We show that optical phase conjugation (OPC) based on third order nonlinear effects for mid-span spectral inversion (MSSI) can be improved by splitting the nonlinear element into two parts and adding an optical filter between them. This band-stop filter suppresses the cross-phase-modulation products that are generated around the pump, which, if not removed, will be shifted to fall around the output OPC signal band. Numerical simulations show that this method reduces the fundamental limitations introduced by OPC by 3 dB, which results in improvement of the maximum signal quality, Qmax, by 1 dB in a 10 × 80-km 4-QAM 224-Gb/s CO-OFDM system with MSSI.
©2013 Optical Society of America
In coherent optical systems, linear impairments such as chromatic dispersion (CD) and polarization mode dispersion (PMD) can be electronically compensated [1–4]. Therefore, fiber nonlinearity is the major limiting factor of transmission distance and bandwidth in long haul high bandwidth optical communication systems [5, 6]. Mid-span spectral inversion (MSSI) using optical phase conjugation (OPC)  near the middle of the link, can mitigate fiber nonlinearity for on-off keyed systems  and polarization multiplexed QPSK systems [9–11]. MSSI has also been proposed for optical OFDM systems . Compared with electronic fiber nonlinearity compensation techniques , MSSI can compensate many WDM channels simultaneously .
Recently, we have experimentally demonstrated an improvement of 4.8 dB in the nonlinear threshold for a 10 × 80-km 604.7-Gb/s 16-QAM CO-OFDM super channel using MSSI . However, the performance at the optimal operating power for maximal signal quality only improved by 0.2 dB compared with a system without MSSI. This was because the OPC module itself introduces a performance penalty. We have presented a detailed theoretical analysis [15, 16] showing that two two-stage nonlinear processes and amplified spontaneous emission (ASE) are the cause of this performance penalty.
In this paper, we present a method of reducing the intrinsic performance penalty seen in optical phase conjugators that use third order nonlinearity. We demonstrate the method by simulating the back-to-back performance penalty of a CO-OFDM system. Our method splits the nonlinear element into two parts; then inserts a band-stop filter (BSF) centered on the pump between them, to remove the XPM products and the pump. The pump is then reinserted into the second part. This novel method reduces the performance penalty due to a two-stage nonlinear process. Numerical simulations using the split-step Fourier method (SSFM) show that our two-part OPC module has a 3-dB better back-to-back maximum Q performance compared with a conventional OPC module. Simulation results also show that this better back-to-back performance results in an improvement of the maximum signal quality, Qmax, by 1 dB in a 10 × 80-km 4-QAM 224-Gb/s CO-OFDM system.
2. MSSI with a mid-way filter
2.1 Conventional OPC
Figure 1(a) shows the block diagram of a system using MSSI near the middle of the link. Figure 1(b) shows the details of a conventional MSSI module. The output of the first half of the link is fed into the MSSI module. The input amplifier of the OPC module boosts the input power. The input signal is then filtered with a band-pass filter (BPF) and is combined with the output of a CW pump. The output of the nonlinear element is passed through another BPF to remove the pump and the original signal, leaving the wanted phase-conjugated signal. The output signal is then amplified before passing to the second half of the link. The details of the coherent transmitter and receiver are discussed in .
Inset (i) in Fig. 1(b) shows the spectrum at the output of the χ(3) nonlinear element, which is a Highly Non-Linear Fiber (HNLF) in this paper. Inset (ii) shows the spectrum at the output of the MSSI module. Two types of nonlinear products, XPM-OPC (dark green) and FWM-OPC (dark blue) [15, 16], fall within the band of the wanted OPC signal, so cannot be filtered out by the BPF. Thus, these two nonlinear products, along with ASE from the erbium doped fiber amplifiers (EDFA), cause a fundamental back-to-back performance penalty in conventional MSSI. As the insets show, XPM-OPC dominates over FWM-OPC .
At IPC 2012, we presented a theoretical analysis of the back-to-back performance limitation of CO-OFDM systems using an OPC modeled with all nonlinear mixing terms . An in-depth analysis shows that nonlinear products generated by two-stage mixing processes impose a fundamental performance limit . In the first stage, XPM products (light green) are generated by mixing between signal × pump × (signal)* tones and FWM products (light blue) are generated due to signal × signal × (signal)* mixing. In the second stage, XPM-OPC (dark green) products are generated by mixing between XPM products × pump × (signal)* and the FWM-OPC (dark blue) products are generated by pump × pump × (FWM tones)* mixing. Here, (x)* denotes the conjugate of the term x. In a conventional OPC, the first stage of these processes generates nonlinear products whose fields grow linearly along the whole length of the HNLF: because the second stage products require the first stage products as an input, they grow quadratically over the length for the HNLF. Thus the output end of the HNLF is responsible for the generation of most of the power in the unwanted products.
2.2 Two-part OPC with mid-way filter
Our novel idea is to suppress the first-stage products at one or more places along the fiber, so the input to the second-stage process is suppressed. This is possible because the first-stage products fall outside the band of the wanted OPC signal. Figure 2 shows the block diagram implementing this idea. The HNLF fiber, length L, has been divided in half, to form two OPC sub-modules. The output of the first OPC sub-module is passed through a band-stop filter to remove the XPM products generated within it. Unfortunately, the pump is also removed. The frequency response of the BSF is shown by the red dashed curve in Inset (i) and its output in Inset (ii). The pump is reintroduced after the filter. This must be coherent with the original pump to ensure that the new conjugate products generated in this second half add in phase with those created in the first half. The combined signal then travels along the second half (HNLF2), a BPF and an output EDFA. Inset (iii) shows the spectrum at the output of HNLF2, which shows that both the XPM and XPM-OPC products have been suppressed by a considerable amount. Inset (iv) shows the spectrum at the output of the second OPC module. The XPM-OPC products are several times smaller than those produced by a single stage OPC module. Thus, it is expected that the system performance should improve significantly using this new two-part OPC module, since the dominant nonlinear limiting factor, XPM-OPC has been suppressed. Obviously, XPM-OPC generated entirely within the first half, cannot be suppressed, as it already falls upon the conjugated signal’s spectrum. The same argument holds for XPM generated in the second half and converted to XPM-OPC in the second half. This implies that multiple filters could be used for even better performance.
3. Back-to-back performance
To quantify the maximum benefit of splitting the nonlinear element into two parts, we first considered a back-to-back system without transmission fiber, as shown in Fig. 1(a). The numerical simulations were conducted using VPItransmissionMaker v8.7. Table 1 gives the simulation parameters.
The OFDM signal was generated using MATLAB, using a 1024-point inverse fast Fourier transform (IFFT); 920 subcarriers were modulated with 4-QAM and a 32-point cyclic prefix (CP) was inserted before each OFDM symbol. The total bit rate was 224-Gb/s, resulting in a net data rate of 200-Gb/s after 12% overhead for FEC and training. At the receiver, a coherent OFDM receiver feeds a digital processor that removes the CP, performs a Fourier transform to separate the subcarriers, equalizes the phases of the subcarriers and then demodulates the subcarriers to recover the data in each subcarrier.
3.1 Improvement in back-to-back performance
Figure 3 shows the back-to-back Q versus input signal power into the HNLF. The blue curve with circles (●) shows the performance of the system with conventional MSSI and the red curve with squares (■) shows the performance with the proposed two-part OPC module. The orange line (─) shows the back-to-back performance without OPC (35 dB), which is limited due to DSP limitations. Splitting the OPC module into two parts with a mid-way filter improves the Q by 3 dB at the optimum signal power. The performance in the nonlinear threshold increases by 6 dB. Unfortunately, there still remains a 7-dB performance penalty because the XPM-OPC products generated within each part via XPM cannot be separated from the desired OPC signal. Also FWM-OPC products and amplified spontaneous emission (ASE) of the input and output EDFAs add to this penalty and cannot be removed by filtering. Further suppression of XPM-OPC products could be achieved using more than one filter, with the associated increase in complexity.
3.2 Dependence on pump power and HNLF length
In a practical OPC module, the product of the nonlinear coefficient of the HNLF and its length, γL, and the pump power are important parameters. Therefore, we have investigated the dependence of the performance improvement on pump power and HNLF length. The nonlinear coefficient, γ, has been kept at 11.5 W−1.km−1. The length of the HNLF, L, is 500 m (Fig. 4(a) ), 1000 m (Fig. 4(b)) or 1500 m (Fig. 4(c)). The optimum signal input power is always used for each point. The results show that for higher pump powers and longer HNLF, the improvement due to suppression of the XPM products decreases. With a higher pump power and/or longer HNLF, the maximum signal quality becomes higher, which makes Qmax of the conventional MSSI modules approach the DSP limit of 35 dB. Thus the improvement using a two-part module is limited in these circumstances. However, as Fig. 4 shows, using a two-part module is more beneficial for higher conversion losses, i.e., for lower γL products and/or for lower pump powers. This may be helpful when designing OPC modules implemented with photonic integrated circuits (PICs) [17, 18], where the γL product term is about 20 times smaller (9900 W−1km−1 × 6 cm)  than the value we have employed to represent a typical MSSI using HNLF (11.5 W−1 km−1 × 1000 m) when Stimulated Brillouin Scattering (SBS) limits pump power.
3.3 Bandwidth dependence
Figure 5 shows the dependence of back-to-back performance improvement on the signal bandwidth. The blue curve with circles (●) shows the maximum signal quality, Qmax with conventional OPC module. The red curve with squares (■) shows Qmax with two-part OPC. It is interesting to note that in the region below 100 GHz, higher signal bandwidths give larger performance improvements with mid-way filtering. This is because, at bandwidths ≤ 100 GHz, the back-to-back performance using conventional OPC is already very high, that is, there is no significant performance penalty. Therefore, the improvement in this region with mid-way filtering is not significant. At higher bandwidths, the improvement saturates at 3 dB, shown by green curve with triangles (▲). These results show that our two-part OPC is more suitable for high bandwidth devices such as PICs [17, 18].
The effect of chromatic dispersion is shown in the dashed lines in Fig. 5. The CD value for this simulation is 0.01 ps/nm/km, which is typical for an OFS HNLF. For signal bandwidths narrower than 400 GHz, CD has almost no effect in the conjugated signal quality. However, for signal bandwidths wider than 400 GHz, the effect of CD degrades the signal quality for a conventional OPC, and reduces the improvement achieved by the two-part OPC. This is because conversion efficiency for the conjugated signal decreases for broad band OPC due to phase mismatch effect of CD.
4. Performance improvement in a transmission system
We have performed a series of simulations to demonstrate that the back-to-back performance improvement translates to an end-to-end performance improvement in a CO-OFDM transmission system, shown in Fig. 1(a). The optical link comprised 10 × 80-km spans of standard single mode fiber (S-SMF) with EDFAs to compensate the span loss. A 60-km dispersion compensation fiber (DCF) has been used just before the MSSI module to achieve nonlinear symmetry in terms of chromatic dispersion, to maximize the benefit of OPC . However, it is clearly impossible to achieve perfect power symmetry with lumped amplifiers . The OPC module is placed after the fifth span. The input power into the OPC module is the optimum power from the back-to-back simulations as shown in Fig. 3, which is 2 dBm for the conventional OPC system and 6 dBm for the two-part OPC system. The input power into the DCF was set to be 4 dB below the OPC input power.
4.1 Improvement in signal quality with transmission system
Figure 6 shows the comparison of transmission performance between systems with conventional OPC (●) and with two-part OPC (■). Results without OPC are also shown (○) to show the benefit of using OPC. The system with conventional OPC shows 1-dB better peak Q performance than the system without OPC. It also shows a 4.5-dB improvement in the nonlinear threshold (NLT) power. The system with two-part OPC module has an additional 1 dB Q improvement at the optimal signal power. Two-part OPC (■) does not change the optimum input signal power compared with conventional OPC (●). This is because, both of the systems are affected by the same link impairments; the improvement from two-part OPC module is due to its improved back-to-back performance.
4.2 Transmission distance dependence
Figure 7 shows the dependence of performance improvement on the transmission distance. Using a pump power of 10 dBm, an improvement of 1.4 dB is obtained at 480 km but gradually decreases to 0.5 dB at a transmission distance of 2400 km. This is because the increasing amount of ASE and nonlinearity generated in the longer links overshadows the back-to-back performance improvement gained by using the two-part OPC module.
4.3 Signal bandwidth dependence in transmission system
Figure 8 shows the signal bandwidth dependence of the performance improvement for the 10 × 80-km transmission system.
Again, the blue curve with circles (●) shows the maximum signal quality, Qmax, from the system with a conventional OPC module and the red curve with squares (■) is for the system with a two-part OPC. The green curve with triangles (▲) shows the improvement in Qmax. The improvement increases with increasing bandwidth and reaches to about 2.0 dB with a signal bandwidth of 866 GHz. In contrast to the back-to-back case (Section 3.3), where the improvement saturated at 3 dB, the improvement in a transmission system increases gradually with signal bandwidth. In a transmission system using OFDM super channel which covers several hundred GHz of signal bandwidth, this method of OPC could become attractive for fiber nonlinearity compensation. Systems with wider bandwidths could be converted in parts, perhaps using an integrated device to save space.
4.4 Effect of pump phase difference
An open question is how the new OPC module will perform in a real implementation, where there could be some phase difference between the pumps used in the first and second parts of the module, thus, we simulated the performance penalty due to phase mismatches. The phase of the second pump was swept from 0 to 360 degrees relative to the first pump. The simulation results are plotted in Fig. 9 . For an absolute phase difference less than 20°, as shown in the shaded region in Fig. 9, the penalty is less than 0.05 dB. However, the penalty increases sharply for larger phase differences. Therefore, our new method of OPC can be implemented practically in a real system, provided that the pump phases can be controlled adequately, perhaps by integrating the system upon a photonic chip [17, 18], or adding an active phase control. The phases could be controlled by monitoring the OPC signal strength and adjusting the phase to maximize this, perhaps using a dither signal on the phase adjustment signal to enable the control system to resolve the direction it needs to adjust in to reach the peak of performance.
An alternative method of implementing optical phase conjugation, by using second-order optical nonlinear process with periodically poled LiNbO3 (PPLN) waveguide has been reported for RZ-DPSK and RZ-DQPSK systems [20–23]. Two cascaded second-order nonlinear processes take place inside a PPLN waveguide to generate the conjugated signal: (i) second harmonic generation (SHG) of the pump from a frequency ωp to 2ωp; (ii) difference frequency generation (DFG) of the SHG by mixing with the input signal ωs, giving conjugated signal at 2ωp–ωs.
One advantage of using PPLN is that no third-order nonlinear impairments such as self-phase modulation (SPM) and cross-phase modulation (XPM) occur in the phase conjugation process . Using PPLN for OPC gave a 1.5-dB improvement in signal quality for a 3200-km 40-Gb/s RZ-DPSK system . Similarly, Jansen et al. gained an improvement of 0.5 dB for a 5000 km system .
A possible disadvantage of using PPLN is that it requires a relatively high pump powers to increase the efficiency of SHG, typically 20-27 dBm [20–23]. These high powers cause photorefractive damage, unless the PPLN is heated above 100°C . In addition, the pump frequency is strictly determined by the period of the poling. OPC using third-order nonlinearity does not have these issues; therefore, with our improvements, it is a viable alternate to PPLN devices. A common analysis framework, including SBS, would need to be developed to quantify the relative performance of these methods.
We have proposed a new design of an OPC to improve the back-to-back performance of CO-OFDM systems using MSSI. The new design reduces the performance penalty introduced by a conventional OPC module by 3 dB. We have shown that this back-to-back performance improvement results in a 1-dB improvement in a 10 × 80-km 4-QAM 224-Gb/s CO-OFDM system. The improvement increases gradually with higher signal bandwidths, which is useful for ultrahigh bandwidth transmission. Finally, we have shown that our new system would have almost no degradation due to the phase difference between the injected pumps, provided that this is controlled to within +/− 20 degrees.
This research was conducted by the Australian Research Council Centre of Excellence for Ultrahigh bandwidth Devices for Optical Systems, CUDOS (Project number CE110001018). We should like to thank VPIphotonics.com for the use of VPItransmissionMaker.
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