Abstract

We investigate polarization mode dispersion (PMD) and polarization dependent loss (PDL) impairments in polarization division multiplexing (PDM) signals with optical polarization demultiplexing and direct detection. We find that the time alignment between the bits in the two polarizations has a significant impact on the PMD impairments, and PMD impairments also depend on the bandwidth of PDM signals, whereas PDL impairments have little dependence on the relative time alignment between the two polarizations and the signal bandwidth. We show that with a proper configuration of the polarization demultiplexing, the PDL-induced crosstalk between the two polarizations can be completely eliminated. The combined effects of PMD and PDL are also studied, and we find that, in the presence of concatenated PMD and PDL, the impairment from one effect does not enhance that from the other.

©2009 Optical Society of America

1. Introduction

Increasing the spectral efficiency of fiber-optic communication systems is an effective way to meet the ever growing demand for transmission capacity and fully exploit the potential of current deployed fiber infrastructure. Polarization division multiplexing (PDM), which transmits two channels with orthogonal states of polarization (SOPs) at an identical wavelength, can double the spectral efficiency and therefore attracts much attention [1-3]. PDM signals are more sensitive to polarization effects in fiber-optic communication systems than signals with a single polarization. Two important polarization effects in a fiber-optic communication system are polarization mode dispersion (PMD) and polarization dependent loss (PDL). PMD mainly arises from the random birefringence in fibers and optical components, in which signals with different SOPs travel at different speeds. PDL usually occurs in optical components, such as isolators and couplers, whose insertion loss varies with the SOPs of input signals. In addition to the penalties from PMD-induced pulse broadening [4] and PDL-induced variation of optical signal to noise ratio (OSNR) [5-8], the main impairments caused by PMD and PDL in PDM signals are the crosstalk between the two polarizations. At the receiver side of PDM systems, the two channels are separated with polarization demultiplexing either in the electronic domain with coherent detection or in the optical domain with direct detection. In the coherent detection scheme, the PMD-induced impairments can be well compensated with digital signal processing [9-11], thus PDL is the primary source of system degradation and has been carefully studied [11] [12]. However, in the direct detection scheme, both PMD and PDL effects put significant limitations on system performance. So far, only limited work has been done on separate PMD or PDL penalties for PDM signals [13-19], and there is no detailed assessment on the combined penalties in literature.

In this paper, we study the PMD and PDL impairments first separately and then jointly, in PDM signals with optical polarization demultiplexing and direct detection. We first analyze the crosstalk induced by PMD and PDL in PDM signals, and then experimental results on 10-Gb/s return-to-zero (RZ) and non-return-to-zero (NRZ) on-off-keying (OOK) signals are presented.

2. Crosstalk Mechanisms

2.1 PMD

PMD causes the output SOP of a fully polarized input signal to vary with frequency. This depolarization means that the two channels originally having orthogonal polarizations cannot be completely separated with a polarization beam splitter (PBS) in the presence of PMD as signals have a certain bandwidth, thus coherent crosstalk is induced in the PDM system. Assuming there is only PMD, after transmission, the signal at the output of a polarizer (one port of a PBS) can be expressed as

Eout(ω)=UpolUpmdEin(ω)
where Ein(ω) is the input complex signal, Upol and Upmd are the Jones matrices to describe PMD and the polarizer, respectively. We assume that a PDM signal with channels A and B at two orthogonal polarization states is launched into a first-order PMD emulator (PMDE). If a PBS aligned at the SOPs of the center frequency components of the signal is used to demultiplex the two channels, from Eq. (1) we can get the output signal at the port A
Aout(ω)=Ain(ω)[cos(ωΔτ2)jcos(2θ)sin(ωΔτ2)]+jBin(ω)sin(2θ)sin(ωΔτ2)
where θ is the angle between the input SOP of A and one principal state of polarization (PSP) of the PMDE, ω is the deviation of the angular frequency component of the signal from its center frequency, Ain(ω) and Bin(ω) are the input signals of A and B, respectively, and Δτ is the differential group delay (DGD) of the PMDE. Three conclusions can be obtained from Eq. (2): 1) Whenθ=0o/90o(PSP launching), there is no crosstalk and when θ=45o, there is the largest frequency dependent crosstalk. The crosstalk increases monotonically when θ increases from 0oto 45oor decreases from 90oto45o; 2) The crosstalk from B to A depends on the bandwidth of B. B with a larger bandwidth will be more depolarized and thus induces larger crosstalk to A; and 3) As most frequency components of a signal are contained in the transition period of pulses, the relative time delay between the two polarization channels has a big impact on the crosstalk.

2.2 PDL

Except for the principal axes launching, after passing through a PDL emulator (PDLE), two originally orthogonally polarized signals become non-orthogonal. We assume that the PDLE is aligned with x and y axes (y axis is the least lossy axis), and a PDM signal is launched into the PDLE as shown in Fig. 1(a) . The normalized input signals are

{Ain=sinθx^+cosθy^Bin=cosθx^+sinθy^
where θ is the angle between the SOP of Ain and y axis of the PDLE in the Jones space.

 

Fig. 1 The effect of PDL on the output angle between the two originally orthogonal PDM channels. (a) Schematic diagram. (b) Evolution of output angle versus input polarization with different PDL values.

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After the PDLE, the normalized output signals are

{Aout=sinθ1αx^+cosθ1+αy^Bout=cosθ1αx^+sinθ1+αy^
where α is related to the PDL value Γ (dB) as

Γ=10log101+α1α

The angle between the output SOPs of channels Aout and Bout can be expressed as

γ=arctan(10Γ20tanθ)+arctan(10Γ20cotθ)
which indicates that the output angle reaches its local minimum if the launched polarization is at 45o, as shown in Fig. 1(b). The loss of orthogonality due to PDL will cause crosstalk between the two channels if only one PBS is used. However, by using two PBSs with each one set to block the signal from the other polarization, the crosstalk can be completely eliminated, at the cost of power reduction of the desired channel [1]. Note that PDL is generally considered as frequency-independent and it alone will not reshape a fully polarized signal; in the presence of modest PMD, the pulse distortion effects related to PDL is considerably small [20] [21]. Therefore, the PDL related intra-channel waveform degradation is not discussed in this paper, but it is included in the experimental results.

2.3 PMD and PDL

A real system has both PMD and PDL, but the combined effects of PMD and PDL on a PDM signal have never been investigated before. Two simple cases are studied here. One is PDL after PMD and the other is PMD after PDL. Although PMD and PDL are distributed in a real system, these two simple cases can help us understand of the interaction between PMD and PDL impairments. The similar simplification of real systems has been implemented to study the combined effects of PMD and PDL on single polarization signals [22].

With a PDLE concatenated after a PMDE, from Eq. (6), when the PDLE input angle (relative to y axis of the PDLE) of a frequency component is θ, the output angle can be expressed as arctan(10Γ/20tanθ). This input-output transformation of the angles can be characterized as the solid curve in Fig. 2 , whose curvature increases as the PDL value increases. As the launch angle increases from 0oto 90o, the corresponding slope of the transformation curve increases from smaller than 1 to larger than 1. There is a sole critical angle whose corresponding slope is 1, i.e., where the output angle variation equals the input angle variation. The critical angle becomes larger as the PDL value increases, and it is always larger than 45oas long as PDL is present.

 

Fig. 2 The SOP transformation induced by PDL.

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For the PMD-degraded PDM signal launched into the PDLE, assuming that the launch angles of the center frequency component and the most deviated frequency component of the same channel are θin1 and θin2, respectively, if both angles are smaller then the critical angle, the output angle difference will be smaller than the input angle difference, which means that a signal depolarized by PMD gets re-polarized by PDL [23].

If the launch angle of one channel is pushed beyond the critical angle and falls into the divergence zone in Fig. 2, the output SOPs of this channel are more divergent and larger intra-/inter-channel penalty is induced, however, as the launch angles of the two channels are complementary, the launch angle of the other channel will be pushed further into the convergence zone with more convergent SOPs and smaller penalty. Meanwhile, as indicated in Fig. 1(b), the output angle between the two channels increases towards 90oas the launch angle of one channel is pushed further into the divergence zone, suggesting that the inter-channel crosstalk induced by the loss of SOP orthogonality is alleviated. Thus, to assess the largest PDL-induced penalty on a PMD-degraded PDM signal, the launch angle can be set as 45orelative to the least lossy axis of the PDLE.

Figure 3 shows the relation of signal SOPs in the case of a PMDE concatenated after a PDLE. Based on Eq. (6), when the launch angle of A is set to be 45orelative to the PSPs of the PMDE in the Jones space, the launch angle of B varies, depending on the relation between SOPs of A and B and the PSPs. The smallest angle between the SOP of B and the PSPs of the PMDE is γ45o when the SOPs of A and B and the PSPs are in the same plane, and the largest angle is 45o when the plane of SOPs of A and B is perpendicular to the PSPs in the Stokes space.

 

Fig. 3 The angles between the SOPs of the center frequency components of the two channels and the PMD vector in the Stokes space. The angles in the Stokes space are twice as large as those in the Jones space (e. g., two perpendicular vectors in the Stokes space are 45oto each other if transferred to the Jones space). Ω1and Ω1: the only pair of PMD vectors which have the smallest angle 2(γ45o) with channel B while perpendicular to channel A; Ω2and Ω2: the only pair of PMD vectors perpendicular to both channels A and B. For all the other vectors with their tips on the circle labeled with arrows, they are perpendicular to channel A and with a angle between 2(γ45o)and 90o relative to channel B.

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There is the largest PMD-induced penalty when the launch angles of the two channels are both 45o, but it is hard to know in an experiment what the launch angle of B is. Practically in most cases, as indicated in Fig. 3, the launch angle of B is within [γ45o,45o], and the potential largest penalty difference between the worst case scenario and an angle-uncertain launch is the difference of PMD-induced intra-channel penalty (pulse broadening penalty) between 45oand γ45o launching, thus we can evaluate the worst case while only one channel is assured to be launched at 45o.

3. Experiment Results and Discussions

3.1 Experimental Setup

The experimental setup is shown in Fig. 4 . A distributed feedback (DFB) laser with a center wavelength of 1561.31nm is modulated with 231-1 pseudo-random binary sequence (PRBS) 10-Gb/s data to generate a 10-Gb/s NRZ-OOK signal. To generate a 50% duty cycle RZ signal, a pulse carver is inserted after the data modulator. After the modulators, the signal is split by a 50/50 coupler into two branches. A delay line (DL) is inserted in one branch to make the bit sequences of the two channels interleaved (the relative time delay is (n+1/2)Tb, where Tb is the bit period and n is an integer) or synchronized (the relative time delay is nTb) in the time domain, and a variable optical attenuator (VOA) is applied in the other branch to equalize the power of the two channels. In each branch the signal is adjusted with a polarization controller (PC) to get the proper polarization, and then combined with the polarization beam combiner (PBC). The PDM signal, whose SOP is controlled with PC3 to demonstrate the worst-case scenarios, is launched to the PMDE or/and the PDLE and both the input and output of the emulators are monitored with the polarization analyzer. When both the PMDE and the PDLE are present, a PC is inserted in between. The output signal is combined with an amplified spontaneous emission (ASE) noise source to vary OSNR. A small portion of signal power is tapped out to an optical spectrum analyzer (OSA) for OSNR monitoring. The polarization demultiplexing is achieved with a PBS and a manually adjusted PC.

 

Fig. 4 Experimental setup of the PDM system. CW: Continuous wave; MOD: Modulator; PC: Polarization controller; VOA: Variable optical attenuator; PBC(S): Polarization beam combiner (splitter); ASE: Amplified spontaneous emission; OSA: Optical spectrum analyzer.

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3.2 Measurement with Only PMD

The system PMD performance is measured in six cases: NRZ one-polarization/interleaved-PDM/synchronized-PDM and RZ one-polarization/interleaved-PDM/synchronized-PDM signals. Each channel is launched 45orelative to the PSPs of the PMDE.

Figure 5 shows the measured OSNR penalties at bit-error-ratio (BER) of 10−3 versus DGD. The right insets of Fig. 5 show typical eye diagrams of the degraded signals. As expected, for the single polarization signal, RZ has better tolerance to PMD than NRZ [24]. However, for the PDM signals, the NRZ signal can tolerate more PMD than the RZ signal in the synchronized case, but has similar tolerance to PMD as the RZ signal in the interleaved case. This can be explained with the eye-diagrams, which show that the crosstalk from B to A mainly occurs in the transition period of the pulses of Band it drops to minimum at the pulse center. When A and B are interleaved, the crosstalks for both RZ and NRZ signals are almost the same and located at the center of each bit slot, whereas in the synchronized case, the crosstalk peak is located closer to the bit center for the RZ signal than that for the NRZ signal. Figure 5 indicates that by properly choosing the modulation format and time delay, the PMD tolerance of a PDM signal can be improved.

 

Fig. 5 Measured OSNR penalties at BER = 10−3 vs. DGD. (a) NRZ-OOK signals. (b) RZ-OOK signals.

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3.3 Measurement with Only PDL

To assess the PDL impairment, each channel of the PDM signal is launched at 45orelative to the least lossy axis of the PDLE, and three cases are measured. Case 1: the PC4 is optimized to get the maximum power from channel A at one PBS port. Based on Eq. (6), there is a maximum crosstalk from channel B and the amount is α2, which is defined as the ratio of signal power from the other channel to that of the desired channel. Case 2: the PC4 is optimized to block B at one port, and there is only A from this port. The crosstalk is eliminated, but the power of A is reduced with a ratio of 1α2. Case 3: the PC4 is optimized to get equal crosstalk at both PBS ports, and the crosstalk is α2/(11α2) for each channel. Note that the demultiplexing setup in Case 2 will be used to analyze the joint effect of concatenated PDL and PMD in the next section.

Figure 6 shows the measured OSNR penalties of the PDM NRZ-OOK signal at BER of 10−3 as a function of PDL value. The result for the RZ signal is similar as the PDL-induced penalties are independent of bandwidth. This bandwidth-independence can be observed in the eye diagrams of Fig. 6, where the PDL value is 3dB. Figure 6 shows that there is a big difference in the PDL penalties among the three cases. With the crosstalk completely eliminated (Case 2), the PDM signal can tolerate a large PDL value. Note that the penalty for the time synchronized case is slightly larger than that for the time interleaved one. This is because the crosstalk in the interleaved case mainly occurs at the edge of the bit slot while in the synchronized case it occurs at the center; and in the latter case the crosstalk has a larger influence on BER.

 

Fig. 6 Measured PDM NRZ-OOK signal OSNR penalties at BER = 10−3 vs. PDL.

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3.4 Measurement with Concatenated PMD and PDL

The joint effects of PMD and PDL are measured in two regimes, i.e., the PMD-PDL regime and the PDL-PMD regime.

In the PMD-PDL regime, the PDM signal is at first launched into the PMDE then the PDLE, with the SOP of the center frequency component of each channel 45orelative to the PSPs of the PMDE and the least lossy axis of the PDLE. At the receiver side, the polarization demultiplexing strategy is to maximally block the unwanted channel by setting the polarizer (one port of the PBS) orthogonal to the SOP of the center frequency component of that channel, as described in Case 2 of Section 3.3. The evolution of the SOPs of the two channels during propagation in the PMD-PDL regime is shown in Fig. 7 . Note that the frequency components deviated from the center one will suffer different loss inside PDLE, but they are symmetric (with the assumption of modest PMD and PDL) with the center one thus its influence on the overall power reduction is small. However, in our experiment there is not such a presumption that this effect is omitted.

 

Fig. 7 The evolution of the SOPs of the signals in the PMD-PDL regime.

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As shown in Fig. 8 , although the PDM signal suffers the largest impairment in each emulator, the overall OSNR penalty is less than the sum of the two separate penalties, and as the PDL value is larger, the PMD-induced penalty is more suppressed. This phenomenon comes from the convergence of the SOPs of the different frequency components in the PMD-degraded signal.

 

Fig. 8 Measured PDM NRZ-OOK signal OSNR penalties at BER = 10−3 with the PMD-PDL regime.

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Figure 9 illustrates the convergence in the form of the measured output degree of polarization (DOP) of one channel versus the PDL value, i.e., the output DOP increases with PDL value when the launch angle is 45o(within the convergence zone); as comparisons, the results of 0olaunching for one channel and 90olaunching for the other channel are presented, also note that for PDM signals in the 0o/90o launching case the output SOP between the center frequency components of both channels remains orthogonal. Therefore, in the worst joint penalty case (45olaunching), the SOP variation induced by the previous PMDE can be partially suppressed by the PDLE, resulting in mitigated pulse broadening effect inside each channel and reduced inter-channel crosstalk as well.

 

Fig. 9 Measured output DOP of one PMD-degraded channel passing through the PDLE versus PDL with different launch angles. Single polarization is used in this measurement.

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In the PDL-PMD regime, the PDM signal is at first launched into the PDLE with the SOP of the each channel 45orelative to the least lossy PDL axis, and then launched into the PMDE with the SOP of A 45orelative to the PSPs of the PMDE. As the launch angle of B is within [γ45o,45o], and Bsuffers less PMD-induced pulse broadening than A, therefore the PMD-induced crosstalk from B to A is smaller than that from A to B. Since the inter-channel crosstalk has a larger impact on BER than intra-channel pulse broadening, the OSNR penalty of A is smaller than that of B, as shown in Fig. 10 .

 

Fig. 10 Measured PDM NRZ-OOK signal OSNR penalties at BER = 10−3 with the PDL-PMD regime.

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With the given experimental setup, the exact launch angle of B is unknown, however, the worst case scenario (when the PMDE launch angle of B is also 45o) can still be evaluated with the measured results. Note that the angle between the center frequency components of the two channels is determined by the PDLE and irrelevant to the PMDE; meanwhile, the polarization demultiplexing strategy for B is to set the polarizer at port B perpendicular to A in the Jones space, thus the crosstalk from A to Bis invariant with regard to how B is affected by the PMDE. Therefore, the penalty difference for B between 45olaunching and γ45olaunching only comes from the different pulse broadening impairment of B. Based on Eq. (6), for a PDM signal 45olaunched into a 3.2dB PDLE, the output inter-channel angle γ is 69o, thus γ45oequals 24o. Note that a 30.92ps PMDE can induce 1.2dB intra-channel pulse broadening penalty if the channel of the PDM signal is launched 45orelative to the PSPs of the PMDE. We assume that B happens to be launched at 24o, the difference of pulse broadening penalty between 24olaunching and 45olaunching can be expressed as 1.2dB ×(1sin248o/sin290o) [25], i.e., 0.54dB. Taking this extra 0~0.54dB penalty into account, the overall OSNR penalty will still not be larger than the sum of the two separate penalties, which is similar to the PMD-PDL regime.

In a real system, PDM and PDL are distributed along the link, which is much complicated to analyze. The simple model of PMD and PDL interaction used in this paper shows that: the sum of the crosstalk-induced penalties from PMD and PDL alone sets the upper limit of the overall crosstalk-induced penalty observed at the end of the link. We believe the conclusion also applies to the distributed model.

4. Conclusion

We have studied the PMD and PDL impairments in PDM signals. We showed that the time synchronized PDM signals can tolerate more PMD than the time interleaved ones, and that signals with larger bandwidth are more sensitive to PMD. We found that PDL impairments have little dependence on the time delay between the two polarizations and signal bandwidth. We showed that PDL-induced crosstalk could cause severe penalties in PDM signals, but with the proper configuration of polarization demultiplexing, the PDL-induced crosstalk can be completely eliminated. The effects of concatenation of PMD and PDL on the PDM signal were studied, and we found that the impairment caused by the combination of PMD and PDL does not enhance the impairments caused by PMD and PDL alone.

Acknowledgment

This work was done at Crawford Hill Laboratory, Alcatel-Lucent, USA. The authors are grateful to acknowledge valuable discussions with R. W. Tkach and R. -J. Essiambre. Zinan Wang acknowledges the support from China Scholarship Council, National High-tech Research and Development Program of China (2007AA03Z447) and National Basic Research Program of China (2003CB314900).

References and links

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9. J. Renaudier, G. Charlet, M. Salsi, O. B. Pardo, H. Mardoyan, P. Tran, and S. Bigo, “Linear fiber impairments mitigation of 40-Gbit/s polarization-multiplexed QPSK by digital processing in a coherent receiver,” J. Lightwave Technol. 26(1), 36–42 (2008). [CrossRef]  

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References

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  1. A. R. Chraplyvy, A. H. Gnauck, R. W. Tkach, J. L. Zyskind, J. W. Sulhoff, A. J. Lucero, Y. Sun, R. M. Jopson, F. Forghieri, R. M. Derosier, C. Wolf, and A. R. McCormick, “1 Tb/s transmission experiment,” IEEE Photon. Technol. Lett. 8(9), 1264–1266 (1996).
    [Crossref]
  2. A. H. Gnauck, G. Charlet, P. Tran, P. J. Winzer, C. R. Doerr, J. C. Centanni, E. C. Burrows, T. Kawanishi, T. Sakamoto, and K. Higuma, “25.6-Tb/s WDM transmission of polarization-multiplexed RZ-DQPSK signals,” J. Lightwave Technol. 26(1), 79–84 (2008).
    [Crossref]
  3. G. Charlet, J. Renaudier, M. Salsi, H. Mardoyan, P. Tran, and S. Bigo, “Efficient mitigation of fiber impairments in an ultra-long haul transmission of 40Gbit/s polarization-multiplexed data, by digital processing in a coherent receiver,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper PDP17. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2007-PDP17
  4. H. Sunnerud, M. Karlsson, C. Xie, and P. A. Andrekson, “Polarization mode dispersion in high-speed fiber-optic transmission systems,” J. Lightwave Technol. 20(12), 2204–2219 (2002).
    [Crossref]
  5. A. Mecozzi and M. Shtaif, “Signal-to-noise-ratio degradation caused by polarization-dependent loss and the effect of dynamic gain equalization,” J. Lightwave Technol. 22(8), 1856–1871 (2004).
    [Crossref]
  6. M. Shtaif and A. Mecozzi, “Polarization-dependent loss and its effect on the signal-to-noise ratio in fiber-optic systems,” IEEE Photon. Technol. Lett. 16(2), 671–673 (2004).
    [Crossref]
  7. C. Xie and L. F. Mollenauer, “Performance degradation induced by polarization dependent loss in optical fiber transmission systems with and without polarization mode dispersion,” J. Lightwave Technol. 21(9), 1953–1957 (2003).
    [Crossref]
  8. O. Vassilieva, T. Hoshida, X. Wang, J. Rasmussen, H. Miyata, and T. Naito, “Impact of polarization dependent loss and cross-phase modulation on polarization multiplexed DQPSK Signals,”in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper OThU6. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2008-OThU6
  9. J. Renaudier, G. Charlet, M. Salsi, O. B. Pardo, H. Mardoyan, P. Tran, and S. Bigo, “Linear fiber impairments mitigation of 40-Gbit/s polarization-multiplexed QPSK by digital processing in a coherent receiver,” J. Lightwave Technol. 26(1), 36–42 (2008).
    [Crossref]
  10. L. E. Nelson, S. L. Woodward, S. Foo, X. Zhou, M. D. Feuer, D. Hanson, D. McGhan, H. Sun, M. Moyer, M. O. Sullivan, and P. D. Magill, “Performance of a 46-Gbps dual-polarization QPSK transceiver with real-time coherent equalization over high PMD fiber,” J. Lightwave Technol. 27(3), 158–167 (2009).
    [Crossref]
  11. C. Laperle, B. Villeneuve, Z. Zhang, D. McGhan, H. Sun, and M. O’Sullivan, “WDM performance and PMD tolerance of a coherent 40-Gbit/s dual-polarization QPSK transceiver,” J. Lightwave Technol. 26(1), 168–175 (2008).
    [Crossref]
  12. M. Shtaif, “Performance degradation in coherent polarization multiplexed systems as a result of polarization dependent loss,” Opt. Express 16(18), 13918–13932 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-18-13918 .
    [Crossref] [PubMed]
  13. L. E. Nelson, T. N. Nielsen, and H. Kogelnik, “Observation of PMD induced coherent crosstalk in polarization-multiplexed transmission,” IEEE Photon. Technol. Lett. 13(7), 738–740 (2001).
    [Crossref]
  14. L. Nelson and H. Kogelnik, “Coherent crosstalk impairments in polarization multiplexed transmission due to polarization mode dispersion,” Opt. Express 7, 350–361 (2000), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-7-10-350 .
    [Crossref] [PubMed]
  15. D. van den Borne, N. E. Hecker-Denschlag, G. D. Khoe, and H. de Waardt, “PMD-induced transmission penalties in polarization-multiplexed transmission,” J. Lightwave Technol. 23(12), 4004–4015 (2005).
    [Crossref]
  16. Z. Wang, and C. Xie, “PMD and PDL tolerance of polarization division multiplexed signals with direct detection,” in Proc. ECOC 2008, Brussels, Belguim, 2008, paper We.3.E.2.
  17. S. Hinz, D. Sandel, F. Wuest, and R. Noé, “PMD tolerance of polarization division multiplex transmission using return-to-zero coding,” Opt. Express 9, 136–140 (2001), http://www.opticsinfobase.org/abstract.cfm?URI=oe-9-3-136 .
    [Crossref] [PubMed]
  18. D. van den Borne, S. L. Jansen, E. Gottwald, P. M. Krummrich, G. D. Khoe, and H. de Waardt, “1.6-b/s/Hz spectrally efficient transmission over 1700 km of SSMF using 40×85.6-Gb/s POLMUX-RZ-DQPSK,” J. Lightwave Technol. 25(1), 222–232 (2007).
    [Crossref]
  19. H. C. Ji, J. H. Lee, H. Kim, P. K. Park, and Y. C. Chung, “Effect of PDL-induced coherent crosstalk on polarization-division-multiplexed direct-detection systems,” Opt. Express 17(3), 1169–1177 (2009), http://www.opticsinfobase.org/abstract.cfm?URI=oe-17-3-1169 .
    [Crossref] [PubMed]
  20. M. Shtaif and O. Rosenberg, “Polarization-dependent loss as a waveform-distorting mechanism and its effect on fiber-optic systems,” J. Lightwave Technol. 23(2), 923–930 (2005).
    [Crossref]
  21. C. Xie, L. F. Mollenauer, and L. Möller, “Pulse distortion induced by polarization-mode dispersion and polarization-dependent loss in lightwave transmission systems,” IEEE Photon. Technol. Lett. 15(8), 1073–1075 (2003).
    [Crossref]
  22. L. Chen, Z. Zhang, and X. Bao, “Combined PMD-PDL effects on BERs in simplified optical systems: an analytical approach,” Opt. Express 15(5), 2106–2119 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-5-2106 .
    [Crossref] [PubMed]
  23. C. R. Menyuk, D. Wang, and A. N. Pilipetskii, “Repolarization of polarization-scrambled optical signals due to polarization dependent loss,” IEEE Photon. Technol. Lett. 9(9), 1247–1249 (1997).
    [Crossref]
  24. C. Xie, L. Möller, H. Haunstein, and S. Hunsche, “Comparison of system tolerance to polarization-mode dispersion between different modulation formats,” IEEE Photon. Technol. Lett. 15(8), 1168–1170 (2003).
    [Crossref]
  25. H. Kogelnik, R. M. Jopson, and L. E. Nelson, Optical Fiber Telecommunications IV-B (Academic, 2002), Chap.15.

2009 (2)

2008 (4)

2007 (2)

2005 (2)

2004 (2)

A. Mecozzi and M. Shtaif, “Signal-to-noise-ratio degradation caused by polarization-dependent loss and the effect of dynamic gain equalization,” J. Lightwave Technol. 22(8), 1856–1871 (2004).
[Crossref]

M. Shtaif and A. Mecozzi, “Polarization-dependent loss and its effect on the signal-to-noise ratio in fiber-optic systems,” IEEE Photon. Technol. Lett. 16(2), 671–673 (2004).
[Crossref]

2003 (3)

C. Xie and L. F. Mollenauer, “Performance degradation induced by polarization dependent loss in optical fiber transmission systems with and without polarization mode dispersion,” J. Lightwave Technol. 21(9), 1953–1957 (2003).
[Crossref]

C. Xie, L. F. Mollenauer, and L. Möller, “Pulse distortion induced by polarization-mode dispersion and polarization-dependent loss in lightwave transmission systems,” IEEE Photon. Technol. Lett. 15(8), 1073–1075 (2003).
[Crossref]

C. Xie, L. Möller, H. Haunstein, and S. Hunsche, “Comparison of system tolerance to polarization-mode dispersion between different modulation formats,” IEEE Photon. Technol. Lett. 15(8), 1168–1170 (2003).
[Crossref]

2002 (1)

2001 (2)

L. E. Nelson, T. N. Nielsen, and H. Kogelnik, “Observation of PMD induced coherent crosstalk in polarization-multiplexed transmission,” IEEE Photon. Technol. Lett. 13(7), 738–740 (2001).
[Crossref]

S. Hinz, D. Sandel, F. Wuest, and R. Noé, “PMD tolerance of polarization division multiplex transmission using return-to-zero coding,” Opt. Express 9, 136–140 (2001), http://www.opticsinfobase.org/abstract.cfm?URI=oe-9-3-136 .
[Crossref] [PubMed]

2000 (1)

1997 (1)

C. R. Menyuk, D. Wang, and A. N. Pilipetskii, “Repolarization of polarization-scrambled optical signals due to polarization dependent loss,” IEEE Photon. Technol. Lett. 9(9), 1247–1249 (1997).
[Crossref]

1996 (1)

A. R. Chraplyvy, A. H. Gnauck, R. W. Tkach, J. L. Zyskind, J. W. Sulhoff, A. J. Lucero, Y. Sun, R. M. Jopson, F. Forghieri, R. M. Derosier, C. Wolf, and A. R. McCormick, “1 Tb/s transmission experiment,” IEEE Photon. Technol. Lett. 8(9), 1264–1266 (1996).
[Crossref]

Andrekson, P. A.

Bao, X.

Bigo, S.

Burrows, E. C.

Centanni, J. C.

Charlet, G.

Chen, L.

Chraplyvy, A. R.

A. R. Chraplyvy, A. H. Gnauck, R. W. Tkach, J. L. Zyskind, J. W. Sulhoff, A. J. Lucero, Y. Sun, R. M. Jopson, F. Forghieri, R. M. Derosier, C. Wolf, and A. R. McCormick, “1 Tb/s transmission experiment,” IEEE Photon. Technol. Lett. 8(9), 1264–1266 (1996).
[Crossref]

Chung, Y. C.

de Waardt, H.

Derosier, R. M.

A. R. Chraplyvy, A. H. Gnauck, R. W. Tkach, J. L. Zyskind, J. W. Sulhoff, A. J. Lucero, Y. Sun, R. M. Jopson, F. Forghieri, R. M. Derosier, C. Wolf, and A. R. McCormick, “1 Tb/s transmission experiment,” IEEE Photon. Technol. Lett. 8(9), 1264–1266 (1996).
[Crossref]

Doerr, C. R.

Feuer, M. D.

Foo, S.

Forghieri, F.

A. R. Chraplyvy, A. H. Gnauck, R. W. Tkach, J. L. Zyskind, J. W. Sulhoff, A. J. Lucero, Y. Sun, R. M. Jopson, F. Forghieri, R. M. Derosier, C. Wolf, and A. R. McCormick, “1 Tb/s transmission experiment,” IEEE Photon. Technol. Lett. 8(9), 1264–1266 (1996).
[Crossref]

Gnauck, A. H.

A. H. Gnauck, G. Charlet, P. Tran, P. J. Winzer, C. R. Doerr, J. C. Centanni, E. C. Burrows, T. Kawanishi, T. Sakamoto, and K. Higuma, “25.6-Tb/s WDM transmission of polarization-multiplexed RZ-DQPSK signals,” J. Lightwave Technol. 26(1), 79–84 (2008).
[Crossref]

A. R. Chraplyvy, A. H. Gnauck, R. W. Tkach, J. L. Zyskind, J. W. Sulhoff, A. J. Lucero, Y. Sun, R. M. Jopson, F. Forghieri, R. M. Derosier, C. Wolf, and A. R. McCormick, “1 Tb/s transmission experiment,” IEEE Photon. Technol. Lett. 8(9), 1264–1266 (1996).
[Crossref]

Gottwald, E.

Hanson, D.

Haunstein, H.

C. Xie, L. Möller, H. Haunstein, and S. Hunsche, “Comparison of system tolerance to polarization-mode dispersion between different modulation formats,” IEEE Photon. Technol. Lett. 15(8), 1168–1170 (2003).
[Crossref]

Hecker-Denschlag, N. E.

Higuma, K.

Hinz, S.

Hunsche, S.

C. Xie, L. Möller, H. Haunstein, and S. Hunsche, “Comparison of system tolerance to polarization-mode dispersion between different modulation formats,” IEEE Photon. Technol. Lett. 15(8), 1168–1170 (2003).
[Crossref]

Jansen, S. L.

Ji, H. C.

Jopson, R. M.

A. R. Chraplyvy, A. H. Gnauck, R. W. Tkach, J. L. Zyskind, J. W. Sulhoff, A. J. Lucero, Y. Sun, R. M. Jopson, F. Forghieri, R. M. Derosier, C. Wolf, and A. R. McCormick, “1 Tb/s transmission experiment,” IEEE Photon. Technol. Lett. 8(9), 1264–1266 (1996).
[Crossref]

Karlsson, M.

Kawanishi, T.

Khoe, G. D.

Kim, H.

Kogelnik, H.

L. E. Nelson, T. N. Nielsen, and H. Kogelnik, “Observation of PMD induced coherent crosstalk in polarization-multiplexed transmission,” IEEE Photon. Technol. Lett. 13(7), 738–740 (2001).
[Crossref]

L. Nelson and H. Kogelnik, “Coherent crosstalk impairments in polarization multiplexed transmission due to polarization mode dispersion,” Opt. Express 7, 350–361 (2000), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-7-10-350 .
[Crossref] [PubMed]

Krummrich, P. M.

Laperle, C.

Lee, J. H.

Lucero, A. J.

A. R. Chraplyvy, A. H. Gnauck, R. W. Tkach, J. L. Zyskind, J. W. Sulhoff, A. J. Lucero, Y. Sun, R. M. Jopson, F. Forghieri, R. M. Derosier, C. Wolf, and A. R. McCormick, “1 Tb/s transmission experiment,” IEEE Photon. Technol. Lett. 8(9), 1264–1266 (1996).
[Crossref]

Magill, P. D.

Mardoyan, H.

McCormick, A. R.

A. R. Chraplyvy, A. H. Gnauck, R. W. Tkach, J. L. Zyskind, J. W. Sulhoff, A. J. Lucero, Y. Sun, R. M. Jopson, F. Forghieri, R. M. Derosier, C. Wolf, and A. R. McCormick, “1 Tb/s transmission experiment,” IEEE Photon. Technol. Lett. 8(9), 1264–1266 (1996).
[Crossref]

McGhan, D.

Mecozzi, A.

A. Mecozzi and M. Shtaif, “Signal-to-noise-ratio degradation caused by polarization-dependent loss and the effect of dynamic gain equalization,” J. Lightwave Technol. 22(8), 1856–1871 (2004).
[Crossref]

M. Shtaif and A. Mecozzi, “Polarization-dependent loss and its effect on the signal-to-noise ratio in fiber-optic systems,” IEEE Photon. Technol. Lett. 16(2), 671–673 (2004).
[Crossref]

Menyuk, C. R.

C. R. Menyuk, D. Wang, and A. N. Pilipetskii, “Repolarization of polarization-scrambled optical signals due to polarization dependent loss,” IEEE Photon. Technol. Lett. 9(9), 1247–1249 (1997).
[Crossref]

Mollenauer, L. F.

C. Xie, L. F. Mollenauer, and L. Möller, “Pulse distortion induced by polarization-mode dispersion and polarization-dependent loss in lightwave transmission systems,” IEEE Photon. Technol. Lett. 15(8), 1073–1075 (2003).
[Crossref]

C. Xie and L. F. Mollenauer, “Performance degradation induced by polarization dependent loss in optical fiber transmission systems with and without polarization mode dispersion,” J. Lightwave Technol. 21(9), 1953–1957 (2003).
[Crossref]

Möller, L.

C. Xie, L. F. Mollenauer, and L. Möller, “Pulse distortion induced by polarization-mode dispersion and polarization-dependent loss in lightwave transmission systems,” IEEE Photon. Technol. Lett. 15(8), 1073–1075 (2003).
[Crossref]

C. Xie, L. Möller, H. Haunstein, and S. Hunsche, “Comparison of system tolerance to polarization-mode dispersion between different modulation formats,” IEEE Photon. Technol. Lett. 15(8), 1168–1170 (2003).
[Crossref]

Moyer, M.

Nelson, L.

Nelson, L. E.

Nielsen, T. N.

L. E. Nelson, T. N. Nielsen, and H. Kogelnik, “Observation of PMD induced coherent crosstalk in polarization-multiplexed transmission,” IEEE Photon. Technol. Lett. 13(7), 738–740 (2001).
[Crossref]

Noé, R.

O’Sullivan, M.

Pardo, O. B.

Park, P. K.

Pilipetskii, A. N.

C. R. Menyuk, D. Wang, and A. N. Pilipetskii, “Repolarization of polarization-scrambled optical signals due to polarization dependent loss,” IEEE Photon. Technol. Lett. 9(9), 1247–1249 (1997).
[Crossref]

Renaudier, J.

Rosenberg, O.

Sakamoto, T.

Salsi, M.

Sandel, D.

Shtaif, M.

Sulhoff, J. W.

A. R. Chraplyvy, A. H. Gnauck, R. W. Tkach, J. L. Zyskind, J. W. Sulhoff, A. J. Lucero, Y. Sun, R. M. Jopson, F. Forghieri, R. M. Derosier, C. Wolf, and A. R. McCormick, “1 Tb/s transmission experiment,” IEEE Photon. Technol. Lett. 8(9), 1264–1266 (1996).
[Crossref]

Sullivan, M. O.

Sun, H.

Sun, Y.

A. R. Chraplyvy, A. H. Gnauck, R. W. Tkach, J. L. Zyskind, J. W. Sulhoff, A. J. Lucero, Y. Sun, R. M. Jopson, F. Forghieri, R. M. Derosier, C. Wolf, and A. R. McCormick, “1 Tb/s transmission experiment,” IEEE Photon. Technol. Lett. 8(9), 1264–1266 (1996).
[Crossref]

Sunnerud, H.

Tkach, R. W.

A. R. Chraplyvy, A. H. Gnauck, R. W. Tkach, J. L. Zyskind, J. W. Sulhoff, A. J. Lucero, Y. Sun, R. M. Jopson, F. Forghieri, R. M. Derosier, C. Wolf, and A. R. McCormick, “1 Tb/s transmission experiment,” IEEE Photon. Technol. Lett. 8(9), 1264–1266 (1996).
[Crossref]

Tran, P.

van den Borne, D.

Villeneuve, B.

Wang, D.

C. R. Menyuk, D. Wang, and A. N. Pilipetskii, “Repolarization of polarization-scrambled optical signals due to polarization dependent loss,” IEEE Photon. Technol. Lett. 9(9), 1247–1249 (1997).
[Crossref]

Winzer, P. J.

Wolf, C.

A. R. Chraplyvy, A. H. Gnauck, R. W. Tkach, J. L. Zyskind, J. W. Sulhoff, A. J. Lucero, Y. Sun, R. M. Jopson, F. Forghieri, R. M. Derosier, C. Wolf, and A. R. McCormick, “1 Tb/s transmission experiment,” IEEE Photon. Technol. Lett. 8(9), 1264–1266 (1996).
[Crossref]

Woodward, S. L.

Wuest, F.

Xie, C.

C. Xie and L. F. Mollenauer, “Performance degradation induced by polarization dependent loss in optical fiber transmission systems with and without polarization mode dispersion,” J. Lightwave Technol. 21(9), 1953–1957 (2003).
[Crossref]

C. Xie, L. Möller, H. Haunstein, and S. Hunsche, “Comparison of system tolerance to polarization-mode dispersion between different modulation formats,” IEEE Photon. Technol. Lett. 15(8), 1168–1170 (2003).
[Crossref]

C. Xie, L. F. Mollenauer, and L. Möller, “Pulse distortion induced by polarization-mode dispersion and polarization-dependent loss in lightwave transmission systems,” IEEE Photon. Technol. Lett. 15(8), 1073–1075 (2003).
[Crossref]

H. Sunnerud, M. Karlsson, C. Xie, and P. A. Andrekson, “Polarization mode dispersion in high-speed fiber-optic transmission systems,” J. Lightwave Technol. 20(12), 2204–2219 (2002).
[Crossref]

Zhang, Z.

Zhou, X.

Zyskind, J. L.

A. R. Chraplyvy, A. H. Gnauck, R. W. Tkach, J. L. Zyskind, J. W. Sulhoff, A. J. Lucero, Y. Sun, R. M. Jopson, F. Forghieri, R. M. Derosier, C. Wolf, and A. R. McCormick, “1 Tb/s transmission experiment,” IEEE Photon. Technol. Lett. 8(9), 1264–1266 (1996).
[Crossref]

IEEE Photon. Technol. Lett. (6)

A. R. Chraplyvy, A. H. Gnauck, R. W. Tkach, J. L. Zyskind, J. W. Sulhoff, A. J. Lucero, Y. Sun, R. M. Jopson, F. Forghieri, R. M. Derosier, C. Wolf, and A. R. McCormick, “1 Tb/s transmission experiment,” IEEE Photon. Technol. Lett. 8(9), 1264–1266 (1996).
[Crossref]

M. Shtaif and A. Mecozzi, “Polarization-dependent loss and its effect on the signal-to-noise ratio in fiber-optic systems,” IEEE Photon. Technol. Lett. 16(2), 671–673 (2004).
[Crossref]

L. E. Nelson, T. N. Nielsen, and H. Kogelnik, “Observation of PMD induced coherent crosstalk in polarization-multiplexed transmission,” IEEE Photon. Technol. Lett. 13(7), 738–740 (2001).
[Crossref]

C. Xie, L. F. Mollenauer, and L. Möller, “Pulse distortion induced by polarization-mode dispersion and polarization-dependent loss in lightwave transmission systems,” IEEE Photon. Technol. Lett. 15(8), 1073–1075 (2003).
[Crossref]

C. R. Menyuk, D. Wang, and A. N. Pilipetskii, “Repolarization of polarization-scrambled optical signals due to polarization dependent loss,” IEEE Photon. Technol. Lett. 9(9), 1247–1249 (1997).
[Crossref]

C. Xie, L. Möller, H. Haunstein, and S. Hunsche, “Comparison of system tolerance to polarization-mode dispersion between different modulation formats,” IEEE Photon. Technol. Lett. 15(8), 1168–1170 (2003).
[Crossref]

J. Lightwave Technol. (10)

M. Shtaif and O. Rosenberg, “Polarization-dependent loss as a waveform-distorting mechanism and its effect on fiber-optic systems,” J. Lightwave Technol. 23(2), 923–930 (2005).
[Crossref]

C. Xie and L. F. Mollenauer, “Performance degradation induced by polarization dependent loss in optical fiber transmission systems with and without polarization mode dispersion,” J. Lightwave Technol. 21(9), 1953–1957 (2003).
[Crossref]

D. van den Borne, N. E. Hecker-Denschlag, G. D. Khoe, and H. de Waardt, “PMD-induced transmission penalties in polarization-multiplexed transmission,” J. Lightwave Technol. 23(12), 4004–4015 (2005).
[Crossref]

D. van den Borne, S. L. Jansen, E. Gottwald, P. M. Krummrich, G. D. Khoe, and H. de Waardt, “1.6-b/s/Hz spectrally efficient transmission over 1700 km of SSMF using 40×85.6-Gb/s POLMUX-RZ-DQPSK,” J. Lightwave Technol. 25(1), 222–232 (2007).
[Crossref]

A. H. Gnauck, G. Charlet, P. Tran, P. J. Winzer, C. R. Doerr, J. C. Centanni, E. C. Burrows, T. Kawanishi, T. Sakamoto, and K. Higuma, “25.6-Tb/s WDM transmission of polarization-multiplexed RZ-DQPSK signals,” J. Lightwave Technol. 26(1), 79–84 (2008).
[Crossref]

H. Sunnerud, M. Karlsson, C. Xie, and P. A. Andrekson, “Polarization mode dispersion in high-speed fiber-optic transmission systems,” J. Lightwave Technol. 20(12), 2204–2219 (2002).
[Crossref]

A. Mecozzi and M. Shtaif, “Signal-to-noise-ratio degradation caused by polarization-dependent loss and the effect of dynamic gain equalization,” J. Lightwave Technol. 22(8), 1856–1871 (2004).
[Crossref]

J. Renaudier, G. Charlet, M. Salsi, O. B. Pardo, H. Mardoyan, P. Tran, and S. Bigo, “Linear fiber impairments mitigation of 40-Gbit/s polarization-multiplexed QPSK by digital processing in a coherent receiver,” J. Lightwave Technol. 26(1), 36–42 (2008).
[Crossref]

L. E. Nelson, S. L. Woodward, S. Foo, X. Zhou, M. D. Feuer, D. Hanson, D. McGhan, H. Sun, M. Moyer, M. O. Sullivan, and P. D. Magill, “Performance of a 46-Gbps dual-polarization QPSK transceiver with real-time coherent equalization over high PMD fiber,” J. Lightwave Technol. 27(3), 158–167 (2009).
[Crossref]

C. Laperle, B. Villeneuve, Z. Zhang, D. McGhan, H. Sun, and M. O’Sullivan, “WDM performance and PMD tolerance of a coherent 40-Gbit/s dual-polarization QPSK transceiver,” J. Lightwave Technol. 26(1), 168–175 (2008).
[Crossref]

Opt. Express (5)

Other (4)

H. Kogelnik, R. M. Jopson, and L. E. Nelson, Optical Fiber Telecommunications IV-B (Academic, 2002), Chap.15.

O. Vassilieva, T. Hoshida, X. Wang, J. Rasmussen, H. Miyata, and T. Naito, “Impact of polarization dependent loss and cross-phase modulation on polarization multiplexed DQPSK Signals,”in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper OThU6. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2008-OThU6

Z. Wang, and C. Xie, “PMD and PDL tolerance of polarization division multiplexed signals with direct detection,” in Proc. ECOC 2008, Brussels, Belguim, 2008, paper We.3.E.2.

G. Charlet, J. Renaudier, M. Salsi, H. Mardoyan, P. Tran, and S. Bigo, “Efficient mitigation of fiber impairments in an ultra-long haul transmission of 40Gbit/s polarization-multiplexed data, by digital processing in a coherent receiver,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper PDP17. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2007-PDP17

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Figures (10)

Fig. 1
Fig. 1 The effect of PDL on the output angle between the two originally orthogonal PDM channels. (a) Schematic diagram. (b) Evolution of output angle versus input polarization with different PDL values.
Fig. 2
Fig. 2 The SOP transformation induced by PDL.
Fig. 3
Fig. 3 The angles between the SOPs of the center frequency components of the two channels and the PMD vector in the Stokes space. The angles in the Stokes space are twice as large as those in the Jones space (e. g., two perpendicular vectors in the Stokes space are 45o to each other if transferred to the Jones space). Ω1 and Ω1 : the only pair of PMD vectors which have the smallest angle 2(γ45o) with channel B while perpendicular to channel A ; Ω2 and Ω2 : the only pair of PMD vectors perpendicular to both channels A and B . For all the other vectors with their tips on the circle labeled with arrows, they are perpendicular to channel A and with a angle between 2(γ45o) and 90o relative to channel B .
Fig. 4
Fig. 4 Experimental setup of the PDM system. CW: Continuous wave; MOD: Modulator; PC: Polarization controller; VOA: Variable optical attenuator; PBC(S): Polarization beam combiner (splitter); ASE: Amplified spontaneous emission; OSA: Optical spectrum analyzer.
Fig. 5
Fig. 5 Measured OSNR penalties at BER = 10−3 vs. DGD. (a) NRZ-OOK signals. (b) RZ-OOK signals.
Fig. 6
Fig. 6 Measured PDM NRZ-OOK signal OSNR penalties at BER = 10−3 vs. PDL.
Fig. 7
Fig. 7 The evolution of the SOPs of the signals in the PMD-PDL regime.
Fig. 8
Fig. 8 Measured PDM NRZ-OOK signal OSNR penalties at BER = 10−3 with the PMD-PDL regime.
Fig. 9
Fig. 9 Measured output DOP of one PMD-degraded channel passing through the PDLE versus PDL with different launch angles. Single polarization is used in this measurement.
Fig. 10
Fig. 10 Measured PDM NRZ-OOK signal OSNR penalties at BER = 10−3 with the PDL-PMD regime.

Equations (6)

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Eout(ω)=UpolUpmdEin(ω)
Aout(ω)=Ain(ω)[cos(ωΔτ2)jcos(2θ)sin(ωΔτ2)]+jBin(ω)sin(2θ)sin(ωΔτ2)
{Ain=sinθx^+cosθy^Bin=cosθx^+sinθy^
{Aout=sinθ1αx^+cosθ1+αy^Bout=cosθ1αx^+sinθ1+αy^
Γ=10log101+α1α
γ=arctan(10Γ20tanθ)+arctan(10Γ20cotθ)

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