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We propose an optoelectronic subsystem for inline compensation of XPM-induced phase noise in long-haul optical links. Based on intensity-dependent phase rotation, these compensators are used to suppress XPM on a span-by-span basis. Using a 7-channel hybrid WDM system as a test case, our simulations show that this technique is effective at suppressing XPM in dispersion managed and unmanaged links for various transmission distances.
© 2015 Optical Society of America
1. Introduction
The capacity of optical communications systems is limited by the ability to mitigate the linear and nonlinear distortions caused by the optical channel. While there are effective methods for digitally correcting linear impairments [1, 2], effects of fiber nonlinearity [3] are significantly more difficult to suppress. In particular, cross-phase modulation (XPM) is seen as the limiting factor in next-generation long-haul communication systems [4, 5] as it is an inter-channel impairment; that is, it is caused by the signal in an adjacent wavelength division multiplexed (WDM) channel [6].
Both optical [7–9] and electronic [10–12] techniques can combat the distortions caused by fiber nonlinearity. Digital back propagation (DBP) [11] in particular has been shown to be an effective method of nonlinear compensation (NLC) in point-to-point links. However, DBP is unable to fully compensate for nonlinearity, as it is fundamentally limited by the interaction between the signal and amplified spontaneous emission noise (ASE) [13]. Additionally, end-span techniques such as DBP are unable to accurately compensate XPM in optically routed links [14], because the NLC algorithm depends upon knowing the waveform at every point along the link; a requirement which cannot be met if channels are added and dropped along the link.
To overcome these limitations, NLC may be performed in a distributed manner, with multiple compensators placed along the link. Periodic NLC would be suitable in an optically routed network, if there is at least one compensator between each pair of switching nodes. Moreover, distributed NLC might provide advantages in mitigating nonlinear phase noise due to signal × ASE mixing because each compensator uses the local signal to calculate the required compensation, rather than the signal at the end of the network, which would be different.
Inline methods for suppressing XPM, rather than compensating for its effects, have been demonstrated using periodic-group-delay dispersion compensating modules [15–17]. These devices introduce a large walk-off between adjacent channels, which significantly reduces the accumulation of XPM along the link. More recently, inline NLC has been demonstrated with all-optical subsystems by Hu et al. using optical phase conjugators [18] and Olsson et al. using phase-sensitive amplifiers [19]. These schemes have been shown to be effective in compensating the distortions caused by XPM, though the high complexity of these devices may limit practical use.
In this paper, we propose a simple optoelectronic method for distributed NLC based on applying a phase rotation proportional to the local instantaneous intensity. While this idea has been explored for pre- and post-compensating intra- [20–22] and inter-channel [23–25] nonlinearities, no studies have examined how its performance when used on a span-by-span basis. For this investigation, the post-compensator described in [23] is placed before every span to compensate XPM. We call these compensators total intensity directed-phase modulators (TID-PMs) as they perform a phase rotation proportional to the total power in a band of channels. In Section 2, we explain the operation of TID-PMs in both idealized and practical implementations, and, in Section 3, verify their ability to suppress XPM in a simple link using numerical simulations. Additional simulations investigate the performance of inline TID-PMs in a 7-channel hybrid WDM system, a 28-Gbaud quadrature phase shift keyed (QPSK) channel surrounded by six 14 Gbit/s on-off keyed (OOK) neighbors, to demonstrate proof-of-concept. Our results show that for a dispersion-managed link, the peak Q of the QPSK channel is increased by 2.4 dB after 1600-km transmission and 2.7 dB for a transmission distance of 3200 km, while peak Q is increased by 1.1 dB in a 3200-km dispersion-unmanaged link.
2. TID-PMs for inline XPM compensation
TID-PMs have previously been demonstrated as a means to post-compensate XPM in both single-carrier [25] and multi-carrier systems [23, 24]. In principle, a TID-PM removes XPM by applying a phase rotation in the opposite direction to the XPM-induced phase shift, thereby cancelling it out. The magnitude of this phase rotation is given by [26]:
where γ is the nonlinear coefficient, Leff is the nonlinear effective length and S(t) is given by:where P(t) is the time-varying optical power entering the TID-PM, hXPM(t) describes how inter-channel walk-off affects the XPM distortion, and * represents the convolution operation. Note that in optically amplified systems, P(t) includes contributions from both the wanted signal and ASE noise.Figure 1 shows the generalized block diagram to implement this equation. First, an optical coupler is used to tap off a small portion of the optical signal and one or more photo-detectors are used to measure its intensity, thereby obtaining an electrical signal which is a fraction of P(t). An electrical amplifier with gain proportional to γLeff amplifies the signal, while low-pass filters with frequency response HXPM(ω), the Fourier transform of hXPM(t), accounts for the effects of walk-off. The electrical signal then drives a phase modulator to correct the distortion caused by XPM and the corrected optical signal is amplified to compensate for coupling and insertion losses.
Fig. 1 Generalized block diagram for TID-PM subsystem. PM: Phase modulator; OA: Optical amplifier. Blue lines represent electrical connections and black lines represent optical connections.
An important factor in this scheme is the calculation of HXPM(ω), which determines the contribution of individual spectral components to the XPM distortion between two channels, taking into account the walk-off between them. Analytically, the effect of walk-off on the XPM between two WDM channels may be calculated following the approach in [26], which considers the case of a continuous wave (CW) probe and an interferer with sinusoidal power modulation with angular frequency ω. In this case, XPM converts the sinusoidal intensity modulation into sinusoidal phase modulation of the CW probe. We start by assuming that chromatic dispersion (CD) does not change the intensity waveform’s shape, but still causes the channels’ waveforms to walk-off one another. This walk-off causes the strength (or XPM efficiency) and phase of the XPM to depend on ω. Using Eqs. (9) and (36) in [26], the XPM efficiency for a dispersion unmanaged N-span link is:
where: α is the fiber attenuation, L is the length of one span and represents the difference in the propagation constants for a CW probe at wavelength λ1 and an interferer at λ2 in a fiber with a CD parameter of D. Similarly, the phase offset over a single span as a result of walk-off is given by Eq. (10) in [26] as:These functions are used as the theoretical basis in determining the optimum HXPM(ω) to compensate the XPM distortion between two channels using inline TID-PM, given by:Practically, an approximation for HXPM-Opt(ω) may be used for inline TID-PM, which we discuss later in this section.There are a number of advantages to using TID-PMs at the beginning of every span rather than at just one end of the entire link. First, we are able to maintain effectiveness in a highly dispersive environment, which was a limitation of lumped phase rotation techniques [14, 22]. While the interaction between dispersion and nonlinearity still occurs, the change in the shape of the signal’s intensity envelope over the nonlinear length of a single span is negligible. From a nonlinear perspective, this means that the dispersion between adjacent TID-PMs can be neglected, resulting in accurate compensation. Secondly, because they use the local waveform, inline TID-PMs are less sensitive to stochastic variations, such as from ASE or optical routing. Finally, we can simplify the calculation for XPM efficiency used in HXPM(ω). Figure 2 plots the XPM efficiency curves for a twenty-span dispersion unmanaged link and a single span. A filter with a frequency response matching Fig. 2(a) would be ideal for NLC over many spans, but this is nearly impossible to achieve. In contrast, by NLC on a span-by-span basis, the amplitude response of the filter should ideally match the response of Fig. 2(b), which is reasonably easy to accomplish. As a result, an inline compensation scheme is able to more accurately account for walk-off than a post-compensator, leading to improved performance.
Fig. 2 XPM efficiency due to walk-off for: (a) a dispersion unmanaged 20-span 1600-km link and (b) a single 80-km span for 50 GHz spacing. The fiber is assumed to have 16 ps/nm.km dispersion.
With ideal components and no constraints on complexity, an inline TID-PM for a single channel of interest would be like that in Fig. 3(a). From Eq. (3), it is clear that the optimal amplitude for HXPM(ω) is affected by the difference in wavelength of the two interacting channels. As a result, each channel should be separately detected and processed for peak performance. The configuration in Fig. 3(a) attempts to achieve this by using a wavelength de-multiplexer to allow each channel to be detected individually. The signal from each channel is amplified and filtered separately, and HXPM-Opt(ω) for the channel applied by a low-pass filter. The compensation signals from individual channels are then summed together to obtain the correction signal for the overall XPM distortion. To obtain the channel of interest for phase modulation, an optical add/drop multiplexer (OADM) is used to drop the channel of interest. It is then operated upon by the phase modulator, and then re-added to the signal. The other channels are unaffected by this process. An optical amplifier compensates for insertion and coupling losses in this device. This process represents a ‘best-case’ scenario for TID-PM performance, which we refer to as the canonical TID-PM. Investigating this canonical TID-PM provides an upper limit to the improvement that can be achieved through inline NLC. Tao et al. [27] have used a similar topology to model XPM as a lumped process just before the receiver; however, they have not proposed that this be used as a method of compensating XPM.
Fig. 3 Block diagram of (a) canonical TID-PM and (b) practical TID-PM. PM: Phase modulator; LPF: Low pass filter; Demux: WDM de-multiplexer; OADM: Optical add-drop multiplexer; OA: Optical amplifier; RF gain: electrical gain. Blue lines represent electrical connections and black lines represent optical connections.
While the canonical TID-PM provides optimal NLC as a result of the individual low-pass filters used to account for each interaction between two channels, it requires a large number of high-bandwidth electrical components for these filters. Additionally, an array of such devices would be required for compensation of an entire WDM system, making physical implementation bulky. A simplification would be to use a single low-pass filter and TID-PM for many channels, though this will reduce the effectiveness of the NLC [23], though we shall show later that this performance reduction is acceptable.
Figure 3(b) shows the block diagram of this ‘practical’ TID-PM. An optical coupler is still used to tap off a portion of the signal for use in the compensation, but in this case, a single photodiode is used to detect the total intensity over the band of channels. A low-bandwidth photodiode may be used because the TID-PM need only remove the low-frequency components of XPM [23]. The photocurrent is electrically amplified, and an aggregate HXPM(ω) for the entire band is applied through a low-pass filter. At low-frequencies (< 1 GHz), the XPM efficiency for channels spaced between 50 GHz and 150 GHz are very similar, so the amplitude response of HXPM(ω) can be readily estimated theoretically. However, the phase response of HXPM(ω) requires more consideration. Considering Eq. (4), the sign of the phase offset on the XPM product changes depending on if the interferer has a higher or lower carrier frequency compared to the CW probe. Therefore, we assume that the aggregate HXPM(ω) has a net phase offset of zero for all modulation frequencies. After the filter, the electrical signal drives a phase modulator that compensates XPM from all of the channels in the band. In this way, we can use low-bandwidth components (i.e. a photodiode, an electrical filter, an RF amplifier and a phase modulator) to suppress XPM in a band of channels.
3. Simulation results
3.1 Single span system
To verify that applying the phase shift described in Eq. (1) accurately compensates XPM, a single span of fiber carrying a CW probe and an OOK-modulated interferer channel placed 50-GHz away was simulated. It is well-known that XPM causes intensity fluctuations in one WDM channel to result in phase noise in adjacent WDM channels [6], so the changing intensity of the OOK interferer causes phase distortions on the CW probe. In the absence of ASE and self-phase modulation (SPM), any phase variations on a CW laser with zero linewidth much be the result of XPM. If we then compare the received phase of the CW laser with and without a TID-PM placed before the span, we can determine its efficacy at compensating XPM.
VPItransmissionMaker v.9.1 was used to simulate an 80-km span of standard single mode fiber (SSMF) carrying the CW probe with a 14-Gbit/s OOK signal, which was chosen as the OOK format has been shown to produce large XPM distortions [28]. The SSMF was modelled with an attenuation of 0.2 dB/km, 16 ps/(nm.km) of dispersion and a nonlinear coefficient (γ) of 1.3 W−1km−1. These parameters were kept constant in all simulations. CD was fully compensated using a piece of lossless dispersion compensating fiber (DCF) with −100 ps/(nm.km) of dispersion and a γ of zero, placed after the SSMF. To ensure there was no ASE or SPM in the system, the loss of the SSMF was compensated for using a noiseless optical amplifier, and the CW probe was launched into the fiber at −10 dBm. In contrast, the OOK interferer had a launch power of 3 dBm to ensure a significant XPM product was developed in the span. The linewidth of all lasers were set to zero so that the received phase of the CW laser is the XPM distortion, and the simulation was confined to a single polarization.
Figure 4(a) shows the 2-channel canonical TID-PM used for NLC. A 90/10 coupler was used to tap off a small portion of the signal for compensation, while Fig. 4(b) plots the optimal HXPM(ω) for the OOK interferer, calculated using Eqs. (3) and (4). The phase modulator and OADM used to isolate the CW probe for compensation were assumed to have no insertion loss. At the receiver, the CW probe was de-multiplexed using a band-pass filter and coherently detected to allow measurement of the received phase.
Fig. 4 (a) System block diagram for 2-channel canonical TID-PM, and (b) the response, HXPM(ω), applied by the low-pass filter to account for walk-off. OADM: optical add/drop multiplexer; PM: phase modulator; LPF: low-pass filter; OA: optical amplifier; RF gain: electrical gain.
Figure 5(a) plots the phase of the CW laser at the end of the span without the use of a TID-PM. There are large fluctuations in this phase due to the XPM caused by the OOK interferer. When a TID-PM is used, however, the magnitude of these fluctuations is greatly reduced, though not removed completely, as shown by Fig. 5(b). Additionally, we compared the spectral components of the root mean squared phase noise by plotting their Fourier transforms (phase noise spectra) in Fig. 6, with a measurement bandwidth of 1 GHz. Figure 6 also plots the phase noise spectrum, for a reduced launch power (−20 dBm) in the OOK channel, to show the spectrum when unaffected by XPM. Without XPM compensation, there are large low-frequency components, indicating a significant XPM penalty. Most of these components are suppressed by the TID-PM, resulting in a spectrum very similar to when the probe is unaffected by XPM.
3.2 Two-channel WDM transmission
Having established that a canonical TID-PM effectively performs NLC over a single span, this system is then cascaded to investigate the benefits of TID-PMs distributed along a multi-span link. Figure 7 shows the system block diagram for the simulated link, which consists of twenty 80-km spans of SSMF carrying a −10-dBm CW probe placed 50 GHz away from a −3-dBm OOK interferer modulated at 14 Gbit/s. This configuration is representative of the ‘best-case’ scenario for NLC using TID-PMs, and places an upper bound on the benefit to be gained from this scheme.
Fig. 7 System block diagram of 1600-km link used to investigate inline TID-PM performance for (a) 0% RDPS and (b) 100% RDPS. The link with 10% RDPS used a combination of inline and end-span DCF.
As done previously, the received phase of the CW laser is used to determine the efficacy of inline TID-PMs for nonlinearity mitigation. Noiseless optical amplifiers (no ASE) were used to compensate the loss of the SSMF, and the linewidth of all lasers was set to zero. CD was compensated using DCF with no loss and no nonlinearity. The DCF was configured to create three dispersion maps with different amounts of residual dispersion per span (RDPS). These maps were 0% RDPS, where DCF was used to fully compensate CD after every span, 10% RDPS, where DCF was used to compensate 90% of the CD developed in a span with the remainder compensated by additional DCF just prior to the receiver, and 100% RDPS, where the accumulated dispersion was fully compensated just prior to the receiver.
Figure 8 shows the phase noise spectra for the three dispersion maps. In all cases, the use of inline TID-PMs significantly reduces the low-frequency power, which leads us to conclude that placing TID-PMs along the link is effective at suppressing fiber nonlinearity, regardless of dispersion map. However, there are residual XPM components after NLC, suggesting that the small amount of dispersion present between adjacent TID-PMs may be a limitation of this technique. These compensation errors can be minimized by leaving some residual dispersion after each span, as evidenced by the smaller low-frequency components after compensation in the 100% RDPS and 10% RDPS links compared with the 0% RDPS link.
Fig. 8 Phase noise spectra for the received phase on the CW probe after a twenty-span 1600-km link for (a) a link with 0% RDPS, (b) a link with 10% RDPS and (c) a link with 100% RDPS. A resolution bandwidth of 1 GHz is used.
To determine how inline TID-PMs affect a channel carrying data, the CW probe laser was replaced with a 28-Gbaud QPSK signal to be transmitted with the same 14-Gbit/s OOK interferer used previously. QPSK was chosen as the test channel because it is a commercial 100 Gbit/s solution and can suffer a large XPM penalty from OOK neighbors [28]. The channels were launched at equal powers into the twenty-span, 1600-km link. CD was compensated using idealized DCF with zero loss and nonlinear coefficient of zero, while erbium-doped fiber amplifiers (EDFAs) with 6-dB noise figures were used to compensate for all losses. The QPSK signal was de-multiplexed with an optical band-pass filter before coherent reception. Signal equalization was achieved with a fractional T/2 spaced CMA equalizer before BER counting. We again used 2-channel canonical TID-PMs for inline XPM compensation, and compared their performance in links with 0% RDPS, 10% RDPS and 100% RDPS.
Figure 9 plots signal quality, Q, of the QPSK channel against launch power per channel with and without inline TID-PMs for the various dispersion maps. In this case, Q was calculated from error vector magnitude (EVM) because an impractically long pattern would have been required to generate enough errors for an accurate calculation of BER. We also include the additive white Gaussian noise (AWGN) limit for reference. At high powers, significant phase noise was observed on the signal, shown in the inset of Fig. 9, causing overestimation of system performance as the constellation points are not Gaussian distributed. Using inline TID-PMs, peak Q is increased by 3.2 dB, 4.5 dB and 3.0 dB for 0% RDPS, 10% RPDS and 100% RDPS respectively. This reinforces the idea that TID-PMs are able to improve performance in links, regardless of the dispersion map. However, the performance in the resonant (0% RDPS) dispersion map is much poorer than the maps with some uncompensated dispersion after each span. This is consistent with observations from the phase noise spectra and confirms that RDPS improves performance by minimizing errors in the NLC.
Fig. 9 Q vs. launch power for the QPSK channel for 0% RDPS (squares) 10% RDPS (diamonds) and 100% RDPS (triangles) in a 1600-km. link Closed markers (solid lines) are links without nonlinearity compensation and open markers (dashed lines) are links using inline TID-PMs. Inset: constellation obtained at a launch power of −4 dBm for the 0% RDPS map when TID-PMs are not used.
3.3 Seven-channel dispersion managed WDM transmission
Although our results show that the canonical TID-PM system significantly improves nonlinear performance, this arrangement is prohibitively complex for large numbers of WDM channels. As such, in order to show that a distributed TID-PM system can be implemented in a practical arrangement, the performance of the TID-PMs presented in Fig. 3(b) is investigated and compared to the canonical case. As shown in Fig. 10, we simulated a seven-channel hybrid WDM system comprising a 28-Gbaud QPSK center channel surrounded by six 14-Gbit/s OOK channels, all on a 50-GHz grid. Such a system could result from upgrading a legacy link, and is an example of ‘worst-case’ nonlinear performance for QPSK [28]. There were either twenty or forty 80-km spans of SSMF, to give total link lengths of 1600 km and 3200 km, respectively. CD is compensated using DCF with an attenuation of 0.6 dB/km, dispersion of −100 ps/(nm.km) and γ of 5.68 × 10−3 W−1km−1; residual dispersion of 100 ps/nm is left after every span (approx. 8% RDPS). At the end of the link, residual dispersion was compensated with additional DCF. EDFAs with a 6-dB noise figure were used to compensate all losses, with gains set so that the launch power into the DCF is 7-dB lower than the launch power into the SSMF to reduce nonlinear effects in the DCF. At the receiver, the QPSK channel is de-multiplexed with an optical band-pass filter before being coherently detected. Equalization is achieved with a fractionally spaced T/2 CMA equalizer before BER counting. The simulation was constrained to a single polarization, and laser linewidths were assumed to be zero.
Fig. 10 System block diagram for 7-channel WDM transmission with (a) inline TID-PMs for XPM compensation and (b) a single TID-PM used to post-compensate XPM.
The practical TID-PMs were modelled with a 90/10 coupler tapping off a small portion of the signal for detection by a single photodiode, the output of which is amplified and filtered before driving a phase modulator with no insertion loss. Figure 11(a) shows the HXPM(ω) function applied by the low-pass filter, which was obtained by concatenating the optimal amplitude response in Fig. 4(b) with a 3rd-order Gaussian filter with a bandwidth of 1 GHz. As mentioned previously, the phase response for the practical TID-PM is set to zero for all modulation frequencies. We evaluated the performance penalty caused by this approximation by comparing the performance of inline canonical and practical TID-PMs. We also compared the performance of the distributed XPM compensators with the post-compensator proposed in [23]. The post-compensating TID-PM had the same structure as the practical TID-PMs, but the effects of walk-off was approximated with the trapezoidal filter shape shown in Fig. 11(b), with a passband of 500 MHz for the 1600-km link and a passband of 100 MHz for the 3200-km link. The phase response for these post-compensator filters was also zero.
Fig. 11 HXPM(ω) as used in (a) all inline practical TID-PMs and (b) the post-compensating practical TID-PM for a 1600-km link. The HXPM(ω) used in the post-compensating TID-PM for a 3200-km link had the same shape, but with a passband reduced to 100 MHz.
Figure 12 plots Q vs. launch power for the QPSK center channel for transmission distances of (a) 1600-km link and (b) 3200-km. Q is calculated from both EVM (open markers, dashed lines) and BER (closed markers, solid lines), using , where erfc−1 is the inverse complementary error function. For 1600-km transmission, while post-compensation provides only 0.5-dB improvement in peak Q over the uncompensated case, inline canonical TID-PMs increase the optimal Q by 3.8 dB and there is a 2.4-dB improvement using inline practical TID-PMs. For the 3200-km link, there is only a marginal (0.2 dB) benefit gained from TID-PM post-compensation, while the inline canonical and practical TID-PMs increase the optimal Q by 3.6 dB and 2.7 dB respectively. The similarity between the results for different distances indicates that the ability of inline TID-PMs to compensate for XPM is independent of link length. Comparing the performance of the two implementations, inline canonical TID-PMs outperform practical TID-PMs by 1.4 dB and 0.9 dB for 1600-km and 3200-km transmission respectively. The penalty in the practical TID-PMs is caused by the approximations used in calculating the nonlinear walk-off, which is the trade-off for significantly reduced complexity.
Fig. 12 Q vs. launch power of the center QPSK channel after a) 1600-km and b) 3200km transmission. Closed markers (solid lines) are Q from BER and open markers (dashed lines) are Q from EVM.
3.4 Seven-channel dispersion unmanaged WDM transmission
A 3200-km dispersion unmanaged link was investigated to determine if the dispersion map is a key factor in the performance of a practical inline TID-PM NLC scheme. The simulated link is shown in Fig. 13, which is similar to the one in Section 3.3 but without the DCF and associated EDFA. CD is instead compensated electronically using the overlap-add algorithm prior to equalization. Additionally, we model the phase modulator in the TID-PM with a 2-dB insertion loss, achievable in commercially available ultra-low loss devices. The insertion loss is compensated by the EDFA immediately after the TID-PM, minimizing its impact on link performance in a manner similar to the treatment of DCF in legacy systems. This was previously not considered as the loss of the phase modulator was much less than the loss of the DCF, so its impact on performance was assumed to be negligible.
We compared the signal quality of the link with no NLC, post-compensation using TID-PM and inline NLC using practical TID-PMs. Figure 14 plots Q vs. launch power for the QPSK center channel, with Q calculated from EVM as the pattern length was again too short to generate a significant number of errors. There is a significant performance increase in the dispersion-unmanaged link compared to the dispersion-managed link, as the addition of DCF increases the link noise figure due to DCF loss (~7dB insertion loss compared with 2 dB for the phase modulator) and increases the correlation between the XPM distortion developed in each span [26]. In the dispersion unmanaged link, NLC using inline practical TID-PMs provides a 1.1-dB improvement in peak Q, which is smaller than seen in the dispersion managed case. This reduction in improvement is likely due to the smaller XPM penalty in the dispersion unmanaged link, as improving Q closer to the AWGN limit is difficult. In contrast, the post-compensation scheme provided negligible benefit in the dispersion unmanaged case, with an improvement of less than 0.1 dB. This is because the waveform into the post-compensator is heavily distorted by the accumulated CD, making it a poor estimate of the waveform that caused the nonlinear distortions.
Fig. 14 Q vs. launch power after 3200-km transmission for uncompensated (square markers), post-compensated (circular markers) and inline TID-PM (triangular markers) systems. Closed markers (solid lines) are the dispersion-managed link and open markers (dashed lines) are the dispersion-unmanaged link.
4. Discussion
From our simulations, we can see that inline TID-PMs are effective for XPM mitigation, and that their performance is robust to a number of link parameters. There is a similar increase in peak Q for different transmission distances in a dispersion-managed link, suggesting the advantage of using inline TID-PMs is unaffected by link length. Additionally, effectiveness is retained for different dispersion maps, with inline TID-PMs suppressing XPM in both dispersion-managed and dispersion-unmanaged links. While the simulations presented here have been confined to a single polarization, we expect application of the Manakov-PMD model [29] will enable this technique to work in polarization multiplexed systems, with the assumption that rich polarization scattering occurs in a single span. Due to the polarization dependent nature of most phase modulators, however, a polarization diverse scheme would be required. Such a scheme may be implementable using two phase modulators, one for each polarization. Additionally, the hybrid WDM link presented here merely represents a test case for proof-of-concept; TID-PMs have been previously demonstrated as a means to post-compensate XPM in orthogonal frequency division multiplexed (OFDM) links [23, 24], suggesting similar applications are possible for inline TID-PMs.
One of the main advantages for distributed NLC is its application to optically routed networks. In optically routed links, channels may be added and dropped along the link, which introduces a large performance penalty in end-span techniques such as DBP [14]. This is because the back propagation algorithm is unaware of the signal dropped at the intermediate node, and thus cannot undo the nonlinear distortions it caused. By using inline TID-PMs, it is possible to measure the waveform entering each span and only compensate the distortions developed in that span. By doing so, inline TID-PMs are not affected by adding and dropping channels, which occurs between the end of one span and the start of the next. Measuring the waveform into every span may also allow inline TID-PMs to reduce the penalty caused by non-deterministic signal × ASE mixing. This requires further study.
There are, however, a number of limitations on the performance of inline TID-PMs. As shown in Section 3.3, the assumption that all channels had identical walk-off characteristics resulted in a performance penalty, which was 1.4 dB for 1600-km transmission and 0.9-dB for the 3200-km link. Additionally, the interaction between CD and nonlinearity may fundamentally limit performance. In the analysis, we assumed that the shape of the waveform is constant over one span, though this is not the case in simulations and in reality. As a result, the TID-PM does not perfectly remove the XPM distortion developed in each span, resulting in imperfect compensation. These errors can be observed in Fig. 8, as the difference between the phase noise spectra in the linear region and when inline TID-PMs are used for NLC, and can be reduced by leaving some residual dispersion after every span.
In spite of these limitations, peak Q was improved by >1 dB in all the cases we investigated, showing that TID-PM has the potential to provide significantly increased tolerance to nonlinear cross-talk in long-haul WDM systems.
5. Conclusion
We have investigated the use of intensity-directed phase modulators distributed throughout a multi-span link as a simple optoelectronic method for nonlinearity management. Our simulations predict that for a test system carrying a 7-channel hybrid WDM signal in a dispersion-managed link, inline TID-PMs increase the peak Q of the center QPSK channel by 2.4 dB after 1600-km transmission and by 2.7 dB after 3200-km transmission. In a dispersion-unmanaged link, inline TID-PMs increase peak Q by 1.1 dB after 3200 km of fiber. These results suggest that inline TID-PMs can effectively mitigate XPM for various link lengths and dispersion maps.
Acknowledgments
We thank VPIphotonics (www.vpiphotonics.com) for the use of their simulator, VPItransmissionMakerWDM V9.1. This work is supported under the Australian Research Council’s Laureate Fellowship scheme (FL130100041) and ARC Centre of Excellence CUDOS (CE 110001018).
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