Uw) = 1P<P?K(w)K(@)" Ho) @aay
= WP<P*[K(@)? HO). ~
With these substitutions, x(w) becomes
X(®) = N<I>|K()7(1 + n<EP p(w) . (4.1.12)

Thus the spectral density of the electric current fluctuations arises directly from (w), which is
proportional to the RIN spectral density of the light. For applications regarding this MAP, K(w)
is referenced to the baseband frequency, and is proportional to the calibration function to be
obtained for the RIN measurement system by application of the standard.

All equations up to this point hold for any kind of light. However, the amplified spontaneous
emission of the RIN standard is represented well by treating it as thermal light. As such it is
governed by Gaussian statistics, for which all space-time correlation functions of the field can be
tepresented by ones of lower-order ([17], section 8.4.1; see also 1.6.3 and 8.5.3 on Gaussian
moment theorem). An important result is that the second-order complex degree of coherence
y(t), from which A(t) is derived, can be found from the first-order space-time correlation
function. Thus the normalized intensity correlations for unpolarized thermal light at a single point
in space ( [17], eqs (8.4.10) and (8.4.24)) can be derived from the degree of coherence:

<AIQAI(t+0)> = Sor ; (4.1.13)

Whereas for polarized thermal light,

16


electron charge and V is voltage), the data should yield a straight line [24]. (The noise power is
2qVAB, which is 2qV in a 1Hz bandwidth.) The voltage values range from 9.39 to 23.66 mV,
with corresponding attenuations from 18 to 14 dB. The first curve is a second-order polynomial
fitted to all data points. The second curve is a linear fit of all points except V = 23.66 mV (which
corresponds to only 12 dB attenuation). The two curves rapidly converge to a straight line with
increasing attenuation (decreasing voltage). At a voltage of 11.82 mV, where the attenuation is
17 GB, the curves are straight lines. This is the normal operating regime for this standard. A
second-order polynomial fit of all points except V = 23.66 mV yields a coefficient of very nearly
zero (slightly negative) for the second-order term. Thus the excess RIN component is too small
to resolve.

A simple argument can be given that further supports our results, and is based on the
manufacturer’s specification of the excess RIN (<- 172 dB/Hz at the operating current of 169 44
mA, where power output is 27.82 mW). At this current and 17 dB attenuation, accounting for all
losses, the optical power incident on the detector is 0.275 mW. Since the Poisson RIN in the
photodetector circuit increases by 1/n, where 7 = 0.77 is the detector quantum efficiency, the
equivalent Poisson RIN at an optical power of 0.212 mW from eq (8.1) is -149.2 dB/Hz. Since
the excess RIN remains <- 172 dB/Hz, the ratio of excess to Poisson RIN would be <0.005
(<0.022 dB).

9. RIN System Calibration Using the Standard and the Laser

To validate the RIN standard and associated MAP, we developed two distinct methods, each
of which uses a precision RIN source, to separately calibrate our RIN measurement system. We
evaluate both methods by comparing calibration results. Because the photon number distributions
differ for the two methods, so too will their calibration functions. By formulating the optical RIN
of each source before it enters the RIN system and the electrical RIN measurement inside, we
derive an equation that relates the response of the system to the two sources. First, we note a
pair of simplifying distinctions between the methods. For the standard, we can consider the

amplitude fluctuations to be of purely second order, that is, devoid of Poisson light, as this

37


Uppy = VAB°(B? C-2B DE+D* F ) var(B(A)) , (7.1.8)

where

4-42
(aay
6P(A)
Be JN
y BA)
8P(A)*
Ce= is
BAYS
TAD
p- Soe TM
7 Bay
ey Oy
7 BAY
aPAy

rey

Resolution bandwidth was shown to be very nearly constant within the wavelength range of
interest, so that the computations were performed at each wavelength using B(A,) = 0.045 nm,
with var(R(A)) = 0.001 nm as determined from the noise-equivalent handwidth. The value of
Ugg used to compute the combined uncertainty is the worst-case value of Uppw calculated
among the RIN measurements for a given filter. These uncertainties are 0.002 dB and 0.006 dB
for filters F1 and F2, respectively. The specific and combined standard uncertainties are shown in
Table 3 for each filter.


ff signal generator rf power meter

Attenuator

C) Attenuator

Electrical
spectrum analyzer

Figure Al. Measurement of the scale fidelity of the electrical spectrum analyzer
using rf signal generator and attenuator, with output power traceable to rf power meter.

90


components that could form a valid standard. The sources compared are listed in column 1 along
with the date of the experiment. The first and second numbers in column 2 represent the average
difference of the Kappas without and with the ESA scale fidelity correction (SFC), respectively
(see Appendix A). Column 3 shows the standard deviation of the average differences of column
2, again, without and with the scale fidelity correction. We list some of the comparisons and their
meanings. Kappa from each of the two amplifiers was determined using all three filters, F1, F2,
and F3, and compared with Kappa from the laser on different days. Thus we might compare
Kappa of EDFA 1+ F1 with Kappa of DFB (experiment of April 27). We also compare Kappa
among various combinations of EDFAs and filters. Thus we compare EDFA1 + F2 with EDFA2
+ F2 (experiment of April 20), EDFA1 + F1 with EDFA1 + F2 (April 29) , and the laser at two
different times: DFB(2) with DFB(3) (experiment of April 13). The behavior for all comparisons
is very similar, with the smallest variation occurring for two different EDFAs using the same filter
(April 23), or the laser with itself (April 23).

We performed a number of comparisons using EDFA1 and EDFA2 with all three filters
in which we calculated the average of the average difference of the two Kappas compared. For
example, we compared each EDFA + filter with the other EDFA using the same filter. We also
compared the laser with different combinations of EDFAs and filters. The results show good

agreement at all frequencies when averaged. The average differences between single data sets, as

shown in Table 4, are quite small.

42



unit bandwidth,6P,(f), measured on an rf spectrum analyzer, with a linear frequency-dependent
calibration function K(f) for the detection system, and divide by electrical dc power P,. We note
that x(f) is proportional to the frequency response of the system, and contains the noise added by

the amplifier. If the excess RIN is much greater than the Poisson RIN, or if we avoid system
losses, the RIN is

K(f) 8P(/)
= (2.3.4)

e

Ri) =

where 6P,(f) is the noise after subtracting the thermal noise floor of the ESA. x(f), can be
obtained from a broadband, flat source of known RIN.

In the electrical domain, the total RIN is also the integral of the RIN over all frequencies, or
over the system bandwidth, BW,

Bw
RIN, = [roe, (2.3.5)
oO

Total RIN can be measured with an electrical filter and an rf power meter in place of the spectrum

analyzer.

3. A RIN Standard Based on Two Different Methods
3.1 Form of the RIN Standard or Primary Method

The form of the RIN standard is shown in Figure 3.1.1. The ASE from an erbium-doped
fiber amplifier (EDFA) is fed through a linear polarizer followed by a narrow band optical filter (1
nm to 3 nm) centered in the 1550 nm range [15,16]. The wavelength spectrum of the ASE from
one of the amplifiers used in this study, EDFA1, is shown in Figure 3.1.2. The EDFA has a built-
in optical isolator and was chosen for its ruggedness. To simplify operation for the customer, we
arranged for a simplified front panel display with only an on/off power switch. The linear polarizer

eliminates the potential for a polarization imbalance between orthogonally polarized modes which

10


Appendix G: Shipping Instructions

The instrument to be shipped should be placed in a padded box with sufficient foam to protect it
from mechanical shock, vibration, and other environmental hazards. The operating manual for the
optical fiber amplifier should be included, as well as specifications for the filter and polarizer. If
appropriate, the customer should specify the operating value of the pump current for the EDFA if it is
adjustable. All cables and connectors needed to calibrate the equipment should be included. All parts
belonging to the instrument will be retumed by NIST.

70


{18] Private discussions with L. Mandel; June, 1999. Mandel acknowledges an error of a factor
of two in eq (9:8.26) of their text; see reference 17. The factor of ¥% in front of the middle

integral should be removed.

[19] Mandel, L. Fluctuations of Light Beams. Progress in Optics, Vol. 2, Wolf, E., ed. New
York: North-Holland Publishing Company—Amsterdam; p. 200; 1963.

[20] Private conversation with A. Girard. EXFO Fiber Optic Test Equipment Corp.; January
1999.

[21] Guide to the Expression of Uncertainty in Measurement. Section H-5: Analysis of Variance,
International Organization for Standardization, pp. 85-87; 1993.

[22] Taylor B.N.; Kuyatt, C.E. Guidelines for Evaluating and Expressing the Uncertainty of
NIST Measurement Results. NIST Technical Note 1297; 1994.

[23] Machida, S.; Yamamoto, Y. Quantum-Limited Operation of Balanced Mixer Homodyne and
Heterodyne Receivers. JEEE Journal of Quantum Electronics, Vol. QE-22, No. 5, p. 617-624;
May 1986.

[24] Cox, M.C.; Copener, N.J.; Williams, B. High sensitivity precision relative intensity noise
calibration standard using low noise reference laser source. JEE Proceedings, Science and

Measurement Technology, Vol. 145, No. 4, pp. 163-165; July 1998.

[25] Box, G.E.P.; Hunter, W.G.; Hunter, J.S. Statistics for Experimenters. New York: John
Wiley; pp. 117-123; 1978.

52


12. References

[1] Agrawal, G.P.; Dutta, N.K. Semiconductor Lasers. New York: Van Nostrand Reinhold; pp.
258-269; 1993.

[2] Obarski, G.E.; Jones, R.D. Relative Intensity Noise Correlates with Beam Profile in an LP11
Mode Vertical-Cavity Surface-Emitting Laser, in Conference on Lasers and Electro-Optics, Vol.
11, 1997 OSA Technical Digest Series, Washington, D.C.: Optical Society of America, pp. 228-
229, 1997.

[3] Coldren, L.A.; Corzine, S.W. Diode Lasers and Photonic Integrated Circuits. New York:
John Wiley; pp. 221-236; 1995.

[4] Petermann, K. Laser Diode Modulation and Noise. Norwell, Massachusetts: Kluwer
Academic Publishers; pp. 157-160; 1991.

[5] Agrawal, G.P. Fiber-Optic Communication Systems. New York: John Wiley; pp. 217, 306;
1992.

[6] Saleh, B-E.A.; Teich, M.C. Fundamentals of Photonics. New York: John Wiley; pp. 405,
489; 1991.

[7] Goodman, J.W. Statistical Optics. New York: John Wiley; pp. 472-477, 1985.

{8] Yariv, A. Optical Electronics in Modern Communications. New York: Oxford University
Press; pp. 449-454, 703-722; 1997.

[9] Obarski, G.E.; Hale, P.D. How to Measure Relative Intensity Noise in Lasers. Laser Focus
World, pp. 273-277, May 1999.

50


The RIN of the standard is determined from measurements of the optical power spectral density
(OPSD) it emits as measured by a high resolution, grating-type, optical spectrum analyzer (OSA). The
RIN is proportional to the autocorrelation of the measured OPSD. Thus the uncertainties that contribute

to the RIN are the repeatability and those that arise from the OSA parameters involved in the
measurement.

The reported results are the average of the NIST calibration measurements made before and after
shipment to the participant, and are summarized in Table I in linear as well as logarithmic units.

Table D1. RIN of the transfer standard (based on 40 RIN measurements).

Frequency range RIN (EDFA + P+ F) Expanded uncertainty
0.1-1.1 GHz V/Hz dB/Hz 1/Hz dB/Hz
1.032510" | -109.9 0.029-107" 0.12
RIN standard Customer's RIN measurement system
C) C) Bias tee Ammeter
>> [of >)
Photo
EDFA +P +F detector 9 ~
pre amp
Electrical
spectrum
analyzer

Figure D1. NIST RIN standard applied to customer’s RIN measurement system.

Folder No. and NIST ID: xx and yy
Date of Report: March 1, 2000
Reference: P.O. No. Mmm, 2/3/00 56


Useful Information for Calibrating the User’s Electrical Spectrum Analyzer
for Scale Fidelity Correction

This section refers to Appendix A of the main document. Application of the RIN transfer standard to
calibrate a RIN measurement system holds true for the rf electrical spectrum analyzer (ESA) set at a
distinct group of function settings, such as sweep time, resolution and video bandwidth, internal
attenuation, etc. Changing a function setting to accomodate a signal requires a new calibration, since
the Kappa then obtained may differ slightly from the original. In addition, each ESA has a unique scale
fidelity factor that accounts for the vertical position of the noise signal on the screen. RIN
measurements for which the rf amplitude noise differs must be weighted with this factor, which like
Kappa, is frequency dependent. The scale fidelity factor can be obtained using an rf signal generator, an
attenuator, the ESA, and an rf power meter. Connector losses should be included and control settings
kept the same as for a RIN measurement. The rf power is recorded at two different positions on the
ESA with and without the attenuator. The scale fidelity correction for signals of varying magnitude can
be expressed as a correction to Kappa at each frequency separately.

Below is an example of how we calibrate the NIST ESA. The attenuation of a 10 dB attenuator is
measured as shown in the top part of Figure A.1 with the signal generator set at 600 MHZ and power
output at -50 dBm. Using the rf power meter the attenuation is measured to be 10.0 dB. With the
signal generator set at 600 MHZ and -—70 dBm, the signal is positioned on the ESA screen as would
occur for an actual noise measurement. The result is recorded with and without the attenuator. When
our ESA is set at 5 dB per vertical division, the scale fidelity, S, is found to increase the difference
between the two readings by 0.15 dB per division. Also, the manufacturer specifies that the amplitude
error must be <0.7 dB over the ten divisions that compose the screen. If the difference between noise
powers at different vertical positions on the screen is 5P, - 5P, (at the same frequency), then the scale
fidelity correction is

OP,

$s, = ———_._—__-
1 8P, +0.03-(6P, - 6P,) (A)

Application of eq (A.1) to Kappa at each frequency (sections 9.1 and 9.2) gives

Folder No. and NIST ID: xx and yy
Date of Report: March 1, 2000
Reference: P.O. No. Mmm, 2/3/00 60


11. Maintaining a Measurement Assurance Program

11.1 Maintaining the RIN Standard

To insure the accuracy and stability of the RIN standard with time, the RIN will be determined
before it is sent to a customer, and again when it is returned. The customer will need only to
connect and disconnect the component chain at a single connector. However, because the
standard must be accurate and valid under substitution of different components, we will perform
any necessary measurements to account for disconnection and reconnection of the components as
deemed relevant for its upkeep. Thus a reference database will be kept to evaluate the long-term
accuracy and stability of the standard.

For example, we began this database by performing a study using EDFA2 with filters F1 and
F2. Eight sets of RIN measurements were taken on seven different days over the course of
several weeks, each set composed of five repeated measurements. Filter F1 was measured on
eight occasions, while filter F2 was measured on four occasions. The five repeated measurements
were taken within a short period of time so that they would be similar within the measurement
occasion. On each occasion the four connectors shown in Figure 3.1.3 were disconnected and
reconnected between each of the five measurements. This relatively small data set, shown in
Figure 7.1.1, fails to indicate the presence of a long-term trend. However, the variability within a
day’s measurements appears to be decreasing. Additional measurements will be required to

monitor the performance of the standard, and validate its long term stability.

11.2 Substitution of Components

Since components composing the standard and the NIST RIN measurement system, such as
the EDFA or the ESA, respectively, can fail and need replacement, it is our intention that this
MAP be validated to account for such changes. We believe that the net effect of any required
changes in components has been accounted for based on our thorough development of the theory
and the precision with which the measurements were performed. Because both the RIN of the
standard as well as the Poisson-limited laser are constant in frequency out to tens of gigahertz,

this MAP should be extendable to such higher frequencies with little or no additional certification.

48


Sy BPA) BPC) ny

BY) B.A, 7
J ) y p . (424)

SPD Ay
[pe

RIN(A) =

This is the most general expression, and accounts for errors in the RIN due to variation in the
wavelength scale (absolute wavelength and wavelength distortion) and resolution bandwidth, as
determined over the entire wavelength span. The shifting parameter does not appear explicitly,
but is defined to exist at the arbitrary shifting value of A;=A,;. Because the RIN of the standard
is very nearly constant from zero shift to many tens of gigahertz, we can simplify this expression

by setting A,= 0, which implies i= 0. This gives

2> ss)
RIN(A=0) = 21 2
PA)

fy ol

7 BA)

(4.2.5)

which is the most general form for the RIN with zero shifting.

Next we consider the shifting equation for the RIN (eq (4.2.4) when the wavelength
distortion is negligible and the resolution bandwidth is constant. Under these conditions,
AA, = AA and B;(A;) = B;; (A;.;) = B for alli andj. Thus the resolution bandwidth is of no

consequence while a AA remains in the denominator. The RIN becomes

aN 2 x OP,(A) OP, Az)
(eo 4.2.6
(Dera) oe
j

20


component is much smaller than the EDFA’s amplified spontaneous emission. For the DFB laser,
the RIN can be considered purely Poisson, as shown previously. Figure 9.1 demonstrates how

each method is applied separately to the RIN measurement system.

9.1 Derivation of the Calibration Equations For the Standard and Secondary Methods

In this section we derive the calibration equations (Kappas, or frequency-dependent
calibration functions) that govern the response of our RIN system to the input RIN of the
standard and the Poisson laser. Let 5P, and SP, be the rf noise measured on the ESA from the
EDFA + F and the laser, and P, ,P, the corresponding electrical dc powers, respectively. Let R,
be the RIN calculated from the optical spectrum of the EDFA + F as measured on the OSA, and
,(@) and k,() the system calibration functions from the EDFA + F and the laser, respectively.
Then for the EDFA + F we must have

6P,()
RA@) = R, = ¥,(@) P = constant . (9.1.1)
Solving for xk, gives
( ) Ry P,
KA@) = .
dO) ~ SD) O12)
For the laser,
Po) _ 2he
R, = k,(@)-—2— = >?” constant , (9.1.3)
- °
so that

38


Application of eq (A.1) to Kappa at each frequency (sections 9.1, 9.2) gives

Kiam” OP)

“ieor ~ $P + 0.03-(P,-OP,) * (A2)

where the subscripts cor and un represent the corrected and uncorrected Kappas, respectively.
This is a most general formula, in which 5P, can be either greater or less than 6P, . If it is
greater, the corrected Kappa increases at the set calibration frequency. If it is less, the corrected
Kappa decreases.

[1] B.N. Taylor and C.E. Kuyatt, “Guidelines for Evaluating and Expressing the Uncertainty of
NIST Measurement Results, NIST Technical Note 1297, 1994 Edition.

For the Director, Report Prepared/Calibrated By:
NIST

G. W. Day, Chief Gregory E. Obarski
Optoelectronics Division Physicist

Sources and Detectors Group

Folder No: bbbb
Date of Report: March 16, 2000
Reference: P.O. No. Tttt ee/yy/nn 69


Measurement Assurance Program for the Spectral Density of Relative
Intensity Noise of Optical Fiber Sources near 1550 nm

Gregory E. Obarski and Jolene D. Splett

National Institute of Standards and Technology
325 Broadway
Boulder, Colorado 80303

This paper provides the documentation to establish a measurement assurance
program (MAP) for the spectral density of relative intensity noise (RIN) of optical
sources. A standard is made available to industry for high-precision calibration of
RIN measurement systems. The device is an erbium-doped fiber amplifier (EDFA)
to which is coupled a linear polarizer followed by a narrow pass-band optical filter.
Measurements show that the spectral density of the RIN is invariant under
attenuation and pump current, and constant from zero to many tens of gigahertz.
These properties render it suitable as a standard for the calibration of high-speed
systems. We characterize the device for use as a standard in the 1550 nm
wavelength range over a radio-frequency (rf) baseband of 0.1 to 1.1 GHz. For the
typical device studied in depth, the magnitude of the RIN is - 109.9 dB/Hz with
uncertainty <0.12 dB over the entire bandwidth. Since the behavior of the RIN
standard can be determined from physical theory, we give a thorough derivation of
the spectral density of RIN in the frequency representation. This derivation has
been absent from the literature. We use this derivation to formulate the needed
numerical RIN equations in spatial wavelength coordinates that are used to
determine the RIN from optical power spectral density measurements made with a
calibrated optical spectrum analyzer. The standard is then applied to calibrate a
NIST RIN measurement system. To further validate the standard we develop a
second calibration method based on a distributed-feedback (DFB) laser having
Poisson-limited RIN. We apply each method to determine the frequency-


Figure 5.2.1.
nm region.

ws

1548.4
1548.2
1548.0
1547.8 4

1547.6 4

Measured wavelength (nm)

1547.4

O Measured wavelength

True wavelength

1567.4

' T ' T ' T y T ’ T ' 1
1547.6 1547.8 1548.0 1548.2 1548.4 1548.6

True wavelength (nm)

Comparison of wavelengths measured by the OSA with the true wavelength in the 1548

1560.6 —
ES tse04 [e) Measured wavelength ‘
£ a True wavelength O
s
S 1se02— °
& J é
o
Be 13600
= 6
ao]
© 15598 4 °
2 J ©
3
S 18896 4
1559.4 a ee To es 1
1559.4 1559.6 1559.8 1560.0 1560.2 1560.4 1560.6

True wavelength (nm)

Figure 5.2.2. Comparison of wavelengths measured by the OSA with the true wavelength in the 1560

mm region.

74


A B c

Laser ' Lossy medium Photo
transmitter | C) such avattenuator ! detector ; Bias tee Ammeter
\ i {
+ . © > 15> Loo)
t i H
H H H
{ 1 t
H : t
Reference plane that Poisson RIN Detector adds
defines total laser RIN increases due shot noise RIN
to losses M
Pre amp
Electrical
spectrum
analyzer

Figure 2.3.1 Basic RIN measurement system.

Nanometer
bandwidth filter

EDFA . .
() Linear polarizer

(with built-in
optical isolator)

Figure 3.1.1. Form of the RIN standard.

71


7054
oo ESA amplitude noise of standard shows the
2 absence of ripple in the 0.5 GHz through 0.6
s GHz range. If present, ripple would appear
o at a spacing of several tens of megahertz. °
2 10
x
2
=
oO
s
o 154
2
fo}
—J
co}
3
2
5 720-4
£
oO
t
OD
uw
728 T T T T 1
0.50 0.52 0.54 0.56 0.58 0.60

Frequency (GHz)

Figure 6.2.3. Absence of ripple on the rf noise from the RIN standard over the frequency bands of
0.5 GHz through 0.6 GHz.

76


. (7.1.3)
d(d-1)

Figure 7.1.1 shows that the variance of the RIN with connector mating over the three week
period is indeed very small. It is 0.002 dB and 0.005 dB for EDFA2 with filters F1 and F2,

respectively.

7.2, Measurement Error From the OSA Parameters

In section 6.6 we showed that the combined errors which may arise from nonlinearity in the
spectral responsivity, and any potential effects of attenuation, could be grouped into a single error
representing an upper bound for the responsivity alone. To determine this upper bound, we
varied the attenuation under constant pump current so that the spectral density level on the OSA
screen varied in direct proportion to the attenuation. We computed the standard deviation of the
RIN values obtained at the six attenuation levels, 0 dB, 3 dB, 6 dB, 9 dB, 11 dB, and 15 dB, from

6. (RIN,- <RIN>Y
U,,, = i TAA
LIN “ 6-1) > ¢ )

without disconnecting or reconnecting any of the fiber components. For filters F1 and F2, the

the following formula,

uncertainties are 0.005 dB and 0.008 dB, respectively. For example, for F1 the uncertainty in the
RIN due to a nonlinear spectral responsivity has an upper bound of 0.005 dB, which will be used
to estimate the total uncertainty in the RIN.

The uncertainty in RIN due to wavelength distortion was determined by applying the
propagation-of-errors formula to eq (4.2.7) with AA = (Ajo, — 4,)/1000 and average wavelength
error of 0.042 nm as determined from the 21 data points of Figures 5.2.1 and 5.2.2. The

31


<AINAKt+1)> = <P? |y(0)/? « (4.1.14)

Returning to unpolarized thermal light, the autocorrelation of the intensity fluctuations in the time

domain is

A)

= <AMQAMED> _ IYO?
<

me 5 (4.1.15)

Now the autocorrelation function of a stationary random process and the spectral density of the
process form a Fourier-transform pair (Wiener-Khintchine theorem). Thus there exists a Fourier
transform of y(t) in the frequency domain that is the normalized spectral density of the optical
field [19],

o(v) = i y(tje 2" dr . (4.1.16)
Since $(v) is single-sided, the inverse relation is

yt) = [opera . (4.1.17)
From eqs (2.1.3) and (4.1.15), the RIN is

RW) = f lY@P eae = f Hw ouev)de . (4.1.18)
mo 0

17


value of 1559.975 nm when read by the wavemeter. The corresponding OSA wavelength
reading was 1559.94 nm. This gives an uncertainty of 0.035 nm (fractional uncertainty of 22-
10°), which falls well within the manufacturer’s specifications for wavelength (+0.5 nm over the
350 nm to 1750 nm range). Wavelength error was measured for many points around both 1548
nm to 1560 nm. For the 21 points shown in Figures 5.2.1 and 5.2.2, the standard deviation is
0.042 nm. This agrees with calibration results obtained by the manufacturer at specific
wavelengths. For example, application of a HeNe laser of wavelength at 1523.1 nm (in air)
yielded a wavelength reading of 1523.13 nm on the OSA. This is an error of 0.03 nm, and in
agreement with our average uncertainty of 0.042 nm. Although the error appears to be small,
application of the propagation-of-errors formula will later show that it contributes significantly to
the total uncertainty in the RIN (section 7.2).

5.3 Nonlinearity of the Optical Power Spectral Density Scale

Since the thermal RIN is a ratio of powers squared (eq 4.2.4), and as such is invariant
under attenuation, absolute power measurements are not required. This simplifies calibration of
the OSA specifically for thermal RIN measurements. However, the potential effect on the
numerical RIN of a nonlinear power spectral density across the wavelength span of the OSA must
be considered. Also, if a slight attenuation effect existed because of wavelength dispersion from
some optical component or connector in the fiber transmission line of the standard, it would
couple with the nonlinearity of the spectral responsivity of the OSA. Thus we determine the effect
on the RIN of spectral responsivity and attenuation in aggregate, and do not attempt to separate
potential contributions that may arise from the two variables. In the simplified eq (4.2.7) for the
RIN, a constant linear scaling error, say €, would cancel if uniformly applied at every noise
power, 5P,(A;), over the entire wavelength span. This follows by substituting «6P,(A;) for each
term. In general, we expect tf to arise mainly from the nonlinear spectral responsivity of the
OSA’s photodetector and any wavelength dispersing components. As such, it is a measure of the
total wavelength or frequency response of the OSA. Thus, on some level of fineness, we expect €;
= €,(A,), so that the uncertainty in noise power will not cancel. In section 6.6, we determine that

Wp; is a small quantity and devise a measurement scheme in which it need not be determined

23


divided by the power squared. If 5p,(A,) is the optical power measured at wavelength A, where
resolution bandwidth is B,(A,), then the optical power spectral density S,A,) at A; is

bP (A)
ay= LL.
SA) BQ) (4.2.1)
INS
Then in the wavelength representation

2 Z
RIN(A) < a [SQ)SQ.+A)dr ; (4.2.2)

0

where P is total optical power, A is wavelength, Z is measurement span, and A is the shifting
parameter in units of wavelength. The integral is not exact since A and v are inversely
proportional (Av = c, from which it follows that AA/Av = -A’/c). Thus a 1 Hz bandwidth will give
a bandwidth in wavelength units of AA = A?/c. This can result in a considerable error in the RIN
when the optical power is significant over ~5 nm or more of the wavelength span. Thus we first
convert from wavelength to frequency units before calculating the RIN.

The total power is obtained from the sum over the incremental power elements in each
resolution bandwidth. The OSA used in these developments measures total power according to

the relation

SPA) 5
B 3(A,)

P->

AA, (4.2.3)

where Ad is the wavelength interval defined by dividing the span by the number of data points
minus one. Rewriting both the autocorrelation of the power spectral density and the optical

power as sums, the RIN evaluated at some arbitrary shift A; is

19


resulting uncertainty is

U,

2
= ¥ OP I 4008004
¢

Sa (S? roo) +57) » (7.15)
& SP(A))? 1 1001 1

A001 apt

where S? ( Ajo) = S? (Ay) = (0.042 nm)’, and j = 1,2,....n, where n is the number of data points.
Since U, is different for each RIN measurement, the U,, used to compute the combined
uncertainty is based on the maximum U, computed for the RIN measurements for a given filter.
The resulting uncertainties are 0.051 dB and 0.017 dB for filters F1 and F2, respectively.

The uncertainty due to variation in resolution bandwidth, U,gw, was computed by applying
the propagation of errors to eq (4.2.5). The propagation-of-errors formula takes the form

_ @RIN \? ,{ arm)? af ORIN)?
Unaw = (2) var(B,(A,)) (2) var(B,(A,)) +. (2) ar(B,(A,))

(7.1.6)

But since var(B, (A,)) = = var(B,(A,) = var(B(A)) , we have

(7.1.7)

Performing the differentiation gives

32


To represent the intensity fluctuations in the time domain, we define A(t) as the autocorrelation in

time of the light intensity fluctuations divided by the square of the average intensity:

<A) A t+t)>
ee (4.1.4)

A(t) =
Then the Fourier transform of A(t) is the spectral density, which we denote by p(w). For
unpolarized thermal light

Vo) - f Mea , (4.1.5)

which is proportional to the RIN.

We now proceed to derive eq (9.8.24) of Mandel and Wolf [17]. Substituting the above
relations into eq (4.1.2) above yields for x(w),

X(@) = f edt Inch f Me) k(t!+0)at!

+7 fi fi R(t )k(t!"\<AM) A(t +t! -t +1))>dt/at")

(4.1.6)
= n<P|K(@)??

+ rf fi fi ES ede
<

= 1<P|K(@)|? + U(@).
If we define a function G(t) as

14


© EDFA1 + Fi
* Laser

Standard deviation / mean (dB)

Figure 10.3.6. Comparison of the frequency dependence of the normalized standard deviation of the four
data sets for Kappa from EDFA1 + F1 (Kappa values shown in Figure 10.3.1) and the corresponding four
data sets from the laser (Kappa values shown in Figure 10.3.3).

°5)

Standard deviation / mean, (dB)

Frequency (GHz)

Figure 10.3.7. Comparison of the frequency dependence of the normalized standard deviation of the four
data sets for Kappa from EDFA2 + Fl (Kappa values shown in Figure 10.3.2) and the corresponding four
data sets from the laser (Kappa values shown in Figure 10.3.3).

88


| ESA amplitude noise of standard
with no apparent ripple.

ESA amplitude noise (dBm, relative units)

T
01 02 03 O04 O05 O06 07 08 09

Frequency (GHz)

Figures 6.2.1. Absence of ripple on the rf noise from the RIN standard over the frequency band of

0.1 GHz through 1.1 GHz.

4675
a
€
5
Q 68.0 4
3
2
& 685
2
o
g
2 «6904
3
2 EE ESA amplitude noise of standard demonstrating
£ lo O the absence of ripple in the 0.7 through 0.85
5 65-4 GHz range. If present, ripple would appear at
4 EP a spacing of several tens of megahertz range.
8 om

70-8 T T T T T T T 1

0.70 072 074 0.76 o7e 0.80 0.82 0.84 oss

Frequency (GHz)

Figure 6.2.2. Absence of ripple on the rf noise from the RIN standard over the frequency band of 0.7

GHz through 0.85 GHz.

75


Kappa (arbitrary scale in dB)

95

T T T T T T T T T “d
04 0.2 0.3 0.4 os 0.6 07 08 0.9 1.0 41

Frequency (GHz)

Figure D2. Graph of the frequency-dependent calibration function, Kappa, obtained for the NIST
RIN measurement system by application of the RIN standard.

Uncertainty Assessment

Estimates of uncertainty for the NIST RIN standard are determined from the repeatability error and the
contributions of the optical spectrum analyzer parameters. All uncertainties related to the standard are

TYPE A evaluations of standard uncertainty, in that each is obtained from measurements. There are no
significant Type B errors [1].

The uncertainties are listed in Table D2. The RIN of the standard is the average of all RIN
measurements used to calculate the repeatability error, Uggp, The uncertainties arising from the optical

spectrum analyzer parameters are nonlinearity spectral responsivity U,, wavelength distortion U,, and
resolution bandwidth Uzay.

Folder No. and NIST ID: xx and yy
Date of Report: March 1, 2000
Reference: P.O. No. Mmm, 2/3/00 58


2.1 Definition of the RIN of an Optical Source

RIN [1, 3, 8] can be precisely calculated from the autocorrelation integral of optical power
fluctuations divided by total power squared. These temporal fluctuations can also be expressed in
terms of their spectral density via the Fourier transform of the autocorrelation integral. An optical
source of output power P(t) and fluctuation 5P(t) has a total RIN, RIN;, given by the ratio of the

mean square of the fluctuation to the square of the average power,

_ <8P(?>

RIN, ;
<P()>?

(2.1.1)

where the time average <6P(t)’> arises from the autocorrelation function A(t) = <6P(t)SP(t + t)
> evaluated at time t = 0. The total RIN, which is dimensionless, can be represented in the
frequency domain by defining a RIN spectral density, which we simply refer to as the RIN. Then
RIN; is also the integral of the RIN, R(v), over all frequencies,

RIN, = i Rw)dv , (2.1.2)
oO

where v is linear optical frequency. This equation holds also for angular frequency units in which
@=2nf, since [R(v)dv = {R(w)dw. The spectral density of the RIN, R(v), is derived by
application of the Wiener-Khintchine theorem [8] to A(t). By equating the right hand sides of eqs
(2.1.1) and (2.1.2), one can show that this spectral density is

R(v) = 2 f Maje?TM at , (2.1.3)


Table 2. RIN for different values of pump current, attenuation, and intensity. To determine the
effect of a nonlinear spectral responsivity, some combinations of pump current and attenuation
were adjusted to give equal values of intensity on the OSA screen.

Pump current (mA) Attenuation (dB) Intensity relativeto | RIN (10 Hz*)
maximum, I,,,,. (dB)

214 0 0 10.296
214 0 0 10.286
187 0 -1 10.294
148 0 -3 10.288
137 0 -4 10.298
100.5 0 -10 10.286
214 1 -1 10.286
214 3 -3 10.304
214 4 -4 10.294
214 10 -10 10.308
187 3 -4 10.308
149 1 -4 10.288
113 3 -10 10.298
185 10 -11 10.306
186 10 -11 10.31

29


Application of the transfer standard to a RIN measurement system

When the RIN of the customer’s device is measured, we first calibrate the NIST RIN system with
the NIST RIN standard. To measure RIN in the electrical domain, we use a bias tee to send the de
photocurrent to an ammeter, while the ac noise is amplified and displayed on a radio-frequency
(rf) spectrum analyzer (Figure F1). The de power is determined with a voltmeter connected across
a 50 Q resister instead of the ammeter. Ifi is the current, v the voltage, and R the resistance, the
de power is P, = Ri? = v/R. The RIN is the noise power per unit bandwidth, 6P,(f), weighted
with the frequency-dependent calibration function K(f) of the detection system (herein referred to
as Kappa), and divided by the electrical dc power P.. Thus,

K(f) 6P.(f)
RIN = ———— = stant
P constant , @.1)

where 6P.(f) is the noise after subtracting the thermal noise floor.

To calibrate the NIST RIN measurement system we apply the RIN standard and measure 6P.(f)
and P,(f). If R, is the RIN of the standard, then from eq (F1) Kappa is

_ Rs PL)

Kf) SP), (F.2)

The RIN of an unknown source is determined by connecting the source to the NIST RIN

measurement system and then measuring 6P,(f) and P.(f). By substituting Kappa into eq (F1), the
RIN is

R .
P, weg &3)

Folder No: bbbb
Date of Report: March 16, 2000
Reference: P.O. No. Tttt ee/yy/nn 65


Table F2. Summary of measurement uncertainties.

EDFA2 + Fl Uncertainty evaluation Standard Standard
Type (A or B) uncertainty (1/Hz) | uncertainty (dB/Hz)

Unep A 0.000561 - 107 0.002
Un A 0.001180 - 107 0.005
U, A 0.012315 - 10" 0.051
Unsw A 0.000419 - 107 0.002
Combined, u, - 0.014475 - 10% 0.06

Expanded, U - 0.029 - 107 0.12

and the contributions of the optical spectrum analyzer parameters. All uncertainties related to the
standard are TYPE A evaluations of standard uncertainty, in that each is obtained from
measurements. There are no significant Type B errors [1].

The uncertainties are listed in Table F2. The RIN of the standard is the average of all RIN
measurements used to calculate the repeatability error, Upgp . The uncertainties arising from the
optical spectrum analyzer parameters are nonlinearity spectral responsivity U,y,, wavelength
distortion U,, and resolution bandwidth Uppy

The repeatability error is calculated from the basic standard-deviation formula. The uncertainties
for the OSA parameters are determined by application of the standard propagation of errors
formula. The combined standard uncertainty u, of the average RIN is determined by combining
the Type A uncertainties (Ugsp, Urn, U;, Upsw ) in quadrature. The expanded uncertainty, U, is
twice the combined standard uncertainty. The values used to calculate the NIST expanded
uncertainties are listed in Table F2.

Folder No: bbbb
Date of Report: March 16, 2000
Reference: P.O. No. Tttt ee/yy/nn 67


Useful Information for Calibrating the User’s Electrical Spectrum Analyzer for Scale
Fidelity Correction

This section refers to Appendix A of the main document. Application of the RIN transfer
standard to calibrate a RIN measurement system holds true for the rf electrical spectrum analyzer
CSA) set at a distinct group of function settings, such as sweep time, resolution and video
bandwidth, internal attenuation, etc. Changing a function setting to accomodate a signal requires a
new calibration, since the Kappa then obtained may differ slightly from the original. In addition,
each ESA has a unique scale fidelity factor that accounts for the vertical position of the noise
signal on the screen. RIN measurements for which the rf amplitude noise differs must be weighted
with this factor, which like Kappa, is frequency dependent. The scale fidelity factor can be
obtained using an rf signal generator, an attenuator, the ESA, and an rf power meter. Connector
losses should be included and control settings kept the same as for a RIN measurement. The rf
power is recorded at two different positions on the ESA with and without the attenuator. The

scale fidelity correction for signals of varying magnitude can be expressed as a correction to
Kappa at each frequency separately

Below is an example of how we calibrate the NIST ESA. The attenuation of a 10 dB attenuator
is measured as shown in part “a” of Figure A.1 with the signal generator set at 600 MHZ and
power output at -50 dBm. Using the rf power meter, the attenuation is measured to be 10.0 dB.
With the signal generator set at 600 MHZ and ~70 dBm, the signal is positioned on the ESA
screen as would occur for an actual noise measurement. The result is recorded with and without
the attenuator. When our ESA is set at 5 dB per vertical division, the scale fidelity, S, is found to
increase the difference between the two readings by 0.15 dB per division. Also, the manufacturer
specifies that the amplitude error must be <0.7 dB over the 10 divisions that compose the screen.

If the difference between noise powers at different vertical positions on the screen is 6P, - 5P,
(at the same frequency), then the scale fidelity correction is

8p
en
1 = SP 4 003-6P,-8P,) ” ap

Folder No: bbbb
Date of Report: March 16, 2000
Reference: P.O. No. Tttt ee/yy/nn 68


Table 1. RIN of optical filters whose transmittance curves have exact mathematical shapes.

Spectral density shape RIN=R Lim{5R/R} as f = 0
Rectangle (1/B)A (7B) 6B/B
Gaussian (C, /B) exp{-C, (f/B)7} 6B/B
Lorentzian (1/B) { 1+ (£/By } 38B/B

In the third column, we list the calculated limit of the variation in the RIN divided by the
RIN as the frequency tends toward zero. For all three cases, the result equals the variation in the
bandwidth divided by bandwidth. Thus a uniform frequency increment, such as provided by an
OSA with a constant-resolution bandwidth, should yield a very precise RIN. RIN calculations
give similar results for intermediate shaped filters. However, the RIN of a filter with an
asymmetric-transmittance shape may behave differently.

6.4 Measured RIN of Three Different Filters When Linked to the Same EDFA

Figure 6.4.1 shows the optical power spectral density from the OSA for the three filters F1,
F2, and F3 used with EDFA2 (each combination a potential RIN standard). Very similar results
are also obtained using EDFA1. Filter F1 is quite rectangular in shape and has 3 dB bandwidth of
1.37 nm. Filter F2 is somewhat rectangular, but spreads more quickly toward the wings; it has
bandwidth 3.42 nm. Although filter F3 spreads very quickly toward the wings, it has a 3 dB
bandwidth of 1.32 nm. Figure 6.4.2 shows that the RIN obtained using all three filters is constant
out to tens of gigahertz. The rectangular shaped filter F1 falls off the fastest, since the RIN is an
autocorrelation function. Increasing the bandwidth (BW) from 1.37 nm to 3.42 nm decreases the
RIN. This agrees with the results of Table 1 in which the RIN behaves according to the inverse
of the bandwidth. For filter F3, however, much of the power density exists far beyond the 3 dB
points, so that the contribution to the RIN of the filter shape outweighs the BW"! dependence.
The RIN of two additional filters (not shown) having well-behaved, symmetrical shapes also
followed a BW" dependence.

Figure 6.4.3 compares the RINs obtained from filter Fl when connected to EDFA1 or to
EDFA2. For both combinations the RIN is very nearly constant to tens of gigahertz. The

26


10.36
*
*
10.35 4 ay
*
10.345 o *
a
Y tos3| * , x“
+ 3
x * *
z 10.32 + * = x
c ** *
10.31 5
«§ *
*
10.30 5 *
*
10291
O6MAY99 16MAY99 26MAYS9 O5JUN99

Measurement date

Figure 7.1.1. RIN of the standard over a three-week period. Circles represent second set of five

measurements taken on May 5, 1999.

80



entire bandwidth, ranges from 0.036 dB/Hz to 0.12 dB/Hz, depending on the filter used. The
EDFA’s built-in optical isolator, along with the property of invariance of the RIN under
attenuation, allows for the convenient use of fiber connectors. We chose a good-quality FC/PC
connector, with all components pigtailed to standard single-mode fiber. The invariance under
attenuation allows the user to achieve noise power levels on their electrical spectrum analyzer
(ESA) to match the values expected when measuring unknown devices.

Accurate specification of the RIN requires that we develop the underlying physical theory
from fundamental principles, then apply it to formulate a numerical representation for the RIN.
We then developed the metrology to describe the interaction of a potential standard device with a
RIN measurement system. This yielded a frequency-dependent calibration function specific to the
RIN system under calibration. To validate the device as a standard, we developed a second
calibration method based on a distributed-feedback (DFB) laser whose RIN is specified by the
manufacturer to be less than - 172 dB/Hz. We demonstrated that under sufficient attenuation, the
RIN of this source becomes Poisson limited. Using this method to calibrate our RIN system also
yielded a similar calibration function (Kappa). By applying the RIN equations for each method to
calibrate the RIN system, we derived an exact expression that equates their calibration functions
and use it to compare the methods. A typical value for the difference between the functions
obtained from each method, as averaged over the 601 frequency points in a span, falls in the range
from 0.04 dB to 0.2 dB. Such values are comparable to the relative uncertainty in the RIN of the
standard (0.12 dB). Application of a statistical F-ratio test demonstrates that the variability in
Kappa of the two methods is similar. Thus the RIN standard compares favorably with the
Poisson-limited laser. We selected the EDFA method for the standard because it is the most
stable, robust, and portable of the two RIN sources. However, in principle either method could
be used for the standard, in that either method would produce nearly equivalent results if applied
to similar RIN measurement systems.

A calibrated RIN system has two immediate applications that illustrate the need for a
measurement assurance program. First, it is needed for precise measurement of the RIN of lasers
used in optical communications systems. This demand is of increasing importance as efforts are

broadened to create lasers with RIN approaching the standard quantum limit. Second, it is useful


dependent calibration function (Kappa) of our RIN system and derive the equation
that relates them. A comparison of the calibration functions obtained from
measurements using the two methods agrees well with the theory developed. The
relative uncertainty in their difference is similar to the relative uncertainty in the
RIN of the standard. Application of a statistical F-ratio test demonstrates that the
variability in Kappa of the two methods is similar. Thus we establish a RIN
standard that compares favorably with a second independent method (Poisson-
limited laser) based on rigorous physical theory, high-precision measurements, and
thorough statistical analyses.

Key words: calibration; measurement assurance; optical fiber sources; Poisson-

limited laser; relative intensity noise; spectral density; transfer standard

1. Introduction

Increasing demand for greater bandwidth in optical communications systems has brought to
fruition laser transmitters and optical fiber amplifiers with very-low relative intensity noise (RIN)
and noise figure, respectively. In this report we present a method for high-precision calibration of
RIN measurement systems (where RIN means the spectral density of the relative intensity noise).
A standard is made available to industry in the form of an erbium-doped fiber amplifier (EDFA)
whose output is coupled to a linear polarizer followed by a narrow-band filter. We characterize a
typical device for use as a standard in the 1550 nm wavelength range over an rf frequency
baseband of 0.1 GHz to 1.1 GHz. However, the spectral density of the RIN is very nearly
constant from zero to many tens of gigahertz, rendering it suitable for calibration of systems of
greater bandwidth. Thus, depending on future requirements of industry, we will be able to certify
the RIN standard at higher bandwidths by using a higher bandwidth pre-amplifier in the RIN
system and applying identical calibration techniques.

The RIN of a typical device studied has a magnitude - 109.9 dB/Hz, which can be decreased
by using a filter of greater bandwidth. The combined standard uncertainty in the RIN, over the


G(t) = fi fi R(t!" )k(t! <A AI +t! -1!"+1)> ala”,

4.1.7
bs <> (4.1.7)
then we observe that U(«) is the Fourier Transform of G(r),
Uw) = <b? f Gt) edt
= PsP? AG(t)) (4.1.8)

wl? / i J BOOMER alae ede,
<q

Since G is a function only of t, we can apply the shifting property of Fourier transforms to the
dummy variables t’, and t” in A I(t + t’ - t” + t) before integrating. If F represents the Fourier
Transform, then the result is

Fiat +t!-t" +0) = AlAUt+ De Het (4.1.9)

so that

Ue) = wef ff HOD KE)<AIMAI +1 > Salonen ot Ode ld Nae

. . . (4.1.10)
web? [ite yet dt! [aCe Ade" f MOAI grrr,

uv

<

15


the noise figure of the optical fiber amplifiers that are essential for building faster and more
efficient optical communications systems. The demand for better techniques to calibrate a RIN
measurement system’s response and sensitivity is also increasing with the appearance of
commercial distributed-feedback lasers and diode-pumped Nd:YAG lasers having very low RIN.
Typical values of RIN range from - 110 dB/Hz to - 130 dB/Hz for inexpensive multimode edge
emitting diode lasers, and less than - 170 dB/Hz for high quality DFB diode lasers.

The RIN of an optical source can arise from a variety of variables and atomic parameters. In
this report, we are interested mainly in the RIN of semiconductor lasers and thermal light sources.
For semiconductor lasers, the most important parameters are frequency, source output power,
temperature, modulation frequency, time delay and magnitude of optical feedback, mode
suppression ratio, and relaxation oscillation frequency [1]. For certain kinds of multimode lasers,
RIN can be greatly affected by system components which have polarization or wavelength-
selective properties [2]. The predominant source of RIN, however, is usually spontaneous
emission. Thus the low-frequency RIN of a laser is a maximum just above threshold, diminishing
with increasing output power. But it can be greatly increased by optical feedback, even at high
output power. For semiconductor lasers such as the DFB laser used for the secondary method of
this MAP, the RIN can be formulated by inclusion of Langevin noise sources in the differential
rate equations for the photon and carrier densities [3, 4]. Semiconductor laser RIN has important
applications in optical communications systems [5]. The source RIN of the standard or primary
method, however, will be shown to arise from the amplified spontaneous emission (ASE) of an
EDFA. Such fluctuations, which are described by Bose-Einstein statistics, can be approximated
by thermal light [6, 7]

Other calibration sources that might apply to calibration of RIN measurement systems are
fast-pulse lasers, broadband sources such as light-emitting diodes, and a heterodyne method in
which the beat frequency of two tunable lasers is used to determine the frequency response of
ultra-high speed photoreceivers. We note that the filtered EDFA method developed herein

contains the information for performing such a frequency-response calibration.


180
160
140 ‘
1204

F-ratlo
8
+

oA 02 03 E 05 06 07 08 0.9 1.0 1
Frequency (GHz)
Figure 10.4.1. F-ratio versus frequency. The F-ratio shown is the variance of each Kappa from the laser

divided by the variance of the Kappa from the EDFA1 + Fl at each frequency. The two reference lines
represent the critical values for the F-test at the 0.05 level of significance.

F-ratio

oA 02 03 0.4 05 0.6 07 0.8 09 1.0 1

Frequency (GHz)

Figure 10.4.2. F-ratio versus frequency. The F-ratio shown is the variance of each Kappa from the laser
divided by the variance of the Kappa from the EDFA2 + FI at each frequency. The two reference lines

represent the critical values for the F-test at the 0.05 level of significance. An F-ratio of 428.863 at 1.08
GHz is not shown.

89


B3-
<
21254 linear fit excluding v = 23.66 mV a
2 al si x
s,,4 — — — 2nd order polynomial using all data ,
2 O data points
8104
z
2°
8 87
Tt
B77
fo]
3 oo
a
os
2
245
=
2 3
o T TT T T TT T T 1
4 6 8 10 12 14 #16 18 20 22 24 26
dc voltage (mV)
Figure 8.1.3. Electrical noise power of laser at 400 MHz versus dc voltage.
EDFA+P+F .
RIN system to be calibrated
Photo
detector
Bias tee Ammeter
or Oo, L__5 Lo)
Poisson limited DFB laser ‘
( Pre amp
Electrical
spectrum
analyzer

Figure 9.1. Calibration of the RIN system using the standard and the laser.

82


Kappa from EDFA1 + Fi (d8)

oA 02 03 0.4 Os 0.6 0.7 08 09 1.0 1
Frequency (GHz)

10.3.1. Kappa determined on four different days from EDFA1 + Fl.

88)

—894

Kappa from EDFA2 + Fi (dB)

a
°
°
+

4/29
—95 T T T T

oA 02 03 0.4 0.5 0.6 07 0.8 09 1.0 11

Frequency (GHz)

Figure 10.3.2. Kappa determined on four different days from EDFA2 + F1.

85


At zero shifting this simplifies to

2D oPay
RIN = Z

=~ 1? (4.2.7)
AA ( > aP,))
In section 7, we apply the propagation-of-errors formula to these equations to estimate the totz

uncertainty in the RIN.

5. Accurate Determination of RIN Requires Precise Calibration of Optical Spectrum
Analyzer Parameters

Since the RIN of the optically filtered EDFA noise is proportional to the autocorrelation of
the optical power spectral density, the optical spectrum must be precisely measured by a well-
calibrated OSA. From the numerical equations for the RIN, the OSA parameters to be evaluated
for uncertainty are resolution bandwidth, wavelength, and power spectral density. The power
spectral density is not a true function because the resolution bandwidth can never be zero. This
condition is acceptable since we can account for all errors in the measurement parameters at each
point numerically. We convert from wavelength to frequency units since we need to reference

the RIN spectrum to the rf-baseband frequency.

5.1 Measurement of Resolution Bandwidth and Its Uncertainty

We determined resolution bandwidth over a wide wavelength range by two distinct methods
using several narrow-linewidth lasers (linewidth << instrument resolution bandwidth). Among
these were a tunable laser (linewidth < 1 MHz) in the 1540 nm to 1580 nm range with wavelength
established by a high-accuracy wavemeter (1 ppm), a 1523 nm HeNe laser (linewidth < 50 MHz,
and previously developed as a secondary wavelength standard), and a 1310 nm YAG laser for
good measure. In the first method, the response of the OSA to the narrow linewidth laser (or
delta function input) is read directly from the OSA. The single-wavelength input is broadened by

the monochrometer, and the resolution bandwidth is equated to the 3 dB bandwidth as read

21


NIST Measurement Services:

Measurement Assurance Program NIST
for the Spectral Density of Relative Bpecial on
Intensity Noise of Optical Fiber 250-57

Sources near 1550 nm

Gregory E. Obarski
Jolene D. Splett

NisT

National Institute of Standards and Technology
Technology Administration, U.S. Department of Commerce NIST CENTENNIAL

a

1007-1061



Kappa from laser (dB)

— 93 Oo 4A6
° 4/23
94, © 4/27
+ 4/29
95 T T T T T T T T T 1
o1 02 08 04 O05 O86 O7 O8 O98 10 14

Frequency (GHz)

Figure 10.3.3. Kappa determined on four different days from the laser.

86


Combinations of sources
and filters compared

Z (eq 10.1.1), in dB

without, with SCF

Standard deviations of the
differences, D, in dB.
without, with SCF

4/20/99; F2 only

EDFA1 + F2 with EDFA2 + F2
EDFA] + F2 with DFB
EDFA2 + F2 with DFB

4/19/99; F3 only

EDFAI + F3 with EDFA2 + F3
EDFAI + F3 with DFB
EDFA2 + F3 with DFB

4/16/99; F1 only

EDFAI + F1 with EDFA2 + F1
EDFA1 + F1 with DFB
EDFA2 + F1 with DFB

4/13/99; F2 and F3

EDFAI + F2 with EDFA2 + F2
EDFAI + F2 with DFB(2)
EDFA2 + F2 with DFB(2)
EDFAI + F3 with EDFA2 + F3
EDFAI + F3 with DFB(3)
EDFA2 + F3 with DFB(3)
EDFAI1 + F2 with EDFA1 1 F3
EDFA2 + F2 with EDFA2 + F3

DFB(2) and DFB(3)

-0.095,  -0.202
-0.111,  -0.147
-0.016,  -0.0014

-0.015, -0.049
0.132, 0.103
0.147, 0.152

0.012, -0.108
0.08, - 0.001328
0.068 0.000864

-0.028, -0.074
0.053, 0.058
0.08, 0.143

-0.0042, -0.056
0.103, 0.076
0.099, 0.131
0.105
0.073
0.051

0.31, 0.327
0.286, 0.292
0.343, 0.333

0.263, 0.27
0.263, 0.269
0.27, 0.279

0.157, 0.164
0.186, 0.188
0.188, 0.191

0.331, 0.349
0.293, 0.302
0.334, 0.35
0.286, 0.295
0.265, 0.271
0.29, 0.301
0.268 0.333
0.28



Teflections within the amplifier, or between it and the span [10]. Recent reports demonstrate
accurate determination of noise figure using electrical methods. Electrical measurement methods
are becoming increasingly important because they include multipath interference effects, which,
however small, are necessary for the higher-speed analog systems.

There are at least two relevant electrical methods for determining optical amplifier noise
figure. The first of these, known as the RIN Subtraction Method [11, 12], requires a laser of low
RIN, such as a DFB laser with RIN spectral density <- 160 dB/Hz. The RIN is measured with a
calibrated RIN system such as the one used in the development of this RIN standard. This method
yields the frequency-resolved noise figure referenced to baseband frequencies, “f.” It is of special
interest here because the RIN explicitly appears in the noise-figure equation. The RIN of the laser
is measured before and after transmission through the amplifier. If R,(f) is the RIN of the laser
(assuming Poisson-limited RIN) and R(f) the RIN of the-amplified signal, then the noise figure is

NA = (RO- RO) Se +GT, (2.2.1)

where P, is optical power, & is laser frequency, h is Planck’s constant, and G is amplifier gain.
This method requires that the RIN of the amplifier be greater than the signal source’s RIN and
detector’s thermal RIN, and also that the signal source’s RIN be greater than the detector’s
thermal RIN.

A second electrical method reports lower RIN uncertainty than the RIN Subtraction
Method, and has been shown to agree well with the polarization nulling (optical) method [13, 14].
An attenuator is used to equalize the power levels on a photodetector with and without the
amplifier present. This results in equal amounts of shot, thermal, and excess RIN levels, all of
which vanish from the noise figure equation upon subtraction of the signals. The net result is a
simplified determination of the noise figure. Both methods are of paramount importance because

each includes contributions to the noise figure of multiple path interference.


here A(t) = <AI(t)AI(t + t)>/ <I>? is the intensity autocorrelation function ( section 4.1.4).
Thus we define the “RIN” of an optical source to be the RIN spectral density, R(v), and the
integral of the RIN to be the “total RIN.”

Our approach is to treat the RIN as consisting of two parts: a Poisson or shot noise
component, and a component we call “excess RIN.” The excess RIN propagates unchanged
through the system while the Poisson RIN depends on system losses. The “Poisson RIN” is the
minimum RIN that can be achieved for classical light. It is often called the standard quantum limit.
Classical light obeys an uncertainty relation for which each conjugate field variable is greater than
or equal to its minimum value. (The perfectly coherent state is defined as the state when both
conjugates are equal and at their minimum.) The excess RIN is non-negative for classical light,
whereas it is zero for Poisson light. RIN is specified in units of 1/Hz, or in logarithmic form as
decibels per hertz. The total RIN is the sum of the spectral integrals of excess RIN and Poisson
RIN [9]; thus, it is dimensionless. To develop a MAP for RIN we characterized two different
kinds of sources; a RIN standard (EDFA + F) having nearly excess-limited RIN, and a laser
having nearly Poisson-limited RIN.

For light obeying a Poisson distribution, the variance in the photon number is proportional to
the photon number. Thus the square of the optical power fluctuations is proportional to the
optical power. When represented by a single-sided noise spectrum (positive frequencies only) the
Poisson RIN is 2hv/P,, where h is Planck’s constant, v is photon frequency, and P, is optical
power. In electrical units it is 2q/i, where q is electron charge, i = nqP,/hv is photocurrent, and
is photodetector quantum efficiency. Thus the Poisson RIN in a real detection circuit increases as

1/n, so an ideal photodetector (n = 1) would detect the laser’s true RIN.

2.2. Application of Laser RIN to Noise Figure of Optical Amplifiers; Electrical Methods
Accurate measurement of EDFA noise figure is required for the design and development of
optical communications systems that rely on amplification to achieve high bandwidths. There is
significant interest in applying optical methods to the measurement of the noise figure because
they can be quickly applied to the amplifiers as they emerge from the production line. Optical

methods, however, are incapable of measuring multipath interference effects which may arise from


Application of the transfer standard to a RIN measurement system

When RIN is measured in the electrical domain, a bias tee sends the dc photocurrent from the
photodetector to an ammeter while the ac noise is amplified, then displayed on a radio-frequency (rf)
spectrum analyzer (Figure 1). The RIN is the noise power per unit bandwidth, 5P,(f), weighted with the
frequency-dependent calibration function K(f) of the detection system (herein referred to as Kappa),
and divided by the electrical dc power P.. Thus

_ KA8PLA)
2

e

RIN = constant , (.1)

where 5P,(f) is the noise after subtracting the thermal noise floor.

To calibrate a RIN measurement system, the customer connects the RIN standard using a quality
FC/PC connector with standard single mode fiber. The 5P,(f) is measured on the rf spectrum analyzer;
measure P.(f) with a high accuracy voltmeter connected across a 50 Q resister. Substitute the value for
the RIN of the standard to obtain Kappa. Solution of eq (1) for K(f) gives

_ RIN-Pf)

= Sp, ©.)

To determine the RIN of an unknown source, the customer applies eq (2) with the values of Kappa

obtained from the standard. Figure 2D is a sample graph of Kappa of the NIST RIN system using the
standard.

Folder No. and NIST ID: xx and yy
Date of Report: March 1, 2000
Reference: P.O. No. Mmm, 2/3/00 57


Therefore,

SaiP 2a , (9.2.4)
SP)  6P,@) 2.

K(@) =

where we dropped the subscripts on Kappa. From this analysis it is clear that x, can be
determined without knowledge of the laser RIN or the quantum efficiency of the photodetector
(measured at 0.77 at the operating wavelength of 1555.9 nm). Note that the variation of Kappa
with frequency for either method is directly proportion to the frequency response of the RIN
system. As such, either method might be used to measure the frequency response of high-speed
photoreceivers. In the next section we use these results to compare the calibration functions

obtained from actual calibrations of our RIN measurement system.
10. Two Methods Applied to the NIST RIN System Give Similar Results

To evaluate the accuracy of the RIN standard we used it to calibrate our rf (electrical) RIN
measurement system, and compared the results with those obtained using the laser. Such a
comparison should help determine the validity of the RIN standard with respect to the secondary
method, in that each method, when applied separately to the RIN system, should yield similar
results. From this we can predict how a typical RIN system will respond to the RIN standard, and
how well the results agree with any conclusions drawn about either method separately. It should

also provide a framework for comparing the statistical uncertainties obtained from each method.

10.1 Quantitative Comparison of Calibration Results from the Two Methods

Since we seek to establish a MAP that allows replacement of various components composing
the standard and the RIN system, we performed calibrations using a variety of components for the
standard, and compared results. Among these are the six combinations that arise from the two
EDFAs and the three filters discussed previously (section 6.4). Use of a single Poisson-limited

laser for the secondary method is justified because the theory and measurement of Poisson light

40


F1 = 1.38 nm BW, nearly a rectangle
F2=3.42 nm BW

oO

.32 nm BW, very broad wings,

Kappa (dE)

T T T T T T T
on 02 03 04 05 06 o7 08 09 10

Frequency (GHz)

Figure 10.1.1. Comparison of Kappas using EDFA2 with filters F1, F2, or F3.

EDFA1+F2
EDFA2+F2
DFB laser

Kappa (dB)

T T T T

T T T T T
0.1 02 03 0.4 Os 06 07 08 09

Frequency (GHz)

Figure 10.1.2. Comparison of Kappas from two different EDFAs + F2 with the laser.

83


nearly invariant under practical attenuation strengths that may arise from component and
connector losses.

However, we must determine any potential effects of attenuation and nonlinear spectral
responsivity in aggregate. The combined uncertainty will be assigned to represent an upper bound
for the uncertainty due to a nonlinear spectral responsivity. Thus we determined the RIN for a
variety of pump currents, attenuation levels, and intensity levels as shown in Table 2. For
example, the effect of a variable attenuation could be studied with the spectral intensity held
constant on the OSA screen by compensating the pump current. For other measurements the
intensity level was allowed to.vary. Column 3 of the Table shows the intensity relative to the
maximum, which occurs at zero attenuation and maximum pump current (214 mA). Thus the
maximum intensity is represented by 0 dB, while 4 dB below the maximum appears as -4 dB.
Such varied conditions, again give nearly the same average value for the RIN, 1.0297 - 107! Hz
(- 109.87 dB/Hz) with a standard deviation of 0.002 - 10"! Hz 7 (0.008 dB/Hz), as when the
intensity levels were allowed to vary. Figure 6.6.2 shows the variation in RIN with pump current
at zero attenuation. The average RIN is 1.0291 - 10°! Hz“ (- 109.87 dB/Hz) and the standard
deviation is 0.0005 - 10"! Hz“ (0.002 dB/Hz). Thus the uncertainty in the RIN due to the

combined uncertainties in spectral responsivity and attenuation in aggregate is indeed small.

28


Table 5. Relative stability of EDFA1 and EDFA2 with respect to the Poisson laser.

Average of the Z’s (dB) Average of standard
deviations (dB)
EDFAI + F, with DFB 0.088 0.046
EDFA2 + F, with DFB 0.103 0.077

10.2 Relative Stability of Two Different EDFAs With Respect to the Poisson Laser

From the data in Table 4, we can compare the accuracy and relative stability of EDFA1 and
EDFA2 with respect to the Poisson laser. The averages for each EDFA were made over all
comparisons with the laser. Specifically, we found the average of the average difference of
Kappas for a specific EDFA with any of the three filters as compared with the corresponding
Kappa from the DFB laser. A comparison of EDFA1 with laser will have the following entries
from Table 4 - column 2, for computing this average: EDFA] + F2 with DFB (5/3, 4/29, 4/20),
EDFA] + F1 with DFB (4/29, 4/27, 4/23), EDFA1 + F3 with (4/23, 4/19, 4/13). Similar entries
occur for comparisons of EDFA2 with the laser. We used the second set of numbers in column 2,
which accounts for the ESA scale fidelity correction. The results are shown in Table 5, where F,,
represents filters F1, F2, and F3. EDFA1 is slightly more stable, with an average of 0.088 dB,
while EDFA2 (the standard) has an average of 0.103 dB. These averages disagree by 0.015 dB,
which is quite small. Recall that we chose EDFA2 for the standard because of its semi-ruggedness
and ease of use.

We note that in determining Kappa the ESA’s noise floor is subtracted. This is an arbitrary
procedure because the noise floor, which is averaged in the measurement process, is the same for
both the standard and the laser. Of importance is that we be consistent in how we define the RIN
system’s response to the standard and the laser.

10.3 Methods Compare Favorably Under Use of Variance Analysis
As was shown in section 9.2 above, Kappa from the laser can be precisely determined without

explicit knowledge of the laser’s RIN. Thus we can compare calibration results from the standard

45


difference in RIN of about 0.012 dB is very small. This demonstrates that filter shape alone does
not determine the RIN. The similar shape of the curves occurs because each arises from the same
filter. The filter bandwidth is probably narrow enough to compensate for a potentially non-zero
slope of the spectral density of a typical EDFA that might occur over a wavelength interval of
several nanometers around the center wavelength of the filter. If such an effect were significant,

the RIN would not be constant.

6.5 Use of Connectors and the Effect of Losses

The net effect of disconnecting and reconnecting the RIN standard will cause a slight
variation in the total optical power transmitted down the transmission line. Connections can be
made by use of either fusion splicing or fiber connectors. Since in principle the RIN is invariant
under attenuation, the effect of using connectors will turn out to be very small. Thus, for
convenience, we chose standard, high-quality FC/PC connectors to mate all of the fiber
components composing a standard. The error due to connector mating is included in the

repeatability error (section 7.1).

6.6 Combined Effects of Attenuation, Pump Current, and Power Spectral Density Levels
If the spectral responsivity of the OSA is nonlinear, an error will occur in measuring
different OPSD levels at the same wavelength. In principle, however, the total variation in the
RIN with respect to power per bandwidth will result from the combination of a nonlinear spectral
responsivity at each sampled wavelength, and any potential effect of attenuation on the RIN itself,
however small. We must consider attenuation because the transmission of the optical spectrum
through connectors and down the fiber transmission line of the standard may be subject to some
wavelength dispersion that could, in principle, alter the RIN spectrum. Such effects should vanish
to first order, but might contribute a small but finite uncertainty to the total RIN. To determine
this error, we devised a scheme in which the RIN standard is attenuated over a wide range of
values at various pump currents. In Figure 6.6.1, the RIN is shown over a range of attenuations
from 0 db to 10 dB. The average RIN is 1.0296 - 10 Hz" (- 109.87 dB/Hz) with standard
deviation of 0.0008 107! Hz" (0.003 dB/Tz). To first order, this result determines that the RIN is

27


Table F1. RIN of customer’s device and uncertainty of RIN expressed in linear and logarithmic

units.
Frequency range | RIN of customer’s device Expanded uncertainty
0.1-1 GHz V/Hz dB/Hz V/Hz dB/Hz
aaa bbb cee ddd

measurements as well as the uncertainties that arise from the OSA parameters involved in the
measurement. Calibrations are performed after all equipment is warmed to steady-state thermal
stability (several hours). The results of the RIN measurements on the customer’s device are

summarized in Table F1, where the expanded uncertainty reported is defined in the section on
uncertainty assessment.

NIST RIN standard

EDFA+P+F

or

EDFA+P+F oO.

Customer's RIN device

OF

NIST RIN measurement system

Photo

detector

Bias tee Ammeter

i > Loot)

—_S

Pre amp

Electrical
spectrum
analyzer

Figure F1. Calibration of the customer’s RIN device using the NIST RIN measurement system

as calibrated by the RIN standard

Folder No: bbbb

Date of Report: March 16, 2000
Reference: P.O. No. Tttt ee/yy/nn

64



in determining the noise figure of optical amplifiers. In the future we plan to develop a standard
(also based on a MAP) specifically for noise figure of optical amplifiers. This latter device will be
used to calibrate optical noise figure measurement systems based on electrical spectrum analyzers.

We will attempt to establish the MAP so that future changes can be made to the various
components that compose the standard and the measurement apparatus with little or no additional
documentation. These might include the EDFA, polarizer, and filter that compose a standard, the
optical spectrum analyzer, and RIN system components such as the pre-amplifier, photodetector,
bias-tee, electrical spectrum analyzer, and voltmeter.

Herein we refer to the EDFA-based standard as the primary method and the Poisson-limited
laser as the secondary method. To distinguish between the use of two different EDFAs and three
filters as components of the standard we use the notation EDFA1, EDFA2, and F1, F2, F3,
respectively. The bulk of our measurements and analysis was performed on results using EDFA2
with F1. Thus the standard has implicit in its definition the use of EDFA2 and F1. For brevity,
instead of denoting the standard by EDFA + P + F, we omit the polarizer, P, and write EDFA +
F, keeping in mind that the polarizer is present unless otherwise specified. Finally, a brief
discussion of RIN expressed in logarithmic units is given in Appendix B for the reader unfamiliar
with this subject.

2. Background

RIN is a concept that is often associated with optical data transmission using diode lasers as
the transmitters. However, the basic ideas of RIN are applicable to all classes of lasers as well as
almost all optical sources. In analog communications, such as cable television, total RIN within
the system bandwidth can limit the signal-to-noise ratio. In high-speed digital systems, RIN can
limit the bit-error-rate (BER) and system performance under certain conditions. A laser’s high-
frequency RIN spectrum often contains a well-defined peak at the relaxation oscillation frequency;
for many classes of lasers this peak can be used to deduce the maximum intrinsic modulation
frequency for a specific laser. Knowledge of RIN can be applied to the design of new lasers to

give improved performance for specific applications. Very low-RIN lasers are used to determine


If S(v) is the power spectral density as measured by the OSA, and P is the total power in the
spectrum, then @(v) = S(v)/P, and the RIN for unpolarized thermal light is

RO -f S(v)S(v +fydv ;

Pp? (41.19)

0

For polarized thermal light we need only introduce the same factor of two as appears in eq
(4.1.14) for the autocorrelation of the intensity fluctuations,

Rf) = 2f Sse . (4.1.20)
0

This derivation establishes the RIN equation of the standard from physical theory. The
magnitude and uncertainty of the RIN will be determined from measurement of the optical power
spectral density of the RIN standard with a well-calibrated OSA. The calibration properties of the
RIN measurement system, which to some extent are arbitrary, will be determined from
measurement and theory by application of the standard and the secondary method (Poisson-
limited laser). The results of the two methods will be compared to verify the equivalence of their
calibration properties. The theory of the Poisson laser is historically known and proven by key

experiments that relate classical and non-classical states of light.

4.2 Numerical Formulation of the RIN in the Wavelength Representation

Having formulated a precise theory for the RIN of the standard, we now develop a
numerical representation that accurately treats the experimental data. This can be done in either
the frequency or the wavelength representation. As the data are recorded with a grating-type
OSA, we seek approximate numerical expressions that will yield the OPSD and the RIN from a
finite basis of data points in the wavelength representation specified by the OSA. In the previous

section, we showed that the RIN in the frequency representation is the autocorrelation of OPSD

18


average difference

Ao —

Difference between Kappas (dB)

TT T T T TT “T T 1
01 02 08 O04 OF 08 O7 O08 O8 10 1.4
Frequency (GHz)

Figure 10.1.3 . Difference between Kappas from the laser and EDFA1 + F2. The data range from -1
to +1 dB. The average difference is 0.056 dB.

84



Appendix D: Sample MAP Certificate

U.S. DEPARTMENT OF COMMERCE
NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY
ELECTRONICS AND ELECTRICAL ENGINEERING

LABORATORY
Boulder, Colorado 80303

MEASUREMENT ASSURANCE PROGRAM (MAP)

for
Spectral Density of Relative Intensity Noise

for
Customer
AaBbCc Corp.
Address

Calibration Summary

This report summarizes the measurement results for the spectral density of Relative Intensity Noise
(RIN) of the NIST transfer standard. The standard is calibrated over the 0.1 GHz to 1.1 GHz frequency
range. However, the spectral density of the RIN (from now on called simply the RIN) is practically
constant up to several tens of gigahertz. The transfer standard is an erbium-doped fiber amplifer
(EDFA) to which is coupled a linear polarizer (P) followed by a narrowband filter (F) (represented as
EDFA + P + F in Figure D1). The EDFA has a built-in optical isolator to ensure that the amplified-
spontaneous emission (ASE) that it emits is free from potential multiple interference effects such as
ripple. High-quality FC/PC connectors and single-mode fiber are used throughout.

Folder No. and NIST ID: xx and yy
Date of Report: March 1, 2000
Reference: P.O. No. Mmm, 2/3/00 55


Attenuation = 15 dB

Attenuation ~ 12 dB.

Attenuation = 10 dB

Kappa (dB)

T T T T T T T
03 04 05 06 07 08

Frequency (GHz)

ot

Figure 8.1.1, Calibration function of the laser versus frequency for various attenuation levels.

2

Attenuation = 16 dB
Attenuation = 13 dB

roo

Attenuation = 10 dB

8 91
3
Es
2-|
£
34
44
°s 1 T T T T T T T T 1
O41 02 03 04 Os 06 O7 08 09 1.0 44
Frequency (GHz)

Figure 8.1.2. Calibration function of the laser versus frequency for similar but different attenuation
levels.

81


Average Kappa (dB)

© EDFA1 + Fi
* Laser

T T T T T T 1
O41 0.2 03 0.4 Os 0.6 07 0.8 og 1.0 1

Frequency (GHz)

Figure 10.3.4. Comparison of Kappa from EDFA] + F1 and the laser. Data were averaged over the four
days shown in Figures 10.3.1 (EDFA1 + F1) and 10.3.3 (laser).

-*)

-90-4

Average Kappa (dB)
1
8

-934 © EDFA2 + Fi
* Laser
-94
-95 T T T T T T T T 1 1
of 02 03 04 O05 O06 OF O8 O98 10 14

Frequency (GHz)

Figure 10.3.5. Comparison of Kappa from EDFA2 + FI and the laser. Data were averaged over the four
days shown in Figures 10.3.2 (EDFA2 + F1) and 10.3.3 (laser).

87


U.S. Department of Commerce
National Institute of Standards

and Technology

325 Broadway

Boulder, CO 80303-3328

Official Business
Penalty for Private Use $300

( We

; weg

ary


Appendix E. Calibration Service

As appropriate, the customer may benefit more from a calibration service (CALSV) than a
measurement assurance program (MAP). To use a CALSV, customers send their own devices to NIST
for calibration instead of renting the NIST standard through the MAP. We refer to the customer’s
calibrated RIN device as a company standard. Although customers purchase their own components,
NIST would be available for consultation on which components to purchase (but as a matter of policy
does not recommend specific brands).

Calibration and traceability of the company standard to NIST would occur as a two step process.
Periodically, perhaps once per year, the customer would send NIST his or her company standard for
calibration. NIST calibrates the NIST RIN measurement system using the NIST standard, and then
within a few minutes this calibrated system is used to calibrate the customer’s RIN device. NIST will
supply the customer with a calibration report, and make any recommendations needed for the customer
to continue possessing a quality RIN standard. This procedure will increase the uncertainty in the RIN
by about 0.03 dB over that of the MAP, which uses the NIST standard to calibrate the customer’s RIN
device directly. The increased uncertainty occurs because, in addition to the uncertainty in the NIST
standard, the uncertainty inherent in the NIST RIN system is also transferred to the customer’s
company standard. However, If the RIN of the source can be approximated by thermal light, such as
the NIST RIN standard, the combined uncertainty is reduced by determining the RIN from the same
method used for the NIST RIN standard. In this method, the theory of the RIN of thermal light is
applied to the optical power spectral density of the device as measured by the NIST optical spectrum
analyzer, which is precisely calibrated as a standard. The latter method will be used at the customer’s
discretion.

62



Table 3: Combined standard uncertainty in the RIN of the standard (EDFA2 with filters F1 and

F2).
EDFA2 + Fl Uncertainty Standard uncertainty Standard uncertainty
type (A or B) in 1/Hz in dB

Unpep A 0.000561 - 107" 0.002

Un A 0.001180 - 10" 0.005

U, A 0.012315 - 10 0.051

Urew A 0.000419 - 107 0.002
Combined, u, - 0.014475 - 107 0.06
Expanded, U - 0.029 - 107 0.12

EDFA2 + F2

Unep A 0.0068325 - 107? 0.005

Um A 0.011804 - 10°77 0.008

U;, A 0.025354 - 10° 0.017

Unaw A 0.009581 - 107? 0.006
Combined, u, - 0.053564 - 10°? 0.036
Expanded, U = 0.10713 - 10° 0.072

8. Achieving the Poisson Limit
For an optical field at wavelength A and optical power P, the Poisson RIN is
2he
RA) = R, = = constant , (8.1)

o

where c is the speed of light and h is Planck’s constant. To achieve the Poisson limit we recall that

any optical source can be rendered Poisson-limited by sufficient attenuation [23]. This occurs

because the Poisson RIN increases with attenuation while the excess RIN remains invariant. Thus

for applications of low-power lasers, the Poisson limit may be useful if the excess RIN is very

small and there is sufficient optical power available after attenuation to meet the power

requirements. However, the true Poisson limit is reached when the ratio of excess to Poisson RIN

35



—— 1.32 nm bandwidth
— - 1.37 nm bandwidth
- - - 3.42 nm bandwidth

Optical power spectral density (dBm)

1545 1548 1551 1554 1557 1560
Wavelength (nm)

Figure 6.4.1. Optical power spectral density of the three filters Fl, F2, and F3 used in this study.

105 —
-110
2 a
+120 4
2
3 125 4
=
~ 430
= F4 (BW= 1.37 nm)
© 35]
— — F2(BW=1.32nm)
140 4 —-- F3(BW=3.42nm)
145
~150 T TOT TH

10 100 1000
Frequency (GHz)

Figure 6.4.2. RIN of Fl, F2, and F3 from near zero to 1000 GHz using EDFA2.

77


approaches zero.

A Poisson-limited source offers two distinct advantages over that of a low-excess-RIN
source. First, the Poisson RIN is manifest in the electrical detection circuit as the simple quantity
2q/i. Second, the calibration of a RIN system can be performed with a Poisson-limited laser
without knowing the RIN explicitly, as will be shown in the following section. To establish a RIN
standard, we need not achieve the true Poisson limit, but require only that the ratio of excess to
Poisson RIN be small. Through attenuation we constrain this ratio to fall within some fixed value,
and thus limit the error it contributes to a RIN system calibration.

8.1 The DFB Laser of the Secondary Method Has Nearly Poisson-Limited RIN

In this section we apply eq (8.1) to a series of RIN measurements under attenuation to show
that the RIN of our laser is nearly Poisson-limited, and contributes only a very small error in the
calibration of our RIN measurement system. Calibration of the RIN system yields a frequency-
dependent calibration function that we call Kappa. Kappa is a dimensionless quantity (precisely
defined in section 9) whose magnitude is not required for the present analysis. To proceed, we
first compare graphs of Kappa obtained from measurements using the DFB laser at several
attenuation levels for which optical power ranged from one half mW to 7 mW. Figures 8.1.1 and
8.1.2 show the frequency dependence of Kappa for the various attcnuation levels. In Figure 8.1.1
the levels are 10, 12, and 15 dB based on a single sweep of the ESA. In Figure 8.1.2 the levels
are 10, 13, and 16 dB, with each curve obtained from an average of nine sweeps. This gives a
smaller spread in the data. The data overlap for all but the 10 dB curve in Figure 8.1.2, which sits
slightly below its neighbors. Thus the overlap of the 15 and 12 dB levels, and the 16 and 13 dB
levels, indicates that the RIN should be very close to the Poisson limit over the entire bandwidth.
At 10 dB, however, the optical power is considerably greater, the Poisson RIN smaller, so that
the ratio of excess to Poisson RIN may be too large to have achieved the Poisson limit. Since all
calibrations made with the laser are at 17 dB attenuation, this result for the Poisson limit should
still hold.

Figure 8.1.3 shows the rf-noise power (in arbitrary units) at 400 MHZ plotted versus de

voltage. Since Poisson noise power manifests in the electrical detection circuit as 2qV (where q is

36


[10] Becker, P.C.; Olsson, N.A.; Simpson, J.R. Erbium-Doped Fiber Amplifiers—Fundamentals
and Technology. New York: Academic Press, pp. 258-263, 1999.

[11] Willems, F.W.; Van der Plaats, J.C. Optical Amplifier Noise Figure Determination by Signal
RIN Subtraction, in Technical Digest—Symposium on Optical Fiber Measurements, Day, G.W.;
Franzen, D.L.; Hickernell, R.K., eds. NIST Special Publication 864, pp. 7-9; Sept 1994.

[12] Willems, F.W.; Van der Plaats, J.C. Experimental Demonstration of Noise Figure Reduction
Caused by Nonlinear Photon Statistics of Saturated EDFAs. IEEE Photonics Technology
Letters, Vol. 7, No. 5, pp. 488-490, May 1995.

[13] Movassaghi, M.; Jackson, M.K.; Smith, V.M.; Hallum, W.J. Noise Figure of Erbium-
Doped Fiber Amplifiers in Saturated Operation. Journal of Lightwave Technology, Vol. 16, No.
5, pp. 812-817, May 1998.

[14] Movassaghi, M.; Jackson, M.K.; Smith, V.M.; Young, J.F.; Hallum, W.J. Accurate
Frequency Resolved Measurement of EDFA Noise Figure. Optical Amplifier Conference Digest,
British Coulumbia; paper # TuD1-1; pp. 130-133, July 1997.

[15] Baney, D.M.; Sorin, W.V.; Newton, S.A. High-Frequency Photodiode Characterization
Using a Filtered Intensity Noise Technique. IEEE Photonics Technology Letters, Vol. 6, No. 10,

p.1258; October 1994.

[16] Baney, D.; Sorin, W. Broadband Frequency Characterization of Optical Receivers Using
Intensity Noise. Hewlett-Packard Journal, pp. 6-12, February 1995.

[17] Mandel, L.; Wolf, E. Optical Coherence and Quantum Optics. New York: Cambridge
University Press; 1995.

51


explicitly. The error due to noise power measurement will be determined by attenuating the input
RIN signal from the standard to fall at predetermined levels on the OSA screen. In addition, RIN
measurements under varying conditions of attenuation and EDFA pump current adjusted to yield
equal values of power density on the screen will also determine that the nonlinearity in the spectral

Tesponsivity is small. Measurements will show that the combined effect is indeed small.

6. Some Properties of the RIN Standard
6.1 Polarization

In section 4.1, we showed that the RIN of the standard was a factor of 2 greater for linearly
polarized than for unpolarized thermal light. Thus for unpolarized light fiber bending could
imbalance the power transmitted between orthogonally polarized modes and change the RIN by a
finite amount. We attempted to measured this effect by changing the curvature of the fiber that
links the various components, but found it to be nearly negligible. Nonetheless, we add the
polarizer to eliminate potential effects which might arise under varying conditions.

We tested the theoretical relationships derived for the RIN for unpolarized and polarized
light. A linearly polarizing isolator determined the polarization behavior of the RIN standard.
Measurement of the RIN with and without the polarizing isolator gave a difference of 3.003 dB in
the noise power measured on the electrical spectrum analyzer (ESA). This compares well with
the 3.0103 dB difference predicted by theory. We note that the RIN system need not be
calibrated to perform this measurement because the calibration function cancels in the equations
that define the difference in the RIN of the two states; it is only necessary that the measurement
be performed at the same ESA settings.

6.2 Absence of Ripple

Low-amplitude ripple for frequencies in the tens of megahertz region was previously
observed in EDFAs and attributed to multiple path interference [20]. To test for ripple on the
RIN standard we visually inspected the RIN spectrum on the ESA at different frequency spans.
Figure 6.2.1 shows the amplitude noise over the total frequency range of interest, 0.1 GHz to 1.1
GHz, with no apparent ripple. Data points are spaced about 1.67 MHZ apart. Resolution and

24


The corrected Kappa at each frequency is

_ Kian OP,

x = BP
ver ~ SP 0.03-GP,- OP,) (A2)

where the subscripts cor and un represent the corrected and uncorrected Kappas, respectively.
This is a most general formula, in which 5P, can be greater or less than 5P,. If it is greater, the
corrected Kappa increases. If it is less, the corrected Kappa decreases.

Appendix B. Addition of RIN

Although RIN is often represented in logarithmic units, it must be added directly in linear
units. A good example is the subtraction of Poisson RIN from total RIN to yield excess RIN. If
these quantities are specified in logarithmic units, each must be converted to linear numbers, then
the subtraction performed. The resulting real number can be converted back to logarithmic form.
Recall that the RIN is defined as the sum of the Poisson and the excess RIN (sections 2.1, 2.3).
Then a laser emitting 0.5 mW optical power (which has Poisson RIN of - 153 dB/Hz) and having
a RIN of - 152.2 dB/Hz) will have an excess RIN of - 160 dB/Hz. But 10 mW of optical power
(-166 dB/Hz of Poisson RIN) with the same excess RIN will have a RIN of - 159 dB/Hz.

Appendix C. Information for Applying the RIN Standard

A calibration should be performed with the user’s electrical spectrum analyzer in a fixed state
of function settings. If a setting is changed to accommodate a noise spectrum of different
magnitude, a new calibration curve must be obtained for the appropriate conditions.

As an example, we give some information on the ESA used in the NIST RIN system. Scale
fidelity can add an uncertainty of 0.075 dB per vertical division, and which requires that we shift
the calibration curve down by this amount. Thus measuring the RIN of two lasers of noise spectra
three divisions apart on the screen, would result in an uncertainty in their calibration curves that
would shift them apart by up to 0.225 dB. But changing reference levels so that the second
spectra would fall at the same vertical position on the screen would add an even greater
uncertainty of 1 dB for our ESA. Changing RBW settings would add an error of 0.5 dB

54


Appendix F: Sample Calibration Certificate

U.S. DEPARTMENT OF COMMERCE
NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY

ELECTRONICS AND ELECTRICAL ENGINEERING LABORATORY
Boulder, Colorado 80303

REPORT OF CALIBRATION BY NIST

for
Spectral Density of Relative Intensity Noise

Submitted to:
ABCDE Corp.
Address

Calibration Summai

This report summarizes the measurement results for the spectral density of relative intensity noise
(RIN) of the customer’s noise source. The source is calibrated over the 0.1 GHz to 1.1 GHz
frequency range. The measurements were performed in two steps. First, the NIST RIN
measurement system was calibrated with the NIST RIN standard. Next, the RIN of the
customer’s device was measured with the calibrated RIN system. The NIST RIN standard is an
erbium-doped fiber amplifer (EDFA) to which is coupled a linear polarizer (P) followed by a
narrowband filter (F). Thus, it is represented by EDFA + P + F as shown in Figure F1. The EDFA
has a built-in optical isolator to ensure that the amplified-spontaneous emission (ASE) that it
emits is free from potential multiple interference effects such as ripple. High-quality FC/PC
connectors and single-mode fiber are used throughout.

The RIN of the NIST standard was determined from measurements of its optical power spectral
density (OPSD) as measured by a high resolution, grating-type, optical spectrum analyzer (OSA).
The RIN is proportional to the autocorrelation of the measured OPSD, and is constant out to
several tens of gigahertz. The uncertainties that contribute to the RIN are the repeatability in RIN

Folder No: bbbb
Date of Report: March 16, 2000
Reference: P.O. No. Tttt ee/yy/nn 63


9.2 Equivalence of the Calibration Functions .............-.-- 25 eee e rere eee 39

10. Two Methods Applied to the NIST RIN System Give Similar Results ..............- 40
10.1 Quantitative Comparison of Calibration Results from the Two Methods ......... 40
10.2 Relative Stability of Two Different EDFAs With Respect to the Poisson Laser . .. . 45

10.3 Methods Compare Favorably Under Use of Variance Analysis ..... : -45
10.4 F-ratio Test Yields Similarity in the Variability of the Calibration Functions ...... 46
11. Maintaining a Measurement Assurance Program ...........-----.- +--+ -200+ - 48

11.1 Maintaining the RIN Standard
11.2 Substitution of Components

12. References

Appendix A. Calibration of the Electrical Spectrum Analyzer, Scale Fidelity Correction ..... 53
Appendix B. Addition of RIN .... 26.0.0... cece ence ne nents

Appendix C. Information for Applying the RIN Standard
Appendix D. Sample MAP Certificate
Appendix E. Calibration Service .... 2.2.0... 0 0 cece cee tnees
Appendix F. Sample Calibration Certificate
Appendix G. Shipping Instructions
Figures ..........2.0-2 20000

iv


Table 4. Comparison of the standard with the Poisson laser; other similar comparisons.

Combinations of sources

Z (eq 10.1.1), in dB

Standard deviations of the

and filters compared differences, D, in dB.
without, with SCF without, with SCF

5/3/99; F2 only
EDFAI1 + F2 with EDFA2 + F2 0.077, 0.049 0.337, 0.355
EDFA! + F2 with DFB 0.091, 0.108 0.301, 0.311
EDFA2 + F2 with DFB 0.013, 0.082 0.343, 0.359
4/29/99, F1 and F2
EDFAI + F2 with EDFA2 + F2 -0.041,  -0.107 0.356, 0.372
EDFAI + F2 with DFB(2) 0.143, 0.161 0.305, 0.316
EDFA2 + F2 with DFB(2) 0.184, 0.268 0.34, 0.358
EDFA1 + F1 with EDFA2 + Fl -0.043,  -0.054 0.212, 0.215
EDFAI1 + F1 with DFB(1) 0.142, 0.064 0.246, 0.249
EDFA2 + F1 with DFB(1) 0.185, 0.118 0.251, 0.254
EDFA] + Fl with EDFA] + F2 0.11 0.279
EDFA2 + F1 with EDFA2 + F2 0.112 0.314

DFB(1) and DFB(2) 0.112 0.295
4/27/99; F1 only
EDFA1 + F1 with EDFA2 + Fl 0.088, 0.079 0.211, 0.214
EDFA1 + F1 with DFB 0.12, 0.042 0.255, 0.258
EDFA2 + F1 with DFB 0.033,  -0.036 0.246, 0.25
4/23/99; F1 and F3
EDFA1 + F3 with EDFA2 + F3 ~ 0.0066, -0.036 0.292, 0.30
EDFAI + F3 with DFB(3) 0.108, 0.094 0.291, 0.299
EDFA2 + F3 with DFB(3) 0.115, 0.13 0.301, 0.311
EDFA1 + F1 with EDFA2 + F1 0.041, 0.041 0.195, 0.198
EDFA1 + F1 with DFB(1) 0.188, 0.113 0.245, 0.248
EDFA2 + F1 with DFB(1) 0.146, 0.071 0.246, 0.249
EDFA1 + Fl with EDFAI + F3 0.074 0.232
EDFA2 + Fl with EDFA2 + F3 0.025 0.252

DFB(1) and DFB(3) 0.0061 0.285

43



are well established, so that we need only determine that the laser’s RIN obeys Poisson statistics.
To compare the standard with the laser we used eq (9.24), which equates their calibration
functions.

First we obtained Kappa for the three filters of different shape and bandwidth using EDFA2.
The results are shown in Figure 10.1.1 for bandwidths of 1.32, 1.37, and 3.42 nm. The shape and
overlap of the three curves confirms that our calculation of the RIN scales with filter bandwidth
and shape as expected from theory. The similarity in all three Kappas indicates that calibration of
the RIN system is independent of the magnitude of the RIN and the shape of the filter. Next we
compared the laser with filter F2 using both EDFA1 and EDFA2. The results shown in Figure
10.1.2 are again similar. Note that measurements were taken sequentially in the shortest time
reasonable to duplicate experimental conditions. When a set of calibrations was performed using
different EDFAs, a matching set was performed with the laser, reinforcing the comparison of the
two methods.

To quantify the calibration results as a comparison of methods between the laser and
combinations of different components intended to compose a valid standard, we determined the
simple average of the difference between Kappas recorded at each frequency over the spectrum.
Let k,; and k,; represent Kappa of the standard and the laser at the ith frequency £, respectively,
and D; is the difference between Kappas, D; = x,; - «,; . Then the average difference, Z, is
obtained by summing over the 601 points in a spectrum,

pL ae 1011
601 601 ( )

Figure 10.1.3 shows a typical distribution of differences obtained for the standard (EDFA1 + F2)
and the laser. The differences range from -1 to +1 dB, with an average difference of 0.058 dB.
The standard deviation of the differences is 0.3 dB, which illustrates the rather large fluctuations
that are characteristic of such rf noise spectra.

In Table 4 we compare calibration results from the laser with various combinations of

41


Kappa (arbitrary scale in dB)

T T T T T T T T T 1
0.4 02 03 04 05 06 07 08 09 1.0 14

Frequency (GHz)

Figure F2. Graph of the frequency-dependent calibration function, Kappa, obtained for the
NIST RIN measurement system by application of the RIN standard.

Uncertainty Assessment

The uncertainty in calibrating the RIN of the customer’s device will depend on whether it is a
broadband source modelled after the NIST standard, or whether it is a laser. For a laser the total
uncertainty is due to the NIST RIN standard plus the uncertainty contributed by the NIST RIN
Measurement system. The latter is the uncertainty in the calibration function (Kappa) and is
determined at the time the calibration is performed. If the RIN of the source can be approximated
by thermal light, such as the NIST RIN standard, however, the combined uncertainty is reduced
by determining the RIN from the same method used for the NIST RIN standard. In this method
the theory of the RIN of thermal light is applied to the optical power spectral density of the device
as measured by the NIST optical spectrum analyzer, which has been accurately calibrated.

The uncertainty estimates for the NIST RIN standard are determined from the repeatability error

Folder No: bbbb
Date of Report: March 16, 2000
Reference: P.O. No. Tttt ce/yy/nn 66


might occur due to fiber bending. The excess RIN of this device is much greater than its Poisson
RIN, so that the total RIN can be considered excess RIN. The shape and bandwidth of the filter
determine the RIN.

Figure 3.1.3 shows the setup for measurement of the standard’s power spectral density
(OPSD) using a diffraction grating-type optical spectrum analyzer. For a single measurement, the
OSA is set to average four sweeps on high sensitivity with the resolution bandwidth set at the
minimum of 0.05 nm. High-quality FC/PC connectors and single-mode fiber are used. Points 1, 2,
3, and 4 represent locations where connectors were routinely disconnected to change
components. We later show that this procedure can change the power loss through the fiber
transmission line, but has no significant effect on the RIN which is invariant under attenuation.
Also, we will show that the EDFA’s optical isolator sufficiently shields it from backreflections due

to the conncctor’s small but finite return loss, and prevents ripple on the output signal of the RIN
standard.

3.2 Source RIN of the Secondary Method

To establish a MAP, a secondary method was used to calibrate our RIN measurement
system. Results were compared with those obtained from the standard (or primary method).
The secondary method was a DFB laser having very low excess RIN, specified by the
manufacturer to be <- 172 dB/Hz at the recommended operating power of 28 mW. In section 6.6
we will show that attenuation of the light to a fraction of a milliwatt results in practically Poisson-
limited RIN. This result follows because under attenuation the excess RIN is invariant but the
Poisson RIN increases. Thus, the RIN of the standard is described by the excess RIN of filtered
ASE, and the RIN of the laser is described by Poisson RIN.

4. Theory of the Spectral Density of the RIN

The spectral density of the RIN of the standard used in this MAP, as approximated by thermal
light, must be derived from physical theory, as the RIN cannot be directly verified through

experimental means. In practice, our theory must yield the RIN from knowledge of the OPSD as

11


Appendix A. Calibration of the Electrical Spectrum Analyzer; Scale Fidelity Correction

A complete calibration of the rf spectrum analyzer is not necessary because all but one
function setting that contributes to a measurement is included in Kappa. Not included, however,
is a scale fidelity factor that accounts for the vertical position of the noise signal on the screen of
the ESA. RIN measurements made for which the rf amplitude noise has different magnitudes
must account for this factor. Like Kappa, this factor also has a frequency dependence.

We computed the scale fidelity factor for our ESA using the procedure illustrated in Figure
Al. Anrf signal generator was set at a predetermined power level with oscillation frequency of
500 MHZ. The power was precisely measured with an rf power meter. A 10 dB attenuator was
then inserted into the transmission line and the power recorded, yielding a magnitude of 10 dB for
the attenuation. This procedure of measuring the power with and without the attenuator was then
applied to the electrical spectrum analyzer. Connector losses were carefully accounted for, and
control settings were the same as for the RIN measurements, including the position of the signal
on the screen. The vertical scale was set at 5 dB per vertical division. Measurement of the rf
signal with and without the 10 dB attenuator occurred at a vertical separation of 9.67 dBm on the
screen. Thus for one division on the screen, the uncertainty in noise power due to the scale
fidelity was (10 - 9.7)/2 = 0.15 dB. (The manufacturer’s specification for the ESA is that the
amplitude error can be no greater than 0.7 dB over the 10 divisions that compose the screen.)

Note that the uncertainty in ESA resolution bandwidth (RBW) is included in the calibration
function; thus it need not be determined separately. Of prime importance, however, is that a
calibration holds true only for a given group of ESA sweep control settings, such as RBW, sweep
time, internal attenuation, etc. Our calibration method neglects only error due to the vertical scale
reading, or scale fidelity factor. A number of calibrations performed at different settings of RBW
or sweep time etc. would give calibration curves of slightly different magnitude, but similar shape
at each setting.

We now determine a scale fidelity correction for comparing signals of varying magnitude,
such as occurs for Kappa from the amplifier compared with Kappa from the laser (see section 9.2
and eq (10.1.1)). The direction of this correction, which is applied at each frequency separately,
is to expand the difference between the two noise powers on the screen. If the difference
between noise powers is 6P, - 5P, (at the same frequency) and S is the correction, then

ap,
S= SP, + 0.03-(8P,- 6P,) ° AD

53


Table D2. Summary of typical measurement uncertainties contributing to the total uncertainty in the
RIN of the standard.

EDFA2 + F1 Uncertainty evaluation Standard Standard
Type (A or B) uncertainty (1/Hz) uncertainty (dB/Hz)

Unep A 0,000561-10" 0.002
Un A 0.001180-1077 0.005
U, A 0.012315-107! 0.051
Unew A 0.000419-107" 0.002
Expanded, U - 0.029-10" 0.12

Combined, u, - 0.014475-10" 0.060

The repeatability error is calculated from the basic standard-deviation formula. The uncertainties for
the OSA parameters are determined by application of the standard propagation of errors formula. The
combined standard uncertainty u, of the average RIN is determined by combining the Type A
uncertainties (Upsp. Uns, U;, Upsw) in quadrature. The expanded uncertainty, U, is twice the combined
standard uncertainty. The values used to calculate the NIST expanded uncertainties appear in Table 2.

Folder No. and NIST ID: xx and yy
Date of Report: March 1, 2000
Reference: P.O. No. Mmm, 2/3/00 59


To relate the fluctuations in photoelectric current Aj(t) that arise from the intensity
fluctuations of the light field AI(t), we define the following quantities: j(t) is the total
photoelectric current in the photodetector circuit at time t, k the distribution of current pulses,
and 7 the quantum efficiency of the detection system. Then the autocorrelation of the current
<Aj(t)Aj(t + t)> at delay or correlation time t is related to the autocorrelation of the intensity

fluctuations by

<A AE +t = nyc fey! +s)
_ (4.1.1)
Pf fhe) We <a anert!-t!+1)>dt'dt" ,

where t’ and t” are just dummy integration variables and the first term represents the shot noise of
the photocurrent ([17], eq (9.8.10)). To later arrive at a functional form for the RIN, we define
some quantities connecting the time and frequency domains. Recall that the spectral density of
the current fluctuations x(«) is the Fourier transform of the photocurrent autocorrelation

function,
x(@) = f <Aj(DA(E+t Pe" dt (4.1.2)

To represent the frequency response of the RIN system, we define the Fourier transform of k(t) as
K(@):

K(w) = faedt . (4.1.3)

13


Contents
Introduction .............--.0-0-22005

Background .. 0.2.0.2... 000 e eee cee nt t ee eee reste
2.1 Definition of the RIN of an Optical Source
2.2 Application of Laser RIN to Noise Figure of Optical Amplifiers, Electrical Methods . .7
2.3 Measurement of RIN ...........000 02.220 c eee 9

ARIN Standard Based on Two Different Methods ................--20--0-0----
3.1 Form of the RIN Standard or Primary Method .
3.2 Source RIN of the Secondary Method ..........----..---

Theory of the Spectral Density of the RIN .........5-.-. 2.0000 e eset eters ll

4.1 Complete Derivation of the Spectral Density of the RIN from the Optical Field
Correlations and the Semiclassical Theory of the Photodetection of Light ......... 12

4.2 Numerical Formulation of RIN in the Wavelength Representation .............-. 18

Accurate Determination of RIN Requires Precise Calibration of Optical Spectrum

Analyzer Parameters .. 1.2.2... 20ers
5.1 Measurement of Resolution Bandwidth and Its Uncertainty
5.2 Measurement of Wavelength Error and Distortion
5.3 Nonlinearity of the Optical Power Spectral Density Scale

Some Properties of the RIN Standard ..... 2.2.0... 0-0 eee eee eee eee eee 24
6.1 Polarization ............. .
6.2 Absence of Ripple . .
6.3 RIN of Various Filters of Exact Mathematical Shape; Dependence on Filter
Bandwidth and Shape ..... 2.2.2.2. 00 e eee
6.4 Measured RIN of Three Different Filters When Linked to the Same EDFA .. .
6.5 Use of Connectors and the Effect of Losses .........-..---- 22000 serene
6.6 Combined Effects of Attenuation, Pump Current, and Power Spectral Density Levels 27

Total Uncertainty in the RIN Standard .............0.-.0-0-. 2022 ee eee ee eee
7.1 Repeatability Error
7.2. Measurement Error From the OSA Parameters
7.3 Combined Standard Uncertainty

Achieving the Poisson Limit .. 2... 62.202. 2 eee cece eee eee ees 35
8.1 The DFB Laser of the Secondary Method Has Nearly Poisson-Limited RIN ....... 36

RIN System Calibration Using the Standard and the Laser ........-....-.-4-0--- 37
9.1 Derivation of the Calibration Equations For the Standard and Secondary Methods . . 38

iii


7.3 Combined Standard Uncertainty

The RIN of the standard is the average of all RIN measurements used to compute Uggp. For
filter F1 with 40 observations <RIN> = 1.0325 -107! Hz". To compute the combined standard
uncertainty of the average RIN, u,, the four uncertainty estimates described in sections 7.1 and
7.2, Upep, Ur, U, aud Uppy, are added in quadrature. Since all four sources of uncertainty use
measured data to compute their values (as opposed to manufacturer’s specifications, for
example), they are all considered Type A uncertainties. (There are no significant Type B
uncertainties.) Although different amplifiers were used to quantify Uggp and U,.y, this should not
influence the uncertainty estimates.

The expanded uncertainty, U, is twice the combined standard uncertainty (U = 2u,), which
represents an approximate 95 % confidence interval for the average RIN [22]. The combined
standard uncertainty and expanded uncertainty for filters F1 and F2 are shown in Table 3. For F1,
the combined standard uncertainty ( 0.014475 - 10" Hz") is 1.4 % of the average RIN (1.0325 -
10" Hz"). The average RIN for filter F2, <RIN> = 6.3712 - 10 “” Hz, was based on 20

observations used to compute Uggp. The combined standard uncertainty (0.053564 - 10°? Hz") is
0.84 % of the average RIN.



RN 4
Z -t0988
ao
S 4
Z -109.90 4 EDFA1 + F1
ig
4 ----+ EDFA2+F1
-109.92 4
109,94 TI] 7] 1
0 1 10
Frequency (GHz)

Figure 6.4.3. Comparison of the RIN from F1 using EDFA1 and EFDA2.

78


directly from the OSA. We refer to the broadened curve as the slit function. Figure 5.1.1 shows
that the slit function for our OSA is fairly smooth from the peak value down to about 25 dB
below peak value, below which it becomes quite irregular. The 1 nm span is centered at 1551 nm,
the resolution bandwidth is set at 0.05 nm, and the tunable laser is set at 3 mW optical power. In
the second method, the noise-equivalent bandwidth (denoted herein by B) is calculated and used
as the definition of resolution bandwidth. If A, is the center wavelength of an arbitrary-shaped slit
function T(A) of peak value T(A,), then

- TaD [T@a, (5.1.1)

where integration is performed over the entire slit function with the background noise subtracted
out. For a perfectly rectangular slit, either method gives the exact answer, while for a distorted
slit, B is more accurate because it accounts for the exact slit geometry.

For each method, the tunable laser was set at predetermined wavelengths and the slit
function displayed on the OSA. The two methods agree as shown in Figure 5.1.2. For either
method, the resolution bandwidth is practically constant over the wavelength range shown. For
the 3 dB method, the average resolution bandwidth is 0.041 nm, with standard deviation of 0.001
nm. For the noise equivalent bandwidth, the average is 0.045 nm, with the same standard
deviation. We use the latter result because our slit function is irregular. Note that the measured

values for the resolution bandwidth are actually smaller than the OSA setting.

5.2 Measurement of Wavelength Error and Distortion

The OSA wavelength scale (horizontal axis) undergoes distortion that manifests itself as a
nonuniform distribution of data points. The absolute error and distortion in the wavelength scale
was determined by comparing the wavelength from a narrow linewidth tunable laser as read by the
OSA with the known wavelength as read by a precision wavemeter. OSA data were averaged

over four sweeps. For example, a wavelength setting of the tunable laser at 1560 nm yielded a

22


Certain commercial entities, equipment, or materials may be identified in this document in order to
describe an experimental procedure or concept adequately. Such identification is not intended to imply
recommendation or endorsement by the National Institute of Standards and Technology, nor is it intended
to imply that the entities, materials, or equipment are necessarily the best available for the purpose.

National Institute of Standards and Technology Special Publication 250-57
Natl. Inst. Stand. Technol. Spec. Publ. 250-57, 96 pages (September 2000)
CODEN: NSPUE2

U.S. GOVERNMENT PRINTING OFFICE
WASHINGTON: 2000

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402-9325



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and the laser by measuring their calibration functions. Our main objective in this section is to
verify that the variations in their calibration functions are similar. Again, all calibrations are
performed using the NIST RIN measurement system.

During a one-day period, we determined Kappa using both the standard and the laser as a pair
of sequential measurement sets taken in the least time possible (~2 min); this is the time needed
to store the data for the standard, disconnect the standard, connect the laser, and collect the new
data. This insures nearly identical environmental conditions (such as temperature and background
rf fields) for the two methods. Stray rf signals can appear unpredictably in a data spectrum, for
example from mobile telephone sources, and their magnitude may vary during the time of a
measurement. They must be averaged out by manual inspection of the data. (The ESA data are
averaged from nine sweeps, which takes about 20 s).

Figures 10.3.1, 10.3.2, and 10.3.3 show the data from four different days for Kappa of
EDFAI + F1, EDFA2 + F1, and the laser, respectively. The different symbols represent the four
measurement occasions. The distribution of Kappa with frequency is fairly repeatable within each
method, and follows a similar pattern when comparing methods. Figure 10.3.4 compares the
average value of Kappa for EDFA1 + F1 with that of the laser, where the Kappas at each
frequency are the calculated averages of the same four data points from Figures 10.3.1 and
10.3.3. Figure 10.3.5 compares the average value of Kappa for EDFA2 + F1 with that of the
laser, where the Kappas at each frequency are the calculated averages of the same four data points
trom Figures 10.3.2 and 10.3.3. Kappa for the laser is slightly lower than that of either EDFA
using F1.

To assess the variation in Kappa for both methods, we calculated the normalized standard
deviation of the four observations at each frequency. Scatter plots of the data are shown in
Figures 10.3.6 and 10.3.7 for the laser compared with EDFA1 + F1 and EDFA2 + F1,
Tespectively. The data indicate that the two independent methods give similar standard deviations
over the entire frequency range, indicating that they are comparable.

10.4 F-ratio Test Yields Similarity in the Variability of the Calibration Functions

We performed a statistical F-test to compare the variability in Kappa between the two

46


7. Total Uncertainty in RIN Standard

We determined the total uncertainty in the RIN standard from the random error or
repeatability of measurements, and the contributions of the OSA parameters to the OPSD
measurement. To determine the OSA’s contribution to the total uncertainty we apply the
propagation of errors formula to the numerical RIN formulas of the preceding section. The OSA
parameters that contribute significant errors are resolution bandwidth, wavelength distortion

(absolute wavelength and wavelength interval), and nonlinear spectral responsivity.

7.1 Repeatability Error

To determine the repeatability uncertainty, five measurements were repeated on several
distinct measurement occasions over the course of several weeks. (EDFA2 with F1 was
measured on eight occasions and EDFA2 with F2 was measured on four occasions.) On each
occasion, the five repeated measurements were taken within a short period of time so that the
measurements would be similar within the measurement occasion. On each occasion, the four
connectors shown in Figure 3.1.3 were disconnected and reconnected between each of the five
measurements. The repeatability uncertainty was computed as outlined in the ISO Guide to the

Expression of Uncertainty [21]. The average RIN for the five measurements on a given day is

<RIN, > = LORIN, . (7.1.1)

For a series of days, the average RIN is

d 5
<Kin> = _ >> RN, (7.1.2)

where d is the number of measurement occasions or days. Thus the repeatability uncertainty is

30


2he | Py
AP, SP,(w) ”

K,(@) = (9.1.4)

where 2hc/AP, is the Poisson RIN of the laser.

9.2 Equivalence of the Calibration Functions
To derive an exact expression equating the calibration functions we note that the Poisson RIN
of the laser increases in the electrical detection circuit by an amount 1/n. Therefore an equivalent

optical RIN for the laser that would yield a Kappa equivalent to that for the standard, with all
other conditions kept constant, is

R 3P (@)
7 = «,(@)- P, ; (9.2.1)

where now k,= k,. Solving for x, gives

RP,

K,(@) = 1 5P,(0) :

(9.2.2)

The photocurrent in the electrical circuit is i= pP, = nqP/hv, where h is Planck’s constant, q is
the electron charge, and p and 1) are the responsivity and quantum efficiency of the photodetector,
respectively. The de voltage is V = ir, where r is resistance. Substituting these expressions for

current and eq (9.1.3) for the Poisson RIN, the quantum efficiency cancels and we obtain

2qV
8P,@) ” (9.2.3)

K,(@) =

39


SP 250-1 Spectral Radiance Calibrations SP 250-24 Standard Cell Calibrations
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video bandwidths are 300 kHz and 300 Hz, respectively. Figure 6.2.2 shows the frequency band
from 700 MHz to 850 MHz devoid of ripple. Data are spread over 0.25 MHZ and video
bandwidth has been reduced to 100 Hz. Finally, Figure 6.2.3 shows a ripple-free noise spectrum
from 500 MHz to 600 MHZ. Data points are spaced every 0.166 MHZ, and video bandwidth is
30 Hz. Sampling other frequency intervals, such as 100 MHz to 250 MHz, and 400 MHz to 550
MHz (neither shown), also yielded no apparent ripple.

To insure that the RIN standard is indeed free of ripple, we compared the calibration
function obtained by applying it to the RIN system with that obtained from a ripple-free
independent source (the Poisson laser of method two, see sections 9.1, 9.2, and 10.1). The
calibration functions from the two RIN sources are nearly identical, demonstrating that the RIN
standard is ripple-free. The absence of a ripple effect indicates that the built-in optical isolator
effectively shields the EDFA from feedback.

6.3 RIN of Various Filters of Exact Mathematical Shape; Dependence on Filter
Bandwidth and Shape

To understand the behavior and properties of the RIN standard, we can solve the exact RIN
equation for filters whose transmittance curves have exact mathematical shapes. Column 2 of
Table 1 shows the results for a Gaussian, a Lorentzian, and a rectangular-shaped transmittance
filter, with A the triangle function, the C’s constants, f the baseband frequency, and B the filter
bandwidth. In all three cases, the RIN is proportional to the product of the the inverse of the
filter bandwidth and a bandwidth-dependent function [16]. It is practically constant to tens or
even hundreds of gigahertz, as expected for frequencies that are small compared to the optical
bandwidth as shown. From the form of the underlying functions, the magnitude of the RIN can be
increased significantly by decreasing the bandwidth.

25


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2.3. Measurement of RIN

We measure RIN in the electrical domain by direct detection, although it can be determined
using optical correlation techniques. A general RIN measurement system with losses is shown in
Figure 2.3.1. The beam passes through a loss medium, such as an attenuator, and is collected by
the photodetector. The RIN, R(v), is to be determined at reference plane A, before any losses.
The Poisson component of the RIN is increased at plane B due to losses, and again at plane C due
to inefficiency in the photodetection process. System efficiency can be combined into one factor
nr = (1 - L), where L is the fractional loss before the detector. The excess RIN, however,
propagates unchanged through the system. If R,(v) is the measured RIN at plane C (which
includes Poisson RIN), then the laser RIN

is
Ry(v) = Rew) - LA ~ ny) - 3.1)

The excess RIN, R,,(v), is determined by subtracting the measured Poisson or shot-noise RIN,
2qfi, from R,(v), giving

2
R.A) = Rev) - 2.3.2)
This last equation is equivalent to subtracting the Poisson RIN from the RIN at plane A,

= _ 2hE
RW) = RAV) Po” (2.3.3)
where & and P, are the laser frequency and power (at plane A), respectively.
To measure RIN in the electrical domain, a bias tee sends the de photocurrent produced in a
photodetector by a test laser to an ammeter, while the ac noise is amplified and then displayed on

a radio-frequency (rf) spectrum analyzer. In the electrical domain we weight the noise power per


kK, OP.

= Lun OF 1

“cor ~ SP —0.03-(6P,- OP,) * (A2)

where the subscripts cor and un represent the corrected and uncorrected Kappas, respectively. This is
amost general formula in which 6P, can be greater or less than 5P,. If it is greater, the corrected
Kappa increases at the set calibration frequency. If it is less, the corrected Kappa decreases.

[1] B.N. Taylor and C.E. Kuyatt, “Guidelines for Evaluating and Expressing the Uncertainty of NIST
Measurement Results, NIST Technical Note 1297, 1994 Edition.

For the Director, Report Prepared/Calibrated By:
NIST

Gordon Day, Chief Gregory E. Obarski
Optoelectronics Division Physicist

Sources and Detectors Group

Folder No. and NIST ID: xx and yy
Date of Report: March 1, 2000
Reference: P.O. No. Mmm, 2/3/00 61


1.0314 =

1.0308 — °
_ °
7 1.0302
uw
x
WH 1.0296 +4
z= °
z 1.0230
« ° Average RIN = 1.0296
1.0284 | Std Dev = 0.0008 = 0.0036 dB
1.0278 4
T T T T T T T T T T 1
° 1 2 3 4 5s 6 7 8 9 10 11

Attenuation (dB)

Figure 6.6.1. RIN of EDFAI + F1 vs. attenuation. Any apparent trend is of no practical significance.

14,0308 |

1.0304 4 ‘Std Dev = 0.0005 = 0.002 dB
1.0300 4

1.0296 4 °
1.0292 4

1.0288 4 °

RIN (1/Hz) x E-11

1.0284 4

1.0280

19276 ott
100 120 140 160 180 200 220
Pump current (mA)

Figure 6.6.2. RIN of EDFAI + F1 vs. pump current of the EDFA.

79


methods. This test computes the ratio of the variances for the two methods and compares this

ratio to critical values from an F-table [25]. To apply the test we define the ratio

F==, (10.4.1)

where S,? and S,” are the sample variances for Kappa of the laser and standard, respectively. If
the variances obtained from the two methods are very similar, then F will not be too large or too
small. Specifically, if F is greater than the 100( 1- a/2)" percentile of the F distribution, or less
than the 100(a/2)" percentile, the variances will be considered significantly different. The value,
“a,” is the probability of incorrectly concluding that the variation in Kappa for the two methods is
different. Usually “a” is a small number since we want the probability of making an error to be
small. The critical values from the F table are F, .,;>.3,; and F,,>.3 ;, where the values 3 and 3 are
the respective degrees of freedom for S,” and S,”. Ifa = 0.05, then the critical values are Fy 075.3, 3
= 15.44 and Foo5,3,3 = 0.07.

To compare methods, we apply the F-ratio test at each frequency. Because the sample sizes
are identical for each method, the critical values are the same for each test. Figure 10.4.1 shows
the distribution of F-ratios with frequency by comparing the laser with EDFA1 + F1. The two
horizontal reference lines on the plot represent the critical values for the F test when a = 0.05.
The majority of the F ratios lie within the critical values, indicating that the two variances are not
statistically different. The F tests at each frequency confirm that the variation in Kappa is similar
for the two methods studied.

We repeated the F-test using EDFA 2+ F1. The results shown in Figure 10.4.2 are
equivalent to those obtained for EDFA1, again confirming that the variation in Kappa is similar
for the two methods. We expect such good agreement because the RIN of both the laser and the
standard (using either EDFA) are both known and constant over the entire frequency band, and

the relationship between their Kappas was precisely determined from physical laws.

47


Also, since the intensity noise of the Poisson-limited laser is predictable and stable, and its RIN is
well known and historically accurate, it too can be considered a RIN standard. However,

because it is not as field employable, it is most useful as a laboratory standard.

We are especially grateful to Wayne Itano for carefully verifying the mathematical expressions
for the RIN of thermal light. We thank the Electronics and Electrical Engineering (EEEL)
Measurement Committee, Richard Jones (chairman), John Kitching, and Wayne Itano for
evaluating various scientific and technical aspects of the manuscript. The first author thanks Paul
Hale for many stimulating discussions related to this work, and for his general interest in the
subject matter. Jack Dupre of Agilent Technologies provided insight on calibration methods for

optical spectrum analyzers. Jack Wang discussed statistical tests for comparing two independent
methods.

49


measured by an optical spectrum analyzer (OSA). Much of the fundamental theory is greatly
developed by Mandel and Wolf [17]. However, it is sketchy in places, and not formulated in
terms of RIN explicitly. It also contains an acknowledged error of a factor of two in one of the
key results [18]. Thus we need to give a complete and accurate derivation of the RIN spectrum in
the frequency and spatial wavelength representations. Although the amplitude fluctuations can be
described by distributions of photon number density with respect to time, this method need not be
applied to the filtered ASE of the EDFA (RIN standard) or the Poisson light of the laser. To
develop a useful formalism we applied the theory of fluctuations to the conversion of optical noise
on the source to electronic noise within the RIN measurement system. The correlation between
the amplitude fluctuations of partially or totally coherent light and those of the associated
photocurrent are well known [17]. In formulating the RIN in terms of the spatial representation,
we note that a fluctuation of the intensity in time gives rise to a frequency component. Such
Fourier frequency components manifest themselves as a spatial wavelength distribution in the
grating-type optical spectrum analyzer used to measure the power spectral density. Thus we seek
to represent the temporal Fourier transform of the amplitude noise as fluctuations in either
frequency or wavelength. Any contribution from the Poisson or standard quantum limit will be
considered negligible compared to the filtered ASE of the EDFA. Since our derivation follows

that of Mandel and Wolf, we use their notation to minimize any confusion that may arise.

4.1 Complete Derivation of the Spectral Density of the RIN From the Optical Field
Correlations and the Semiclassical Theory of the Photodetection of Light

From the general form for the autocorrelation of the photocurrent fluctuations ([17], section
8.4.1, eq (9.8.10)), we derive the spectral density of the current fluctuations in terms of
measurable quantities ([17], eq (9.8.24)) which is omitted from the text. We then apply the
properties of the degree of coherence of the light ficld ([17], section 8.4.1) to express the RIN as
an autocorrelation of a power spectral density function. For completeness we give the results for
both polarized and unpolarized light, although we use only polarized light for the standard.
Unless specified, all integrals in both the time and frequency representations are double-sided;

thus their limits run from minus to plus infinity.