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We analyze the effect of polarization-dependent loss (PDL) on the performance of the polarization-division-multiplexed (PDM) signals in direct-detection systems. We present the theoretical analysis of the sensitivity penalty caused by PDL-induced coherent crosstalk and compare the results with experimental data obtained by using a simple variable PDL emulator based on a LiNbO3 Mach-Zehnder modulator. Also presented is the performance degradation caused by the polarization misalignment between the received signals and the polarization beam splitter at the receiver in the presence of PDL.
©2009 Optical Society of America
1. Introduction
In recent years, there have been lots of efforts to increase the capacity of wavelength-division-multiplexed (WDM) systems by using polarization-division-multiplexing (PDM) technique [1]-[5]. By carrying two independent data traffics in two orthogonal polarization states (but operating at the same wavelength), the PDM can double the aggregate data rate of WDM systems without increasing the transmission bandwidth. For a given data rate, the PDM can be also used to halve the symbol rate to cope with transmission impairments including chromatic dispersion (CD). Thanks to the capability of doubling the spectral efficiency, many recent experiments have utilized the PDM technique in combination with multi-level modulation formats [1]-[4].
The receiver of the PDM systems is typically composed of a polarization tracking module and a polarization beam splitter (PBS) to properly separate the two orthogonal polarization states of the signals and to send them to their respective receivers [3]-[5]. For coherent receivers, the post-detection digital signal processing (DSP) unit can replace the polarization tracking module [1]-[2]. However, this has been nowadays performed off-line in high-speed lightwave communication system experiments because the symbol rate of the systems can be beyond the reach of modern analog-to-digital converters and DSP units [1]-[2]. For direct detection receivers, automatic polarization tracking modules are essentially required to track the polarization variation of the incoming signals. A small error of the polarization misalignment between the incoming signal and the PBS leads to power penalties for both PDM tributaries [6]. Very recently, automatic polarization tracking has been successfully demonstrated in a PDM direct-detection system with 5,200-km circulating loop [5].
However, polarization mode dispersion (PMD) and polarization dependent loss (PDL) are known to induce coherent crosstalk to direct-detection PDM transmission systems. In the presence of PMD, the polarization states of the signal become a function of wavelength. This implies that for a modulated signal which has a certain optical bandwidth proportional to modulation data rate, the polarization states are not maintained throughout the signal spectrum. Therefore, the signal spectral components away from the carrier wavelength become crosstalk to the other tributary channel since the polarization axis of the PBS is aligned to the polarization state of the carrier [7]. On the other hand, PDL serves to cause the power imbalance between the polarization states, which, in turn, leads to different optical signal-to-noise ratio (OSNR) to the tributaries [8]-[9], [12]-[13] and/or to break the orthogonality of the two polarization states [10]-[11]. Unless the PDL axis is exactly aligned to the one of the two orthogonal polarization states of the signals, the orthogonality of the two polarization states are not maintained and consequently coherent crosstalk occurs at the receiver. This coherent crosstalk between the two tributaries would not be problematic in the coherent detection scheme since the crosstalk can be fully compensated for by the DSP unit with the help of the retrieved optical phase information. Thus, when it comes to the PDL effects on PDM signals, many researches have mainly dealt with the OSNR degradation by PDL [8]-[9], [12]-[13], which cannot be mitigated regardless of receiver types and set the ultimate limit of the PDL-induced performance degradation.
For direct-detection scheme, however, the optical phase information is lost at the receiver and consequently the crosstalk cannot be compensated. Thus, both the OSNR degradation and the coherent crosstalk can limit the performance of PDM direct-detection systems. To see how much both effects affect the performance of PDM direct-detection systems, we performed a computer simulation with a lumped PDL element as shown in the inset of Fig. 1. We changed the angle between the axis of the PDL element and one of the polarization states of the PDM signals (i.e., x-polarization) from 0 to 90°. This allows us to isolate the coherent crosstalk-induced penalty from the OSNR degradation. For example, when the angle is 45°, the polarization mixing becomes largest and only the coherent crosstalk degrades the system performance (it should be noted that there is no additional OSNR degradation in this case because both polarization tributaries experience the same loss before the signal OSNR is set by the EDFA). On the other hand, only OSNR degradation affects the system performance when the angle is 0° or 90°. The simulation results of Fig. 1 show that in PDM direct-detection systems the coherent crosstalk-induced penalty is larger than OSNR degradation-induced one. A couple of researchers have recently analyzed through experiment the effects of PDL on PDM direct-detection systems [8]-[9]. However, they have mainly focused on the OSNR degradation in their systems and there has been no in-depth study on the PDL-induced polarization mixing between the PDM tributaries.
Fig. 1. Computer simulated receiver sensitivity penalty vs. the angle between the polarization state of PDM signal and principal axis of the 1-dB PDL element. NRZ: Non-Return-to-Zero.
Hence we analyze the PDL-induced receiver penalty of the direct-detection PDM systems. The amount of the coherent crosstalk as well as the orthogonality degradation in the PDM systems are theoretically analyzed as functions of PDL and the polarization angle between the PDM signal and the PDL element. The results are confirmed with experimental measurement. For our experiment, we utilize a simple variable PDL emulator based on a LiNbO3 modulator. A wide range of PDL value can be obtained up to 35 dB simply by adjusting the bias voltage. The result shows that a PDL of 0.9 dB causes a 1-dB power penalty in the PDM direct-detection systems. We also show that the polarization misalignment between the PDM signal and the PBS at the receiver makes the systems more sensitive to PDL.
2. Coherent crosstalk by PDL in PDM systems
Fig. 2. Polarization states of the PDM tributaries after (a) polarization multiplexing with a PBC, (b) passing through the transmission line with PDL, and (c) polarization demultiplexing with a PBS.
Figure 2(a) shows the orthogonal polarization states of the PDM tributaries obtained after polarization multiplexing with the polarization beam combiner (PBC) located at the transmitter. Then, the power of each tributary (P and S) can be described as
We define θ as the angle between the x-axis (y-axis) and the polarization state of one of PDM tributaries shown as S (P) in Fig. 2(a). However, these polarization states can be distorted by PDL elements in the fiber-optic transmission line. Without loss of generality, we assume that PDL attenuates only the x-components of the tributaries, as shown in Fig 2(b). Thus, after passing through the transmission line with PDL, the power of each tributary can be expressed as
where α is the PDL expressed in a linear scale. Fig. 2(b) shows the polarization states of the two tributaries after the PDL element. It shows that the orthogonality between P and S was impaired by φ+γ. From the relationship of tan2 (θ−φ) = P′x/P′y and tan2 (θ + γ) = S′y/S′x in Fig. 2(b), φ and γ can be calculated by using Eq. (3) as
When P′ and S′ are demultiplexed by using the PBS at the receiver, the polarization states of them can be illustrated as Fig. 2(c). Also shown in this figure is that the PDL generates new components (shown as solid gray arrows) when P and S were reduced to P′ and S′ respectively. They are coherent crosstalks and cause power penalties. To analyze this PDL-induced coherent crosstalk, we defined the signal-to-crosstalk ratio (SCR) as the ratio of the power of each tributary to the power of the coherent crosstalk expressed as
where Ψ1 (and Ψ2) are the angles between the polarization axes of the PBS and P′(and S′), respectively. To optimize the performances of both tributaries, the polarization states of P′ and S′ are typically controlled in a way that they experience the same amount of loss in the PBS by using the polarization controller during polarization demultiplexing. Thus, each tributary would have identical SCR and the same signal power after demultiplexing. Since the SCR of P′ and S′ is identical and Ψ2 can be replaced with φ+γ−Ψ1, two equations in Eq. (4) can be rewritten as
Thus, Ψ1 (and Ψ2) can be obtained as
Then, the PDL-induced power penalty for maintaining a given value of Q (e.g., Q=6 corresponding to a BER of 10-9) can be now calculated as [14]
Here, we assume that there is no optical coherence between the PDM tributaries. If there is optical coherence between the tributaries, which can be found in PDM systems using a single light source, Eq. (7) can be used to estimate the time-averaged power penalty. This is because the phase difference between the tributaries at the receiver can slowly change over time.
When there is an error in polarization control for demultiplexing the PDM tributaries, which can be denoted as a small change (δ) in the angle between the polarization axes of the PBS and P′ (and S′), the SCR of P′ (and S′) and crosstalk penalty can be expressed accordingly using Ψ′1 (and Ψ′2) as
Figure 3 shows the calculated power penalty of the PDM signal as functions of the PDL and the polarization misalignment angle (δ) between the PBS and the tributaries (P′ and S′). The resultant penalty of the PDM signal was represented as an average value of the penalties in the two tributaries. To illustrate the worst case scenario, we set θ to be 45°. The result shows that the presence of PDL makes the PDM systems sensitive to the polarization misalignment at the receiver. For example, a 2-dB power penalty arises in the absence of the misalignment when the PDL is ~1.1 dB. However, when the misalignment is 3°, only a PDL of 0.5 dB gives rise to the same amount of penalty.
Fig. 3. Power penalty in decibel caused by PDL and the polarization misalignment between of the PBS and the PDM signals.
3. Generation of various PDL values
For the generation of various values of PDL in our experiment, we modified a typical
LiNbO3 modulator. Although a LiNbO3 modulator is an inherently
polarization-sensitive device, the Ti-diffused waveguide could still propagates the
signals in both TM and TE polarizations. However, in modern fiber-optic communication
systems, a polarizer is usually inserted inside the modulator package to maximize the
extinction ratio by suppressing the signal in TE polarization (for z-cut modulators). In
our experiment, we removed the polarizer from the modulator in order to use the
LiNbO3 modulator as a PDL emulator by using different transmittances of TE
and TM polarizations. Figure 4(a) shows the
measured transmittance traces of the proposed PDL emulator in comparison with the
calculated results. The Vπ of the TE polarization was measured to be four
times larger than that of TM polarization. The difference between the transmittances of
two polarization states represents a PDL. The result indicates that the proposed PDL
emulator could generate PDL from 0 to 35 dB simply by adjusting the bias voltage of the
modulator. Obviously, the maximum PDL value is limited by the extinction ratio of the
modulator. Figure 4(b) shows the PDL values
measured as a function of the bias voltage by using a commercial PDL meter (FIBERPRO
PL2000). The symbols (
Fig. 4. (a) The measured transmittances of PDL emulator. (b) Measured PDL value as a function of bias voltage.
This problem could be easily solved by using feedback control and locking the dc bias to an arbitrary point of the transmittance of the PDL emulator. By using a feedback control of bias voltage, we were able to maintain the PDL value within ± 0.02 dB of error for > 1 hour.
4. Experimental results and discussions
Fig. 5. Experimental setup for the measurement of PDL-induced coherent crosstalk. PD: Photodetector, RFSA: RF spectrum analyzer.
We first measure the PDL-induced coherent crosstalk as functions of PDL and the polarization angle between the PDM signal and the PDL element by using an experimental setup depicted in Fig. 5. We used two distributed feedback (DFB) lasers operating at the same wavelength (1552.12 nm) and applied pilot tones at 100 and 105 kHz to these lasers, respectively, by adding small sinusoidal currents to the injection currents. This was to measure the amplitudes of coherent crosstalk by detecting the pilot tones. The outputs of these lasers were polarization-multiplexed by using a PBC and the polarization controllers (PC1 and PC2). The multiplexed signal was then sent to the PDL emulator described at the previous section. The polarization angle between the PDM signal and the principal axis of the PDL emulator was set to be 45° by using PC3 in the experiment. The polarization analyzer located after the PDL emulator was used to monitor the state of polarization (SOP) of the PDM signal and to adjust the PC3. The polarization analyzer was also used for observing the PDL during the crosstalk measurement. We demultiplexed the PDM signal by using a PBS with PC4 and measured the amplitudes of pilot tones by using an RF spectrum analyzer. We also set the SCRP and SCRS to be identical by adjusting PC4 for optimizing the performances in both PDM tributaries.
Fig. 6. PDL-induced coherent crosstalk as a function of the angle between the polarization state of PDM signal and principal axis of the PDL emulator. The PDL value was changed from 1 to 5 dB by using the proposed PDL emulator.
Figure 6 shows the measured PDL-induced coherent crosstalk in comparison with the theoretically calculated lines obtained by Eq. (4). The data were also compared with the numerically simulated results obtained by using a commercial simulator (VPI) in order to confirm the calculated results at various polarization angles between the PDM signal and principal axis of the PDL emulator. The results show that the crosstalk would increase with the PDL value and it becomes the maximum when the polarization state of the PDM signal is 45° from the principal axis of PDL emulator. The results also show that a small (~1 dB) PDL in the transmission line could induce a coherent crosstalk as large as 25 dB. Such a large crosstalk would inevitably cause power penalty. We measured the performance degradation caused by the PDL-induced crosstalk using the setup shown in the Fig. 7. In this experiment, we modulated the DFB laser with a 10-Gb/s non-return-to-zero (NRZ) signal (PRBS: 231-1) using a LiNbO3 intensity modulator (IM), and then divided the modulated signal into two paths by using a 3-dB coupler. A 3-km long single mode fiber (SMF) was placed in one path for the decorrelation between the PDM tributaries. The powers of the signals in two paths were equalized by using an optical attenuator.
Fig. 7. Experimental setup for the measurement of the effect of PDL-induced coherent crosstalk on the PDM direct-detection systems.
These signals were then polarization multiplexed by using a PBC, and sent to the PDL emulator at 45° from its principal axis. In the receiver side, we demultiplexed the tributaries by using PC5 and PBS. The extinction ratio and receiver sensitivity for both tributaries were measured to be 13.8 dB and -19.3 dBm in the back-to-back. The power penalty was measured while varying the PDL value. Fig. 8 shows that the measured data agrees well with the theoretically calculated curve using Eq. (7). The results show that the power penalty was measured to be 1 dB when the PDL was ~0.9 dB. The PDL would be particularly problematic in long-haul transmission systems because there are a number of cascaded optical devices with PDL. Considering the accumulated PDL could be easily increased up to several decibels in a long-haul transmission line (e.g., 9.2 dB in the transmission link consists of 11 nodes [15]), the PDL-induced coherent crosstalk could be a significant limiting factor in the highspeed PDM systems such as for 100-Gb/s Ethernet.
5. Conclusion
We have presented the theoretical and experimental analysis of the sensitivity degradation caused by polarization-dependent loss in polarization-division-multiplexed direct-detection systems. The PDL of the fiber-optic transmission line could impair the orthogonality between the polarization-division-multiplexed tributaries and generate coherent crosstalk on the signal in the opposite polarization state during the demultiplexing in the receiver. The results show that 0.9-dB PDL could generate coherent crosstalk of -25 dB, which, in turn, degrades the receiver sensitivity by 1 dB. It has been also shown that the presence of PDL makes the systems sensitive to the polarization misalignment between the PDM signal and the polarization beam splitter at the receiver Although coherent receivers can mitigate the effect of PDL-induced coherent crosstalk by using electrical digital signal processing technology, the effect of the PDL could be still significant to the polarization-division-multiplexed highspeed transmission systems when the bit rate of each tributary increases more than 10 Gb/s (beyond reach of modern analog-to-digital converters and digital-to-analog converters).
Acknowledgments
This work was supported in part by the IT R&D program of MKE/IITA, [2008-F017-01, 100Gbps Ethernet and optical transmission technology development]. The work of H. –C. Ji was supported by the Information and Telecommunication National Scholarship Program of IITA, the Ministry of Information and Communication (MIC), Korea.
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