Inter-channel nonlinear phase noise compensation using optical injection locking

We propose optical injection locking (OIL) to enable compensation of the interchannel nonlinear phase noise, which is dominated by cross-phase modulation (XPM). In this paper, injection locking is used to create a local oscillator for a homodyne receiver from a residual carrier. The locking is fast enough to follow XPM-phase distortion, but slow enough to reject the signal bands, which are spaced slightly away from the pilot. The homodyne receiver thus partially cancels XPM, as it is common to the signals and the pilot. An experimental 7-channel WDM system gives 1-dB (0.7-dB) improvement in the peak Q of the center channel, for QPSK (16-QAM) modulated OFDM subcarriers, and increased the transmission reach by 320 km. The optimum performance was achieved at an injection ratio of −45 dB, with the injected power as low as −24.5 dBm. © 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement OCIS codes: (060.2330) Fiber optics communications; (060.2920) Homodyning; (140.3520) Lasers, injectionlocked. References and links 1. P. P. Mitra and J. B. Stark, “Nonlinear limits to the information capacity of optical fibre communications,” Nature 411(6841), 1027–1030 (2001). 2. E. Ip and J. M. Khan, “Compensation of dispersion and nonlinear impairments using digital backpropagation,” J. Lightwave Technol. 26(20), 3416–3425 (2008). 3. E. Ip, “Nonlinear compensation using backpropagation for polarization-multiplexed transmission,” J. Lightwave Technol. 28(6), 939–951 (2010). 4. R. Dar and P. J. Winzer, “On the limits of digital back-propagation in fully loaded WDM systems,” IEEE Photonics Technol. Lett. 28(11), 1253–1256 (2016). 5. E. Temprana, E. Myslivets, V. Ataie, B. P.-P. 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Richardson, and R. Slavík, “Homodyne OFDM with optical injection locking for carrier recovery,” J. Lightwave Technol. 33(1), 34–41 (2015). 20. O. Lidoyne, P. Gallion, and D. Erasme, “Analysis of a homodyne receiver using an injection locked semiconductor laser,” J. Lightwave Technol. 9(5), 659–665 (1991). 21. J. Jignesh, B. Corcoran, J. Schröder, and A. Lowery, “Polarization independent optical injection locking for carrier recovery in optical communication systems,” Opt. Express 25(18), 21216–21228 (2017). 22. A. Fragkos, A. Bogris, D. Syvridis, and R. Phelan, “Amplitude noise limiting amplifier for phase encoded signals using injection locking in semiconductor lasers,” J. Lightwave Technol. 30(5), 764–771 (2012). 23. O. Lidoyne, P. Gallion, C. Chabran, and G. Debarge, “Locking range, phase noise and power spectrum of an injection-locked semiconductor laser,” IEE Proc., Optoelectron. 137(3), 147–154 (1990). 24. R. A. Shafik, Md. S. Rahman, A. H. M. R. 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Introduction
The transmission reach of optical communication systems is restricted by nonlinearities in optical fibers [1].In a multi-channel environment, these nonlinearities cause both intrachannel interference and inter-channel interference.Intra-channel nonlinear interference, such as self-phase modulation (SPM), can be compensated to a large extent by digital methodslike digital back-propagation (DBP)-which attempt to undo propagation effects by numerically solving a nonlinear Schrödinger equation [2,3].On the other hand, inter-channel nonlinear interference, e.g. from cross-phase modulation (XPM) and four-wave mixing (FWM), are difficult to model with significant precision for effective compensation, based on full-field digital propagation [4]; although, in optimized laboratory experiments, there are clear benefits from compensating inter-channel nonlinear interference [5].Digital methods based on virtual propagation are also computationally intensive for inter-channel nonlinear interference, due the need to process extremely wide-bandwidth signals.They are also compromised when channels are added or dropped in optically routed networks [4].Thus, inter-channel nonlinear interference remains a problem for optically routed networks, despite significant research in developing multi-channel DBP algorithms and modelling inter-channel interference (e.g [6,7].).Dar et al. showed that this inter-channel nonlinear interference noise (NLIN) cannot strictly be considered as circularly symmetric (CS) Gaussian noise, but can be dominated by phase noise in systems with many short-spans: the CS Gaussian noise model is only appropriate when longer distances are covered by fewer spans [8].For multi-channel signals with sufficient channel spacing (>30 GHz), FWM becomes negligible [9] and XPM dominates the inter-channel NLIN.The XPM model developed in [10] indicates a reduction in the bandwidth of inter-channel phase modulation by dispersion-induced walk-off between the WDM channels, which depends on the channel spacing.Thus, the spectral width of the XPM-induced phase distortion is limited in dispersion-unmanaged links [11][12][13].Specifically [12], shows that the XPM bandwidth for 50-GHz channel spacing with QPSK modulation is ~1.6-GHz full-width half-maximum, with a roll-off of 2.8 dB per GHz of modulation bandwidth in a 20-span, 1600-km link.
There have been various approaches to compensate for inter-channel nonlinear effects; for example, phase conjugation, including using optical phase conjugation per-span [14], and phase sensitive amplifiers [15].However, these approaches require sophisticated equipment in the field.Other approaches take advantage of the limited bandwidth of the XPM-induced phase fluctuations.For example, a low-bandwidth phase modulator, driven proportional to the combined intensity of all of the WDM channels, can be installed along the link to mitigate XPM [12].Alternatively, pilot-tone based techniques have been proposed, in which the pilot tone picks up XPM along the link, enabling the XPM to be cancelled digitally at the receiver [16][17][18], but with added processing latency.
In this paper, we propose using optical injection locking (OIL) to identify the XPMinduced fluctuations from the residual carrier, which can then be cancelled in a coherent receiver.We show that in an OFDM system with a central 2.5-GHz guard-band, OIL carrier recovery can improve peak Q by 1-dB and associated improvement in transmission reach without adding latency in the DSP, by adding optical injection locking to the receiver hardware.
Section 1 describes the concept of nonlinearity compensation using optical injection locking.Section 3 discusses the experimental setup used for the concept verification and the results observed for various injected power, link distances and modulation schemes.Finally, Section 4 draws the conclusions.

Concept
The nonlinear phase noise, as discussed in the previous section, is dominated by the crossphase modulation (XPM) for systems with more number of spans of shorter lengths (< 100 km).Further, this XPM distortion is limited in bandwidth for dispersion-unmanaged links.The XPM efficiency vs. modulation frequency, ω, is where: ƞ XPM is the XPM efficiency, α is the fiber attenuation, Δβ = D(λ 1 -λ 2 ) is the difference in the propagation constants of a continuous wave probe at wavelength λ 1 and its interferer at λ 2 ; D is the chromatic dispersion parameter of the fiber; N is the number of spans in the link and L is the length of each span.Figure 1a plots the XPM efficiency for N = 4 and 40 spans, each of 80 km for a total length 320 km (red line) and 3200 km (blue line) respectively.The frequency spacing is 50 GHz.The CD parameter D = 16 ps/nm km.Note that the horizontal axis in Fig. 1a relates to the frequency of the intensity fluctuations within the neighboring channel, not the channel spacing itself.We observe that the XPM efficiency increases in magnitude with the link distance due to accumulation.As transmission distance increases, the magnitude of the XPM transfer function increases as nonlinear distortions accumulate, but the bandwidth of intensity fluctuations transferred via XPM is reduced (Fig. 1a).The XPM concentration in the main lobe of the XPM efficiency spectrum reduces with the length and the XPM effects becomes restricted in bandwidth.This can be attributed to the walk-off caused by the CD and a largefrequency spacing between the channels.As such, we can expect the XPM to phase modulate the CW probe wavelength only at relatively low frequencies.
The concept of OIL based nonlinearity compensation was inspired from pilot-based nonlinearity compensation methods [16][17][18].A pilot frequency tone is added in a guard band of the signal.The pilot tone acts as a CW probe signal and is subjected to the same cross-phase modulation (XPM) distortions that is suffered by the signal subcarriers across the fiber link.As such, if this pilot tone is filtered out at the receiver, the XPM on it can be used to cancel out the XPM distortions on the signal.Refs [16][17][18].performed this filtering and cancellation digitally after coherently receiving the signal in an intradyne receiver.In this work, our intention was to achieve this XPM compensation without increasing the DSP latency.We need to select the pilot tone and use it as a local oscillator to a coherent receiver so that the XPM common to the signal and pilot cancel one another before digitization of the signal.To select the pilot tone in analog domain before digitization, we could use an optical bandpass filter, but frequency drifts in in the signal may lead to the OBPF amplitude-modulating the extracted pilot tone, or passing portions of signals sidebands along with it.Thus, we need a mechanism that locks to the frequency of the signal and allows for phase transfer in a specific bandwidth.This motivates us to use optical injection locking, as shown in Fig. 1b.The OIL selects the XPM-modulated pilot (a residual carrier) so it can be used as a local oscillator in a coherent receiver.Because OIL-based carrier recovery can replicate the phase information of the incoming signal up to several GHz, depending on the injected power, the recovered carrier at the output of OIL contains the phase noise information (linear and nonlinear) [19][20][21].At the same time, the output of the OIL frequency locks to the incoming signal carrier frequency.Thus, the OIL acts as an optical bandpass filter for phase modulation (not amplitude modulations), whose center frequency is locked on to the incoming signal's carrier frequency, avoiding the frequency drift problems in passive OBPF.
The self-phase modulation (SPM) in the system is not bandlimited and occupies a relatively wider bandwidth, as ∆β→0 in Eq. ( 1).The OIL suppresses the phase-transfer beyond the phase-transfer bandwidth, the proposed system cannot completely compensate for the SPM in the system.As such, we do not expect our approach to significantly compensate for intra-channel distortions, such as the nonlinear interactions between the OFDM subcarriers.In our work, we choose digitally generated orthogonal frequency division multiplexing (OFDM), because it enables guard bands to be easily defined around the residual carrier.Our method can, however, be generalized to any system using a guard-band.

Polarization-independent injection locking sub-system
Figure 2 shows the experiment in detail.The received signal is split: half to a coherent homodyne) receiver, and half injected in the cavity of a local oscillator (LO) laser via a circulator.The OIL slave LO laser was a Gooch and Housego EM650 distributed feedback laser.If the free-running frequency of the LO laser (f2) and the frequency of the injected signal (f 1 ) are within the locking range, the LO signal locks on to the frequency of the injected signal, essentially suppressing its phase noise and removing the CFO.This OIL cavity is aligned to a defined of polarization (SOP).As a result, proper locking can be achieved only when the incoming signal's state of polarization is aligned with that of the LO laser cavity.We proposed a module in [21] that, when added before the circulator (dashed box in Fig. 2), makes the OIL system independent of the incoming signal's polarization i.e. the module outputs a signal with a constant SOP.This signal, ŝ is then aligned with the LO cavity using a polarization controller, thus maintaining the injection lock despite of polarization drifts in the link.The blue box in Fig. 2 shows the complete polarization-independent OIL setup.The polarization controller in the signal path was used in preliminary set-up measurements to ensure polarization independence of the injection-locking module, but left in a random state for the rest of the experiment.
The results presented in [21] show that this polarization-injection locking system, when used with a self-homodyne receiver, in a back-to-back configuration over a range of OSNRs, performs almost identically to using an ECL as local oscillator in a standard intradyne receiver.This shows that the optical injection locking stage shows no obvious advantage in terms of compensating for laser phase noise when using high-precision (~100 kHz linewidth) ECLs, indicating that any improvement in performance after transmission is likely from compensation of nonlinear phase noise.This we intend to show in the following sections

Optimum phase-transfer bandwidth (BOIL)
The phase-transfer bandwidth of the OIL (B OIL ) is critical.The phase transfer bandwidth is a separate consideration to the frequency detuning locking bandwidth.The phase transfer bandwidth is the bandwidth of phase modulation that is unaffected by the injection locking process.The frequency detuning locking bandwidth defines the allowed detuning of the incoming carrier from the free-running frequency of the slave laser before locking fails entirely.Within the phase transfer bandwidth amplitude modulation is highly attenuated [22].If the phase-transfer bandwidth (B OIL ) is less than the XPM bandwidth (B XPM ), the system performs sub-optimally as the detected signal still contains traces of XPM distortions at frequencies outside the OIL bandwidth (illustrated in Fig. 3a).Reducing the (B OIL ) further leads to complete loss of lock and the system fails.At the same time, if the phase-transfer bandwidth of the OIL (B OIL ) is higher than the guard band frequency range (B guard ), it allows for some portion of the signal's sidebands to influence the local oscillator signal, causing degradation (Fig. 3b).Hence, there is an optimum B OIL at which the proposed system needs to be operated.The phase-transfer function of the OIL is important as it reflects the frequency range and the degree of the XPM-dominated nonlinear phase noise that can be cancelled upon coherent reception.To that end, a spectrally flat 20-Gbaud single-carrier QPSK-modulated signal (inset of Fig. 4), generated using zero-padded oversampling, was injected into the OIL at various P inj .An unmodulated portion of the transmit laser was passed to the local oscillator port of the coherent receiver, to allow for homodyne detection experiments, otherwise the output of the OIL laser was used as the LO.The phase transfer function was then simply taken as the phase modulation spectrum measured from the output of the injection locked laser.We then take this as an indication of the injection locking bandwidth of the OIL set-up under injection with a wide-band signal.Through inspection of Fig. 4, the phase transfer function of the injection locked laser seems to have a Lorentzian distribution, as have free-running lasers, but with a much wider bandwidth.To illustrate this, we fitted a Lorentzian curve to the transfer curves, shown in dashed lines in Fig. 4. Inspecting the separate curves for different injected powers (P inj ), we note that the phase transfer bandwidth (B OIL ) is broader with increasing injected power, as expected for low injection ratio locking [19,20].We note that at higher injection ratios (P inj = −20 dBm, a −40 dB injection ratio), the phase transfer at low bandwidths is not complete (<0 dB).This may affect the optimal injection ratio in the systems we investigate in later sections of the paper.The optimum value of B OIL will depend on the performance of the laser used for injection locking [23].
Frequency drifts between the slave laser and incoming signal can be compensated using slow feedback loops [19], to overcome limitations in the injection locking bandwidth (as distinct from the phase transfer bandwidth measured in Fig. 4).In our free-running case, we observed a locking bandwidth of around 2 GHz, although we did not make a rigorous measurement of this parameter in all cases.
Figure 4 also shows the theoretical XPM bandwidth for 40 spans (3200 km link) calculated using Eq. ( 1) and scaled to the phase transfer measurements.Ideally, these phase transfer characteristics of OIL would be flat within the BOIL bandwidth, to faithfully transfer the XPM phase modulation to the coherent receiver.However, the Lorentzian shape of the phase transfer means that the higher-frequency XPM components are attenuated.Nonetheless, the attenuation is minimal for the main XPM lobe in Fig. 4 and so we should still expect significant cancellation of XPM.The attenuation can be compensated by increasing the P inj at the risk of passing portions of signal sidebands through, as highlighted in Fig. 3.We will investigate this optimum P inj or optimum injection ratio in the next section.

Experimental setup for transmission experiments
We experimentally identified the optimum phase-transfer bandwidth (B OIL ) and the optimum injected power P inj for various link lengths and signal parameters.Figure 5 shows the experimental setup.An ECL array of seven continuous-wave (CW) lasers, each with 150-kHz linewidth and 15-dBm output power, was used.The center frequencies were 50-GHz apart, from 192.95 THz to 193.25 THz.The CW carriers were combined using an 8 × 1 polarization maintaining coupler, then modulated using a 20-GHz bandwidth IQ modulator (Complex MZM) with a 25-Gbaud OFDM signal with 100 sub-carriers from a 156-point FFT.The modulator drive was generated with a 60-Gsa/s 20-GHz bandwidth arbitrary waveform generator.A central guard-band of 2.5 GHz (10 sub-carriers was added to prevent the transfer of the phase of the data-carrying subcarriers through the OIL set-up, providing an overall signal bandwidth of 27.5 GHz.The effective symbol rates of both the QPSK and 16-QAM is 25 Gbaud, and we assumed a 7% and 20% FEC overhead for these signals, respectively.This then gives a net rate per polarization of 46.7 Gb/s for QPSK and 83.3 Gb/s for 16-QAM.To de-correlate the neighboring channels, the multichannel signal was dispersed by ~14 symbols using an 80-km fiber and a Teraxion DCML dispersion compensation module, which flattens the intra-channel differential group delay within each channel, while maintaining interchannel delay.The de-correlated WDM signal was then passed through a recirculating loop that consists of four 80-km spools of standard single-mode fiber (ITU G.652D).The number of re-circulations was controlled by two acousto-optic modulators (AOMs) to achieve transmission over multiples of 320 km.The noise bandwidth in the system was limited to 400 GHz using a WaveShaper (WSS 1).The power launched into each span was controlled by the output powers of the EDFAs numbered 1 to 5. The output of the recirculating loop was passed through WSS 2, set to select the center channel.The received signal is injected into the polarization-independent OIL described in Section 3.1 and shown in Fig. 2. The output of the OIL is used as the local oscillator (LO) for a coherent receiver, whose outputs were sampled by an 80 GSa/s oscilloscope feeding offline digital signal processing (DSP).
The DSP used to recover the signal (Fig. 6) includes: blind chromatic-dispersion compensation based on a coarse knowledge of the known distance and typical fiber dispersion using the overlap-save method; preamble-enabled frame synchronization using crosscorrelation for the known preamble and received signal waveform; training-based channel estimation using the difference between the sent and received training waveforms to determine the channel response for single-tap sub-carrier equalization; M th -power phase estimation for constellation recovery.

Optimum injection ratio
To confirm the optimum injection ratio, we measured the dependence of the performance of the recovered signal (using quality factor Q as a metric) on the injected power (P inj ) for a fixed transmission distance.P inj represents the total signal power, including the residual carrier.The injection locking extracts a residual carrier from a guard-band in the middle of the signal, with the carrier-to-signal power ratio << 0 dB, set to be close to the point where injection locking was lost.The residual carrier was produced by biasing the CMZM slightly away from the null point, in order to pass a small amount of unmodulated light through to provide the seed for injection locking.
We use signal quality factor (Q) as a metric to determine optimum injection ratio for the carrier recovery system under test.By measuring Q, we include in our measurement the effects of non-ideal phase transfer through injection locking, as highlighted in Section 3, which help define the efficacy of our carrier recovery system.The Q of the recovered M-QAM signal is calculated from the error-vector magnitude (EVM) as a metric of system performance [24].For a given EVM, the resulting BER for different M-QAM formats will change depending on the modulation order M. By taking the Q as extracted from measured EVM, the corresponding modulation-level-dependent BER was calculated using Eq. ( 2).At high EVMs, insufficient bit-errors are present over a reasonable time-frame, given the processing time of off-line DSP.To ensure that EVM wass a reliable measure of performance, we checked that when there were a significant number of errors at low OSNRs, the Q from EVM matches with Q calculated from BER, as  (dB) For the measurements shown in Fig. 7, we picked a distance for transmission and used a receiver-side EDFA to ensure that the receiver had sufficient input power.We then adjusted the injection ratio by adjusting the P inj using a VOA (see Fig. 2).Each curve on the plot was then measured for different launch-powers, to probe the noise-limited and the nonlinear regimes.
Figure 7a shows performance against injection ratio plot for 320-km link.We observed an optimum injection ratio, in line with behavior predicted in Section 3.2.At the same time, the launch-power was also varied from −1 dBm to 7 dBm and the Q plotted.The Q increases globally from PL = −1 dBm to 3 dBm and decreases from P L = 3 dBm to 7 dBm, as expected for a nonlinear transmission system.The performance is maximum for P L = 3 dBm (dark blue squares).Along the x-axis, the performance for all curves reaches a maximum value at P inj = −24.5 dBm, corresponding to an injection ratio of −45 dB, with the slave laser producing + 20 dBm of output power in free-running mode.This would then seem to indicate that a −45 dB injection ratio is optimal over a range of transmission distances when the launch power in the link is such that the Q of the received signal is close to its maximum value.
There are several inferences we can make from this result.As the injection ratio where performance is optimized does not seem to change with either launch power or transmission distance, this suggests that the optical signal-to-noise ratio plays only a minor role in determining the optimal injection ratio.Moreover, this also suggests that chromatic and polarization mode dispersion have little impact on the injection ratio that maximizes system Q, which is understandable as the injection locking stage is polarization independent and the bandwidth of injection locking should be nominally independent of dispersion of the injected signal.
In short, as the properties of injection locking are generally dependent on the strength of the injected tone, and even in the case of low OSNR, the power contribution of optical noise over the phase-transfer bandwidth is likely quite low, it may be expected that the injection ratio at the receiver is independent of the propagation distance.This is reflected in the relatively close match in the behaviors of the −1-dBm launch power curve at 1920 km, the 2-dBm launch power curve at 2560 km, and the 3-dBm curve at 2880 km.
At this optimum injection ratio (Pinj = −24.5 dBm), Fig. 4 showed that the phase response has full-width half-maximum (FWHM) of 1 GHz with 2.8-dB/GHz roll-off up to 2 GHz.The performance drop on the low-power-side of the optimum in Fig. 7 is due to a reduction in the phase-transfer bandwidth of OIL (B OIL ) as shown in Fig. 3a, causing loss of phase information.If the injected power is reduced further, the system oscillates between locked and unlocked states: at lower powers, it experiences a complete loss of lock.The performance drop for injection ratios higher than the optimum is due to the increase in the phase transfer bandwidth of the OIL (B OIL ) to have a significant component outside the guard band (B gaurd ), which leads to transfer of the signal sidebands' phase on to the generated LO distorting the detected signal (Fig. 3b).
Similar trends were observed for longer distances (Figs.7b-d).The Q performance is again maximum for P L = 3 dBm and the optimum injection ratio is again found to be −45 dB.The overall performance decreases with distance, as expected as noise and nonlinear distortions increase with transmission distance.Interestingly, we observe that the optimal injection ratio is independent of the launch-power and the link distance.Comparing this to the expected range of XPM bandwidths for the different distances trialed, this would seem to suggest a broader phase transfer bandwidth would be preferred, for shorter distances, which should imply a change in injection ratio.The conclusion that the injection ratio-and hence phase transfer bandwidth-should be static with changing XPM bandwidth is similar to the set filter bandwidths used in [12].This is an important and a useful property of the proposed system for optically routed networks where it is very difficult to determine the length of fiber traversed by a particular channel.In addition to this, the launch-powers may also vary in an optical network depending on the link length between subsequent repeaters, so the fact that the same optimum injection ratios are found for a variety of launch powers indicates that our method is robust to these launch power variations.As the operation of the proposed OILbased system is independent of both transmission reach and launch power, would then seem to be suitable for use in optically routed networks, provided the injection ratio can be set (in this case to −45 dB), e.g. by using a power-controlled receiver-side EDFA.

Transmission of QPSK and 16-QAM modulated WDM signals
To gain insight on the transmission reach improvements enabled by partially compensating nonlinear distortions, we selected a distance and we swept the launch-powers.Curves were then plotted to understand the performance gain due to the nonlinearity-compensation. Fig. 8. Q vs. launch power with QPSK modulation.The injection ratio for the OIL was fixed at −45 dB, i.e. the optimum value shown in Fig. 7.The link distance was also varied to observe the maximum reach that can be achieved while the peak Q is greater than 7% hard FEC limit (Q = 8.5 dB, BER = 3.8 × 10 −3 ). Figure 8 shows the performance plots for QPSK modulation.Similar to our observations in Fig. 5, the performance reaches the maximum at P L = 3 dBm and then drops when increased further in to the nonlinear region (P L > 3 dBm).
Figure 8 shows the performance comparison of proposed system with a regular intradyne system without any nonlinearity compensation.The intradyne system uses a spectral peak search method for carrier frequency offset (CFO) compensation.At lower launch-powers, the OIL shows marginal improvement that increases with increase in the nonlinear effects at higher launch powers.We note that the differences in peak Q between the systems with and without OIL means that the low launch power points for longer distances are unable to be measured in the amplifier-noise dominated regime, which results in the observed performance improvement for the OIL system even at low launch powers.The performance gain for higher launch-powers, thus, verifies the compensation of the nonlinear phase noise by the proposed OIL setup.Figure 8 shows that the performance for 3200 km does not reach the HD-FEC limit with the regular intradyne system, whereas, the OIL system with 3200-km link crosses the HD-FEC limit for a good range of launch-powers (2-4 dBm).In this case, we note that the 3200-km system with OIL performs very similarly to the 2880-km system without OIL, indicating that OIL can indeed improve system reach.While the distances we transmit over are fundamentally a product of the laboratory set-up that we measure with, the relative improvement between systems with and without injection locking indicate that OIL is able to compensate for nonlinear phase noise, and that this can translate into improved system reach.
We next measured the performance for 16-QAM modulation, which is being discussed as a potential candidate for high-throughput next-generation optical networks.This is important in the context of nonlinearity compensation, because as nonlinear interference is modulationdependent [8], the effect of nonlinearity on higher-order QAM is worse than for QPSK. Figure 9 plots the measured Q for the recovered 16-QAM signal against the launch-power sweep for links of 640 km to 1920 km.The previously used HD-FEC limit was not met when transmitting 16-QAM signals over links longer than 320 km, even for the OIL system.As a result, we consider a 20% soft-decision FEC limit (BER = 2.7×10 −2 , Q = 12.1 dB, 20% overhead) for 16-QAM modulated signals [25].As shown in Fig. 9, the peak Q over 1600-km transmission for an intradyne system without OIL does not meet the pre-FEC requirements for SD-FEC, whereas with OIL system this condition is met.Again, this indicates that reach can be improved through the use of OIL, here with 16-QAM modulated signals.Table 1 shows the peak-Q-improvement by the proposed OIL system in the peak-Q.The QPSK signals experienced 0.95-1.1 dB improvements, whereas the 16-QAM system experienced 0.7-0.8dB improvement.A marginal increase in peak-Q-improvement with transmission distance was observed in both systems.This improvement saturates at 1-dB for QPSK and at 0.8-dB for 16-QAM.

Discussion
The OIL system gave a 1-dB improvement over a regular intradyne system in the nonlinear regime for QPSK modulated signal.The best Q was always obtained at 3-dBm (4-dBm) launch-power for QPSK (16-QAM) modulated signal.The performance improvement in the nonlinear regime confirms the nonlinearity compensation by the proposed OIL-based method.
Comparing our results to digital pilot tone-based compensation methods, the proposed method gave a 0.2-dB gain in peak-Q over demonstrations of digital carrier extraction methods, which give 0.5-dB [17,18] and 0.8-dB [16] improvements over non-compensated links.We believe that the peak-Q improvement in those systems was limited by receiver imperfections, possibly related to the resolution of the ADCs.Moreover, the 0.2-dB improvement we observe over digital pilot recovery systems carrying QPSK was achieved without adding extra steps into the receiver-side digital signal processing (DSP), thus avoids the introduction of extra processing latency, with reasonable increase in hardware complexity.
There are several avenues toward optimising the performance of our system, and to establish rigorous design rules for nonlinear cross-talk suppression using this technique.In this investigation, we used a low signal-to-carrier-power ratio, that was close to what we found experimentally to be the minimum necessary to ensure locking.However, the carrierto-signal-power ratio could be significantly increased without significant degradation to the required OSNR at the receiver, and we expect that this may help expand the injection locking bandwidth without causing significant penalty from signal leakage.A rigorous study of this trade-off would help establish further design rules for our demonstrated system.
Similarly, there are expected trade-offs between the width of the guard-band employed to host the residual carrier, and performance, especially when holistically including the impact on overall capacity.At higher injection ratios, the leakage of data sidebands into the recovered carrier reduce performance.Clearly, with a wide guard-band, this effect could be reduced, but at the cost of lost capacity.This change in guard-band is also likely to influence the optimal carrier-to-signal power ratio.A full investigation of this trade-off would benefit from using mutual information as a metric.In addition, design of injection locking carrier recovery may change somewhat when using widely tunable lasers.These are some issues that would need to be addressed before commercial translation is a feasible option.
Compensation of inter-channel nonlinearities is proving to be a practically difficult task for multi-channel DBP [4][5][6], as it requires accurate models of the inter-channel interference along the link.By extracting nonlinear phase distortions optically at the receiver, we attempt to remove the requirement for accurate nonlinear channel models over wide bandwidths.In addition to this, by recovering phase distortions from the signal itself, the proposed system potentially allows for the cancellation of some stochastic nonlinear distortions that are extremely difficult to predict.For example, the proposed method should also cancel the low frequency components (those that fall within the phase transfer bandwidth of the OIL) of both the nonlinear phase noise generated due to amplified spontaneous emission's (ASE) interaction with the nonlinearities (the Gordon-Mollenauer effect).
The motivation to find alternatives to nonlinearity compensation techniques that rely on knowledge of the nonlinear fiber channel has also spurred investigations into in-line nonlinearity compensation techniques [12,14,15].By requiring modification to optical equipment at the receiver-side only, our proposed system does not require modifications to equipment at multiple locations along the link, potentially simplifying implementation.
Commonly, the effectiveness of nonlinearity compensation schemes decrease as the transmission distance increases, for many reasons [4].Here, we see either no change to efficacy, or a marginal improvement.We note that the characteristic XPM transfer curve in dispersion uncompensated links shrinks in bandwidth as distance increases [10][11][12].This would then suggest that as transmission distance increases, more of the XPM distortion lies within the phase transfer bandwidth of the injection locking stage.This would suggest an improving level of nonlinear distortion cancellation.However, as transmission distance increases, so to do amplitude distortions from nonlinear effects, which are not likely to be transferred through injection locking.These characteristics may explain why, on balance, our technique seems to provide an unchanged amount of peak-Q improvement in the systems investigated.We believe this warrants further investigation.
The proposed system is capable of mitigating the XPM distortion because of its limited bandwidth, but most of the wide-band SPM remains uncompensated.In contrast to wide-band inter-channel nonlinearity, DBP can significantly mitigate intra-channel nonlinear distortion (such as SPM).As such, the peak-Q and the nonlinearity tolerance can be further increased by adding a digital-backpropagation algorithm in the DSP that takes care of the SPM distortions.
Open questions remain as to whether this technique could be used to improve capacity.If only a small family of FEC options are considered, then the improvement in peak-Q afforded by OIL may be useful in using lower overhead codes (e.g.switching from 20% SD-FEC to 7% HD-FEC).If adaptive modulation or FEC codes are used, then the improvement in peak-Q may be used to improve capacity for a given transmission distance.The trade-off between peak-Q improvement and the central guard band's bandwidth need to be investigated.The proportional spectral efficiency loss for a given guard band will improve with higher bandwidth signals; here we used a 25-Gbd signal, signals with baud rates over 60-Gbd (e.g [26].) are becoming common, and rates up to 100-Gbd are being reported by some groups (e.g [27].).

Conclusions
An all-optical processing approach for nonlinear phase noise compensation, using optical injection locking, has been proposed and experimentally verified on an OFDM signal in a WDM system.The method resulted in 1-dB (QPSK) and 0.7-dB (16-QAM) improvement in Q in the nonlinear power regime, compared with a conventional intradyne receiver.With an injection ratio of −45 dB, the transmission reach of the system was increased by one loop of the recirculating loop (320 km) for a given FEC limit.Thus, the proposed system can extend the transmission distance of optical communication networks, and only requires a sub-system modification at the receiver, rather than additional components in the field.

Fig. 3 .
Fig. 3. Spectral effects of OIL's phase-transfer bandwidth on received signals when a) B OIL < B XPM and b) B OIL > B guard .