## Abstract

We analyzed the mechanism of the interplay between PDL and fiber nonlinear effects in 112Gb/s DP-QPSK systems and showed that PDL can generate large data-dependent optical peak power variations that can worsen nonlinear tolerance and cause an additional 1.4dB Q-penalty.

©2011 Optical Society of America

## 1. Introduction

Dual polarization coherent systems are considered to be an attractive solution for 100Gb/s optical transmission. In such systems coherent receiver with digital signal processing (DSP) is the key enabling technology, which can completely compensate for some impairments such as chromatic dispersion (CD), polarization mode dispersion (PMD) and PDL-induced loss of orthogonality. However, DSP cannot completely compensate for signal degradation due to polarization dependent loss (PDL) and nonlinear (NL) effects. Therefore, PDL and NL effects become the most dominant sources of signal degradation in DP-QPSK systems.

PDL can cause power inequality between polarization tributaries, resulting in loss of optical signal to noise ratio (OSNR) degradation. Nonlinear effects can cause significant penalties due to signal depolarization induced by data-dependent state of polarization (SOP) rotation. This type of degradation occurs on a very fast rate, which makes it difficult to compensate with DSP.

In the past the impact of NL and PDL effects has been investigated separately [1–3]. However, there is a valid concern about the interplay between NL and PDL effects and its impact on system design. Up to date, there is only one report on combined NL + PDL study, which reported additional OSNR penalties due to interaction between PDL and fiber nonlinearities [4].

In this work we provide more insight on the mechanism of the interplay between NL and PDL effects in 100Gb/s dual polarization quadrature phase shift keying (DP-QPSK) systems and discuss the critical factors that can impact signal degradation. We show that PDL can worsen nonlinear tolerance by generating large data-dependent optical peak power variations, which can cause additional Q-penalty that needs to be considered in system design.

## 2. System model

In order to accurately estimate the interplay between NL and PDL effects we used distributed simulation model. This model closely approximates real system and takes into account the interaction between PDL, ASE noise and NL effects. It contains one PDL element per node with polarization controller in front of it to set the desired signal state of polarization. Then each PDL element is followed by a fiber link. We investigate the interplay between NL and PDL effects in 50GHz-spaced three-channel 112Gb/s DP-QPSK DWDM system with coherent detection (see Fig. 1 ). The fiber link consists of 15 spans x 60 km NZ-DSF fiber with slightly under-compensated dispersion map, where nonlinear phase noise is the dominant source of signal degradation. The fiber input power is set to −2dBm/ch, for which Q-penalty is approximately 1.5dB. The received OSNR in this work is kept at 18dB. Table 1 summarizes simulation parameters. At the end of the transmission line, the performance of the center channel is evaluated. The DSP in the coherent receiver performs compensation of the accumulated residual chromatic dispersion, polarization demultiplexing using constant modulus algorithm (CMA) and carrier phase recovery using a Viterbi-Viterbi algorithm. The BER values of each polarization channel are obtained by direct error counting and the total BER of polarization multiplexed signal is averaged over BER’s of each individual channel and then converted to Q factor.

## 3. Mechanism of the interplay between NL and PDL effects

We start investigation of the mechanism of the interplay between NL and PDL effects with the analysis of the impact of PDL on DP-QPSK signals. After that, we will add impact of fiber nonlinearity by transmitting PDL-distorted signal through optical fiber. Signal degradation due to PDL strongly depends on the angle between PDL and signal polarization axes [1,2]. There are two angles at which PDL can affect system performance most severely, but in different ways: 0 and 45 degrees. We will analyze the mechanism of DP-QPSK signal degradation in particular for these two cases.

#### 3.1 Signal and PDL element are aligned at θ = 0°

In the first case when signal and PDL polarization axes are aligned at 0 degree angle, the PDL attenuates the polarization component aligned with the high-loss PDL axis, which results in power inequality between polarization tributaries and loss of OSNR. Figure 2(a) shows Q-penalty increase of X-polarization channel, which is aligned with high-loss PDL axis, for various PDL values. In this case Y-polarization channel, which is aligned with low-loss PDL axis, enjoys Q-factor improvement due to signal power increase during optical amplification. As can be seen from Fig. 2(a) the total signal degradation due to PDL is dominated by the lowest power (and the lowest OSNR) tributary.

When this PDL-impaired signal propagates through optical fiber, each polarization component experiences different amounts of nonlinearity due to different power levels induced by PDL. Typically, the polarization tributary with higher power level suffers from larger nonlinear signal degradation compared to the polarization tributary with lower power level. Figure 2(b) shows Q-penalty increase for each polarization component as a function of fiber input power for a PDL = 4dB. Here, Q-penalty difference between two polarization components induced by PDL can be clearly observed at low fiber input power (low NL regime), where PDL effects are dominant. With increase of the fiber input power, the Y-polarization component with higher power suffers from larger Q-factor degradation due to NL effects, while lower power component suffers from smaller NL effect. The Q-penalty difference due to PDL significantly reduces at higher fiber input power where NL effect somewhat balances out PDL-induced impairments. Here once again the Q-factor of the total signal is dominated by lower power channel, resulting in smaller Q-penalties due to nonlinear impairments.

Finally, we investigate Q-penalties of the total polarization multiplexed signal as a function of fiber input power for PDL values 0, 2, 4 and 6dB (see Fig. 2(c)). We can clearly see that Q-penalty curves for different PDL values are parallel to each other, resulting in total Q-penalty due to combined NL and PDL effects be equal to the sum of Q-penalties of each degradation factor: Q-pe(NL + PDL) = Q-pe(NL) + Q-pe(PDL). This shows that for this particular case when signal and PDL axes are aligned at 0 degrees, there is no indication of additional penalties due to interplay between NL and PDL effects.

#### 3.2 Signal and PDL element are aligned at θ = 45°

The second type of signal degradation due to PDL occurs when signal and PDL axes are aligned at non-zero degree angle. Here, in addition to loss of OSNR loss of orthogonality between polarization tributaries occurs, which leads to generation of polarization crosstalk components. The worst case scenario occurs when signal and PDL axes are at 45 degrees with respect to each other. Figures 3(a) and 3(b) demonstrate the impact of PDL on orthogonality of polarization multiplexed signal when signal is rotated by 45 degrees counter-clockwise and clockwise with respect to PDL axes, respectively. Here, let us assume that PDL element has two orthogonal axes with high-loss PDL axis aligned with x-axis and low-loss PDL axis aligned with y-axis of the frame of reference. Then, two originally orthogonal X- and Y-polarization components of the input polarization multiplexed signal slightly rotate towards low-loss PDL axis resulting in reduced or increased relative angle between polarization tributaries (shown in the diagrams as X′ and Y′). The generated polarization crosstalk components are also shown.

Since in DP-QPSK systems the information is encoded in phase of the optical signal, these crosstalk components could be in-phase, out-of-phase or at ± π/2 with the main polarization component. For those symbols whose crosstalk components are in-phase or out-of-phase constructive or destructive interference could occur, resulting in generation of large data-dependent optical peak power variations. Figures 4(a) and 4(b) show examples of the optical waveforms for the cases when signal and PDL axes are aligned at 0 and at 45 degrees, respectively, with red and green arrows pointing out to the peak power variations due to polarization crosstalk. Since polarization diversity coherent receiver can effectively separate each polarization component, these crosstalk components and associated with it peak power variations have no impact on the signal when considering PDL effect separately from nonlinear effect. However, they can become important during transmission of PDL-impaired signal in optical fiber with Kerr nonlinear effects.

The amount of optical peak power variation depends on the PDL amount and on the angle *θ* between signal and PDL axes. For simplicity let us assume a single PDL element with PDL value in decibels expressed as PDL[dB] = 10·log((1 + *η*)/(1-*η*)), where *η* is linear PDL parameter. Then, using Jones matrix representation, the optical field U(z,t) of the signal after being rotated by an angle *θ* with respect to PDL polarization axes and after passing through PDL element can be expressed as:

Therefore, the optical intensity |U|^{2} of the signal after PDL is equal to:

The last term in the equation shows that PDL-induced peak power variation is proportional to the PDL value *η* and angle *sin2θ*, indicating that there are no peak power variations at *θ* = 0degrees and maximum peak power variations at *θ* = 45degrees. This finding is confirmed by numerical simulation as shown in Figs. 4(a) and 4(b).

#### 3.3 Interplay between NL and PDL effects

When such PDL-impaired optical signal propagates in optical fiber with Kerr nonlinear effects, these peak power variations can generate symbol-dependent nonlinear phase noise. Figure 5(a) shows Q-penalty as a function of the angle between signal and PDL axes for PDL of 2, 4 and 6dB and fiber input power −2dBm/ch. Here, the interplay between NL and PDL effects manifests in large Q-penalty increase with angle, which also increases with increase in PDL values. The Q-penalty difference due to interplay between PDL and nonlinearity is shown in Fig. 5(b). As we explained above, at 0degree angle the Q-penalty increase is simply due to PDL impact only such that the Q-penalty of combined effects is simple sum of each degradation factors: Q-pe(NL + PDL) = Q-pe(NL) + Q-pe(PDL). However, when the angle between PDL and signal axes increases up to 45 degrees, an additional penalty Q-pe(NL&PDL) in the amount of 0.8, 1.1 and 1.4dB for PDL of 2, 4 and 6dB, respectively, is observed due to interplay between NL and PDL effects. This effect can be expressed as: Q-pe(NL + PDL) = Q-pe(NL) + Q-pe(PDL) + Q-pe(NL&PDL). This additional penalty is attributed to the phase noise generation due to PDL-induced optical peak power variations.

Finally, we investigate the interplay between PDL and fiber nonlinearity as a function of fiber input power for PDL = 4dB. Figure 6 shows that Q-penalty of a signal rotated at 45 degrees angle with respect to PDL polarization axes increases faster than that of 0 degrees angle, which is due to additional PDL-induced optical peak power variations. This effect is somewhat easy to understand. As we know, the most dominant source of nonlinear impairments in optical fiber transmission comes from the Kerr effect, where intensity dependence of the refractive index gives rise to intensity dependent phase shift. The propagation of the polarization multiplexed signal in optical fiber under assumption that nonlinear effects are averaged over Poincare sphere and neglecting PMD can be described by Manakov equation [5]:

*U*is the electric field column vector,

*β*is the chromatic dispersion coefficient,

_{2}*γ*is the fiber nonlinear coefficient,

*z*is the distance along the fiber. The last term in the equation comes from Kerr nonlinearity, which leads to a phase rotation that is proportional to the intensity of the optical signal. Thus, when signal is aligned with PDL axes at 0 degrees angle, the signal degradation and associated with it Q-penalty increases with increase of the fiber input power (optical intensity). When the signal is rotated by 45 degrees with respect to PDL axes, the PDL-induced additional optical intensity variations result in larger signal degradation and, thus, increased Q-penalty. This Q-penalty increase is steeper compared to 0 degree angle case due to faster nonlinear phase noise generation rate with increase of fiber input power in high nonlinear regime.

## 4. Summary

We numerically investigated the interplay between NL and PDL effects in 112Gb/s DP-QPSK systems and identified three factors contributing to signal degradation, i.e. impact of PDL, NL and interplay NL&PDL effects. We show that significant interplay can occur when the axes of PDL elements are rotated by 45 degrees with respect to the signal polarization axes, which can cause up to 1.4dB additional Q-penalty due to PDL-induced large data-dependent optical peak variations. We also showed that this additional Q-penalty can increase even faster with increase of fiber input power.

## References and links

**1. **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 *Proceedings of IEEE Conference on Optical Fiber Communications* (Institute of Electrical and Electronics Engineers, San Diego, 2008), paper OThU6 (2008).

**2. **T. Duthel, C. R. S. Fludger, J. Geyer, and C. Schulien, “Impact of Polarization Dependent Loss on Coherent POLMUX-NRZ-DQPSK,” in *Proceedings of IEEE Conference on Optical Fiber Communications,* (Institute of Electrical and Electronics Engineers, San Diego, 2008), paper OThU5 (2008).

**3. **C. Xie, “Polarization-Dependent Loss Induced Penalties in PDM-QPSK Coherent Optical Communication Systems,” in *Proceedings of IEEE Conference on Optical Fiber Communications *(Institute of Electrical and Electronics Engineers, San Diego, 2010), paper OWE6 (2010).

**4. **O. Vassilieva, I. Kim, and T. Naito, “Systematic Investigation of Interplay between Nonlinear and Polarization Dependent Loss Effects in Coherent Polarization Multiplexed Systems,” in *Proceedings of ECOC’2010*, Torino, Italy, paper P4.08 (2010).

**5. **C. R. Menyuk and B. S. Marks, “Interaction of Polarization Mode Dispersion and Nonlinearity in Optical Fiber Transmission Systems,” J. Lightwave Technol. **24**(7), 2806–2826 (2006). [CrossRef]