4,

3, 2.25, 2, 1.75 and 1.5. A total of 106 Monte-Carlo realizations were used.

falling within region 3 in Fig. 2. The above applications of importance sampling fo- cused on the probability distributions of first- and secondorder PMD only as simple examples of the method. It

is also possible, however, to directly apply the method to the calculation of PMD-induced power penalties and out- age probabilities [14]. In particular, in a study of PMD

compensation with a single fixed DGD element, it was

demonstrated that for realistic power penalties of 1 dB the optimal value of the compensator's DGD is two to three times larger than (Ax). The results also show that it is not sufficient to determine the impact of a design upon

the average penalty, because this is not directly related to the outage probability. It is therefore crucial to accurately

model the tail of the probability density function of the power penalty, and importance sampling is a technique

that makes such a study feasible.

7. Conclusions

We have described the application of importance sampling to Mc nte-Carlo simulations of the PMD generated

by birefringent sections connected by either polarization scramblers or rotatable connectors. Importance sampling

biases the random simulations so that configurations with

large first- and/or second-order PMD occur more fre- quently than they would normally. As a result, the method

allows rare PMD events to be simulated much more effi- ciently than with standard methods. Importance-sampled

Monte-Carlo techniques therefore provide a natural and

effective means to assess PMD-induced impairments in optical transmission systems at realistic bit-error rates.

Acknowledgments

We thank J. N. Damask, A. Galtarossa, I. T. Lima and

C. R. Menyuk for many interesting and valuable discussions. This work was supported in part by the National

Science Foundation under grant numbers DMS-0101476

and DGE-9987577.

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F. Prieto, C. W. Zimmer, IEEE J. Lightwave Tech. 16, 757

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9. P. Bratley, B. L. Fox and L. E. Schrage, A guide to simulation (Springer-Verlag, New York, 1987)

10. G. S. Fishman, Monte Carlo: concepts, algorithms and applications (Springer-Verlag, New York, 1996)

1 1. G. Biondini, W. L. Kath and C. R. Menyuk, IEEE Photon.

Tech. Lett. 14, 310 (2002).

12. S. L. Fogal, G. Biondini and W. L. Kath, OFC2002, paper ThAl; IEEE Photon. Tech. Lett, to appear (2002)

13. S. L. Fogal, G. Biondini and W. L. Kath, OFC2002, paper ThA2

14. I. T. Lima, G. Biondini, B. S. Marks, W. L. Kath and C. R. Menyuk, Photon. Tech. Lett. 14, 627 (2002).

15. D. Marcuse, C. R. Menyuk, and P. K. A. Wai, J. Lightwave

Tech. 15, 1735 (1997)

16. R. Khosravani, I. T. Lima, P. Ebrahimi, E. Ibragimov, A.E.

Willner, and C.R. Menyuk, Phot. Tech. Lett. 13, 127

(2001)

17. J.N. Damask, OFC2000, paper ThB3

18. A. Galtarossa, L. Palmieri, M. Schiano, and T. Tambosso,

Opt. Lett. 25, 1322 (2000)

19. A. Papoulis, Probability, Random Variables and Stochastic Processes (McGraw-Hill, New York, 1965)

20. A. Owen and Y Zhou, J. Amer. Stat. Assoc. 95, 135

(2000).

21. E. Veach, Robust Monte Carlo Methods For Light Trans- port Simulation, Ph.D. thesis (Stanford University, 1997).

22. G. J. Foschini, L. E. Nelson, R. M. Jopson, H. Kogelnik, IEEE Photon. Tech. Lett. 12, 293 (2000).

23. B. D. Hughes, Random Walks and Random Environments

(Clarendon Press, Oxford, 1995).

24. M. Karlsson, J. Lightwave Tech. 19, 324 (2001)

25. I. T. Lima, R. Khoshravani, P. Ebrahimi, E. Ibragimov, A. E. Willner, and C. R. Menyuk, OFC2000, paper ThB4

186
Investigations on the relation between PMD coefficient and cable

installation year in Deutsche Telekom fiber plant

H.-J. Tessmann, D. Breuer, H.M. Foisel, H. Reiner*, and H. Cremer*

T-Systems/Deutsche Telekom, Technology Center, Goslarer Ufer 35, D-10589 Berlin, Germany, email:

d.breuer@t-systems.com

*T-Com/Deutsche Telekom, Am Kavalleriesand 3, D-64295 Darmstadt, Germany

Abstract: PMD data based on measurements of about 10'000 fiber sections within Deutsche Telekom

fiber plant are analyzed. The relationship of the PMD coefficient and the installation year of the deployed

fiber cables over a time period from 1985 till 2001 is investigated.

1 Introduction

Today network operators are facing the challenge of offering higher capacity to deal with the steadily

growing demand of customers for transmission bandwidth at even reduced costs. In particular, during the

last years a rapid capacity expansion of the core network with WDM links up to 600 km transporting up to 100 wavelength channels at 2.5 Gbit/s or 10 Gbit/s on a single fiber was necessary. To keep pace with

this increasing capacity demand some carriers already performed field trials at 40 Gbit/s per wavelength

[1]. For data rates per channel at and beyond 10 Gbit/s the assessment of the parameters of the installed

fiber plant is a critical element for a carrier in the process of deploying these new terabit optical transport

systems.

The impairments limiting the transmission performance generally include fiber loss, chromatic dispersion,

polarization mode dispersion (PMD) and fiber non-linearities. From these limitations PMD is quite often considered as the most severe limiting effect, since it is complicated to compensate for. However, there is only rare data about PMD in a carriers installed fiber plant available. In this paper we present PMD

measurements carried out in the installed fiber plant of Deutsche Telekom, which consists solely of G.652

fiber. The measurements were performed all over Germany during the last three years on nearly 10'000

fiber sections whereby these fiber cables were installed from 1985 till 2001. In this paper PMD

measurement results are presented and a correlation of the PMD values with the initial operation and

cable vintage (installation year) are shown. Moreover, based on published specifications the assessment

of Deutsche Telekom fiber plant regarding 10 Gbit/s and 40 Gbit/s WDM transmission will be discusses.

2 Measurements and PMD specifications

The PMD measurements in the backbone network of Deutsche Telekom were performed with

commercially available, interferometer based field measurement systems from EXFO (FTB 300/400 with

the Polarization Mode Analyzer module FTB-5500). The broadband LED light source (module M2100

from EXFO) had a center wavelength of 1545 nm and a spectral width of 60 nm. To measure each

individual cabled fiber receiver and transmitter are placed on opposite ends of the span, no loop-back was

used. In each PMD measurement the cabled fiber section's mean DGD in picoseconds (ps) was

measured. For characterization of the first order PMD coefficient in ps/Vkm, the fiber length of each

investigated fiber section was also measured by OTDR measurements. Typically, in a selected cable all not-in-service fibers were measured.

Table 1 shows DGD's and PMD coefficients for 2.5, 10 and 40 Gbit/s based on the International Telecommunication Union (ITU-T) proposed guidelines for PMD limitation to maintain acceptable error

187
rates [2]. The maximum DGD has to be lower than 1/10 of the bit duration. During the measurement

process the fibers with the least PMD-values and attenuation were reserved for future high speed links.

Bit rate (Gbit/s) DGD (ps) PMD-coefficient (ps/Vkm)

2.5 40 2.0

10 10 0.5

40 2.5 0.125

Table 1: Relation ship between bit rate and proposed max. DGD and PMD coefficient for a 400 km link according to ITU-T recommendations [2].

It is noticeable to mention that for pre-1994 cables PMD was not yet specified by cable manufacturers.

The fiber and cable manufacturers started to add the PMD value to their specifications around 1995. For

today's G.652 cabled fibers a PMD coefficient of 0.5 ps/Vkm is guaranteed. However, the typical fiber PMD, without any cabling effects, can have PMD coefficients less than 0.1 ps/Vkm. Considering the PMDlimits in tablel and the above specifications from manufacturers there were considerable concerns about

the suitability of the installed fiber plant regarding 40 Gbit/s and even 10 Gbit/s.

3 Results and Discussion

During the last three years 9770 cabled G.652 fibers in the backbone network of Deutsche Telekom have

been characterized with respect to PMD. The cable vintage of the measured fibers ranged from 1985 to 2001 . Fig. 1 shows a histogram of the PMD coefficient of all measured fibers. Please note that for showing the tail distribution in Fig. 1 from 0.5 to 3.5 ps/Vkm the class width was

increased from 0.02 ps/Vkm to 0.5 ps/Vkm. The mean measured PMD-coefficient of all fibers is 0.17

20

18

16 „ 14

S?o

12

O)

iS 10 c

4>" 8 a

°- 6

4

Total Measurements:

PMD-Coefficient - Average:

PMD-Coefficient - Maximum:

9770

0.17 ps/km A0.5 4.79 ps/Vkm

Iclass width 0.02 ps/Vkm | class width 0.5 ps/Vkmw

PMD Coefficient (ps/Vkm)

Fig. 1: Histogram of PMD coefficient (ps/Vkm) for all 9770 measured fibers

ps/Vkm and the maximum measured value is 4.79 ps/Vkm. Directly from this graph it is noticeable that the

majority of the measured fibers will fulfill the ITU-T recommendation for 10 Gbit/s.

Based on all measured fibers Fig. 2 provides a summary of the assessment of the fiber plant for various

link length according to the ITU-T recommendations in tablel. Only fiber PMD was considered. For 2.5

Gbit/s transmission nearly all fibers (98,5%) are suitable up to the maximum considered link length of 1000km. For today's installed terrestrial 10 Gbit/s WDM-systems with typical link length up to 600 km

nearly all fibers (89%) of the fiber plant are accessible and even for next generation systems with link length of about 1000 km still 86% of the cabled fibers support 10 Gbit/s operation. In particular, Fig.

2

188
reveals that for future systems operating at 40 Gbit/s 63% of Deutsche Telekom fiber plant can be used

for typical length up to 600km.

In a next step a possible correlation between cable vintage and mean PMD coefficient was analyzed (see

1000 km

Link Length

Fig. 2: Percentage of fibers suitable for 2.5 Gbit/s, 10 Gbit/s and 40 Gbit/s over various link length

Fig. 3). For each cable vintage the mean PMD value was determined from at least 200 to a about 1000

measured individual fiber sections of different cables from different manufacturers installed in the same

0,45

Cable Vintage

Fig. 3: Mean and variance of PMD coefficient as a function of cable vintage.

year. In the early years usually cables from four different cable manufacturers were deployed.

As depicted in Fig. 3 there are 3 regions of almost constant PMD values. The first region with a high

average PMD value of 0.32 ps /Vkm is for pre-1991 cables. The second one covers a time period from

1992 to 1998 with a typical PMD value of 0.13 ps/Vkm and the third region for post-1999 cables shows an even lower PMD coefficient of about 0.05 ps/Vkm which is attributed to improved manufacturing

189
processes caused by more stringent carrier requirements on cabled fiber PMD. Also a significant drop of the PMD variance with cable vintage could be observed.

However, jased on these results, particularly the improvement in PMD from 0.32 to 0.13 ps/Vkm for cable

vintage of 1991 to 1992, could not be directly correlated to the introduction of the PMD specification from

the manufacturers in 1995, but maybe correlated to an improvement in the fiber/cable manufacturing

process. Anyway, the deployment specifications for fiber cables were not significantly modified during this time frame to explain the observed behavior.

A more thoroughly analysis of the three PMD regions is presented in Fig. 4 where the percentage of

100,0%

PMD-coefficient [ps/Vkm]

Fig. 4: Percentage of fibers in the different PMD classes for different cable vintages (installation years)

according to Fig. 3.

cabled fibers for the three regions with respect to different PMD coefficients is shown. Also the mean PMD value for each region is depicted. In region 1 the PMD classes from 0.3 ps/Vkm to 0.7 ps/Vkm occur

with 1%. For region 2 (cable vintage 1992 till 1998) the percentage of the investigated fibers is about

0.1% for PMD-coefficients greater 0.46 ps/Vkm. The region 3 shows no value greater than 0.44 ps/Vkm

and the classes over 0.18 ps/Vkm are less than 1%. But as obvious from Fig.4 even for "old" fibers (pre1991) low PMD values (<0.125 ps/Vkm) suitable for 40 Gbit/s transmission can be found.

3 Conclusions

Deutsche Telekom has accomplished a thoroughly investigation of the installed fiber plant with respect to future transmission requirements. About 10'000 cabled fiber sections have been measured and the fibers with lowest PMD were identified and reserved for high capacity transmission. The data indicate that no

direct correlation of the first-oder PMD coefficient value with the rollout of the PMD specification by the

fiber and cable manufacturers is feasible. Even for cables which were installed during 1985 till 1991 a reasonable number of fibers is suitable for 40 Gbit/s transmission. For 10 Gbit/s selected fibers are used,

thus PMD does not impose any limitations and therefore avoiding expensive exchange of fibers.

References

[1] press release: http://www.lucent.com/press/0501/010523.nsa.html

[2] ITU-T G.650

190
Pulsed measurement of polarization mode dispersion

in field-installed optical fibers

Asbj0rn O. Kleivstul, asbjorn.kleivstul@telenor.com,

Telenor R&D, Snarayv. 30, 1331 Fornebu, Norway,

and Aasmund S. Sudbo, sudbo@unik.no,

University Graduate Center - UniK, P O Box 70, 2027 Kjeller, Norway.

Abstract: Polarization mode dispersion (PMD) has

been measured in optical fibers in field-installed cables. Two methods that allow simultaneous

measurement of many fibers in parallel accessing one end of the cable have been investigated.

Agreement with measurements based on Jones

matrix eigenanalysis (JME) is observed for both

methods.

Introduction: The fixed analyser (FA)

method [1] is well established for measuring

polarization mode dispersion (PMD) in

optical fibers. With this method, the

transmission coefficient of the fiber is measured as a function of wavelength, for

polarized input light and with an analyzer

(polarizer) in front of the detector. The

polarization analysed spectral response

(PASR) curve thus obtained has oscillations,

and the PMD is determined by the number

of oscillations of the curve. Instead of the

transmitted light, the light reflected back to the input end from the far end of the fiber

may be measured [2], i.e., a two-way

spectral response may be measured. Using

pulsed illumination, several fibers in parallel

may be measured simultaneously with one

source and one detector, provided the fiber

lengths are different, so that the pulses from

different fibers arrive at different times at the detector. We have shown [3] that a twoway measurement on four fibers in parallel

may be performed with a tuneable optical

time-domain reflectometer (OTDR) with a

polarizer and a power splitter. We show that a minor modification of the measurement

setup in [3] also allows a one-way

transmission measurement to be made. For

a field-installed cable, the measurements

may be performed by an operator only

having access to one end of the cable. We

demonstrate measurements on four fibers in

parallel, performed on fibers in field- installed cable.

tuneable

laser modulator

pulse generator

fibres

p

2 n P

3 n s 4 0

computer 1 OTDR

Figure 1: Experimental setup for measuring

polarization mode dispersion (PMD) in many optical fibers in parallel, using a tuneable optical time domain reflectometer (OTDR) with power splitter(s) and a polarizer (P). C: optical circulator, o/e: detector, (a) one-way. (b) two-way, as in [3J.

Measurement setup: The measurement setup

described in [3] was used for making two191
way measurements of PMD. In this setup,

all the fibers to be measured are connected

to a tuneable OTDR with a power splitter.

To make one-way measurements, the far ends of the fibers were connected to a power

splitter followed by a polarizer, as shown in Fig. 1(a), and the output power returned to the OTDR via a separate fiber in the cable.

For comparison, the setup adapted from [3]

is shown in Fig. 1(b).

A computer tuned the laser in wavelength

steps of 0.25 nm from 1520 to 1580 nm,

started the OTDR measurement for each

step, and read the height of each pulse in the

OTDR trace corresponding to a fiber. The

OTDR pulse width used was 1 us. For each

pulse representing a fiber, the pulse height was recorded as a function of wavelength,

yielding the polarization analysed spectral

response (PASR) of the corresponding fiber. The number of extrema in the response

curve for each fiber was counted manually.

Both one-way- and two-way measurements

were performed. With strong polarization

mode coupling in the fiber, the PMD within

a frequency interval Av(7.5 THz in our measurements) is < At > = kN / Av , (1)

where N is the number of extrema in the

PASR, k = 0.403 for one-way, and k = 0.247

for two-way transmission [2]. (There is a misprint in Eq. (1) of [3], where 0.298 is written instead of 0.247, but the correct value was used in the data analysis in [3].)

The relative rms uncertainty in the measured

<Ax> is(TJ{A<u)=VI4n , (2)

where k'= 0.72 for one-way, and k'= 0.88

for two-way transmission [2].

For reference, we also measured PMD in the

fibers with the one-way Jones-matrixeigenanalysis (JME) method [4], using a commercially available polarimeter.

A total of 1 6 cabled standard (ITU type

G.652) single-mode fibers were measured.

The fibers were measured in groups of 4, as shown in Fig. 1 , with each member of the

group from a different cable or an uncabled

fiber spool, to obtain a group of 4 fibers with

different lengths. The fibers were selected

from 9 different installed cables.

Results: Fig. 2 shows typical results from a measurement on 4 fibers with a one-way

setup. An example of a PASR of a fiber

with N = 1 7 extrema is shown in the bottom

figure. Fig. 3 shows corresponding results

for the two-way setup, with 7V= 29 extrema

1540 1550 1560 Wavelength (nm) 1570

Figure 2: Pulses observed in one-way measurement

with fourfibers (A, B, C, and D) at two wavelengths

(top and middle), and sample polarization analysed

spectral response ofonefiber (bottom).

192
35

1520 1530 1540 1550 1560 1570 1580 Wavelength (nm)

Figure 3: Likefigure 3, obtained with two-way

measurements.

in the PASR. Our results are compiled in

Fig. 4. Each data point (ring) represents the

average of two measurements made on a

field-installed fiber, and the PMD value

measured with the OTDR (one-way and

two-way) is plotted against the PMD value

measured with the JME method. We have

included two error bars in the top figure

(one-way measurements), 6gat/V2 tall, with

Gat computed from Eq. (2). (The v2 is introduced by an assumption of each data

point representing two statistically

independent measurements). For a given

PMD value, corresponding error bars for the

two-way measurements would be about 5%

smaller than for the one-way [2]. Considering the error bars, accurate comparison between the two measurement

methods cannot be made. The average ratio

between the OTDR measurement results and

the JME results is 1.012 ± 0.083 for the oneway measurements, and 0.957 ± 0.098 for

the two-way. The '±' represents 3 standard

deviations of the average (not of individual

measurements).

One-way

Two-way

o

°0 05 1 1.5 2 2.5 PMD measured with JME method, ps

Figure 4: Polarization mode dispersion (PMD)

measured with the tuneable reflectometer (OTDR)

plotted versus PMD measured with a polarimeter,

using each ofthe setups in Fig. 1. The straight lines represent perfect agreement.

Discussion: In [3] we estimated that it should be possible to measure tens of fibers

in parallel with our setup, assuming shot

noise limited detection and perfect Fresnel

reflection from the fiber ends. Both

assumptions may be difficult to meet in

practice. An advantage of the setup shown

in Fig. 1(a) compared to the one in Fig. 1(b)

is that we do not have to rely on an unknown

reflection from the far end. By using the

far-end power splitter we obtain an OTDR

signal that is more than 25 times larger than

we can ever obtain with reflections from

glass-air interfaces. (Somebody, however,

has to go to the far end and mount a power

splitter and a polarizer before the

measurements can be performed.)

193
As discussed in [3], for large N, the time

needed to perform a measurement on N

fibers is proportional to N . An alternative

then is to use a fiber switch instead of the

power splitter, in which case the time

needed to perform a measurement is proportional to N.

One purpose of our measurements was to find how well the two OTDR methods and

the JME method for measuring PMD agreed on our field installed cables. Our

measurements indicate agreement within a

factor of 0.96, and are not nearly extensive

enough for an accurate verification of any

disagreement between the three methods.

Most of the measurements shown in Fig. 2

yielded PMD values considerably less than 1 ps, corresponding to few oscillations in the

PASR curve, with correspondingly large

uncertainty in the measured PMD.

Eq. (2) seems to indicate that two-way

measurements are more accurate than one- way, because they yield PASR curves with more extrema. Actually, the opposite may

be true for long fibers, because of the

reduced signal obtained in two-way

measurements due to fiber attenuation.

Conclusion: We have demonstrated one- way and two-way measurements of

polarization mode dispersion (PMD) on

optical fibers in field installed cables, using

a tuneable optical time domain reflectometer

(OTDR). The measurements were

performed on groups of four fibers in

parallel, and access to both ends of the fiber was not required during the measurement.

Within our measurement uncertainty, we

have observed agreement between the two

OTDR methods and the JME method. Even

though individual measurements have

limited accuracy, the measurement method

is well suited for surveying the overall PMD

status of an operator's network.

References:

1 POOLE, C. D., and FAVIN, D. L., 'Polarization-Mode Dispersion

Measurements Based on Transmission

Spectra Through a Polarizer,' J. Lightwave

Technol, 1994, 12, (6), pp. 917-929.

2 GALTAROSSA, A., PALMIERI, L., SCHIANO, M., and TAMBOSSO, T., 'Single-End Polarization Mode Dispersion

Measurement Using Backreflected Spectra

Through a Linear Polarizer,' J. Lightwave

Technol., 1999, 17, (10), pp. 1835-1842.

3 KLEIVSTUL, A. O. and SUDB0, A. S., 'Simultaneous measurement of polarization

mode dispersion in several optical fibers in

parallel,' Electronics Letters, vol. 37, no. 10, pp. 621-623,2001.

4 HEFFNER, B. L., 'Automated

Measurement of Polarization Mode

Dispersion Using Jones Matrix

Eigenanalysis,' IEEE Photonics Technol.

Lett., 1992, 4, (9), 1066-1069.

194
Analysis and comparison of measured DGD data

on buried single-mode fibers

Christopher Allen

1

, Pradeep Kumar Kondamuri1

, Douglas L. Richards2

, and Douglas C. Hague2

'Lightwave Communication Systems Laboratory

Information and Telecommunications Technology Center (ITTC)

The University of Kansas, Lawrence, Kansas 66045

2 Sprint Corporation, Overland Park, Kansas

Abstract

Temporal and spectral measurements were made on

three different 95-km fibers within a slotted-core, direct buried, standard single-mode fiber-optic cable over many days to characterize DGD variability. From this data we observed that DGD varies slowly over time but

rapidly over wavelength. This data showed good

agreement with a Maxwellian distribution. The

frequency-averaged mean DGD varied by about 1 0% or

less during the periods that included significant

temperature swings. Outage analysis showed that for system tolerances of three times the mean DGD,

outages will occur typically every 3 to 8 years with mean outage durations ranging from about one to two

hours. From this analysis we conclude that high-DGD

episodes are spectrally localized and will be

exceedingly rare and short lived. Introduction

Polarization-mode dispersion (PMD) may be a major

impediment for network operators seeking to increase

the per channel data rate on long-haul fiber-optic links. While the differential group delay (DGD, or Ax) in buried fiber had negligible impact at 2.5-Gb/s signaling

rates, upgrades to lOGb/s, 40 Gb/s and beyond will require increasingly more attention. While there are PMD challenges facing carriers operating at 10 Gb/s,

these challenges are not as severe as originally feared. Major carriers are successfully deploying 10-Gb/s

dense-wavelength division multiplexed (DWDM) links across the core of their networks. A marked

improvement in the DGD tolerance of 10 Gb/s long- reach receivers (to about 40 ps) will likely satisfy most

length demands, obviating the need for PMD

compensation (PMDC). Signaling rates of 40 Gb/s and

beyond will most likely require some form of mitigation

in long-haul applications, such as robust modulation

schemes or PMDC.

To ensure signal quality on their fiber at higher bit rates, network engineers must anticipate the impact of PMD

on the various fiber routes. An understanding of the

variability of both the DGD and the principal states of

polarization (PSPs) is required to specify appropriate transmission parameters. Factors such as the mean DGD, PMD correlation time and bandwidth, as well as

second-order effects together with performance

prediction models can provide this understanding.

The availability of measured PMD data on installed, buried fibers is limited. In this paper we present

measured DGD data for buried, standard single-mode

fiber to improve our understanding of the variability of

PMD. While PMD is a vector quantity, with a magnitude (DGD) and a direction (PSP), we are only

focusing on the DGD. The statistical distribution and

behavior of PSPs has been extensively studied and is shown to be correlated to DGD behavior [1,2]. Experimental setup

Experiments were conducted to measure the instantaneous DGD on three different 95-km fibers (1,

2, and 3) within a slotted-core, direct buried, standard single-mode fiber-optic cable made available by Sprint.

A polarization analyzer employing the Jones-MatrixEigenanalysis (JME) method was used for measurements at wavelengths from 1510 nm to 1625

ran with a spectral resolution of 0.1 nm (about 12.5 GHz). Measurements on fiber span 1 were repeated

approximately every 3 hrs and they were carried on for about 86 days whereas on fiber spans 2 and 3 they were

repeated approximately every Y/i hours and carried out

for about 14 and 9 days, respectively. Over the 86 days

(from Nov. 9, 2001 through Feb. 2, 2002) 692

measurements were made on fiber span 1 across the 1150 discrete wavelengths representing 795,800

measured values. For fiber spans 2 and 3 the corresponding number of DGD measurements is about 271,600 and 181,700.

Plots of DGD vs. wavelength and time

Figures 1, 2, and 3 show in a color-coded format normalized DGD data (i.e., DGD/mean DGD) measured on the three fiber spans, respectively. From the plots it

is clear that for buried fibers DGD changes with time

but not at a rapid rate. This variation is random and

differs from fiber to fiber. It is also evident that the DGD varies significantly with wavelength and relatively

high-DGD events are spectrally localized. A histogram of the normalized DGD data on fiber span

1, shown in Figure 4, is seen to have shape consistent with a Maxwellian distribution, as expected. A curve

representing a Maxwellian distribution for a 1 -ps mean DGD is also plotted for comparison.

195
Figure 1. Measured, normalized DGD vs. wavelength and time

for fiber span 1 (86 days of data).

Figure 2. Measured, normalized DGD vs. wavelength and time

for fiber span 2 (14 days of data).

(C)

Figure 3. Measured, normalized DGD vs. wavelength and time

for fiber span 3 (9 days of data).

1

0 0.5 1 1.5 2 2.5 3 DGD / mean DGD

Figure 4. Histogram of measured, normalized DGD data on fiber span 1.

Similar histograms were obtained for the data on the other two fiber spans (plots not shown here) and they

also showed good agreement with a Maxwellian

distribution.Mean DGD variation with time

To observe the time-dependent nature of DGD more

closely, 1 150 DGD measurements over all wavelengths were averaged together to obtain frequency-averaged

DGD data, denoted as <DGD>x. normalized by the

overall mean DGD (averaged over both time and

frequency), denoted as «DGD>x>t. Since temperature

is a known driver in changing DGD changes, hourly air temperature data for the region were collected as well. The variation of frequency-averaged DGD and

temperature with time on the three fiber spans is shown

in Figures 5, 6 and 7. From Figure 5 it can be observed

that frequency-averaged DGD varies by only about

±10% over 86 days of observations that included

significant temperature swings. Since the entire length

of the fiber is buried, the diurnal temperature variations do not represent the fiber temperature. Statistical analyses reveal no significant correlation between long- term temperature variations and the frequency-averaged mean DGD.

196
Ail! ^

Tm i et,-»I 9, 2001 - Frfa 2, 2002) Figure 5. Frequency-averaged DGD and temperature vs. time for

fiber span 1.

US

' 1,1 i«

I

• awM

a*

•r- t-

:

•

-4 J -t- •-36 f"

I t 4 * I fl 11 rimr i.ik 1 1 iMwf «, :ucc - Mn in :ik : Figure 6. Frequency-averaged DGD and temperature vs. time for

fiber span 2.

I 1 % J 1 9 * f I TtHM Ctfajtl I .Wis 3», 2002 - May 2?, 2002) Figure 7. Frequency-averaged DGD and temperature vs. time for

fiber span 3. System outage analysis

An outage event is one which exceeds the given

threshold value of DGD, Ax,h

. The outage probability Pout, expressed in minutes/year, can be calculated from

the Maxwellian probability distribution function (pdf), fx(0 as

P(Ax > Ax lh ) = 1 - ffx (Ax)d Ax (2)

and then multiplying the number of minutes in a year. As Pout is based on the Maxwellian pdf, it may be

expressed as a function of one independent variable M=Ax/A/(mean DGD) as Pout(M) and is clearly fiber independent and will be the same for all installations.

In cases where the probability of an outage is quite

small, Pou, represents the annualized outage probability

based on long time records, however no insight is provided regarding the outage rates and their durations. Accurate estimation of the impact of PMD on network

availability requires statistical analysis of the DGD

variability. Caponi et al. [3] showed how the mean time

between PMD-related outages could be estimated from

the temporal characteristics of DGD variations and the Maxwellian probability density function. The mean

outage rate, R<,ut (defined as the mean number of outage

events per unit time with units of events/year), is found

using [3]

R. = | ft (threshold) ] ft

. (Ax')|Axj dAx' (3)

where Ax' is the time derivative of the DGD, and ff( ) is the pdf of Ax'. Caponi et al. observed Ax and Ax' to be

statistically independent and also found that RoUt is cable and installation dependent.

Figure 8 shows the calculated outage probability, Pout, and the mean outage rate, R<,ut, for a given system

threshold relative to the mean DGD on the three fiber spans.

h

f J

5 10 D

.11

1— —i - r —- Haul — • Rain an n*ar,l Knul 'in Sf9tii

Hflitt .in ^Jin'J : \

i

- r

1 .^^......'Sy!--

H i It li,

** 1 * I ! M 1 1 k 1 * liliitl 1 « (Ml f i 1. 1 1 1 j ' ) i i < » • • i . . l. . . . | , |H| , <^t* ~

13III7 23 3 13 4 43

Threshold f Mean DGD

Figure 8. Calculated outage probability, Pou„ and mean outage

rate, RoU,, versus Threshold/Mean DGD.

197
o

1 i , i i i 1 1.5 2 U 1 i.5 4 4,5 5 TTirestwId J Mean DGD

Figure 9. Calculated mean outage duration, Toul, as a function of Threshold/mean DGD.

Table 1. Predicted mean time between outages (MTBOs) and mean outage durations for different DGD tolerances 3*<DGD> 3.7*<DGD>

Span 1 MTBO

Outage duration

6.39 years 136 min1 648 years 108 min

Span 2 MTBO

Outage duration

3.25 years 69 min833 years 55 min

Span 3 MTBO

Outage duration

7.91 years 138 min2000 years 133 min

The mean duration of DGD-induced outages can be

determined using statistical analysis as well. Caponi et

al. [3] showed that the mean outage duration, Tout, is

1"out — ^out out (4) which has units of minutes. Figure 9 shows the calculated mean outage duration,

Tout, as a function of system threshold relative to the mean DGD. Since Tout is found using R^,, which is cable and installation dependent, Tout will also be cable and installation dependent.

From the above analysis, we can estimate the mean

outage time between outages (MTBOs) and mean

outage durations for various DGD tolerances for these

fiber spans. Table 1 lists these values for system

thresholds of three and 3.7 times the mean DGD.

For comparison, Nagel et al. [4] predicted that for the

1 14-km buried link they studied, the DGD will exceed

three times its mean value once every 3.5 years and

estimated a mean outage duration of between 10 and 20

minutes for their link. From data measured on 37-km of

buried cable, Caponi [3] predicted the DGD will exceed

three times the mean DGD once every 2.5 years with a mean outage duration of 56 minutes. Conclusions

We have measured DGD data on three different 95-km

fibers within a slotted-core, direct buried, standard single-mode fiber-optic. From these measurements we

observed that DGD varies slowly over time but rapidly over wavelength or frequency. Episodes of higher-that- average DGD were observed and seen to be spectrally localized and of limited duration. To investigate the role of changing temperature on mean DGD variations, frequency-averaged DGD data were compared to temperature histories. The frequencyaveraged DGD varied by only about ±10% over 86 days

of observations that included significant temperature

swings.

From this data predictions were made regarding the

probability, and frequency of outage occurrence. While

the statistics of Maxwell ian processes adequately

describe the annualized outage probability, further analysis of the DGD data revealed the mean time

between outages and mean outage durations. For

outages characterized by high DGD episodes (DGD

more than three times the mean DGD), we found that the mean outage rates and durations for these three

fibers to be similar. Our findings agree with reports by

others that DGD excursions of three or more times the mean DGD are infrequent and relatively short lived. This finding is significant for network operators who

must assess the impact of PMD on network reliability. Acknowledgment

This work was funded by Sprint Corporations

Company, L. P. A special tribute is paid to Francis Yarkosky, for his leadership and support.

References

[1] Karlsson, M. and J. Brentel, "Autocorrelation function of

the polarization-mode dispersion vector," Optics Letters, 24(14), pp. 939-941, 1999.

[2] Karlsson, M., J. Brentel, and P. A. Andrekson, "Longterm measurement of PMD and polarization drift in installed fibers," Journal of Lightwave Technology,

18(7), pp. 941-951,2000.

[3] Caponi, R., B. Riposati, A. Rossaro, and M. Schiano,

"WDM design issues with highly correlated PMD spectra of buried optical fibers," Proc. OFC 2002, Anaheim, CA,

ThI5, pp. 453-455, 2002.

[4] Nagel, J. A., M. W. Chbat, L. D. Garrett, J. P. Soigne, N.

A. Weaver, B. M. Desthieux, H. Bulow, A. R. McCormick, and R. M. Derosier, "Long-term PMD

mitigation at 10 Gb/s and time dynamics over high-PMD

installed fiber," Proc. ECOC 2000, Munich, Germany

Vol. 11(4.2.1), pp. 31-32, 2000.

198
Statistical evaluation of polarization-dependent losses and polarization-mode

dispersion in an installed fiber network

C.J.K. Richardson1 , R. J. Runser

2

, M. Goodman2

, L. Mercer3

'Laboratory for Physical Sciences, University of Maryland, College Park, MD

2 Laooratory for Telecommunication Sciences & Telcordia Technologies, Adelphi, MD

3 Naval Research Laboratory, Washington, D.C.

ABSTRACT: The statistical probability distributions of the differential group delay, the

differential attenuative slope, and the polarization-dependent loss are determined from

measurements of Jones matrices acquired as a function of time for several wavelengths within a

single channel of several links on an installed metropolitan optical wavelength division

multiplexed network. Analysis of the measured results forms a statistical picture that is not in

conformity with theoretical descriptions that predict Maxwellian distributions.

The statistical behavior of pulse broadening in optical networks through the interaction of

polarization-mode dispersion (PMD) and polarization-dependent loss (PDL) is needed by network

operators and laboratory scientists in order to understand and predict real-world outage

probabilities and to expand the limits of operation of installed networks to accommodate higher

data rates and new modulation formats. It is known that the interaction between polarization mode

dispersion and polarization dependent loss can combine to disperse an optical pulse by an amount

that is greater than the contribution to dispersion made by birefringence alone. [1-3] Here we

analyze the change in differential group delay (DGD), the differential attenuative slope (DAS),

and the PDL of an installed fiber link on the Advanced Technology Demonstration Network

(ATDNet) as a function of time. The measurements provide a means to compare the statistical transmission characteristics of a functional network link in a real-world environment with

theoretical statistical models. To our knowledge, only one other measurement of PMD on an

installed fiber span has been reported[4], but is the first to investigate a functional metropolitan

area network and the first to consider PDL in addition to PMD.

Experiments were conducted on the ATDnet optical test bed, which is a transparent, 8

channel, wavelength division multiplexed network in the Washington, D.C. metropolitan area. Fig. 1 describes the experimental setup. The loop under test consisted of a round trip through a

pair of 40 km SMF-28 fiber spans between two nodes, the LTS and DARPA/ISI, which have gain

clamped Erbium-doped fiber amplifiers (EDFA) located at the midpoint. The test signal was

passively multiplexed into the WDM fiber at the LTS. At the DARAP/ISI node, the WDM

channel under test was separated from the network using a commercial 1 00 GHz wide wavelength

division demultiplexer and patched directly into the output multiplexer for return to the LTS.

EDFA's were located on both trunk sides of the optical add drop multiplexers at the loop-back

location. Upon return to the LTS, the signal was split and filtered using a 200 GHz demux and

sent to the measurement apparatus.

199
26.6km 13.1km m

ED FA

Bridge

Fig. 1 Experimental test of a loop back between DARPA/ISI and LTS on ATDNet.

The CW optical signal was generated and detected in the same location using a tunable

external cavity semiconductor laser. The output Stokes parameters from three input polarization

states that were measured by an HP8509B polarization analyzer were used to calculate the Jones

matrices of the fiber loop for twelve different wavelengths within a 1 00 GHz passband centered

around ATDNet X6. Measurements of the Jones matrix were obtained every 5 seconds for

approximately 7 days. The DGD and the DAS are determined using the Pauli spin matrix

equivalence[5] to examine the operator TMT

_1 where T represents the frequency dependent Jones

matrix of the network link under test, and the subscript co denotes differentiation with respect to the angular optical frequency. In general, the operator TWT

_1 calculated from measured data is not

traceless. However, the Jones matrices can be represented as T(co)=exp[-A(co)-iB(oj)]T0(co) where

T0(co) is the measured Jones matrix and T(co) contains the polarization dependent information of

interest here. The factors A and B are determined from the average values calculated from the

Jones matrix at each wavelength under test. Satisfying the traceless condition allows the real (Q.)

and imaginary (A) components of the PMD vector to be expressed in terms of the Pauli spin

matrices, which can be determined from T^T

-1 by inspection using

, (T(co0 +5co)-T(co -5co)) . . . ir- --n TT1 ^ 1 i-2 —T (co ) = -—TQ + iAl-d. (1)

25co

V o)

2

L J The magritude of Q is the DGD while the magnitude of is A the DAS. The derivative of the

Jones matrix is completed using a center difference 2-point scheme, which is then averaged to obtain a single first-order value of the DGD and the DAS. This approach was selected to minimize the error associated with calculating the derivative and the influence of error resulting

from time-dependent variations in the Jones matrix. The magnitude of the PDL vector is determined by converting the measured Jones matrix into a 4x4 Mueller matrix and calculating the

maximum and minimum transmission components.

As shown in Fig. 2, measurements of the transmission characteristics indicated a dynamic

behavior in the DGD, DAS, and PDL that evolved over time. Upon inspection of the fiber route

for this link, it was discovered that there was a bridge crossing between the two nodes. To

investigate the influence of possible environmental factors, the component of the average wind

speed that is perpendicular to the bridge span was obtained for time duration of these

measurements. It is apparent that there may be a causal relationship between this environmental

variable and the transmission characteristics as suggested by the correlation. These observations

are a departure from the formulation of conventional theoretical descriptions that use a fully

200
stochastic model to describe the polarization dependent transmission characteristics for PMD and

residual PDL.

0 i—,—i—i—i—.—i—i

i—ii—.—i—i—

i

0 24 48 72 96 120 144 166 Ellapsed Time (Hr)

Figure 2. Temporal evolution of the DGD, DAS and PDL compared to one vector component of the average wind

speed (gray bars) and gust speed (circles) measured from the National weather service. A causal relationship between

wind speed and the transmission characteristics is suggested by the apparent correlation.

One would expect that the histograms of these measured components to vary from the expected

Maxwellian distribution. Figures 3 and 4 show the normalized histograms of the DGD, the DAS,

and the PDL compared with a normalized Maxwellian distribution that is calculated using the

mean value of each quantity.

0.0100 |

.

1 . 1

. 1.

1

0 10 20 30 40 DGD (ps)

Figure 3 The normalized histogram of the DGD (filled distribution) and the normalized Maxwellian curve (solid line)

that is calculated using the mean DGD.

201
Understanding the actual statistical behavior of links under the influence of dynamic real- world conditions is required to develop a complete model of the polarization evolution that is representative of an installed fiber plant. These measurements suggests that upgrading capacity

and bit rate on fiber plant may depend upon the condition and placement of its installation. Given

that a large portion of the installed fiber plant in metropolitan areas is older, SMF-28 fiber,

designed to support low bit rate (<10 Gb/s), single wavelength channel applications, dynamic

compensation and novel modulation techniques may be required along certain spans to enable

capacity upgrades in the presence of these effects. The results shown here will be presented and compared to measurements on other links of

the ATDnet and as well as on BOSSNET, a long haul WDM testbed. Other statistical quantities

relating to the DGD and the DAS such as magnitude and vector correlations will be explored.

References:

[1] B. Huttner, C. Geiser, and N. Gisin, "Polarization-induced distortions in optical fiber

networks with polarization-mode dispersion and polarization-dependent loss," IEEE

Journal of selected topics in quantum electronics, vol. 6, pp. 317-329, 2000.

[2] Y. Li and A. Yariv, "Solutions to the dynamical equations of polarization-mode dispersion

and polarization-dependent losses," Journal of the Optical Society of America B, vol. 17,

pp. 1821-1827, 2000.

[3] N. Gisin and B. Huttner, "Combined effects of polarization mode dispersion and

polarization dependent losses in optical fibers," Optics Communications, vol. 142, pp. 1 19-

125, 1997.

[4] M. Karlsson, J. Brentel, and P. Andrekson, "Long-term measurement of PMD and

polarization drift in installed fibers," Journal of Lightwave Technology, vol. 18, pp. 941-

951,2000.

[5] J. P. Gordon and H. Kogelnik, "PMD fundamentals: Polarization mode dispersion in

optical fibers," PNAS, vol. 97, pp. 4541-4550, 2000.

202
Programmable Polarization-Mode-Dispersion Generation

J. N. Damask, P. R. Myers, T. R. Boschi

YAFO Networks, 1340F Charwood Rd., Hanover, MD 21076, jdamask(&vafonet. com

Abstract: Combination of programmable polarization-mode-dispersion generation with numerically

generated PMD statistics, field measurements of temporal PMD evolution profiles, and PMD measurement

instrumentation rounds out a complete suite of tools that can provide reliable tests as to the long-term

performance of an optical transmission system or any active subsystem such as a receiver or PMD

compensator.

1. Introduction

It is an unfortunate misconception in much of the optical telecommunications industry that simply

because fiber-generated polarization-mode-dispersion (PMD) is arbitrarily complex, testing a

receiver for PMD tolerance needs to be arbitrary or complex [1-7]. The reality is that much

detailed performance information can be derived from systematic measurements with a robust

programmable PMD generator, numerically generated PMD statistics, and field measurements of temporal PMD evolution profiles. In particular, the total outage probability (TOP) of a receiver,

transmitter / receiver pair, or entire system can be estimated by combining measurements of receiver sensitivity to first-, second-, and higher-orders of PMD with PMD probability statistics [8]. The mean-time-between failure (MTBF) and mean-duration of failure (MDoF) can also be

estimated when the temporal PMD-evolution profile of a fiber link is measured [9-10]. The

estimators TOP, MTBF, and MDoF form evaluation metrics necessary for apples-to-apples

comparisons between system designs as well as for development of PMD mitigation techniques.

The paradigm followed in this paper requires direct measurements of receiver performance

against PMD stress. PMD statistics are relegated to analysis rather than laboratory inputs. Direct measurements of receiver performance are essential due to the many factors that make numeric

simulation of the receiver unreliable. Typical link receivers use square-law detectors, electrical band-limiting filters, and limiting amps. State-of-the-art receivers can also use active phase and

threshold adjustments to tune performance. Moreover, a receiver in an optical link is sensitive to

linear effects, including noise accumulation, chirp, chromatic dispersion, polarization-dependent

loss, PMD, and jitter; and non-linear effects, including nonlinear pulse propagation, nonlinear

polarization rotation, and forward-error correction. To date, the industry has developed actual or

at least de facto standards on how to test for most of these impairments, isolated or combined.

PMD testing, however, has remained an outlier. The metrics to gauge a successful PMD generator implementation include: a) a complete

addressable PMD space; b) stable PMD (and SOP) at any state; c) predictable PMD generation;

d) repeatable PMD generation; e) access to 1

s,-order PMD, to 2

nd -order PMD components

depolarization and polarization-dependent chromatic dispersion (PDCD), and higher PMD orders;

f) good optical performance such as insertion loss and PDL. Conspicuously absent is any

requirement to match PMD statistics. A complete addressable PMD space means that any PMD

state can be generated without regard to the iikelihood that a fiber would arrive at that state.

203
2. Mapping a Transceiver for PMD Tolerance

The first step to qualifying a transmitter / receiver pair for PMD tolerance is to create a Tx/Rx

map. Figure 1 illustrates a basic test setup to automatically generate a PMD tolerance map. A

map is created by inserting a programmable PMD source between the transmitter and receiver. In order to cover all projections of the input state of polarization (SOP) onto the PMD vector, a

polarization scrambler is added before the PMD source. In cases where the receiver is preceded

by a polarization-tracking subsystem, such as a PMD PMD

compensator, a second polarization scrambler is required after the PMD source to scramble the

output Principal State of Polarization (PSP) of the PMD

source. An actual system link or a lumped model of one is located

after the PMD source and

TxI

Pol Scr SourcePol Scr I System Rx

BERTS

Computer Control

Fig. 1: Schematic diagram of an automated test set to create a PMD

tolerance map of the Tx/Rx pair. A map may use 200 PMD states.

scramblers. A typical lumped model is a noise source and low-PMD fiber spool to establish a known OSNR and level or chromatic dispersion. A BERT set is used to measure error rate, Q, or Q-penalty, depending on the application. Computer control is used to coordinate error measurements with the PMD state, OSNR setting, etc. One point to note is that the dwell time at any PMD state needs to be long enough for the first polarization scrambler to cover the Poincare

sphere. In practice this can take about 5 minutes using a commercially available fiber-based

scrambler. Haunstein has performed detailed analysis to show that polarization scrambling is about as pessimistic as launching known, worst-case polarization states [11]. The number of PMD states addressed to create a map depends on the application. The

first map of any receiver would likely cover 200 pre-determined, well separated states. It is reasor.able to suppose that a program can be written to adaptively measure states to trace performance contours; however, no such program has been written to date. Once a receiver

profile is known, spot sampling is typically performed to check for consistency. Figure 2 shows

two Tx/Rx maps, each measured using 150 PMD addresses in DGD, SOPMD space. The

SOPMD space was depolarization only. Regions of similar color indicate the same error-rate. Each map took about 13 hours to measure. The mapped receivers are clearly characteristically

different. In the first case, the receiver is largely sensitive to both DGD and SOPMD. In the

I

a

30 « 50 60 DO) (ps)

mats

2000

20 .» 40 50 60 70 DGD(ps)

Fig. 2: Two receiver maps made with a programmable PMD source. Each map is generated with 150 states. The

map on the left exhibits sensitivity to both DGD and SOPMD. The right map is much more tolerant to SOPMD.

204
0>0 0.5 1j0 1.5 2.0 2.5 3.0 DGO / <t>

3.5 day

50 min

0) 30 sec Oi

S3= 0.3 sec

3.0 ms

30 us

0.3 \is

1 1

- Receiver A

Receiver B /

5 10 15 20 25 30 Mean Fiber PMD <t> (ps)

35

Fig. 3a Computer generated universal joint probability contours of 1

st - and 2

nd-order PMD statistics at one optical frequency for a fiber having 2000 sections. The labels indicate the area that remains outside of the associated

contour. The DGD axis scales with <t>, the fiber mean DGD, while the SOPMD axis scales with <x>

2

. Fig. 3b Estimates of TOP over measured PMD space. Since the JPDF scales with <x>, TOP is calculated for any mean fiber PMD given a single BER map across PMD space.

second case, the receiver is quite insensitive to SOPMD but rolls off with DGD alone. Both

receivers are of typical design and built using commercially available components. The PMD

maps qualitatively reveal actual differences in the two receiver designs. Aided by a receiver map,

a receiver designer can work to improve the PMD tolerance.

3. Measurement-Based Estimation of Total Outage Probability

Figure 2 showed the qualitative difference between two receivers. Quantitative metrics, such as

the Total Outage Probability (TOP), can be estimated by combining receiver maps with a pre- calculated Joint Probability Distribution Function (JPDF) for DGD and SOPMD. Figure 3a shows

a calculated JPDF. The function is universal because the DGD scales as the mean fiber PMD

and the SOPMD scales as the square. This function was numerically calculated using 1 billion

fiber instances where each fiber comprised 2000 sections [12]. The contours are of constant

probability. Importance-sampling techniques have been developed by Kath [13] to calculate far more rare contours in DGD, SOPMD space. Such extensive JPDFs are definitely desirable for outage probability calculations. TOP is calculated using the equation

TOP((x)) = Xl(PenaltyT^ > TOL) ?r(%,%„',(%)) ( 1

)

where Pr(x, t^; <t>) is the probability of address { x, tm } given a fiber mean PMD of <x>. I is the

indicator function, and TOL is some chosen tolerance for penalty. What is interesting with Eq. (1)

is that TOP scales continuously with <t>. Figure 3b shows TOP estimates for the two receiver

maps of Fig. 2. The TOP estimates plot outage probability against the parameter axis <t>. The

plots cut off below DGD < 10 ps because the JPDF as used does not have enough visibility into events below 1E-4 and because the paucity of measured points at low PMD values. Work still needs to be done to evaluate the confidence bounds for the TOP values.

205
4. Measurement-Based Estimation of MTBF and MDoF

Total outage probability is a useful metric to estimate the expectation value how many severely

errored seconds in a unit period of time, e.g. a year, one would encounter due to PMD. However,

this metric doesn't really apply in a protected network. A protected network will typically switch to the backup line within 50 ms. After the switching event, the downed line can remain PMDPMD Trajectory Field Data

3500

impaired for hours without affecting traffic (however, of course, the backup route now

runs unprotected). The question then

becomes how many switching events are

likely (MTBF), and what is the average

duration of an outage (MDoF), given a TOP

estimate [9]. This question can be addressed

combhing a receiver map, which

characterizes the receiver behavior, the

JPDF, which provides the PMD statistics, and

a fiber temporal evolution profile (TEP).

A TEP can be directly measured on a

particular fiber route by taking a series of PMD vs. wavelength scans over a longer

period of time. The work reported in [9] conjectured, and supported through

experiment, that the temporal change of DGD

was itself independent of the magnitude of DGD. From this observation they calculated a

correlation time of DGD change and used to that to estimate MTBF and MDoF. Work done at Yafo and reported in [10] extends the conjecture to assert that temporal change in DGD and

SOPMD are independent of any instantaneous DGD, SOPMD magnitudes. Long-term test data was measured by Yafo on a carrier network to determine the autocorrelation time of DGD,

SOPMD change. The experiments supported the conjecture of separability. Figure 4 shows a

particularly severe PMD evolution in time. Once the TEP is estimated, numerical calculations are

45 60 DGD (ps)

Fig. 4: Measured temporal trajectory of DGD, SOPMD

at one frequency on an installed fiber, with the JPDF for <30>ns fiher

! m<~

Wswtangti) Hat Slat* Satactxv SWWfla'JJ-w. BED (pil

F »3- 1 :

Fig. 5: GUI interfaces for 12-stage and 15-stage incoherent PMD emulators. Left, contours of wavelength-flat states

for 12 equal-length stages over 10.0 ps per stage. Wavelength-flat states are those where the DGD and SOPMD are independent of frequency. The outer contour is governed by two groups of six stages. Right, contours of wavelengthflat states for a binary-weighted 15-stage emulator. The stages were 2x1 ps, 2x2 ps, and 1 1x4 ps. While the 15-stage

state space is more complete than the twelve stage. Neither implementation offers continuous motion in PMD space.

206
used to find MTBF and MDoF distributions. While this work is fully reported in [10], the findings

generally are that short durations at severe states are more common than long durations.

Therefore, as TOP increases, the number of switching events expected in a network increases.

5. Incoherent PMD generation

Two types of incoherent programmable PMD sources have been built by the authors. The first type uses 12 equal length birefringent crystal stages, constructed to be passively athermal [14,

15]. The second type uses 15 stages, where the first stage pair is one-quarter the nominal length,

the second pair is one-half the nominal length, and the remaining 11 stages are full length. Half- wave waveplates are inserted between each stage to programmatically induce polarization modemixing. Both source types are predictably operated in wavelength-flat states. A wavelength-flat

state is one where neither the DGD nor SOPMD spectra vary with wavelength. This can only be

achieved when the stages are arranged in two groups. Within a group the extraordinary crystal axes are aligned. The group lengths and the angle of the waveplate located at the interface of the

two groups determines the DGD and SOPMD.

Figure 5 shows the GUI interface used to select the PMD states in DGD, SOPMD space.

The interface on the left shows the 21 wavelength-flat trajectories available for a 12-stage PMD

source. The interface on the right shows the -134 wavelength-flat trajectories available for the

particular 15-stage PMD source built at Yafo. The obvious purpose of the 15-stage design is to increase the coverage of wavelength-flat states within the outer envelope. Both sources have

been used to generate receiver maps at both 10G and 40G. The maps shown in Fig. 2 were

generated using a 12-stage source.

6. Coherent PMD generation

While the programmable sources of the last section have been used for years, there is need for advanced methods of PMD

generation that provide predictable generation

of PDCD. The preceding sources are called incoherent because the birefringent phase

from one stage to the next is unknown at the

time of construction. A new generation of PMD

sources have been developed at Yafo where

the three critical PMD parameters, the DGD of a stage, the mode mixing between stages,

and the birefringent phase of each stage, are

established during construction. An important way to construct a PMD source is where all the DGD stage values are an integral multiple of a unit value, e.g. equal, and where the birefringent

phase of each section is the same. An instrument so constructed generates coherent PMD.

A coherent multi-stage PMD source has been built by the authors where the birefringent

phase is corrected using a classic "A-Vi-V* phase shifter as in [16, 17, 18]. During construction, the

birefringent phase of a section is measured, then the phase shifter is engaged to correct for any

error. Serial application of this procedure results in a fully coherent instrument. As the phase

shifters in the instrument can be actuated, the frequency position of the PMD spectrum can be

25

UWS.O 154S.4 1S4S.8 1M4.6 1M7.Q Wavelength (nm)

Fig. 6: Continuous frequency shift of a coherent DGD

spectrum while the spectral shape remains intact. In a

test, either the PMD source or the signal laser needs

to sweep frequency. Here it is the source that sweeps.

207
shifted without changing the shape of the

spectrum. Figure 6 shows a DGD spectrum that has been frequency shifted over a free-spectral range. The ability to frequency shift the PMD

spectrum is essential when the spectrum exhibits

structure. Without this ability, the transmitter laser frequency would have to be swept in order to experience the structure of the spectrum.

Another feature of this coherent multi-stage source is that DGD and SOPMD can be

independently controlled at the center frequency.

Such independence allows the PMD state to be

continuously addressed across DGD, SOPMD

space, unlike the incoherent generators of the

preceding section. Also, in combination with the

frequency shift ability, the SOPMD magnitude can be resolved into depolarization and PDCD

components. The user can then choose a fixed value of DGD and span the range of available

depolarization and PDCD values. In this way, the coherent PMD generator can address three- dimensional PMD space: {DGD, depol, PDCD}. Figure 7 shows three generated spectra of DGD

and SOPMD. The DGD value at center frequency is fixed at 35 ps while the SOPMD changes

from maximum towards a narrow-band zero value.

15*8.0 IS48J 1S48.4 15+6.6 1549.0 1549.2 Wavelength (ran)

Fig. 7: Three measured PMD spectra from a

coherent multi-stage PMD source. At center frequency DGD and SOPMD are independent. The

PMD spectra exhibit structure. Combined with frequency shifting, a receiver can be inspected across a wide range of PMD states.

Acknowledgement: The authors wish to thank our colleagues G. Gray, P. Leo, D. Longbottom, K. Rochford, G. Simer, as well as the rest of the Yafo engineering staff.

References

[1] I. T. Lima Jr et al, "Polarization Mode Dispersion

Emulator," in Proc. OFC 2000, 2000, Paper ThB4.

[2] S. Lee et al, "A short recirculating fiber loop testbed

with accurate reproduction of Maxwellian PMD

statistics," in Proc. OFC 2001, 2001, Paper VVT2.

[3] I. T. Lima Jr. ef al, "Comparison of Polarization Mode

Dispersion Emulators," J. Lightwave Techno., vol. 19, no. 12, pp. 1872, Dec. 2001.

[4] C. H. Prola Jr ef al, "PMD emulators and signal

distortion in 2.48 Gb/s IM-DD lightwave systems," IEEE Photon. Technol. Lett., vol. 9, pp. 842, June

1997.

[5] S. Lanne ef al, "Demonstration of adaptive PMD

compensation for 40Gb/s," in Proc. OFC '01, Amheim, CA 2001 , Paper TuP3.

[6] Y. Xie ef al, "Enhanced PMD mitigation using FEC

coding and first-order compensator," in Proc. OFC

'01, Anaheim, CA 2001 , Paper WAA2.

[7] W. Shieh, "Accelerated Outage Probability Testing for PMD Induced Impairment," IEEE Photo. Technol.

Lett., vol. 12, pp. 1364, October 2000.

[8] A. Ayer ef al, "Mapping PMD quantifies system

performance," WDM Solutions, April 2002.

[9] R. Caponi ef al, "WDM design issues with highly correlated PMD spectra of buried optical cables," in Proc. OFC '02, Anaheim, CA 2002, Paper Thl5.

[10] P. J. Leo ef al, "Estimation of system outage statistics due to polarization mode disperion," submitted to Symposium on Optical Fiber Measurements, NIST, Boulder CO, Sept. 24-26, 2002.

[11] Haunstein, "Fast PMD penalty measurement using

polarization scrambling," in Proc. OFC '02, Anaheim,

CA 2002, Paper WQ6.

[12] P. J. Leo, internal communication.

[13] S. L. Fogal ef al, "Multiple importance sampling for

first- and second-order PMD", in Proc. OFC '02, Anaheim, CA 2002, Paper ThA1

.

[14] J. N. Damask, "A Programmable Polarization-Mode

Dispersion Emulator for Systematic Testing of 10 Gb/s PMD Compensators," in Proc. OFC '00, Baltimore, MD 2000, Paper ThB3.

[15] J. N. Damask, "Apparatus and method for controlled generation of polarization mode dispersion," US

Patent US6,377,719.

[16] J. Evans, "The Birefringent Filter," J. Opt. Soc. Amer.,

vol. 39, no. 3, pp. 229, 1949.

[17] C. Buhrer, Applied Optics, vol. 27, no. 15, pp. 3166,

1988, and vol. 33, no. 12, pp. 2249, 1994.

[18] J. N. Damask, "Methods and apparatus for frequency

shifting polarization mode dispersion spectra", US

Patent Application US20020080467.

208
Measurement of Differential Group Delay Profiles in Fibers

and in LiNb03 Distributed PMD Compensator

S. Bhandare 1

, D. Sandel 1

, R. Noe 1

, H. Hermann2

, H. Suche2 and W. Sohler

2

'Department of Optical Communication and High Frequency Engineering, department of

Applied Physics, University of Paderborn, Warburger Str. 100, 33098 Paderborn, Germany

Abstract: Frequency-dependent reduced Miiller matrix measurement enables to calculate

the corresponding Jones matrix and hence the impulse response of the devices with

polarization mode dispersion. From the later, the differential group delay profiles are determined by inverse scattering. These allow to identity, emulate and compensate the

effects of higher-order PMD that persists after compensation of first-order PMD.

Introduction: Polarization mode dispersion (PMD) continues to impair high data rate in

optical communication. It is conveniently modelled as a concatenation of differential

group delay (DGD) sections connected by variable polarization transformers. Jones

matrix measurement over optical frequency has allows to verify the structure having only

3 known DGD sections [1]. Moller has synthesized a 2x2 Jones matrix filter that has the

inverse of a PMD fiber characteristic for broadband PMD compensation [2], by

generalizing the basic work done by Harris [3]. Experimental validation of such a filter seems not to have been reported so far nor seems a PMD medium with complicated

structure have been analysed. This method of determining the DGD profiles would be of

particular help for identifying and emulating the effects of higher-order PMD and for the

non-destructive characterization of distributed PMD compensators in LiNbC«3.

Measurement Setup and Principle: A measurement setup basically consists of tunable

laser source, an electrooptic polarization transformer, and a polarimeter (see Fig. 1). Tunable laser source is connected to the input of polarization transformer. Fiber pigtailed

and packaged electrooptic polarization transformer is based on X-Cut, Z-propagation

LiNb03 [4] and is fabricated in house. It is used to generate 8 different polarization

states, which are equally distributed onto the Poincare sphere. These are given as input to the device under test (DUT). A polarimeter is connected to the DUT output. The laser is swept in the steps of 10 GHz between the 1525 nm and 1545 nm where it had no mode

hops. The frequency-dependent 3x3 rotation matrix R of the device, i.e. rows and

columns 2 to 4 of its Miiller matrix are thereby determined. Each of the n (= 8 in our

case) normalized input (in) Stokes vectors results in corresponding output (out) Stokes

vectors. Both vector groups are arranged in form of a matrix

The rotation matrix R is then obtained by

r=s0X(s,X)~'-

Compared to a more compact method [5] with two launched polarizations this gives a

better immunity against polarization measurement errors. Any existing nonorthogonality

of R is removed by singular value decomposition of R according to R = u s v

+

,

209
where u, v are orthogonal (or more generally: unitary) matrices and s is a diagonal matrix

with the singular values. R is then redefined as an orthogonal matrix

R = u v

+ From this frequency-dependent rotation matrix, R, frequency-dependent Jones matrix, J,

is obtained in the form

A B

* * B A

\a\ + B =1

Inverse Fourier transform yields the time-dependent Jones matrix with impulse response

as its elements. Its first column is the finite impulse response to a horizontally polarized

pulse while last column is the finite impulse response to an orthogonally polarized pulse

(vertical). It is sampled with a 785fs period. The structure is analysed on the basis of

sections having DGDs equal to this value.

Tunable

Laser

Electro optic Device — Polarization Under —i*- Polarimeter

Transformer Test

Fig. 1: Experimental setup for DGD profile measurement

The complex ratio between the field components of the first sample (and/or the last sample) allows to calculate retardation, (p, and orientation angle, of the mode converter

present at the DUT output. Once it is known, the mode conversion effect can be easily

removed from the overall impulse response by multiplication by a Jones matrix that is inverse to that which describes the mode conversion. The matrix that is used to describe

this mode conversion effect is considered to be that of an elliptical retarder (ER).

\cos(pll + jVx sin<p/2 j(V2 + jV^smcp 1

2

j(V2 - j V3 ) sin (p 1 2 cos (pi 2- jVx sin <p / 2

V simply equals to V = [0 cosy sinyf and its elements Vi, V2 , and V3 represent the

relative strengths of 0°, 45° and circular birefringence, respectively. Thereby the first sample is confined to one field component and the last sample is confined to an

orthogonal one. Now a time shift of the samples in one field component is possible. It corresponds to a DGD section with principal states-of-polarization (PSPs) equal to these

field components, preceding the already-known mode conversion. The pure time shift

(without differential phase shift) means that the DGD section exhibits a retardation

between the PSPs that is an integer multiple of 2n at the center frequency of the optical

scanning range. It has been shown in [6] that this is not a restriction. The time shift results in a new impulse response which is shorter by one sample. It allows to determine an initial mode conversion which precedes the first DGD section. The impulse which

generates the response and all local slow PSPs, are assumed to be horizontal (Qj

direction, marked by an input arrow in Fig. 2). Experimentally, the inverse scattering

range was chosen as 31.4ps. An inverse scattering algorithm will always display a full length DGD profile (40 sections).

The DGD or PMD profile of concatenated retarders is a concatenated sequence of inputreferred PMD vectors Q, with Q, = R<,i2, . Rotation matrix R<( represents the

210
concatenated retarders preceding the retarder with PMD vector ft, . ft, is the normalized

Stokes vector of a PSP multiplied by the DGD. This holds also for the total PMD vector

ft total =2,ft, , DGDt0Xa] = ft total. In order to allow a zero length of the last DGD section

we mark its direction by an output arrow. It indicates the CW input polarization that

would be necessary to hit the slow PSP of that section.

DGD profiles in Fibers: At first a back-to-back measurement without DUT was

performed. In this case, all PMD vectors (=rods) should be cancelled by oppositely

directed adjacent ones. This is indeed the case (see Fig. 2). The DGD profile travels 20

sections forth, then another 20 sections back on the same path, as if returning from a dead

end. As a consequence, one has the impression to see only 20 sections, which in reality

hide the other 20 sections. Input arrow tip and output arrow back end coincide within

<100fs which is a measurement error since the true DGD was ~0fs. So the simplified

back-to-back DGD profile is a frequency-independent polarization transformation

specified by the arrows.

Input-referred DGD profile for back to bBCk measurement

ni

IP*]

End _

Origin %

Fig. 2: DGD profile back-to-back. DGD

sections run forward and backward

along the same path, ending at origin.

-0.4 -0.6 Q2 [ps] Next DUT (Fig. 3) was a ~1 1 m long polarization-maintaining fiber (PMF) with ~25ps of

DGD. It yielded a straight, 25.12ps long line (32 sections) followed by a short dead end

(2x4 sections).

Input-referred DGD profile for ~25ps PMF

Q2

[PS]

Origin

End j

Input-referred DGD profile tor 2 PMFs with 50% mode conversion

£21

IPS]

End

(^Origin

q: tps]

Fig. 3: DGD profile of one ~25ps DGD

section

Fig. 4: DGD profile of two DGD sections

(22ps + 6ps) with 50% mode conversion.

90° angle is clearly seen.

Figure 4 shows a DGD profile when two pieces of PMF with ~22ps and ~6ps of DGD are

211
concatenated with 50% mode conversion (45° rotation) in between. The long section and

the short section, which also contains a short dead end (2x1 section), are clearly seen. Angle between sections was -90° as expected.

DGD profiles of a distributed PMD compensator in LiNbC^: Fiber pigtailed X-cut,

Y-propagation LiNb03 PMD compensator was fabricated in house, similar to those in

[7]. 70 in-phase and quadrature TE-TM mode converters were distributed along a 94 mm

long waveguide. Insertion loss was 4 dB and PDL was 1.1 dB. Required voltage times

length product for full mode conversion in a single quadrature, with half of the length

belonging to the other quadrature being unused, was 375V-mm. An average DGD was

about 25ps. Without any voltages applied the DGD profile was similar to that of Fig. 3. Fig. 5(a) shows the DGD profile bent in a full circle when two full mode conversions

distributed along the whole chip occur in one quadrature. A dead end with approximately

2x4 sections is also seen because the total DGD value of the chip is less than the inverse

scattering range. In the pigtail-shaped profile of Fig. 5(b) only one and half mode

conversions occur, but they are concentrated at about 3/4 of the total DGD. This

demonstrates the versatility of the distributed PMD compensator with respect to emulation and compensation of higher-order PMD.

Input-referred DGD profile for single loop In UND03 PMDC

Input-referred OGD profile for pigtail shape loop in PMDC

Origin

Fig 5: DGD profile of the LiNb03 PMDC with (a) 2 full mode conversions (b) 1.5 mode

conversions distributed over the whole length ofthe chip

Conclusion: An inverse scattering algorithm for the characterization of devices with

polarization mode dispersion has been implemented. This has allowed the nondestructive measurement of various DGD profiles in fibers and in distributed PMDC in

LiNb03. It can be used as a base for the generation and compensation of higher-order

PMD effects using the proposed PMDC based on the X-cut, Y-propagation LiNbC»3.

Acknowledgement is made to Deutsche Forschungsgemeinschaft for partial funding and

Siemens AG or hardware support.

References:

[1] B.L.Heffner: IEEE PTL 5, 814 (1993)

[2] L. Moller: IEEE PTL 12, 1258 (2000)

[3] S.E.Harris et al: JOSA 54, 1267 (1964)

[4] R.Noe etal: IEEE JLT 6, 1199 (1988)

[5] L.E.Nelson et al: Proc. ECOC II, 10

(1999)

[6] R.Noe et al: IEEE JLT 17, 1602 (1999)

[7] R.Noe et al: Electron. Lett. 35, 652

(1999)

212
Estimation of system outage statistics due to polarization mode dispersion

Paul J. Leo

1

, Daniel L. Peterson Jr.

2

, and Kent B. Rochford 1

1 YAFO Networks, 1340F Charwood Rd., Hanover, MD 21076

2 Transmission Engineering, WorldCom, 2400 N. Glenville, Richardson, TX 75082

Abstract: Measurements of fiber DGD and SOPMD over time and measurements of receiver tolerance

to PMD are combined with a random-walk simulation model to estimate the rate and duration of PMDinduced system outages.

1. Motivation

Polarization mode dispersion (PMD) complicates the assessment of network performance because of its time-varying nature. Quantitatively, PMD is defined as the mean differential group delay (DGD) over wavelength and the statistics for DGD and second-order PMD (SOPMD) contributions are well known [1]. The joint probability distribution function (J-PDF) of DGD and SOPMD, calculated from a simulation of 1 billion fibers, is shown in Figure 1. The

cumulative probability contours show

the likelihood that an instantaneous pair

(DGD, SOPMD) occurs. One can

overlay boundaries demarcating high

DGD & SOPMD combinations that cause transmission impairment, and

calculate the probability that such

impairment occurs. This process, however, gives no insight into the

frequency and duration of events. For example, the instantaneous states at a

given channel wavelength breach the

0.9999 contour 0.01 % of the time. Does

this occur as one 9 s event every day, one 53 minute event each year, or some

combination of events? To answer this question we have combined numerical

techniques with temporal

measurements of DGD and SOPMD on

an installed fiber to simulate the path

that DGD and SOPMD values take as

they evolv ) over time. We measured

the receiver tolerance to DGD and

SOPMD to determine the boundary on

the J-PDF beyond which a system outage may occur. Performing a simulation of DGD/SOPMD evolution

and monitoring crossings of the outage boundary allows us to gather statistics describing the occurrences and durations of PMD-induced outage events.

2. Random-walk model

Recently Caponi used measured temporal DGD data to estimate the mean outage rate and the mean

outage duration in a 9.4 ps embedded fiber [2]. The analysis was based on their observation that the

Maxwellian probability distribution of the DGD and the probability distribution of the change in DGD (in

units of ps/hr) were uncorrelated. This allowed the application of the analytic one-dimensional level crossing problem [3] to determine the mean outage rate. We extend this method to a two-dimensional (2-D) random-walk model that includes the dependence of both DGD and SOPMD on outage occurrence and provides the statistics for outage events. Our method

includes a powerful self-consistency check of the measured rate-of-change distribution of DGD/SOPMD

(the accuracy of which is typically limited by the paucity of experimental data). The data that we collected on two 36ps underground fibers was properly filtered in frequency and time to exclude correlated

DGD

Figure 1. The joint probability density function (J-PDF) for DGD and

SOPMD occurrences in a 25 ps PMD fiber. Also shown (and

described in Section 2) is a starting value (DGD, SOPMD) and

possible next values after obtaining a step size R(t,) from the

distribution of measured rates of change. The sloped line demarcates the PMD values for which performance of a measured

receiver is unacceptable.

213
measurements and to provide an effective 4.73yrs of data. These data verified the previous authors

observation that the magnitude of change in the DGD was uncorrelated with the instantaneous value of DGD. Analogously, when considering both the DGD and SOPMD, we found that the step size taken on a normalized 2-D J-PDF in a given time interval was also independent of the instantaneous (DGD, SOPMD)

value. However the experimental data indicated a strong correlation of the direction of the change on the

J-PDF.

Our 2-D random-walk model consists of starting at an arbitrary position in the J-PDF. The instantaneous

step size R(tj) is chosen from a random variable that is an analytic fit to the experimentally measured

distribution of step sizes. To determine which direction to move, a circle of radius R(tj) (Figure 1) is then

drawn about the current position (DGD(ti),SOPMD(tj)) and the J-DPF evaluated on the perimeter of that

circle. The step direction is determined by a random selection weighted by the J-PDF values on the circle of radius R(tj).

To improve computational efficiency the "weighted circle" that determines the direction was sampled at

1 1 .25° arc intervals and the J-PDF was discretized into a 400x500 grid. Sampling the weighed circle at smaller int3rvals or sampling the J-PDF on a courser grid provided similar results. By keeping a record of the (DGD, SOPMD) visited in a simulation, histograms of the simulated probability distribution of DGD and

SOPMD can be constructed and compared to the expected distributions of the DGD and SOPMD [1]. We found that discrepancies between the simulated and expected distributions could be corrected by

adjusting the tail of the analytic fit to the measured DGD/SOPMD data. The tails of these distributions correspond to the largest step sizes, and these rare steps are not well characterized by the limited amount of experimental data. To obtain accurate statistics of these very rare large DGD/SOPMD changes

requires a prohibitively long measurement of the DGD and SOPMD on a given fiber. Thus we have

employed a self-consistent feedback procedure, whereby the long-range tail of the stepsize distribution is adjusted so that the correct DGD /SOPMD statistics result from the simulation. We believe this provides some advantage over the integral technique where the stepsize distribution is assumed to be correct a

priori over its entire range. Figure 2 shows the DGD and SOPMD results obtained from two step-size

distribution fits and compares these to the expected probability distributions for DGD and SOPMD. The

step size distribution "Fit 1" falls off as exp(x

0 25

) and using it for the simulation overestimates the

probability of high DGD and SOPMD (Figure 2). Our simulations used a fit that decreases as exp(x°

15

) (Fit 2).

As the simulation runs, the (DGD, SOPMD) states walk about the J-PDF. If an outage boundary is exceeded, i.e. the PMD state is one that produces penalties sufficient to cause a transmission system

Instantaneous DGD / <DGD> Instantaneous SOPMD / <SOPMD>

Figure 2. DGD and SOPMD probability densities obtained from random-walk simulations, plotted against the known probability distributions for two choices of rate-of-change fits. Fit 1 overestimates the step sizes for rare events.

214
outage, we record the outage time and, by monitoring when the PMD state again crossed the boundary,

the duration of the outage event. We use this data to form histograms of outage occurrences and

durations. As a final check a one-dimensional random walk (considering only DGD) was performed using

this procedure, and the predictions for the mean outage rate and duration were found to be in excellent agreement with those obtained using the integral method [2].

3. Measurements of DGD/SOPMD evolution and system penalties.

Our random walk method requires a measurement of the first- and second-order PMD over time in a

target fiber to obtain the PMD rate of change distribution. In addition, measurements of the effect of PMD

on OC-192 system performance are needed to set an outage boundary. For our target fiber, we chose a 3-span, 1 10km route buried along railroad tracks in Texas. Two fibers from the first span were loopedback and connected to a tunable laser and commercial polarimeter to perform Jones Matrix Eigenanalysis

(JME) measurements [4]. At each wavelength the Jones Matrix was measured, and appropriate

numerical derivatives calculated over pairs of wavelengths to obtain DGD and SOPMD. A 20 nm

wavelength range (using 20 pm steps) was measured every 1.6 hours for 174 hours on this 36 ps PMD

fiber. (Sample spectra are shown in Figure 3). The measurement was repeated using a 36ps fiber pair on the third span with similar results. We estimate that the DGD and SOPMD values have better than

10% uncertainty, based on laboratory measurements of a stable programmable PMD generator [5]. These data sets were used to form the time-derivatives required for the simulation. 2400 System penalties from PMD are measured using noise-loaded bit-error- rate (BER) measurements. The BER is measured at several optical signal-tonoise ratios (OSNRs) by attenuating the

10Gb/s NRZ transmitter signal just

before an optical amplifier. First, we obtain

the back-to-back characteristic of the

transmitter/receiver pair with no

impairments. Next a programmable

PMD generator, located between

polarization scramblers, is placed after the transmitter. The BER vs. OSNR

curves are then measured for various

combinations of DGD and SOPMD. The 1540 1544 1548 1552 1556 1560 Wavelength (nm)

Figure 3. A sample of the DGD and SOPMD spectra for one measurement interval. system penalty for each PMD is defined as the

increase in OSNR (compared to the back-toback curve) for which BER=10"12

. All receivers show increasing penalty with increasing DGD. The tolerance to SOPMD is less predictable and we have observed that a remarkable number of commercial receivers also show increasing penalty with

increasing SOPMD (at a fixed DGD).

Each system has an OSNR margin that is allotted to various parameters that degrade performance (for example, chromatic dispersion, self-phase modulation, PMD, etc.). For our example, we allow 3 dB of OSNR penalty to be allotted to PMD; thus values of PMD that have > 3 dB penalty are unacceptable and

considered an outage. An outage boundary based on mapping the PMD penalties on a commercial

receiver is shown in Figure 1 as a nearly vertical line rising from 45 ps DGD; states to the right of this line show > 3 dB penalty.

4. Results

We used the outage boundary shown in Figure 1 that includes the additional receiver dependence on SOPMD; thus any (DGD, SOPMD) pairs to the right of this line are considered outages. Each simulation was run for an equivalent to 700yrs (« 6 million steps) and results scaled to a 20 year period. The

resulting outage histograms for a fiber with 25 ps PMD are shown in Figure 4. Our random walk model

215
Outage Duration (hrs) Time Between Outages (hrs)

Figure 4. Histogram of outage events on a 25 ps PMD fiber scaled for a 20 year time period. The random-walk

simulation provides statistics for the duration of outages and the time between outage events.

predicts that outages will occur an average of 38 times per year. The mean outage time is 10 hours,

though the outage durations ranged from 4 mins to 6.7 days on this fiber. We verified our random-walk model by comparing with the measured outage performance of the

characterized receiver over the installed fiber we measured in the field. A 1+1 bi-directional OC-192

system was provisioned on the 110 km, 3-span route using fiber with a 25ps PMD. Chirped NRZ was

transmitted through amplifiers at each span termination to a commercial receiver similar to the type

mapped for PMD tolerance. No forward error correction was used during the tests. Bit error-rate (BER)

performance was measured using the raw SONET data stream. Over a 25 day period, outage events

occurred on three separate instances; day 2, day 12 and day 17, or roughly once every 8.3 days. As a comparison, our simulation of outages on a 25 ps fiber for this receiver suggests an outage would occur

every 9.6 days.

5. Conclusions

A new random-walk model uses probability distributions derived from measured fiber data to provide new

insight into the effects of PMD on system performance over time. This method includes a self- consistency test to judge the quality of measured data. Measured system degradation due to PMD,

mapped by using a programmable PMD source, can be used to set thresholds defining outages. Running

this random walk model with an outage threshold provides statistics that describe the quantity and

duration of PMD-induced outages over time.

These methods are useful for evaluating the effect of rare outage events caused by PMD. This can be

applied to the characterization of receivers and PMD compensators, and calculations of service

availability in the presence of time-varying phenomena such as PMD.

6. References

1. G.J. Foschini, L.E. Nelson, R.M. Jopson, and H. Kogelnik, "Probability densities of second-order polarization

mode dispersion including polarization dependent chromatic fiber dispersion," IEEE Photon. Technol. Lett., 12, p.293 (2000).

2. R. Caponi, B. Riposati, A. Rossaro, M. Schiano, "WDM design issues with highly correlated PMD spectra of buried optical cables," in Proc. OFC '02, Anaheim, CA, 2002, Paper Thl5.

3. A. Pap->ulous, Probability, Random variables, and Stochastic Processes, 3

rd ed., McGraw-Hill, New York (1991).

4. B.L. Hefner, "Automated measurement of polarization mode dispersion using Jones matrix eigenanalysis," IEEE

Photon. Technol. Lett. 4, p. 1066 (1992).

5. J. Damask, "Apparatus and method for controlled generation of polarization mode dispersion," US Patent - US6,377,719.

216
Low-coherence interferometric measurement of differential' group delay

and its dispersion to second-order in polarisation maintaining fibre

Donal A. Flavin1 Roy McBride2 and Julian D.C. Jones

3

Department of Physical and Quantitative Sciences, Waterford Institute of Technology, Waterford. Ireland.

Department of Mechanical and Chemical Engineering, Heriot-Watt University, Riccarton, Edinburgh EHI4 4AS. UK

Department of Physics, Heriot-Watt University, Riccarton, Edinburgh EH 14 4AS. UK

Abstract

We present an interferometric technique for measurement of differential group delay (DGD) and its dispersion in polarisation maintaining fibres for a wavelength range of over 200 nm. The approach yields measurements from analysis of the phases of the Fourier transforms of a pair of interferograms, obtained

in a tandem interferometer. The technique is demonstrated to measure DGD and its dispersion to secondorder, with measurements immune to asymmetry in the interferogram being processed.

Introduction

In recent publications, the incorporation of polarisation maintaining fibre (PMF) elements in active schemes for PMD mitigation has been widely reported [1]. There has also been realisation that pulse

shape and distortion in such systems is governed not alone by the PMD vector but also by its higher-order

dispersion [2,3]. This leads to a critical interest in characterisation of the dispersion of differential group

delay (DGD) of PMF. Interferometric time domain techniques are often used to characterise fibre birefringence dispersion [4,5]. Typically two interferograms, corresponding to the individual propagation

modes of the sample, are captured. Such approaches require a sequence of measurements at a range of

wavelengths to determine birefringence over a broad wavelength range.

Here we propose and demonstrate an in-line interferometric scheme for measurement of DGD and

DGD-dispersion to second-order on PMF sections over a broad wavelength range, based on only two

OPD scans in a tandem interferometer. From the phases of the Fourier transforms of the interferograms, we determine the DGD parameters for a broad wavelength range, extending over 200 nm beyond the PMF's cut-off wavelength.

Tandem interferometry for DGD and DGD-dispersion measurement in PMF

Representing the propagation constants of the fast and slow eigenmodes of polarisation-maintaining

fibre as j3/a)) and /^(co) respectively, we define the differential propagation constant /3«5(co) as

fj s (co) = (lj(co)-

P

s {co) ; each term is explicitly dispersive. The corresponding differential phase

accumulated over a length L is then <ps (co) = fi 5 (co) L . The DGD and the i

th -order dispersion of DGD,

represented as z5 (co) and Tg } (co) respectively, can each be defined in terms of fi 5 (co) and its derivatives

relative tu optical frequency:

, dp6 (co) 1 dfe(a» 0) dfifV) _ 1 d<pl

+i) (co) rs (co)=— = -— , t5 (co) = - — (i)

dco L dco dco{ ' L dco

The experimental arrangement in Fig. 1 is designed for DGD and DGD-dispersion measurement on

the length Lxy of PMF element between points X and Y. The technique is based on the capture of two

217
interferograms; the first interferogram arises from mode-coupling induced at X , and the second for the case when the coupling point is transferred to Y.

Light from the low-coherence source is linearly polarised, and launched into the fibre to populate

only one of its eigenmodes. A localised transverse stress is applied at test point X, thus causing partial

coupling of light to the second eigenmode. The beam transmitted through the polariser A is then a linear combination of the eigenmodes propagating between X and the analyser, i.e. from the point at which the eigenmodes separate to the point of their recombination. This beam is made to illuminate a temporally-scanned

Michelson interferometer, and the resulting low-coherence interferogram is detected at Dl.

s EEH PMF

HeNe

Ml

M3

M4

UD2 lil

Reference

Interferometer

BS

MTS

Dl

This arrangement behaves as a tandem structure: the primary

interferometer is formed by the section

between X and the analyser, incorporating

the PMF section of length Lx and the air- lens section path of length Lc ; the Michelson acts as the local reference

interferometer. Scanning the OPD in the Michelson then produces a set of central and satellite interferograms associated with tandem

interferometry [6], provided the DGD in the PMF section exceeds the coherence length of the source.

Fig.l The optical configuration: S, low-coherence source,

linearly polarised with polarisation adjusted to populate only

eigenmode of the PMF; Ml, M2, M3, M4, mirrors; A, polariser;

Dl, D2, photodetectors: MTS, translation stage.

The captured satellite interferogram can be represented as [7]:

hsati?) <* RefcdOOl =Re ^G(co)exp{-upxs (o))}exp{-wn}d(o (2)

where x is the group delay imbalance in the reference interferometer, yXd (t) is the dispersed mutual

coherence function, G(co) is the normalised source spectrum, and (pxs (a>) is the differential phase

accumulated over the lengths Lx and Lc. From Eqn.2, we can derive ^xs (co) from the phase of the inverse Fourier transform of the satellite interferogram. Similarly, repeating the experiment for the case where the mode coupling is induced at Y

rather than X, gives a satellite interferogram /ysat (T) , from which we can determine the differential phase (j)YS (a>) for transmission through the PMF section of length LY and the air-lens section Lc.

The differential propagation constant Ps (co) for the Lxy section is then measurable in terms of ^>x5 {(o)

and (f) YS (a>) , and can be expanded in a Taylor expansion about a reference frequency coQ:

&(©) = J- {0^ (<o)-^5 Vo) (o)-(D0 )/i\ (3)

where j3^''((y 0

) are the i

th derivatives of (3 s (co) with respect to o> at co = Q)o- The residual birefringence

within the length Lc is common-mode and does not enter Eqn. 3.

Thus, in principle, a single polynomial fit to the phase {<px& {co)-<pY5 {(o)\ yields measurements of

the section's DGD, ts {(Oq

) = ^''(ft)0 ), and /""-order dispersion, t

{s

l) (Q)0

) = f}

{5

i+l> (a>0 )

, for any optical

frequency co0 in the source spectral range. However, for both satellite interferograms, though digital

218
signal processing will recover phase values for <j) xs (co) and </) y5 (ct;) at a series of uniformly distributed frequencies across the source spectrum, the individual

phase measurements are recovered modulo-2;r radian. Neverthe'ess, by sampling the interferograms within the Nyquist criterion, there is no ambiguity in the differences between the neighbouring phase measurements. Thus, though the measurement of

obtained from the polynomial fit is ambiguous, the required measurements of DGD and its dispersion at optical frequency (O=(o0

, obtained from

the values /^"(cOq) and higher derivatives off3 s (a)

,

are measured without ambiguity.

Experiment and Signal Processing

The fibre under test was York HB 750, with a

cut-off wavelength of 640 nm. The combination of a miniature tungsten-halogen lamp with Si photodetectors gave a detectable spectral range from

278 THz to 480 THz, (625 nm to 1075 nm), thus

facilitating our study over a wavelength range well beyond the cut-off wavelength of the fibre. In the experiments reported here, the points X and Y were 10.491m and 3.601m from the end-facet; thus the section '.ength Lxy was 6.890 m. Precision

calibration of the OPD scan was achieved by

processing the complex-valued analytic signal of the high coherence interferogram derived from the HeNe

laser and simultaneously captured during the scan

[8]. The presence of high-order dispersion of DGD

was immediately evident from the visibility profiles

of the interferograms. Figs. 2 (a) and 2(b)

respectively illustrate windowed central and satellite interferograms obtained for an OPD scan in the reference interferometer for mode coupling at the test point X; in each case the window is « 1000

femtoseconds ( = 300 |im). The central interferogram is consistent with a source coherence

time of ~ 50 fs (coherence length of = 17 |im). The

corresponding satellite interferogram shows

dramatic high-order dispersion-induced asymmetry

and broadening, with an interferometric signal

extending over a range exceeding 800 fs.

Fig. 3 (a) shows the sequence of phase values

200 400 600 800 OPD (femtoseconds)

Fig. 2: Windowed sections of the central and

satellite interferograms

r 1550

- 1540

- 1530

- 1520 ? - 1510 it

- 1500

- 1490

- 1480 > - 1470

- 1460

- 1450 350 375 400 425 450

Optical frequency (THz)

475

340 360 380 400 420 440 460 480 500

Optical frequency (THz)

Fig . 3: (a) unwrapped differential phase, <j)xs, over the range 353 THz to 475 THz (630 nm to 850

nm) recovered from the processing of the interfer- ogram of Fig.2 (b), together with the DGD, Ts ((0) , measurement at 0.2 THz intervals within the range;

the inset shows the individual DGD measurements

for the range from 402 THz to 403 THz.

(b) the first- and second-order DGD-dispersion measurements at 0.2 THz intervals over the full range

219
for (j) xs (co) , recovered modulo-27t, from the unwrapped phase of the Fourier transform of the satellite interferogram of Fig. 2(b) over the frequency range 353 THz to 475 THz (630 nm to 850 nm). The phase can be readily corrected for the nonzero OPD by processing the HeNe interferogram in the interval between true zero, as identified by the central interferogram, and the window origin [9].

Corrected phase curves for the interferograms arising from coupling at X and Y were obtained and

subtracted to yield the phase data for {(px5 (co) - <pYS (ft))}. From our earlier considerations, the DGD and

DGD-dispersion at a specific frequency co0 is measured unambiguously from the polynomial fit to this phase data. We performed third-order fits to the data for a sequence of reference frequencies at intervals of 0.2 THz over the range 353 THz to 475 THz. Thus we obtained measurements of DGD, Ts (co) , and

DGD-dispersion to first and second order, T^'(ft)) and T^

2) (ft)) respectively, for the full frequency range. These measurements are represented on Fig. 3(a) and Fig. 3(b). The precision of the group delay

measurement is better than 0.2 femtoseconds, corresponding to a precision of = 0.08 fs/m in the DGD

measurement for the 6.89 m PMF section. .

Discussion and Conclusion

The technique yields DGD and dispersion measurement over a broad wavelength range from the processing of the single pair of interferograms. In comparison with "centroid location" techniques, it obviates the need for a set of experiments using a narrow range of wavelengths at a series of different mean wavelengths. It also minimises the limitations associated with broad source bandwidth and

consequent interferogram overlap of interferograms corresponding to the individual propagation

eigenmodes [4]: in our case the critical separation is between the central and satellite interferogram; the former narrows with increased bandwidth and the latter broadens in a direction away from the central interferogram Further the technique benefits from increased bandwidth, which improves the accuracy of

the polynomial fitting to the phase curve. We have reported an interferometric technique for in-line measurement of DGD and DGD-dispersion

to second-order over a broad wavelength range (630 nm to 850 nm) for sections of polarisation

maintaining fibre. The measurements are obtained by tandem interferometry, from the processing of a

single pair of interferograms, arising from induced mode coupling at the extremities of the section. The

DGD and dispersion are determined from polynomial fits to the phase of the Fourier transforms of the interferograms arising from two OPD scans in the reference interferometer. The measurements are immune i d the dispersion induced broadening and asymmetry of interferograms.

References

1. D. Penninckx and S. Lanne, Optical Fiber Communication Conference 2001, OSA,Technical Digest),

TuP,pp. 1.1-1.4.

2. H. Kogelnik, L. E. Nelson, J. P. Gordon, and R. M. Jopson, Opt. Lett, 25, 1, pp. 19-21, 2000.

3. A. Eyal, Y. Li, W. K. Marsall and A. Yariv, Opt. Lett., 25, 12, pp. 875-877, 2000.

4. P. L. Francois, M. Monerie, C. Vassallo, Y. Durteste, and F. R. Alard, Journal ofLightwave

Technology., 7, 3, pp 500 - 513, 1989.

5. L. Thevenaz, J-P Pellaux, N. Gisin, and J-P. VonDerWeid, Journal ofLightwave Technology, 7, 8, pp.1207- 1212, 1989.

6. Y. J. Rao and D. A. Jackson, Measurement Science & Technology, 7,7, pp.98 1-999, 1996

7. D. A. Flavin, R. McBride and J.D.C. Jones, Optical Communications, 156, pp. 367 - 376, 1998.

8. D. A. Flavin, R. McBride, J. G. Burnett, A. H. Greenway and J. D. C. Jones, Optics Lett., 19, 24, pp. 2167-2169, 1994.

9. D. F. Murphy and D. A. Flavin, Applied Optics. 39, 25, pp. 4607-4615, 2000.

220
AUTHOR INDEX

A 1m. T ADe, i. on8 / Achten, F.J 1 A 1 101

/\iien, ^nns>iopner 1iyj

Ampem-Lassen, E. iuy

Argyros, Alexander

Barlow, Arthur J. on i a< Zy, 1UD

Barreiro, C. 1 <"7 lj 1 rjarton, U.w. in

tsarton, M.J. in

Bassett, Ian M. 135

Batagelj, Bostjan 11 D a\ LCI , vj

.

1 no

Bernard, F. /y

OlldllUalC, o. L\jy

OlllglC IV1. Biondi, Gino 1 0 1 lot

Boisrobert, C. /IQ K1 4y, jj

DOSCnl, 1 .K. TA1 ZVj

Breuer, D. 1 C7 18/

Campbell, C. 79

Castle, Richard Zy

Chapeleau, X. 4y, j

j

Chung, Youngjoo 1 1 "3

Clausen, Carl Baslev A 1 41

^urwiii, j\.ns>idn i_>. 7

Craig, D.L. 139

Craig, Rex M. 121, 125

Cremer, H. 1 C"7 18/

IvalllasK., J .IN

.

Das, Mini 91

de Hon, B.P. 101

de Riedmatten, H. ID 1 Dragomir, N. 1 AO iuy

Dyer, Shellee u.

A C 1 1< 4j, Izj

Eiselt, Michael 41

Elsey, J. 37

Espejo, R. Joseph 45

Evans, Alan 1

Flavin, Donal A. 217

Fleming, S. 57

Foisel, H.M. 187

Fougeres, A. 157

Fowlkes, J. 139

Frazao, 0. 87

Oaarde, reter B. 143

Gautier, J.-D. 157

Geraghty, David 25

Ghalmi, S. 61

Giles, Randy 19

Gisin, Nicolas 117, 157

Golowich, Steven E. 95

Golub, I. 177

Goodman, M. 199

Gray, Stuart 1 Grosche, E.G. 83

Guttman, Jeffrey L. 33

Hackert, Michael J. 105

Hague, Douglas, C. 195

Haldimann, A. 157

Hallam, Andrew G. 29

Han, Young-Geun 1

1

1

1 1

J

Harris, Subrena 169

Hermann, H. 209

T T 1 O Honkanen, Seppo 25

T T 1 TV A Humphreys, D.A. 79

Huntington, S.T.

1 AO 109

T T~\ * J Ives, David 169

Jasapara, J. 129

Jones, Julian D.C. 217

Kalinowski, HJ. 87

Kaneshima, K. 15

Kang, Jin U. 113

Kath, William L. 181

Kawanami, K. 15

Kawanishi, Satoki 69

Kim, Chang-Seok 113

Kleivstul, Asbj0rn 0. 191

Knudsen, Stig N. 143

Kofler, Jonathan D. 173

Kondamuri, Pradeep Kumar 195

Law, S.H 37

Le Ny, R. 49, 53

Leduc, D. 49, 53

Legre, Matthieu 117

Leo, Paul J. 213

Lopes, P. 87

Lupi, C. 49

Ma, Ning 147

Madasamy, Pratheepan 25

McBride, Roy 217

Meissner, J. 83

Mena, P. 151

Mercer, L. 199

Michna, M.L. 109

Miyagi, K. 15

Mori, Kunihiko 75

Morikuni, J. 151

Morioka, Toshio 75

Morrell, Mike 25

Muktoyk, Mark 1 Murdoch, S.G. 161

Myers, P.R. 203

Namihira, Y. 15

Newbury, Nathan R. 7

Nicholson, J.W. 61

Noe, R. 209

Nogueira, R. 87

Nugent, K.A. 109

Paek, Un-Chul 113

Palsdottir, Bera 143

Patel, P. 79

Peterson Jr., Daniel L. 213

Peyghambarian, Nasser 25

Phan, T.N. 37

Pietra, G. 15

Pinto, J.L. 87

Poon, Andrew W. 147

Prat, Josep 65

Qian, Yujun 143

Ramachandran, S. 61

Reiner, H. 187

Richards, Douglas L. 195

Richardson, C.K. 199

Ritger, A. John 95

Roberts, A. 109

Rochford, Kent B. 213

Rogers, A.J. 165

Runser, R.J. 199

221
bandel, D. 209

Santos, J.L. 87

Santos, Maria C. 65

oardesai, Jti.r. 139

Satyanarayan, M.N. 91

Scarmozzino, R. 151

ocnnier, m. w. on0 / oCnOlQci, f. 1 C"7 lj 1 Shake, Ippei 69

onatalm, o. V. 165

Simova, E. 177

Sohler, W. 209

Soler, Mar^al 65

Sova, Raymond M. 113

Suche, H. 209

Sudb0, Aasmund S.

1 A 1 191

i>wann, William C 125

Tadakuma, M. 15

Takada, Atsushi 75

Takara, Hidehiko 69

i ayior, m.Lf. 139

Tessmann, H.-J. 187

Thyagarajan, K. 91

1 kach, Robert W. A 1 41

van Stralen, M.J.N. 1 A 1 101

Vidmar, Matjaz 11 Vinegoni, C. 15

Wegmuller, Mark 117, 157

Whitlock, B.K. 151

Wicks, M. 53

Williams, Paul A. 43, 1 15

Yamazaki, Etsushi 75

Yan, M.F. 61

Zhao, Y.C. 57

Zheng, W. 139
APPENDIX I - PROGRAM

Scxaa

Tuesday, September 24, 2002

8:30 Opening Remarks: Gordon Day, NIST, Symposium General Chair

Session I. Nonlinear Effects, Chair: William Reed, OFS Fitel

8:45 INVITED: The Unique Measurement Challenges of Raman Amplifiers, A. Evans, S. Gray, M.

Muktoyuk, Corning, Inc.

9: 15 Comparison of Stimulated and Spontaneous Scattering Measurements of the Full Wavelength

Dependence of the Raman Gain Spectrum, N.R. Newbury, K.L. Corwin, NIST

9:30 Fiber Nonlinear Coefficient Measurement Scheme Based on FWM Method with Externally

Modulate DFB Laser Source, B. Batagelj, M. Vidmar, University of Ljubljana

9:45 A Comparison of Six Techniques for Nonlinear Coefficient Measurements of Various Single

Mode Optical Fibers, Y. Namihira, K. Miyagi, K. Kaneshima, University of the Ryukyus, M.

Tadakuma, Furukawa Electric, C. Vinegoni, University of Geneva, G. Pietra, Pirelli Labs

Innovation, K. Kawanami, Muroran Institute of Technology

10:00 BREAK

Session II. Fiber Geometry, Chair: Ka Kha Wong, Northstar Photonics

10:30 INVITED: Monitoring the Optical Network, Randy Giles, Lucent Technologies

1 1:00 Burial Depth Measurement for Ion-Exchanged Glass Waveguides with Different Widths, P. Madasamy, University ofArizona, M. Morell, NP Photonics, D. Geraghty, S. Honkanen, N.

Peyghambarian, University ofArizona

11:15 Accuracy of MFD and Aetr Measurements Using Far-Field Scanning, A.J. Barlow, R. Castle,

PerkinElmer Optoelectronics, A.G. Hallam, Halcyon Optical Services

1 1 :30 Mode-Field Diameter and "Spot Size" Measurements of Lensed and Tapered Specialty Fibers,

J.L. Guttman, PHOTON, Inc

1 1:45 Anomalies in Online Fibre Measurements and Their Implications for Fibre Array Manufacture,

S.H. Law, T.N. Phan, Australian Photonics CRC, G.W. Barton, University ofSydney, M.J.

Barton, J. Elsey, Australian Photonics CRC

12:00 LUNCH

Session III. Group Delay and Dispersion, Chair: Andrew Inenaga, JDS Uniphase

1:30 Performance Characterization of Components with Group Delay Fluctuations, M. Eiselt, C.B.

Clausen, R.W. Tkach, Celion Networks

1:45 High-Resolution Group Delay Measurements of a Hydrogen Cyanide Gas Cell Using LowCoherence Interferometry, S.D. Dyer, R.J. Espejo, P.A. Williams, NIST

2:00 Group Delay and Spectral Response of Free Space Optics Mux/Demux Measurement Using

OLCR, X. Chapeleau, Universite de Nantes, NetTest, D. Leduc, C. Lupi, R. Le Ny, C. Boisrobert,

Universite de Nantes

2: 15 High Accuracy Relative Group Delay Measurements of a Chirped Grating (NIST Telecom Round

Robin), X. Chapeleau, D. Leduc, Universite de Nantes, M. Wicks, NPL, R. Le Ny, C. Boisrobert,

Universite de Nantes

2:30 Direct Dispersion Slope Measurement by Mach-Zehnder Interferometer on Short Length Optical

Fibre, Y.C. Zhao, S. Fleming, Australian Photonics CRC

2:45 Dispersion Measurements on Multiple Kilometer-Length Few-Mode Fibers with an RF Spectrum

Analyzer, J.W. Nicholson, S. Ramachandran, S. Ghalmi, M.F. Yan, OFS Laboratories

223
3:00 Group-Delay Measurements with RF Optical Frequency Scanning, M.C. Santos, J. Prat, M. Solar,

Universitat Politecnica de Catalunya

3:15 BREAK

Session IV. Time and Frequency Measurements, Chair: Janet Jackel, Telcordia

3:45 INVITED: Optical Waveform and Q-Factor Measurement using Optical Sampling for UltraHigh Speed TDM Systems, H. Takara, I. Shake, S. Kawanishi, NTT Network Innovation

Laboratories

4: 15 Frequency-Controlled Supercontinuum Lightwave Source Applied to Optical Measurements with

High Frequency Accuracy, K. Mori, T. Morioka, A. Takada, E. Yamazaki, NTT Network

Innovation Laboratories

4:30 Recent Developments of Excited-state Optical Frequency Standards for Telecommunications,

D.A. Humphreys, C. Campbell, F Bernard, P. Patel, NPL

4:45 Fiber Bragg Gratings as Wavelength References - Development and Characterization, E.G.

Grosche, PTB, J. Meissner, Advanced Optics Solutions

5:00 Simultaneous Measurement of Transverse Strain and Temperature Using FBG Written in HiBi

Fiber, I. Abe1 ' 3

, M.W. Schiller

3

, R. Nogueira1 ' 2, P. Lopes

1 , O. Frazao

4

, J.L. Santos

4

, J.L. Pinto 1 ' 2

, H.J. Kalinowski , Universidade de Aveiro, Instituto de Telecomunicacdes, Centro Federal de

Educacao Tecnologica do Parana,

4INESC Porto

5:15 A Simple and Direct Method to Estimate Long Period Grating Parameters, K. Thyagarajan, M.

Das, M.N. Satyanarayan, Indian Institute of Technology

5.30 SESSION CLOSE

7:00 RECEPTION, REGAL HARVEST HOUSE

Scxaa

Wednesday, September 25, 2002

Session V. Multimode Fiber and Fiber Characterization, Chair: Mike Hackert

8:30 INVITED: A Simplified Model of Modal Dispersion in Multimode Fiber, A.J. Ritger, OFS

Fiber Optics, S.E. Golowich, Bell Laboratories

9:00 DMD Measurement and Simulation on Short Length, 850-nm Laser-Optimised, 50 urn Core

Diameter, GfMM Optical Fibres, F.J. Achten 1 , M. Bingle2' 3

, B.P. de Hon2, M.J.N, van Stralen

1

, ! Draka Fibre Technology,

2 Eindhoven University of Technology,

3EM Software and Systems

9: 15 Determination of Skew in Multimode Ribbon Fibers, A.J. Barlow, PerkinElmer, M.J. Hackert,

Corning, Inc. 9:30 Phase Imaging Methods for Optical Fiber Characterization, A. Roberts, University of Melbourne,

G. Baxter, N. Dragomir, Victoria University, ST. Huntington, E. Ampem-Lassen, M.L. Michna,

K.A. Nugent, University ofMelbourne

9:45 Measurement of Fiber Birefringence Using Lyot-Sagnac Interferometer, C.S. Kim, Y.G. Han,

R.M. Sova, J.U. Kang, Johns Hopkins University, U.C. Paek, Y. Chung, Kwangu Institute of

Science and Technology

10:00 BREAK

Session VI. Polarization and Engineered Fibers, Chair: Julie Taylor, NPL

10:30 Determination of the Degree of Polarization Based on a Coherent Quantum Measurement, M.

Legre, M. Wegmiiller, N. Gisin, University of Geneva

10:45 Visualizing the Limitations of Four-state Measurement of PDL and Results of a Six-State

Alternative, R.M. Craig, NIST

1 1 :00 Four-State Measurement Method for Polarization Dependent Wavelength Shift, W.C. Swann,

S.D. Dyer, R.M. Craig, NIST

224
11:15 INVITED: Measurement of Dispersion in Photonic Bandgap Fibers, J. Jasapara, OFS

Laboratories

11:45 Counting Modes in Optical Fibres with Leaky Modes, A. Argyros, I.M. Bassett, Australian

Photonics CRC

12:00 LUNCH:

Session VII. Cavities and Resonances, Chair: Simon Fleming, University of Sydney

1:30 INVITED: Measurement of Multipath Interference and Resulting Optical Communication

System Penalty, D.L. Craig, M.G. Taylor, W. Zheng, J. Fowlkes, H.P. Sardesai, CIENA

Corporation

2:00 Predicting MPI in Raman Optical Amplifiers by Measuring the Rayleigh Backscattering

Coefficient, P.B. Gaarde, Y Qian, S.N. Knudsen, B. Palsdottir, OFS Fitel Denmark

2: 15 Measurement of Multimode Resonances in Hexagonal Optical Micro-Pillar Cavities, N. Ma,

A.W. Poon, Hong Kong University of Science and Technology

2:30 INVITED: Measurement Requirements for Optical and Optoelectronic Model Verification,

Validation, and Calibration, J. Morikuni, P. Mena, B.K. Whitlock, R. Scarmozzino, RSoft Design

Group, Inc. 3:00 BREAK

Session VIII. OTDR and Component PMD, Chair: Greg Schinn, EXFO

3:30 Photon-Counting OTDR at Telecom Wavelength: High-Resolution and Long-Distance

Measurements, F. Scholder, A. Fougeres, J.D. Gautier, C. Barreiro, A. Haldimann, H. de

Riedmatten, M. Wegmuller, N. Gisin, University of Geneva

3:45 Coherent Speckle in Direct-Detection OTDR, S.G. Murdoch, NetTest

4:00 Full Measurement of the Spatial Distribution of PMD Using Backscatter, A.J. Rogers, S. V.

Shatalin, University of Surrey

4: 15 Polarisation Mode Dispersion in Restricted Optical Bandwidth: An Evaluation of Measurement

Techniques, S. Harris, D. Ives, NPL

4:30 Measurement and Mitigation of Multiple Reflection Effects on the Differential Group Delay

Spectrum of Optical Components, P.A. Williams, J.D. Kofler, NIST

4:45 7t-Shifted All-Fire Sagnac Loop for Characterization of Femtosecond Polarization Mode

Dispersion, E. Simova, I. Golub, Institute for Microstructural Sciences

5:00 SESSION CLOSE

goes

Thursday, September 26, 2002

Session IX. PMD - Field Measurements, Chair: Arthur Barlow, PerkinElmer

8:30 INVITED: Using Importance Sampling to Assess the Effects of PMD on System Performance,

W.L. Kath, G. Biondini, Northwestern University

9:00 Investigations on the Relation Between PMD Coefficient and Cable Installation Year in Deutsche

Telekom Fiber Plant, H.-J. Tessmann, D. Breuer, H.M. Foisel, H. Reiner, H. Cremer, Deutsche

Telekom

9:15 Pulsed Measurement of Polarization Mode Dispersion in Field-Installed Optical Fibers, A.O.

Kleivstul, Telenor R&D, A.S. Sudb0, University Graduate Center-UniK

9:30 Analysis and Comparison of Measuree DGD Data on Buried Single-Mode Fibers, C. Allen, P.K. Kondamuri, University of Kansas, D.L. Richards, D.C. Hague, Sprint Corporation

225
9:45 Statistical Evaluation of Polarization-Dependent Losses and Polarization-Mode Dispersion in an

Installed Fiber Network, C.J.K. Richardson, University ofMaryland, R.J. Runser, M.Goodman,

Laboratoryfor Telecommunication Sciences and Telecordia Technologies, L. Mercer, NRL

10:00 BREAK

Session X. PMD - System Applications, Chair: Casey Shaar, NetTest

10:30 INVITED: Programmable Polarization Mode Dispersion Generation, J.N. Damask, P.R. Myers,

T.R. Boschi, YAFO Networks

1 1 :00 Measurement of Differential Group Delay Profiles in Fibers and in LiNb03 Distributed PMD

Compensator, S. Bhandare, D. Sandel, R. Noe, H. Hermann, H. Suche, W. Sohler, University of

Paderborn

11:15 Estimation of System Outage Statistics Due to Polarization Mode Dispersion, P.J. Leo, YAFO

Networks, D.L. Peterson Jr, WorldCom, K.B.Rochford' YAFO Networks

1 1:30 Low-Coherence Interferometric Measurement of Differential Group Delay and its Dispersion to Second-Order in Polarisation Maintaining Fibre, D.A. Flavin, Waterford Institute of Technology,

R. McBride, J.D.C. Jones, Heriot-Watt University

1 1 45 SYMPOSIUM CLOSE

The Symposium is held in the auditorium of the Department of Commerce Laboratories, 325 Broadway,

Boulder, Colorado. Attendees must register in advance and make accommodation arrangements. Details, can be obtained from Wendy Ortega, NIST, (303) 497-4500, FAX (303) 497-5208,

ortegaw@boulder.nist.gov, or on the web at http://www.boulder.nist.gov/div815/current.htm.

SYMPOSIUM COMMITTEE (G.W. Day, NIST, General Chair, P.A. Williams, NIST, Program Chair)

A. Barlow, PerkinElmer S.C. Fleming, U. of Sydney

D. Franzen, NIST N. Gisin, U. of Geneva

M. Hackert T.A. Hanson, Corning

A. Inenaga, JDS Uniphase J. Jackel, Telcordia

K. Okamoto, NEL W. Reed, OFS Fitel G. W. Schinn, EXFO C. Shaar, NetTest

J. Taylor, NPL K.K. Wong, Northstar Photonics

226
ill X Technical Publications

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