For differential decoding, direct detection of DPSK signal needs a delay line interferometer with a free spectral range normally equal to the transmitted bit-rate. We numerically demonstrate that free spectral range optimization can increase tolerance to fiber Kerr nonlinearities for 40 Gbit/s RZ-DPSK transmission, especially for multi-format (RZ-DPSK and RZOOK) systems, in which Kerr nonlinearities is quite serious mainly due to cross-phase modulation. The optimal delay time of the delay line interferometer in DPSK signal demodulation is shorter than one bit-period. Joint optimization of free spectral range and optical filter bandwidth will further enhance system tolerance to nonlinear transmission.
©2008 Optical Society of America
Differential phase-shift keying (DPSK) format has been studied extensively in recent years [1–4]. With 3 dB benefit in receiving sensitivity and superior tolerance to fiber nonlinearities compared to on-off keying (OOK) format, DPSK attracts great attentions for long-haul wavelength-division multiplexing (WDM) transmission operating at higher data rate, especially 40 Gbit/s and beyond . The DPSK receiver commonly consists of a delay line Mach-Zehnder interferometer (DLI) and a balanced photodetector. Usually, there is a 1-bit delay between two DLI arms. The phase of the preceding bit is compared with that of the current bit to convert the phase modulation into intensity modulation, which can be detected by the balanced photodetector.
Corresponding to 1-bit delay time, DLI free spectral range (FSR) is equal to the transmitted bit-rate, which has been generally recognized as the optimal case for achieving maximal overlap of the two adjacent bits for interference . It has been shown that bit delay mismatch will incur performance degradation due to inter-symbol interference (ISI) [6–8]. However, recently it has been brought forward that FSR optimization, inducing bit delay mismatch, can increase optical filtering and chromatic dispersion (CD) tolerance [9–14]. Ref.  showed that in the presence of CD, offsetting the FSR in RZ-DPSK signal demodulation increases CD tolerance with no adverse effect on PMD tolerance or frequency offset penalty. Ref.  presented that optimal FSR may be greater than bit-rate when optical filtering is involved. In Ref. , a low crosstalk demodulator is introduced with FSR larger than bitrate. Ref.  demonstrated that tolerance to narrow optical filtering and CD can both be increased by decreasing the differential delay of DLI to less than one bit-period. Much recently, Ref.  further showed the combined influence of large FSR and tight optical filtering in the demodulation of NRZ-, RZ-and CSRZ-DPSK leading to increased CD tolerance. The above studies all focus on back-to-back configuration, except that Ref.  exhibited a 43 Gbit/s NRZ-DPSK transmission experiment over a 1440 km commercial 10 Gbit/s WDM system. However, Ref.  only discussed FSR optimization under optical filtering effects and didn’t refer to fiber nonlinearities. Actually, none of previous studies on FSR have considered nonlinear WDM transmission. This subject, however, is of high importance as it has been shown that Kerr nonlinearities of self-phase modulation (SPM) and cross-phase modulation (XPM) will degrade DPSK system performance [1, 3, 15]. The FSR optimization might be advantageous to counteract performance degradation in nonlinear transmission.
In this paper, we numerically investigate FSR optimization for 40 Gbit/s RZ-DPSK transmissions of single-/multi-channel systems and multi-format (RZ-DPSK and RZ-OOK) WDM systems. Generally speaking, the optimal delay time of DLI is shorter than one bitperiod in the presence of serious fiber Kerr nonlinearities. Conjunct optimization of FSR and optical filter bandwidth further improve system performance in nonlinear transmission.
2. System setup
The transmission system setup in our simulation is shown in Fig. 1. We consider three kinds of 40 Gbit/s transmission systems: single-channel RZ-DPSK system, RZ-DPSK WDM system, and multi-format WDM system. For WDM transmission, the wavelength of the center channel is 1553.60 nm and the channel spacing is 100 GHz. The fiber link consists of identical spans, each of which includes nonzero dispersion-shifted fiber (NZDSF), dispersion compensation fiber (DCF) and an erbium-doped fiber amplifier (EDFA). The parameters of the NZDSF are: span length Lspan=100 km, dispersion D =4.5 ps/nm/km, attenuation α =0.21 dB/km and nonlinearity γ =1.32/W/km. DCF is linear and without loss, whose length is chosen to fully compensate for the dispersion of NZDSF. The span loss is totally compensated by the EDFA. The average launch power in each channel is set as Pave=0.9 dBm so that for DPSK signal the mean nonlinear phase shift induced by SPM is rad after Nspan=30 spans. Here is the effective length per span.
The direct detection receiver of DPSK signal consists of a third-order Gaussian optical filter with 3 dB bandwidth of 80 GHz, followed by a DLI, a balanced photodetector and a fifth-order Bessel electrical low-pass filter with 28 GHz bandwidth. Our numerical simulations are performed with VPItransmissionMaker7.1. A De Bruijn sequence of 4096 bits is chosen to contain sufficient bit patterns to capture nonlinear interaction details for the system scenarios in this paper .
3. Simulation results and discussion
In this Section, we first present the results of FSR optimization considering fiber Kerr nonlinearities of SPM and XPM. Then we show that the optimal FSR has no relation with nonlinear phase noise. Finally, we discuss the joint optimization of FSR and optical filter bandwidth.
3.1 FSR optimization in the presence of SPM and XPM
In nonlinear transmission shown in Fig. 1, the inline amplifier is set noiseless for only considering fiber nonlinearities of SPM and XPM. Amplified spontaneous emission (ASE) noise is added at the receiver end to set the desired optical signal-to-noise ratio (OSNR) in a resolution of 0.1 nm. The nonlinear transmission results in OSNR penalty, referencing to the back-to-back measurement, at bit-error-rate (BER) target of 1e-3. We calculate OSNR penalties at different delay time. The optimal delay time is thus determined by the minimal OSNR penalty. In Fig. 2(a) and Fig. 2(b), the optimal delay time and its corresponding OSNR penalty improvement are shown, respectively, as a function of transmission distance.
For single-channel RZ-DPSK transmission, SPM effect is not strong enough to cause optimal delay time shift, which is still one bit-period of 25 ps. Meanwhile for RZ-DPSK WDM system, XPM due to neighboring channels becomes serious after 2500 km transmission, leading to optimal delay time a little shorter than 25 ps. This phenomenon is much more evident for multi-format WDM system. Owing to much greater XPM effect induced by two adjacent RZ-OOK channels, optimal delay time is no more 25 ps just after 1000 km transmission. It decreases with transmission distance increasing, indicating that larger fiber Kerr nonlinearities result in shorter optimal delay time, corresponding to larger FSR. Figure 2(b) shows that optimizing DLI delay time is more beneficial for multi-format WDM system to enhance nonlinearity tolerance. For pure DPSK systems, however, the improvements are much less. Figure 3 shows eye diagrams after 3000 km nonlinear transmission of RZ-DPSK single-channel and WDM systems without ASE noise. Compared with Fig. 3(a), more eye closure is observed in Fig. 3(b) due to ISI induced by XPM. However, since the ISI is not too much in this case, the improvement by optimizing delay time is not evident. Figure 3(c) shows the eye diagram after optimizing delay time, corresponding to the last point of the red curve in Fig. 2(b). We can hardly tell the difference between Fig. 3(b) and Fig. 3(c).
Figure 4 further demonstrates the details in the case of multi-format system after 3000 km transmission. Figure 4(a) clearly shows that the optimal delay time of DLI is not 25 ps but 20.5 ps, which yields an OSNR penalty reduction of more than 1.7 dB. In addition, the optimization range is about 2 ps according to 0.1 dB OSNR penalty redundancy, which is easy for practical implement. The eye diagrams shown in Fig. 4(b) and Fig. 4(c), in which eye of 20.5 ps opens up much more clearly than that of 25 ps, evidently prove the performance enhancement by FSR optimization.
By reducing DLI delay time, part of bit interferes onto itself providing deterministic constructive interference, which has been confirmed in Ref.  for minimizing ISI induced by CD. Similarly in nonlinear transmission, ISI induced by XPM can also be mitigated by decreasing delay time. The non-constant intensity of RZ-OOK channel changes randomly with different bit patterns, causing much more serious XPM-induced ISI than the case of pure DPSK WDM system, which can explain why greater improvement can be obtained in multi-format WDM systems.
Recently, we numerically proved that XPM-induced impairments can be successfully suppressed with optimum dispersion mapping . In Table 1, the OSNR penalties for 3000 km multi-format WDM transmission systems with resonant and optimum dispersion maps are summarized, respectively. The resonant map with 25 ps DLI delay time corresponds to Fig. 4(b) and that with 20.5 ps DLI delay time is for Fig. 4(c). FSR optimization yields an OSNR penalty reduction of 1.76 dB. The optimum precompensation was found to be Dpre = -360 ps/nm for residual dispersion per span Dres=20 ps/nm. In this case, optimal delay time of DLI is 25 ps as expected. With optimum dispersion map, XPM effect is well suppressed and a nonlinear OSNR penalty remains only 0.56 dB, indicating an OSNR improvement of 5.11 dB. In comparison with optimum dispersion map, optimizing FSR offers less nonlinear tolerance increase. However, optimum dispersion map, applied in the whole transmission link, is more complicated and costly than FSR optimization implemented at the receiver end.
3.2 FSR optimization in the presence of nonlinear phase noise
We choose 3000 km RZ-DPSK WDM system with resonant map to investigate FSR optimization in the presence of nonlinear phase noise. ASE noise is added at each EDFA along the fiber link. Nonlinear phase noise is thus induced by the interaction between ASE and fiber Kerr nonlinearities. The noise figure of the EDFA in each span is set to be 7.2 dB, resulting in an OSNR of ρs=25.5 (14 dB) after 30 spans transmission. The OSNR is defined as ρs=Pave/(NspanS 0 Bd). S 0 is the amplifier noise spectral density in a single polarization. Bd is the optical noise bandwidth which is set the same as the bit-rate of 40 Gbit/s. In Fig. 5, the red curve stands for the case with both Kerr nonlinearities and nonlinear phase noise. For comparison, we add ASE noise at the receiver end instead of each EDFA, shown as the black curve in Fig. 5, taking only fiber Kerr nonlinearities into account. The optimal delay time for the two cases is nearly the same, so that introducing nonlinear phase noise won’t influence the choice of optimal delay time. However, it should be noted that the performance improvement by optimizing FSR is limited for both two cases, as shown in Fig. 2 (b).
3.3 Optimization of both FSR and optical filter bandwidth
We take the 3000 km multi-format WDM system with resonant map as an example to further study the relationship between FSR and optical filter bandwidth. Joint optimization of both of them has been proved to increase CD tolerance . The OSNR penalty at BER of 1e-3 is again used as a criterion and the results are summarized in Fig. 6. For all values of optical filter bandwidth, 25 ps is no longer the optimal delay time. The increase of optimal delay time (decrease of FSR), corresponds to larger optical filter bandwidth, which is consistent with Ref. [13, 14]. The reason is that the optimization of both FSR and optical filter bandwidth is actually optimizing the bandwidth of two filters, optical filter and DLI. When one filter bandwidth is getting wider, the other should be narrower to filter out noise. Note that the optimal optical filter bandwidth is around 80 GHz at the back-to-back measurement. After nonlinear transmission, it is from 85 GHz to 100 GHz. With joint optimization of both FSR and optical filter bandwidth, the minimal OSNR penalty is 3.8 dB, which is further reduced by more than 0.1 dB, compared with its equivalent in Fig. 4(a).
We have studied FSR optimization in the presence of fiber Kerr nonlinearities. The numerical results show that the optimal DLI delay time is shorter than one bit-period provided serious fiber Kerr nonlinearities. The optimal FSR scales with the strength of Kerr nonlinearities. FSR optimization can distinctly increase nonlinear tolerance of DPSK signals in 40 Gbit/s multi-format WDM systems, e.g., OSNR penalty can be reduced by more than 1.7 dB after 3000 km transmission. For pure DPSK systems, however, the effect of FSR optimization is quite limited, due to less XPM effects compared to that of multi-format WDM systems. Nonlinear phase noise has no influence on the choice of optimal delay time. Optimizing FSR together with optical filter bandwidth will further enhance system tolerance to fiber Kerr nonlinearities.
This work was supported by National Hi-tech Research and Development Program of China (863 Program) (No. 2006AA01Z253 and No. 2006AA01Z261). The authors also acknowledge the donation of VPI software suite from Alexander von Humboldt foundation.
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