PMD Compensator and PMD Emulator
by Yu Mimura *, Kazuhiro Ikeda *, Tatsuya Hatano *,Takeshi Takagi *, Sugio Wako * and Hiroshi Matsuura *As a technology for increasing the capacity to meet the growing demandfor communications in recent years, dense wavelength-division multiplexing(DWDM) is being implemented in tandem with achieving higher transmission rates on eachchannel. At next-generation transmission rates of 40 Gbps, it is expected that polarization mode
dispersion (PMD) will be the main factor in the deterioration of transmission characteristics.
Both first-order PMD and higher-order PMD can affect the performance of a high-speed opticaltransmission system. A PMD emulator capable of generating PMD up to the second-order isuseful in estimating the performance degradation due to PMD and in optimizing the devices
that compensate for this type of degradation. The present work is a programmable device
based on variable Faraday rotators (VFRs) that is capable of emulating first-order and two
components of second-order PMD. Various PMD conditions can be generated by the emulator
and the measured values agree with theoretical simulations. Further, we propose a much simpler
configuration for the PMD compensator (PMDC) with higher-order PMD canceller (HOPC),
unifying the monitor sections of the PMDC and HOPC into one power monitor. Test results for ourconfiguration in a 10-Gbps evaluation system are also reported.

ABSTRACT1.

INTRODUCTION

In response to the need for larger capacities in longhaul optical digital transmission, greater channel density
has been achieved by wavelength division multiplexing(WDM), and the bit rate for each channel is also being
increased.
At 40 Gbps, which is in the next generation oftransmission rates, polarization mode dispersion (PMD),
which does not present a problem at bit rates of 10 Gbps
and below, can impose significant limitations on the
distance over which transmission is possible 1). Further,at the distances served by 10-Gbps transmission, which
is currently becoming the mainstream technology, there
are concerns that using fibers installed in previous years
may, depending on the amount of PMD, cause problems
in terms of system configuration 2).
In recent years there have been many programs tostudy PMD compensation (PMDC) 1), 3), 4). PMD arises
from random birefringence, induced either by increasing
the core eccentricity of single-mode fibers or by internal
stress due to changes in lateral pressure or temperature.
This gives rise to a phenomenon known as differential
group delay (DGD), in which two orthogonal polarization
modes, which should, in theory, be degenerating in fact*

Transmissions & Components Dept., FITELPhotonics Lab.

diverge. In these programs, the PMDC may be controlledeither as the DGD element in the PMDC, completely
compensating for DGD in the transmission line, or, as the
input state of polarization (SOP) aligned to the principal
state of polarization (PSP) 2). However, both of thesecompensation methods were only for DGD, which is firstorder PMD.
PMD also contains higher-order components, and secondorder PMD (SOPMD) impairment to pulse propagationand the system penalty cannot be neglected 2), 5). A PMD
emulator, which is capable of generating a desired
and stable PMD up to the second order, is useful inestimating the performance degradation due to PMD
up to the second order and to optimize the devices
compensating for this type of degradation. Up to now,
several techniques have been proposed to emulate
PMD by the use of polarization rotators in combination
with polarization maintaining fibers (PMF) or birefringent
crystals 6), 7). However, these techniques have difficulties
controlling second-order PMD because of the frequency
dependence of these effects. The present work relates
to a programmable device capable of emulating firstorder PMD and two components of second-order PMD
based on a variable Faraday rotator (VFR). Various PMD
conditions can be generated by the emulator and themeasured values agree with theoretical simulations.
F u r t h e r, c o m p e n s a t i n g f o r s e c o n d - o r d e r P M D
completely requires a complicated configuration, such

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PMD Compensator and PMD Emulator

as a PMD emulator consisting of many DGD sections.
Such a configuration can be expensive, and control
speed becomes a problem. On the other hand, PMDC
with a higher-order PMD canceller (HOPC) 8) is one
type of PMDC, which, while unable to provide complete
compensation for second-order PMD, has a simple
configuration. The HOPC is only a polarizer that functions
as a suppresser of PMD depolarization, with a polarization
controller for SOP alignment to the transmissive axis of
the polarizer. Therefore, a combination of conventional
first-order PMDC with HOPC includes second-order PMD
mitigation and is simple in configuration.
In this paper, we propose a much simpler configuration
for a first-order PMDC with HOPC, unifying the feedback
monitors for the PMDC and for the HOPC into one powermonitor. Test results for our configuration in a 10-Gbps
evaluation system are also reported.

Specifically, the DGD and SOPMD generated by two
DGD sections may be represented as

2.

3.

SECOND-ORDER PMD

First- and second-order PMD vectors may be representedbyτ = τ· q→→→τ ω = τω· q + τ · q ω
→

(1)
(2)

→

where: the subscript indicates differentiation, ω isthe optical angular frequency, τ is the DGD, and→q is the unit Stokes vector aligned with the PSP.
The absolute value of the second-order PMD vector
is the SOPMD, the first term of the right side is apolarization-dependent chromatic dispersion (PCD)
component which is parallel to the first-order PMD
vector, and the second term of the right side is apolarization state depolarization (PSD) component whichis perpendicular to the first-order PMD vector. The units
for SOPMD, PCD, and PSD are ps 2 , ps/nm, and ps
respectively, but in this paper all are shown in units of ps2
for simplicity.
For a PMD emulator that uses a concatenation ofbirefringent elements such as polarization maintaining
fiber (PMF) or birefringent crystal, the PMD vector canbe calculated recursively 7). For the device consistingof m sections, first- and second-order PMD may be
represented bymτ = Σ R (m , n + 1 )τ n

(3)

→

n =1
m

τω = Σ R (m , n + 1 )(τ nω + τ n × τ (n ))
→

→

→

n =1

τ = √ τ12 +τ22 +2τ 1τ 2cos2τω = τ 1τ 2sin2θ

(6)
(7)

where: τ1 and τ2 are the DGD of the two DGD sections,and θ is the rotational connection angle. The DGD and
SOPMD are independent of frequency. In this case,because the SOPMD vector is always perpendicular to
the first-order PMD vector, SOPMD has only the PSD
component.
In contrast, the DGD and SOPMD generated by the
concatenation of more than two DGD sections, have aperiodic characteristic with respect to frequency, and the
SOPMD has two components. The free spectrum range(FSR) of a device is determined by the length of each
DGD section.

SECOND-ORDER PMD EMULATOR

3.1 Configuration
The PMD emulator consists of four DGD sections
concatenated by three VFRs, which function aspolarization rotators 9). Figure 1 shows a schematic of thedevice, which can generate first- and second-order PMD.
In order to achieve a single FSR, all DGD sections havethe same DGD value of 7.5 ps. The resulting FSR is 133.3
GHz, and all phases of all DGD sections are tuned to it. In
order to shift the DGD and SOPMD spectra in frequency
while keeping the spectral profile constant, a common
frequency shift has to be applied to all FSRs. This can beachieved by a phase shifter, or by temperature control of
the DGD sections. Although the number of DGD sectionsin the PMD emulator constructed here is four, that
number can be reduced by setting VFR angles to zero.
For example, setting any two angles to zero reduces thenumber of DGD sections to two.
Because there is a natural correlation among DGD,
PCD, PSD and SOPMD, these variables cannot be
individually set to any arbitrary value. However, by thesimultaneous non-linear fitting of more than one target
profile, the rotational connection angles can be calculated.
In the emulator constructed here the rotational connection
angles of the VFRs can be set to the angles determinedby fitting, and the error of the rotational connection
DGD

(4)

→

where: τ n is the first-order PMD vector output by→n -th DGD section, τ (n ) is the first-order PMD
vector output by first n DGD sections, and R is
defined with rotation matrix for the n-th DGD
section (Rn ), such that

R (m , n ) = RmRm-1 ...Rn (m >n )R (m , m ) = Rm
R (m , m+1 ) = identity matrix(5)

Variable Faraday Rotator

Figure 1

Schematic for the first- and second-order PMD
emulator with VFRs.

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PMD Compensator and PMD Emulator

causes measurement error. Precision measurement of
PMD and SOPMD can be effected by this system. The
response time of the VFR for a π /2 rotation is less than 60
ms.

TunableLaser

Polarimeter

DUT

Variable Faraday Rotator

Figure 2

Schematic for the first- and second-order PMD
measurement system with VFR.

angle with respect to the calculated value is less than ±3
degree.
The tunable DGD range of the PMD emulator is 0 to 30
ps, variable SOPMD range is 0 to 260 ps2, and insertion
loss of the device is 1.7 dB.
3.2 PMD Measurement System
Figure 2 shows the configuration of the PMD
measurement system, which is based on the generalpolarization analysis method. The VFR is used as apolarization controller following a polarizer, which controls
input SOP. A polarimeter is used as a Stokes analyzer,
which analyzes output SOP. The PMD vector is analyzed
by the Muller matrix method (MMM) 10), and is determinedby measuring the two output Stokes vectors resulting
from two orthogonal input Stokes vectors, and the firstand second-order PMD values and the components of
SOPMD are calculated.
Two Stokes vector measurements performed at
different wavelengths are required to determine the PMD
vector at one wavelength. Because the SOPMD vector
is the derivative of the PMD vector, determining the
SOPMD vector at one wavelength requires Stokes vector
measurement at one more wavelength. Determining
SOPMD requires the measurement of at least two
Stokes responses at three wavelengths. For an accurate
determination, these measurements have to be completed
before the PMD, the SOPMD and the polarization statesof the DUT change. Utilizing a VFR that has a short
response time for input SOP control, measurement time
can be shortened and it is possible for measurement not
to be affected by changes in the polarization state, which

3.3 Results of Evaluation
With a fixed DGD spectrum, the SOPMD spectrum waschanged by different values. The target DGD value was
20 ps at 1548 nm, and the target SOPMD values were 75,
100, and 125 ps2. For each of the cases, a set of angles
for the VFRs was calculated by simultaneous non-linear
fitting:
SOPMD 75 ps2 : 31.0, 67.5, 31.0 [deg.]
SOPMD 100 ps2 : 26.4, 65.2, 26.4 [deg.]
SOPMD 125 ps2 : 21.8, 63.5, 21.8 [deg.]
Figure 3 shows DGD and SOPMD by emulator andtheory, and the two sets of values are consistent. Eachmeasurement was carried out five times, and the data
proved to be repeatable. Figure 4 shows the absolutevalues of PCD and PSD separated from SOPMD when
the target SOPMD was set to 100 ps 2, demonstrating
good agreement between the measured and theoreticalvalues. Because PCD is zero at the center frequency,
SOPMD includes only the PSD component at thatfrequency. The ratio of PCD to PSD increases as the200

Absolute of PCD, PSD (ps 2 )Polarizer

25

Absolute of PCD (Emulator)

Absolute of PCD (Theory)

PSD (Emulator)

PSD (Theory)

150
125
100
75
50
25
0
1547.21547.41547.6

1547.81548.01548.2

1548.4

1548.6

1548.8

Wavelength (nm)Figure 430
Emulator SOPMD= 75 ps2
Emulator SOPMD=100 ps2
Emulator SOPMD=125 ps2

175

200

Theory SOPMD= 75 ps2
Theory SOPMD=100 ps2
Theory SOPMD=125 ps2

175

Absolute values of PCD and PSD separated
from an SOPMD value of 100 ps2.

Emulator SOPMD= 75 ps2
Emulator SOPMD=100 ps2
Emulator SOPMD=125 ps2

Theory SOPMD= 75 ps2
Theory SOPMD=100 ps2
Theory SOPMD=125 ps2

150

SOPMD (ps 2 )

DGD (ps)

2015
10125 ps2

125

100 ps210075

75 ps2

50
5

25
0

0
1547.21547.41547.6

Figure 31547.81548.01548.2

1548.4

1548.6

1548.81547.21547.41547.6

1547.81548.01548.2

1548.6

1548.8

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Wavelength (nm)Wavelength (nm)a) DGDb) SOPMD

1548.4

DGD and SOPMD for SOPMD values of 75, 100 and 125 ps2 by emulator and theory.

25

PMD Compensator and PMD Emulator

frequency deviates from the center frequency.
We also found that when the same frequency shift wasapplied to all FSRs, the DGD and SOPMD spectra shiftedin frequency but kept the spectral profile. That is, the ratioof PCD to PSD at any one wavelength can be changed
keeping SOPMD constant by shifting the spectra. This
enables us to investigate the influence of two components
of SOPMD on the transmission system.
The two-section configuration of the emulator can
generate flat PMD spectrum in frequency. As mentioned
above, setting any two angles to zero reduces the numberof DGD sections to two. For example, when the angleof the first and third VFRs are set to zero, a two-section
configuration of 15 ps + 15 ps is realized, and when theangles of the first and second VFRs are set to zero, a twosection configuration of 22.5 ps + 7.5 ps is realized. If theangle of the first VFR is set to 90 deg, the first and second
DGD sections cancel each other, so the two-section
configuration of 7.5 ps + 7.5 ps is realized with the last
two DGD sections.
The two-section configuration of the emulator was
also investigated. As in the four-section configuration
test, target SOPMD was set to 75, 100, and 125 ps2.
Consistent with the theory, the measured SOPMD, DGD,
PCD, and PSD were constant (not shown).
The above two tests demonstrate that, for a fixed
SOPMD value, different PCD and PSD profiles can beachieved by changing the number of DGD sectionsin the emulator. The emulator ’s repeatability andprogrammability are useful for systematic testing and forthe study of the real-time behavior of higher-order PMD.

4.

SECOND-ORDER PMD COMPENSTOR

4.1 Configuration
In the conventional PMDC with HOPC shown in Figure 5a) the compensator was configured with a PMDC 4) andan additional HOPC, which are completely independentof each other, while our novel PMDC with HOPC is shownin Figure 5 b) 8), 11). The first polarization controller and
the PMF compose the first-order PMDC and the second
polarization controller and a polarization beam splitter(PBS) compose the HOPC. The differences between
our configuration and the conventional one are in themonitoring and control method. We use the other output
port (not the signal port) of PBS to control both the firstorder PMDC section and HOPC section.
In the conventional PMDC with HOPC shown in Figure5 a), the degree of polarization (DOP) is monitored
for control of the polarization controller of the PMDC,
and output power from the polarizer is monitored forcontrol of the polarization controller of the HOPC. Thus
each polarization controller maximizes DOP and power
individually, but if the polarization controller of the HOPC
always maximizes power, maximizing DOP means
the same as maximizing power, because DOP means
polarization uniformity over the signal spectrum. If thepolarization controller of the PMDC maximizes the powera) Conventional
Polarizer

PMF
PC

PC

Feedback

DOP monitor(maximizes DOP)

Feedback

1st-order PMD compensator

Power monitor(maximizes power)

2 nd-order depolarization cancellerb) Novel (simplified)
PBS

PMF
PC

PC
Feedback

Feedback

Power monitor(minimize power)

1st-order PMD compensator and2 nd-order depolarized component canceller

Figure 5

Configurations of conventional and novel PDMCs.

that is maximized by the polarization controller of the
HOPC, it means that the DOP of the signal is maximized.
Therefore, we can unify DOP monitoring and powermonitoring. Additionally, we monitor the other port of the
PBS to reduce the number of components, and control thetwo polarization controllers so that the monitored poweris minimized. This has the same meaning as maximizing
the power from the signal port of the PBS. Thus, secondorder PMD mitigation can be realized with a simplified
configuration b) just as with configuration a).
4.2 Second-Order PMD Mitigation
It has been reported that the penalty due to second-order
PMD is mainly caused by PSD components 2), 5), so here
we consider only PSD components. Theoretically, in acase in which the PSP is linearly polarized and aligned to
x-axis and the direction of PSD depolarization is aligned
to the direction while maintaining linear polarization, theoutput pulse which undergoes second-order PMD can be
represented by the equation 2).
Eout (η ) = K— {2φ + (η -τ )(û *+û )√2+[ ∆φ + (η -τ -κ )-∆φ -(η +τ -κ )]û
+[ ∆φ + (η -τ +κ )-∆φ -(η +τ +κ )]û *}(8)

where: η is time normalized by the bit time, τ isnormalized DGD, κ is normalized PSD and K isconstant.
In this case, the direction of input SOP is aligned to the
S 1 direction in Stokes space, which is the same as thePSP, and the direction of PSD depolarization is S 1 -S 2 ,û and û * represent left and right circular polarization
respectively, the φ ± terms independent of κ are split pulses
due to DGD, and the ∆φ ± terms dependent on κ areadditional split pulses due to PSD.
The PMDC operates to align the PSP to the input SOP,
and the HOPC operates to align the polarization axis to
the PSP, so only the x component is transmitted by thepolarizer.

[ ]

1 0
(*)
*
0 0 · û = (û +û )/2

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PMD Compensator and PMD Emulator

10GbpsTx (NRZ)

PMD
emulator-1.54dBm
Pol. con.

Pol. con.

(c)
(b)
(a)

(e)

1E-5

(d)

PMF (40ps) for
compensation

PBS-7.65dBm-25~29dBm

Power
meter

1E-9

Variable
attenuator-16~20dBm

1E-11

Rx

2 nd-order depolarizedcomponent canceller

Figure 6

Feedback
controller

1E-7

Controller

-20.0

Error
detector

4.3 Test Results
The 10-Gbps non-return zero (NRZ) test system that weused is shown in Figure 6. We configured the feedback
loop using two polarization controllers, which are ourproprietary magneto-optic polarization controller 12). We
used two states generated by the PMD emulator, namely
30-ps DGD without SOPMD and 30-ps DGD with 441 ps2
SOPMD that consists of only a PSD component. Since theemulator we used here is made up of only two sections,
SOPMD has only PSD components, and DGD and
SOPMD have no frequency dependence.
Because our first-order PMDC operates so that the
total PSP is identical to the input SOP to the system, thesum DGD of the transmission line and the PMF in thecompensator varies in response to the connection angle
between them. And second-order PMD is affected by
DGD, so the penalty caused by second-order PMD varies
depending on the input SOP. Therefore, we took theaverage BER with respect to input SOP when we used the
PMDC with HOPC. In the case of no PMDC, we took theworst BER.
The BER test results are shown in Figure 7. The curves
are (a) back to back, (b) DGD 30 ps + SOPMD 441 ps2
with our PMDC with HOPC (average with regard to the
input SOP), (c) DGD 30 ps + SOPMD 441 ps2 with only
first-order PMDC (average), (d) DGD 30 ps (worst case),(e) DGD 30 ps + SOPMD 441 ps2 (worst case).
Curve (b) is the data for the novel configuration we
propose and (c) is the data without PMDC. We can seethat our simplified PMDC with HOPC can suppress
the second-order PMD effect in the same way as the

-19.0

-18.5

-18.0

-17.5

-17.0

-16.5

-16.0

(a) Back to Back(b) DGD 30 ps + SOPMD 441 ps2 with our PMDC with HOPC
(average with regard to the input SOP)(c) DGD 30 ps + SOPMD 441 ps2 with only 1st-order PMDC (average)(d) DGD 30 ps (worst case),(e) DGD 30 ps + SOPMD 441 ps2 (worst case)

When the PMDC and HOPC are properly controlled, thetransmitted pulse may be represented as

Since the ∆φ ± terms dependent of κ are cut in half, thecomponents of split pulses due to PSD are mitigated. The
effect of PMDC with HOPC in mitigating second-order
PMD is shown analytically.

-19.5

Power (dBm)

Configuration of NRZ test system.

E(η ) = K
— {2φ + (η -τ )
√2
(10)
1
+
[ ∆φ + (η -τ -κ )+∆φ + (η -τ +κ )2-∆φ - (η +τ -κ )-∆φ -(η +τ +κ )]}(û *+û )BER

1st-order PMD compensator-0.82dBm

Figure 7

BER test results.

conventional configuration. The amount of suppression
is not so dramatic (around 30% of the power penalty),
but this method is very simple and inexpensive. It isnecessary to check whether this device is adequate foruse in actual transmission system or not.

5.

CONCLUSION

We have proposed a PMD emulator on a variable Faraday
rotator (VFR), and have confirmed that it is capable ofgenerating a stable PMD spectrum. The two componentsof second-order PMD measured by the measurement
system developed here agree with the theoretical
calculations.
We also have proposed a novel simplified configurationconsisting of a first-order PMDC with higher-order PMD
canceller (HOPC). The operation of this device has beenchecked in a 10G-NRZ evaluation system, and it has beenfound that it can suppress the second-order PMD effectconsisting of a PSD component.
It is certain that requirements in terms of transmission
rates will increase as time goes on, and we cannot
avoid the problems either of higher-order dispersion
compensation or higher-order PMD compensation. A
second-order PMD emulator will be useful for reachinga deeper understanding of second-order PMD effectand optimizing second-order compensators in theirdevelopment.

REFERENCES
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3) T. Takahashi et al.: “Automatic compensation technique fortimewise fluctuation polarization mode dispersion in in-line
amplifier systems”, Electron. Lett., 30 (1994), 348.

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PMD Compensator and PMD Emulator

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