Abstract

Compensation of nonlinear distortion of polarization-multiplexed (PolMux) signals in optical fiber is evaluated experimentally using all-optical signal pre-distortion and fiber loop phase-conjugation at the transmitter. An improved bit error rate is shown for high baud rate, 80 Gb/s RZ-DPSK PolMux signals before transmission in a 728 km long dispersion-managed fiber link employing a direct detection receiver. The partial compensation of nonlinear distortion for both single channel and 3 × 80 Gb/s WDM PolMux signals is observed, despite the impact from the inter-polarization nonlinearity and the associated polarization scattering. Evidence of the limited compensation of inter-polarization nonlinearity is shown.

© 2013 OSA

1. Introduction

Polarization multiplexed (PolMux) signal transmission using the dual orthogonal principle polarization states in optical fiber has attracted broad interest for doubling the spectral efficiency of communication systems [1]. The tradeoff is the greater susceptibility to nonlinear distortion from the intensity dependant Kerr effect. As a countermeasure, schemes for compensating the distortion have been explored to extend the maximum transmission distance. A promising solution is the use of high-speed digital signal processing (DSP) at the receiver (Rx), which has shown the partial compensation of an amount of distortion limited by the circuit complexity, size, and power consumption needed for its implementation [2,3].

An alternative that can avoid the bandwidth and complexity limitations of DSP is all-optical processing using nonlinear optics. This has been widely investigated for single polarized signals using schemes such as optical phase conjugation (OPC) for mid span spectral inversion (MSSI) [48] or transmitter (Tx) based pre-compensation [4,9]. However, the viability for all-optical compensation of PolMux signals is uncertain. A challenge is the impact of the inter-polarization nonlinearity in the fiber link on potentially altering the signal phase evolution that determines the effectiveness of OPC for compensating the distortion [7]. All-optical processing also differs from the typical DSP approach of computing the Manakov equation to apply an effective negative nonlinearity that is averaged over all the possible states of polarization of the signal on the Poincaré sphere.

In this paper, all-optical compensation of the nonlinear distortion of PolMux signals is investigated experimentally. A Tx based scheme for distortion pre-compensation using pre-distortion and fiber loop OPC (Tx-OPC) demonstrates an improved transmission performance for single wavelength channel and 3 × 80 Gb/s PolMux WDM RZ DPSK signals in a 10 span, 728 km long dispersion-managed (DM)-fiber link with a direct detection Rx and no DSP. Measurements show the impact of inter-polarization nonlinearity on the achievable BER improvement, and its limited compensation, and that the main limit on performance is not the link’s linear birefringence.

2. Background

The Kerr induced inter-polarization nonlinear effects in optical fiber can severely degrade the transmission performance of PolMux signals, in contrast to the lesser and indirect impact on conventional single polarization (non-PolMux) signals [10]. For WDM PolMux channels for example, the intensity dependant cross polarization modulation (XpolM) can induce a bit-pattern dependant nonlinear rotation of the signal polarization and an associated polarization scattering over the Poincaré sphere, which in turn degrades the orthogonality of PolMux channels leading to a crosstalk BER penalty at the Rx [1113]. This is on top of the nonlinear distortions affecting non-PolMux signals of self phase modulation, cross phase modulation (XPM) and four wave mixing (FWM). These effects can arise as both intra-channel and inter-channel nonlinearities [5], especially at the higher baud rates where the propagation distance needed for significant dispersion becomes short relative to the Kerr nonlinear length.

For PolMux signals, Mecozzi and Matera [14] have shown by theory and numerical simulation that the intra-channel nonlinearities of XPM and FWM between colliding neighboring symbols within the same channel for highly dispersive transmission can induce a bit-pattern dependant polarization scattering in an analogous manner to XpolM for WDM systems. This can alter the XPM between polarization channels on top of the effects of fiber propagation loss and dispersion, to in turn degrade the symmetric evolution of the signal phase distortion that OPC requires in general to maximize the compensation. Further complications may also arise from polarization mode dispersion due to the fiber birefringence, which to first order, is the differential group delay (DGD) between the principle states of polarization stemming from their slightly different refractive index. The varying channel delay from span to span can alter the inter-polarization nonlinearity, just as walk-off between WDM channels due to the group velocity dispersion (GVD) in fiber affects XPM.

The dominant nonlinear effect depends on factors such as the signal baud rate, data format, and the link dispersion map [13, 14]. For high baud rate signals such as 40 Gbaud RZ DPSK with 33% pulse duty cycle, and transmission in standard single mode fiber (SSMF), the intra-channel nonlinearities of XPM and FWM are enhanced due to the short pulse dispersion length of ≈1 km, compared to the typical effective fiber span length for nonlinear transmission (Leff), which is ≈22 km for a propagation loss of ≈0.2 dB/km [9]. For WDM signals, the inter-channel XPM on the other hand is reduced due to the walk-off length between co-propagating WDM channels being <1 km in the case of a 100 GHz grid spacing. For DM-links, studies have also shown PolMux signals typically have a reduced nonlinearity tolerance compared to transmission links without in-line dispersion compensation [13, 14].

3. Design and Experiment

The all-optical compensation of nonlinear distortion of PolMux signals was investigated with the Tx-OPC scheme shown in Fig. 1(a) and Fig. 1(b), whereby nonlinear signal propagation in a pre-distortion stage preceding OPC is designed to induce an opposite phase distortion to that in the link [4, 9]. For a fiber link of N spans, each with total input power, Pin, the total input power, PNL, to a predistortion fiber of length LNL is tuned to induce an equivalent total average nonlinear phase shift in the link by approximately PNL·γNL·LNL = 〈ϕT〉·K·M = N·Pin·γs·Leff, where γNL and γs are the nonlinearity coefficients for the predistortion and link fibers, respectively, 〈ϕT is the induced average total nonlinear phase shift in the fiber link for each WDM and polarization channel of total number K and M, respectively, with M = {1, 2}, and PNL and Pin are assumed to be the signal powers that are path averaged over LNL and Leff, respectively [4].

 

Fig. 1 (a) Schematic of dispersion-managed link with pre-compensation of fiber nonlinearity for PolMux signals by Tx-OPC. (b) Experimental set-up of Tx-OPC with nonlinear pre-distortion in SSMF before fiber loop OPC. (c) Optical spectra of fiber loop output for either 1 × or 3 × 80 Gb/s PolMux input signal at total applied PNL of 80 and 281 mW, respectively, and ≈1551 nm wavelength to generate phase conjugate at ≈1559 nm by FWM pumped by a CW laser. (Inset) First span input after EDFA for both with, and (blue lines) without Tx-OPC. (d) Set-ups of the 100 GHz spaced WDM 3 × 40 Gbaud RZ DPSK signal source, and the (e) direct detection receiver with a polarizer for polarization demultiplexing.

Download Full Size | PPT Slide | PDF

Maximizing the cancellation of the phase distortion by OPC relies on matching the signal phase distortion induced before and after OPC by ensuring the signal power and dispersion in the predistortion stage evolves symmetrically with respect to the link over Leff. For a dispersion-managed (DM) fiber link with a periodic dispersion map, such as obtained by compensating each fiber span’s dispersion with the insertion of dispersion compensating fiber (DCF), the dispersion symmetry can be satisfied with a predistortion stage consisting of a single length of fiber of the same type as in the link [9]. In the case of the dispersion map deviating from periodic, the signal power and dispersion evolution could be mirrored in principle by a more complicated predistortion stage containing multiple fiber spans between EDFAs in an architecture resembling conventional MSSI.

The Tx-OPC module was implemented for PolMux signals as shown in Fig. 1(b). The pre-distortion stage contained a 9 km long SSMF terminated with a Faraday mirror (FM). So by the retro-reflection transmission via an optical circulator, an LNL of 18 km (close to Leff) was obtained with half the required SSMF length, and with cancellation of the linear birefringence [15, 16], which ensured a polarization stable input to the following OPC stage. Notably, the induced nonlinear polarization rotation in the pre-distortion stage remained [15].For the following OPC, a bi-directional nonlinear fiber loop was implemented based on a similar scheme demonstrating wavelength conversion [17] and dispersion compensation [18]. As shown in Fig. 1(b), the PolMux signal’s two orthogonal polarization states (x and y) were demultiplexed by a polarization beam splitter (PBS) and counter-propagated through a nonlinear fiber loop to generate their respective phase conjugated wave. This was by FWM in a 100 m long highly nonlinear fiber (HNLF) with a CW laser whose polarization state at the PBS input was angled so that half of its power was aligned to each counter-propagating signal, x and y. The HNLF parameters for the nonlinear coefficient, loss, zero dispersion wavelength and dispersion slope were 21 W−1km−1, 0.5 dB/km, 1551 nm, and 0.02 ps/nm2.km, respectively. The CW laser had an input power to the fiber loop of ≈250 mW and its wavelength was set to ≈1555 nm, so that for an input signal center wavelength of ≈1551 nm, its phase conjugate formed at ≈1559 nm as shown in Fig. 1(c). At the fiber loop output from an optical circulator, the PolMux signal was extracted by bandpass optical filters (BPF’s) and launched into the link. Without Tx-OPC, the signal wavelength was set to match 1559 nm. Figure 1(c) (inset) shows the link input signal spectra for both with and without Tx-OPC.

The longest possible DM link was assembled from the available fiber spools to form a total of ten spans, with the first five spans ranging in length from 38 to 85 km and consisting of SSMF and a similar large effective area fiber with ≈20% larger dispersion parameter. The following five spans each contained 80 km of SSMF. With the OPC module inserted, the additional chromatic dispersion in the pre-distortion stage was compensated for by extending the last span from 85 km to 99 km, which increased the total link length to 728 km. To reduce the buildup of ASE noise, a BPF was inserted directly after the EDFA at the input of half of the spans (i.e. the 1st, 4th, 5th, 6th and 8th span), and an EDFA preceded each DCF for all except the 3rd, 4th, 7th and 10th span. For all experiments, the input power to each DCF was kept at an optimized low power for minimizing the BER at the link output.

At the Tx, PolMux signal generation was emulated as shown in Fig. 1(b) by splitting the output of a 40 Gbaud RZ DPSK source with a 50:50 coupler and multiplexing both copies using a polarization beam combiner (PBC) after setting their polarization state to be orthogonal via polarization controllers (PC). The PolMux circuit included a time delay line (ΔT), optical switch (SW) and variable optical attenuator (VOA) for data decorrelation, polarization identification at the Rx, and power equalization, respectively.

The signal Tx itself that directly preceded the PolMux circuit had the set-up shown in Fig. 1(d). The center channel of a WDM signal (Ch. 2) was generated from a CW laser at either 1551 or 1559 nm wavelength corresponding to with or without Tx-OPC, respectively. This was modulated by a pair of Mach Zehnder (MZ) modulators that in succession carved pulses of 40 GHz repetition and 33% duty cycle, before applying 40 Gb/s DPSK encoding with a binary 231-1 pseudo random bit sequence (PRBS) as the electrical drive signal. The neighboring WDM channels (Ch. 1 and 3) were produced by simultaneously modulating two CW lasers at 100 GHz carrier frequency offset from Ch.2 using a phase modulator (PM) driven by the complementary output of the same PRBS source. This was followed by an electro-absorption modulator (EAM) for 40 GHz pulse carving. All channels were combined with a multiplexer (MUX) and aligned to be co-polarized at the output of a polarizer. For the single channel measurements, the neighboring channels were switched off, leaving only Ch. 2.

At the link output, the signal was polarization demultiplexed by a polarizer (PLZ) inserted before a direct detection Rx. The Rx set-up, as shown in Fig. 1(e), contained an EDFA, 43 GHz DPSK demodulator (DMOD), 0.5 nm BPF, and VOA before a single photodetector (PD). Polarization-state selection was by manual control of a polarization controller (PC). Since Tx-OPC improves the quality of the signal arriving at the receiver, it is expected to also benefit the performance of communication links using the alternative coherent detection in place of differential demodulation and square law direct detection.

4. Results and discussion

Signal transmission in the fiber link was evaluated at a high Pin for 〈ϕT on the order of π where nonlinear distortion was severe. For all BER measurements, the received power to the photo detector was fixed at −2.4 dBm (unless plotting BER versus received power), and the PolMux ΔT was set to minimize the BER, in which case, polarization interleaving was taken advantage of [14]. The optimized polarization interleaving reduced the bit pattern dependant cross polarization modulation to enable the lowest possible BER for a given launch power. The performance improvement by Tx-OPC for without polarization interleaving where the BER is further degraded may differ, just as for comparing the BER improvement at a higher signal transmission power.

The impact of inter-polarization nonlinearity in the link is evident in Fig. 2 from the BER sensitivity to Pin compared to non-PolMux transmission (implemented by blocking the x polarization beam in the PolMux circuit using the switch). The major transmission performance degradation for polarization multiplexed signals at an equivalent power per polarization channel is highlighted by plotting the BER against Pin per polarization channel (Pin /M), rather than the total combined signal power. It shows over the range of Pin, PolMux signals tolerate only ≈Pin/3 per polarization channel for achieving the same output BER. In both cases, Tx-OPC with PNL optimized for minimum BER allowed around twice the Pin for achieving the same BER. Although error free transmission was not achieved for PolMux signals, the results show the use of Tx-OPC can effectively reduce the BER to below the typical FEC limit of ≈2 × 10−3. The degradation compared to non-PolMux signals is expected from the intra-channel polarization scattering for high baud rate signals in highly dispersive fiber [14]. As for previous single polarization measurements [9], the BER curves are expected to converge for decreasing Pin as the fiber nonlinearity diminishes. Extending the BER to lower Pin was limited in this case by the adjustable output power range of the link EDFAs. Nevertheless, the focus on the nonlinear regime at higher Pin highlights the effectiveness of Tx-OPC for compensating severe nonlinear distortion, to permit for example a longer span length between optical amplifiers along the link.For each Pin with Tx-OPC, PNL was optimized to minimize the BER. At (Pin /M) = 8 mW, the BER was minimized at a total applied PNL of 126 mW (63 mW per polarization channel) for the PolMux case, and 115 mW for single polarization transmission. This was of similar order to the predicted 98 mW per polarization channel from the approximate relation in Section 3.

 

Fig. 2 Transmission performance for 40 Gbaud RZ-DPSK signal in 10 span DM-link (solid lines, filled points) with nonlinearity compensation by Tx-OPC, and (dashed lines, empty points) without Tx-OPC. Output BER versus Pin for (colored curves) single polarization 40 Gb/s signal, and (black curves) 80 Gb/s PolMux signal for (triangle points) x and (circles) y polarization channels. The diamond and box points are PolMux 3 × 80 Gb/s WDM centre channel (Ch. 2) x and y polarization channels, respectively.

Download Full Size | PPT Slide | PDF

The impact of Tx-OPC on the output signal eye diagrams and optical spectra are shown in Fig. 3(a) for Pin = 10 mW. The corresponding BER shows the use of Tx-OPC reduced the BER floor by over 2 orders of magnitude. The nonlinear fiber loop for OPC alone was confirmed to minimally degrade the PolMux signal. This was evaluated by comparing the back to back (B2B) measurement of the signal BER both before and after the Tx-OPC module with its 9 km pre-distortion SSMF removed. The penalty in the received power for achieving a BER of 10−9 compared to the PolMux signal input was minor at <1 dB as Fig. 3(b) shows.

 

Fig. 3 1 × 80 Gb/s PolMux signal transmission in 10 span link with Pin = 10 mW. (a) 40 Gbaud signal eye diagrams at photoreceiver output, and optical spectra after polarization demultiplexing of x polarization channel, and (b) minimum BER versus received optical power for (solid lines, filled points) with Tx-OPC at optimum PNL, and (dashed lines, empty points) without Tx-OPC, in the case of (black lines) fiber link transmission, and (colored lines) B2B with fiber link removed, for (triangle points) x and (circle points) y polarization channels.

Download Full Size | PPT Slide | PDF

For link transmission both with and without OPC, a slight performance difference was observed between the x and y polarization channels, indicating a polarization dependant loss in the link. With OPC, the imbalance was also sensitive to the input polarization state of CW pump into the fiber loop stage determining the FWM conversion efficiencies for the counter-propagating x and y polarization channels.

The transmission performance was also investigated for PolMux WDM 3 × 80 Gb/s RZ DPSK signals to assess the potential further degradation from the inter-channel nonlinearities of both XPM and XpolM between WDM channels. In this case, Pin was set to an average total of 28 mW corresponding to ≈4.7 mW per WDM channel per polarization. This corresponded to a significantly large 〈ϕT of ≈π/2. Due to the EDFAs in the first five spans having an output power limitation of maximum Pin ≈16 mW, a higher Pin = 40 mW was set for the last five spans to achieve the target average. Measurements at higher signal powers were limited by the inability of the BER analyzer to measure a significantly worse BER. Figure 4 compares the link output signal eye diagrams, spectra and BER for with and without Tx-OPC. It shows the signal quality was improved for both polarizations states of all WDM channels at the same total PNL of 276 mW. The equivalent Q2 factor improvement calculated from the BER as Q2 = 20·log10√2·erfc−1(2 × BER)] was between 1.9 and 4 dB for both polarizations of all channels. Both interpolarization nonlinearity and XPM are expected to grow for an increasing number of WDM channels, nevertheless, Fig. 2 shows the performance for WDM versus single channel transmission doesn’t degrade as severely as for PolMux versus non-PolMux signals.To verify the BER improvement by Tx-OPC was attributable to pre-distortion stage nonlinearity, as opposed to solely pre-compensating the link GVD (pre-GVD), the Tx-OPC module was substituted with a DCF of equivalent pre-GVD (−275 ps/nm). The DCF input power was optimized to minimize the link output BER, and the pre-GVD module output power was attenuated to approximately match the Tx-OPC case. The BER plotted in Fig. 5 shows Tx-OPC outperformed the pre-GVD module despite Tx-OPC adding extra fiber nonlinearity in the pre-distortion stage. For the 3 × 80 Gb/s PolMux signal, the Q2 factor improvement compared to the pre-GVD module was also measured to be 0.7 and 1.7 dB for the x and y polarizations of the center channel, respectively. The analysis by Mecozzi et al. [19] has shown the performance advantage of pre-GVD in general is dependent on the data modulation format, and diminishes significantly for DQPSK compared to DPSK.

 

Fig. 4 PolMux 3 × 80 Gb/s RZ DPSK signal output from 10 span DM-link for (solid lines) with Tx-OPC at PNL = 276 mW, and (b) without Tx-OPC. (a) Optical spectra after polarization demultiplexing, and center channel (Ch. 2) 40 Gb/s eye diagrams from Rx, and (b) output BER for (triangle points) x and (circle points) y polarization channels.

Download Full Size | PPT Slide | PDF

 

Fig. 5 1 x 80 Gb/s PolMux signal BER measured at fixed received power after 10-span DM-fiber link for PolMux input signal to either (solid lines) Tx-OPC, or (dashed lines) pre-GVD module at the Tx for (triangle points) x and (circle points) y polarization channels, showing the improved BER by Tx-OPC despite the added pre-distortion nonlinearity

Download Full Size | PPT Slide | PDF

Evidence of the compensation of inter-polarization nonlinearity was investigated by comparing the transmission of a 1 × 80 Gb/s PolMux signal with the Tx-OPC module shifted from the output of the PolMux circuit in Fig. 1(b) to its input. By doing so, the inter-polarization nonlinearity was confined to the PolMux signal transmission in the link only and not the predistortion stage as well. Figure 6(a) shows, however, that over the range of Pin with optimized PNL, the link output BER remained comparable in both cases. Since the added interpolarization nonlinearity in the predistortion stage for Tx-OPC of PolMux signals did not degrade the overall transmission performance, it indicates it was partially compensating the contribution from the link, instead of only further degrading the signal.

 

Fig. 6 1 × 80 Gb/s PolMux signal transmission in 10 span DM-fiber link with Tx-OPC inserted (black lines) after PolMux circuit for dual polarization channel input, or (colored lines) before PolMux circuit for single polarization channel input. (a) (solid lines, filled data points) Minimum BER versus Pin and (dashed lines, open data points) corresponding UNL for PNL normalized to (N·Pin·Leff·M*/(M·LNL), and (b) BER versus normalized PNL at fixed Pin = 10 mW. Triangle and circle points are for x and y polarization channels, respectively.

Download Full Size | PPT Slide | PDF

It is also interesting to compare the optimum PNL per polarization channel for minimizing the BER. At Pin = 10 mW, the BER was minimized at a total applied PNL of 80 mW and 61 mW in the case of Tx-OPC of a PolMux and single polarization input signal, respectively. Figure 6(a) plots PNL normalized to the equivalent 〈ϕT with γNL ≈□γs as given by UNL = (PNL·LNL/M*)/(N·Pin·Leff/M), where M = 2 for the transmission link, and M* represents the number of polarization channels propagating in the predistortion stage, and equals either 1 or 2 for Tx-OPC of a single polarization or PolMux signal, respectively. It showed over the range of Pin, the optimum normalized PNL per polarization channel for minimizing the BER was slightly lower for Tx-OPC of PolMux signals and further below the expected unity value estimation. Also, sweeping PNL for the case of Pin = 10 mW in Fig. 6(b) showed the signal degradation was more pronounced at higher PNL for PolMux Tx-OPC. These results indicate a limited compensation capability.The impact of the differential group delay (DGD) in the link, and its potential mismatch to the pre-distortion stage was also investigated. This was performed by comparing the PolMux transmission performance in a shorter, 99 km long, single-span DM-fiber link so that the effective accumulated DGD within Leff would be less. This follows from the expectation that over long distances the accumulated DGD increases in proportion to the square root of the total transmission distance [20]. Figure 7 compares the output BER after transmission of a 1 × 80 Gb/s PolMux signal in both the 99 km and 728 km long links when plotted against Pin·N for a corresponding approximately equivalent normalized 〈ϕT. The BER was minimized at a similar PNL in both cases of 64 mW and 67 mW for N = 10 with Pin = 10 mW, and N = 1 with Pin = 100 mW, respectively. The comparable BER curves measured for both with and without Tx-OPC indicated that DGD wasn’t the main performance limitation in these experiments.The results show a BER improvement by Tx-OPC despite an imperfect power and dispersion symmetry. A marginal boost in performance could be expected by improving the power symmetry using a predistortion stage with distributed gain instead of loss, and extending LNL to match the link span length to account for the nonlinearity induced beyond Leff in each span. A link of only SSMF would also ensure the dispersion and nonlinearity are more accurately matched to the predistortion stage. The wavelength dependence of the signal dispersion map and corresponding dispersion symmetry would remain due to the non-zero dispersion slope of optical fiber. The impact of major dispersion asymmetry was tested by offsetting the signal dispersion map on the dispersion axis through simply compensating for the dispersion of the predistortion stage after the 1st span of the link instead of the last. In doing so, for the transmission of single polarization signals, the BER improvement by Tx-OPC was observed to be lost. Even with optimum signal dispersion and power evolution, the impact of polarization mode dispersion and the polarization dependence of XPM, FWM, and XpolM would disrupt the symmetric phase evolution needed for optimum distortion compensation.

 

Fig. 7 Output BER measured at fixed received power versus the product Pin × N/M for 1 × 80 Gb/s PolMux signal transmission in (black lines) 10 span and (colored lines) single span fiber link for (solid lines) with and (dashes) without Tx-OPC of PolMux input signal, showing the similar performance for comparable 〈ϕT. Triangle and circle points are for the x and y polarization channels, respectively.

Download Full Size | PPT Slide | PDF

5. Conclusions

The compensation of nonlinear distortion of 80 Gb/s PolMux RZ-DPSK signals was demonstrated by all-optical signal pre-distortion and fiber loop phase conjugation. An improved output BER for both single wavelength channel and 3 × 80 Gb/s WDM signals was observed after the transmission in a 728 km long fiber link employing a direct detection receiver and no DSP. This was despite the impact from the inter-polarization nonlinearity and the associated polarization scattering of the signal field. Measurements showed the limited compensation of inter-polarization nonlinearity and that the primary limit on the achievable BER improvement was not due to DGD in this case.

Acknowledgments

M.D. Pelusi was supported by the Australian Research Council (ARC) Future Fellowship program. This research was also supported by the ARC Centre of Excellence for Ultrahigh bandwidth Devices for Optical Systems (project number CE110001018).

References and links

1. T. J. Xia, “Optical channel capacity – From Mb/s to Tb/s and beyond,” Opt. Fiber Technol. 17(5), 328–334 (2011). [CrossRef]  

2. S. J. Savory, G. Gavioli, E. Torrengo, and P. Poggiolini, “Impact of interchannel nonlinearities on a split-step intrachannel nonlinear equalizer,” IEEE Photon. Technol. Lett. 22(10), 673–675 (2010). [CrossRef]  

3. W. Yan, Z. Tao, L. Dou, L. Li, S. Oda, T. Tanimura, T. Hoshida, and J. C. Rasmussen, “Low complexity digital perturbation back-propagation,” in Proc. ECOC 2011, paper Tu.3.A.2, 2011.

4. S. Watanabe, S. Kaneko, and T. Chikama, “Long-haul fiber transmission using optical phase conjugation,” Opt. Fiber Technol. 2(2), 169–178 (1996). [CrossRef]  

5. A. Chowdhury, G. Raybon, R.-J. Essiambre, J. H. Sinsky, A. Adamiecki, J. Leuthold, C. R. Doerr, and S. Chandrasekhar, “Compensation of intrachannel nonlinearities in 40-Gb/s pseudolinear systems using optical-phase conjugation,” J. Lightwave Technol. 23(1), 172–177 (2005). [CrossRef]  

6. S. L. Jansen, D. van den Borne, P. M. Krummrich, S. Spälter, G.-D. Khoe, and H. de Waardt, “Long-haul DWDM transmission systems employing optical phase conjugation,” IEEE Sel. Top. Quantum Electron. 12(4), 505–520 (2006). [CrossRef]  

7. P. Minzioni, “Nonlinearity compensation in a fiber-optic link by optical phase conjugation,” Fiber Integr. Opt. 28(3), 179–209 (2009). [CrossRef]  

8. P. Minzioni, V. Pusino, I. Cristiani, L. Marazzi, M. Martinelli, C. Langrock, M. M. Fejer, and V. Degiorgio, “Optical phase conjugation in phase-modulated transmission systems: experimental comparison of different nonlinearity-compensation methods,” Opt. Express 18(17), 18119–18124 (2010). [CrossRef]   [PubMed]  

9. M. D. Pelusi, “WDM signal all-optical precompensation of Kerr nonlinearity in dispersion-managed fibers,” IEEE Photon. Technol. Lett. 25(1), 71–74 (2013). [CrossRef]  

10. R. Khosravani, Y. W. Song, Y. Xie, L.-S. Yan, A. E. Willner, and C. R. Menyuk, “Bit-pattern-dependent polarization rotation in first-order PMD-compensated WDM systems,” Opt. Commun. 257(1), 191–196 (2006). [CrossRef]  

11. L. F. Mollenauer, J. P. Gordon, and F. Heismann, “Polarization scattering by soliton-soliton collisions,” Opt. Lett. 20(20), 2060–2062 (1995). [CrossRef]   [PubMed]  

12. B. C. Collings and L. Boivin, “Nonlinear polarization evolution induced by cross-phase modulation and its impact on transmission systems,” IEEE Photon. Technol. Lett. 12(11), 1582–1584 (2000). [CrossRef]  

13. C. Xie, “Impact of nonlinear and polarization effects in coherent systems,” Opt. Express 19(26), B915–B930 (2011). [CrossRef]   [PubMed]  

14. A. Mecozzi and F. Matera, “Polarization scattering by intra-channel collisions,” Opt. Express 20(2), 1213–1218 (2012). [CrossRef]   [PubMed]  

15. C. Vinegoni, M. Wegmuller, B. Huttner, and N. Gisin, “Measurement of nonlinear polarization rotation in a highly birefringent optical fibre using a Faraday mirror,” J. Opt. A, Pure Appl. Opt. 2(4), 314–318 (2000). [CrossRef]  

16. M. Martinelli, “A universal compensator for polarization changes induced by birefringence on a retracing beam,” Opt. Commun. 72(6), 341–344 (1989). [CrossRef]  

17. P. Martelli, P. Boffi, M. Ferrario, L. Marazzi, P. Parolari, R. Siano, V. Pusino, P. Minzioni, I. Cristiani, C. Langrock, M. M. Fejer, M. Martinelli, and V. Degiorgio, “All-optical wavelength conversion of a 100-Gb/s polarization-multiplexed signal,” Opt. Express 17(20), 17758–17763 (2009). [CrossRef]   [PubMed]  

18. L. Marazzi, P. Parolari, P. Martelli, R. Siano, P. Boffi, M. Ferrario, A. Righetti, M. Martinelli, V. Pusino, P. Minzioni, I. Cristiani, V. Degiorgio, C. Langrock, and M. M. Fejer, “Real-time 100-Gb/s POLMUX RZ-DQPSK transmission over uncompensated 500 km of SSMF by optical phase conjugation,” in Proc OFC/NFOEC 2009, paper JWA44 (2009). [CrossRef]  

19. A. Mecozzi, M. Tabacchiera, F. Matera, and M. Settembre, “Intra-channel nonlinearity in differentially phase-modulated transmission,” Opt. Express 19(5), 3990–3995 (2011). [CrossRef]   [PubMed]  

20. F. Curti, B. Daino, Q. Mao, F. Matera, and C. G. Someda, “Concatenation of polarisation dispersion in single-mode fibres,” Electron. Lett. 25(4), 290–292 (1989). [CrossRef]  

References

  • View by:
  • |
  • |
  • |

  1. T. J. Xia, “Optical channel capacity – From Mb/s to Tb/s and beyond,” Opt. Fiber Technol. 17(5), 328–334 (2011).
    [CrossRef]
  2. S. J. Savory, G. Gavioli, E. Torrengo, and P. Poggiolini, “Impact of interchannel nonlinearities on a split-step intrachannel nonlinear equalizer,” IEEE Photon. Technol. Lett. 22(10), 673–675 (2010).
    [CrossRef]
  3. W. Yan, Z. Tao, L. Dou, L. Li, S. Oda, T. Tanimura, T. Hoshida, and J. C. Rasmussen, “Low complexity digital perturbation back-propagation,” in Proc. ECOC 2011, paper Tu.3.A.2, 2011.
  4. S. Watanabe, S. Kaneko, and T. Chikama, “Long-haul fiber transmission using optical phase conjugation,” Opt. Fiber Technol. 2(2), 169–178 (1996).
    [CrossRef]
  5. A. Chowdhury, G. Raybon, R.-J. Essiambre, J. H. Sinsky, A. Adamiecki, J. Leuthold, C. R. Doerr, and S. Chandrasekhar, “Compensation of intrachannel nonlinearities in 40-Gb/s pseudolinear systems using optical-phase conjugation,” J. Lightwave Technol. 23(1), 172–177 (2005).
    [CrossRef]
  6. S. L. Jansen, D. van den Borne, P. M. Krummrich, S. Spälter, G.-D. Khoe, and H. de Waardt, “Long-haul DWDM transmission systems employing optical phase conjugation,” IEEE Sel. Top. Quantum Electron. 12(4), 505–520 (2006).
    [CrossRef]
  7. P. Minzioni, “Nonlinearity compensation in a fiber-optic link by optical phase conjugation,” Fiber Integr. Opt. 28(3), 179–209 (2009).
    [CrossRef]
  8. P. Minzioni, V. Pusino, I. Cristiani, L. Marazzi, M. Martinelli, C. Langrock, M. M. Fejer, and V. Degiorgio, “Optical phase conjugation in phase-modulated transmission systems: experimental comparison of different nonlinearity-compensation methods,” Opt. Express 18(17), 18119–18124 (2010).
    [CrossRef] [PubMed]
  9. M. D. Pelusi, “WDM signal all-optical precompensation of Kerr nonlinearity in dispersion-managed fibers,” IEEE Photon. Technol. Lett. 25(1), 71–74 (2013).
    [CrossRef]
  10. R. Khosravani, Y. W. Song, Y. Xie, L.-S. Yan, A. E. Willner, and C. R. Menyuk, “Bit-pattern-dependent polarization rotation in first-order PMD-compensated WDM systems,” Opt. Commun. 257(1), 191–196 (2006).
    [CrossRef]
  11. L. F. Mollenauer, J. P. Gordon, and F. Heismann, “Polarization scattering by soliton-soliton collisions,” Opt. Lett. 20(20), 2060–2062 (1995).
    [CrossRef] [PubMed]
  12. B. C. Collings and L. Boivin, “Nonlinear polarization evolution induced by cross-phase modulation and its impact on transmission systems,” IEEE Photon. Technol. Lett. 12(11), 1582–1584 (2000).
    [CrossRef]
  13. C. Xie, “Impact of nonlinear and polarization effects in coherent systems,” Opt. Express 19(26), B915–B930 (2011).
    [CrossRef] [PubMed]
  14. A. Mecozzi and F. Matera, “Polarization scattering by intra-channel collisions,” Opt. Express 20(2), 1213–1218 (2012).
    [CrossRef] [PubMed]
  15. C. Vinegoni, M. Wegmuller, B. Huttner, and N. Gisin, “Measurement of nonlinear polarization rotation in a highly birefringent optical fibre using a Faraday mirror,” J. Opt. A, Pure Appl. Opt. 2(4), 314–318 (2000).
    [CrossRef]
  16. M. Martinelli, “A universal compensator for polarization changes induced by birefringence on a retracing beam,” Opt. Commun. 72(6), 341–344 (1989).
    [CrossRef]
  17. P. Martelli, P. Boffi, M. Ferrario, L. Marazzi, P. Parolari, R. Siano, V. Pusino, P. Minzioni, I. Cristiani, C. Langrock, M. M. Fejer, M. Martinelli, and V. Degiorgio, “All-optical wavelength conversion of a 100-Gb/s polarization-multiplexed signal,” Opt. Express 17(20), 17758–17763 (2009).
    [CrossRef] [PubMed]
  18. L. Marazzi, P. Parolari, P. Martelli, R. Siano, P. Boffi, M. Ferrario, A. Righetti, M. Martinelli, V. Pusino, P. Minzioni, I. Cristiani, V. Degiorgio, C. Langrock, and M. M. Fejer, “Real-time 100-Gb/s POLMUX RZ-DQPSK transmission over uncompensated 500 km of SSMF by optical phase conjugation,” in Proc OFC/NFOEC 2009, paper JWA44 (2009).
    [CrossRef]
  19. A. Mecozzi, M. Tabacchiera, F. Matera, and M. Settembre, “Intra-channel nonlinearity in differentially phase-modulated transmission,” Opt. Express 19(5), 3990–3995 (2011).
    [CrossRef] [PubMed]
  20. F. Curti, B. Daino, Q. Mao, F. Matera, and C. G. Someda, “Concatenation of polarisation dispersion in single-mode fibres,” Electron. Lett. 25(4), 290–292 (1989).
    [CrossRef]

2013 (1)

M. D. Pelusi, “WDM signal all-optical precompensation of Kerr nonlinearity in dispersion-managed fibers,” IEEE Photon. Technol. Lett. 25(1), 71–74 (2013).
[CrossRef]

2012 (1)

2011 (3)

2010 (2)

2009 (2)

2006 (2)

R. Khosravani, Y. W. Song, Y. Xie, L.-S. Yan, A. E. Willner, and C. R. Menyuk, “Bit-pattern-dependent polarization rotation in first-order PMD-compensated WDM systems,” Opt. Commun. 257(1), 191–196 (2006).
[CrossRef]

S. L. Jansen, D. van den Borne, P. M. Krummrich, S. Spälter, G.-D. Khoe, and H. de Waardt, “Long-haul DWDM transmission systems employing optical phase conjugation,” IEEE Sel. Top. Quantum Electron. 12(4), 505–520 (2006).
[CrossRef]

2005 (1)

2000 (2)

B. C. Collings and L. Boivin, “Nonlinear polarization evolution induced by cross-phase modulation and its impact on transmission systems,” IEEE Photon. Technol. Lett. 12(11), 1582–1584 (2000).
[CrossRef]

C. Vinegoni, M. Wegmuller, B. Huttner, and N. Gisin, “Measurement of nonlinear polarization rotation in a highly birefringent optical fibre using a Faraday mirror,” J. Opt. A, Pure Appl. Opt. 2(4), 314–318 (2000).
[CrossRef]

1996 (1)

S. Watanabe, S. Kaneko, and T. Chikama, “Long-haul fiber transmission using optical phase conjugation,” Opt. Fiber Technol. 2(2), 169–178 (1996).
[CrossRef]

1995 (1)

1989 (2)

M. Martinelli, “A universal compensator for polarization changes induced by birefringence on a retracing beam,” Opt. Commun. 72(6), 341–344 (1989).
[CrossRef]

F. Curti, B. Daino, Q. Mao, F. Matera, and C. G. Someda, “Concatenation of polarisation dispersion in single-mode fibres,” Electron. Lett. 25(4), 290–292 (1989).
[CrossRef]

Adamiecki, A.

Boffi, P.

Boivin, L.

B. C. Collings and L. Boivin, “Nonlinear polarization evolution induced by cross-phase modulation and its impact on transmission systems,” IEEE Photon. Technol. Lett. 12(11), 1582–1584 (2000).
[CrossRef]

Chandrasekhar, S.

Chikama, T.

S. Watanabe, S. Kaneko, and T. Chikama, “Long-haul fiber transmission using optical phase conjugation,” Opt. Fiber Technol. 2(2), 169–178 (1996).
[CrossRef]

Chowdhury, A.

Collings, B. C.

B. C. Collings and L. Boivin, “Nonlinear polarization evolution induced by cross-phase modulation and its impact on transmission systems,” IEEE Photon. Technol. Lett. 12(11), 1582–1584 (2000).
[CrossRef]

Cristiani, I.

Curti, F.

F. Curti, B. Daino, Q. Mao, F. Matera, and C. G. Someda, “Concatenation of polarisation dispersion in single-mode fibres,” Electron. Lett. 25(4), 290–292 (1989).
[CrossRef]

Daino, B.

F. Curti, B. Daino, Q. Mao, F. Matera, and C. G. Someda, “Concatenation of polarisation dispersion in single-mode fibres,” Electron. Lett. 25(4), 290–292 (1989).
[CrossRef]

de Waardt, H.

S. L. Jansen, D. van den Borne, P. M. Krummrich, S. Spälter, G.-D. Khoe, and H. de Waardt, “Long-haul DWDM transmission systems employing optical phase conjugation,” IEEE Sel. Top. Quantum Electron. 12(4), 505–520 (2006).
[CrossRef]

Degiorgio, V.

Doerr, C. R.

Essiambre, R.-J.

Fejer, M. M.

Ferrario, M.

Gavioli, G.

S. J. Savory, G. Gavioli, E. Torrengo, and P. Poggiolini, “Impact of interchannel nonlinearities on a split-step intrachannel nonlinear equalizer,” IEEE Photon. Technol. Lett. 22(10), 673–675 (2010).
[CrossRef]

Gisin, N.

C. Vinegoni, M. Wegmuller, B. Huttner, and N. Gisin, “Measurement of nonlinear polarization rotation in a highly birefringent optical fibre using a Faraday mirror,” J. Opt. A, Pure Appl. Opt. 2(4), 314–318 (2000).
[CrossRef]

Gordon, J. P.

Heismann, F.

Huttner, B.

C. Vinegoni, M. Wegmuller, B. Huttner, and N. Gisin, “Measurement of nonlinear polarization rotation in a highly birefringent optical fibre using a Faraday mirror,” J. Opt. A, Pure Appl. Opt. 2(4), 314–318 (2000).
[CrossRef]

Jansen, S. L.

S. L. Jansen, D. van den Borne, P. M. Krummrich, S. Spälter, G.-D. Khoe, and H. de Waardt, “Long-haul DWDM transmission systems employing optical phase conjugation,” IEEE Sel. Top. Quantum Electron. 12(4), 505–520 (2006).
[CrossRef]

Kaneko, S.

S. Watanabe, S. Kaneko, and T. Chikama, “Long-haul fiber transmission using optical phase conjugation,” Opt. Fiber Technol. 2(2), 169–178 (1996).
[CrossRef]

Khoe, G.-D.

S. L. Jansen, D. van den Borne, P. M. Krummrich, S. Spälter, G.-D. Khoe, and H. de Waardt, “Long-haul DWDM transmission systems employing optical phase conjugation,” IEEE Sel. Top. Quantum Electron. 12(4), 505–520 (2006).
[CrossRef]

Khosravani, R.

R. Khosravani, Y. W. Song, Y. Xie, L.-S. Yan, A. E. Willner, and C. R. Menyuk, “Bit-pattern-dependent polarization rotation in first-order PMD-compensated WDM systems,” Opt. Commun. 257(1), 191–196 (2006).
[CrossRef]

Krummrich, P. M.

S. L. Jansen, D. van den Borne, P. M. Krummrich, S. Spälter, G.-D. Khoe, and H. de Waardt, “Long-haul DWDM transmission systems employing optical phase conjugation,” IEEE Sel. Top. Quantum Electron. 12(4), 505–520 (2006).
[CrossRef]

Langrock, C.

Leuthold, J.

Mao, Q.

F. Curti, B. Daino, Q. Mao, F. Matera, and C. G. Someda, “Concatenation of polarisation dispersion in single-mode fibres,” Electron. Lett. 25(4), 290–292 (1989).
[CrossRef]

Marazzi, L.

Martelli, P.

Martinelli, M.

Matera, F.

Mecozzi, A.

Menyuk, C. R.

R. Khosravani, Y. W. Song, Y. Xie, L.-S. Yan, A. E. Willner, and C. R. Menyuk, “Bit-pattern-dependent polarization rotation in first-order PMD-compensated WDM systems,” Opt. Commun. 257(1), 191–196 (2006).
[CrossRef]

Minzioni, P.

Mollenauer, L. F.

Parolari, P.

Pelusi, M. D.

M. D. Pelusi, “WDM signal all-optical precompensation of Kerr nonlinearity in dispersion-managed fibers,” IEEE Photon. Technol. Lett. 25(1), 71–74 (2013).
[CrossRef]

Poggiolini, P.

S. J. Savory, G. Gavioli, E. Torrengo, and P. Poggiolini, “Impact of interchannel nonlinearities on a split-step intrachannel nonlinear equalizer,” IEEE Photon. Technol. Lett. 22(10), 673–675 (2010).
[CrossRef]

Pusino, V.

Raybon, G.

Savory, S. J.

S. J. Savory, G. Gavioli, E. Torrengo, and P. Poggiolini, “Impact of interchannel nonlinearities on a split-step intrachannel nonlinear equalizer,” IEEE Photon. Technol. Lett. 22(10), 673–675 (2010).
[CrossRef]

Settembre, M.

Siano, R.

Sinsky, J. H.

Someda, C. G.

F. Curti, B. Daino, Q. Mao, F. Matera, and C. G. Someda, “Concatenation of polarisation dispersion in single-mode fibres,” Electron. Lett. 25(4), 290–292 (1989).
[CrossRef]

Song, Y. W.

R. Khosravani, Y. W. Song, Y. Xie, L.-S. Yan, A. E. Willner, and C. R. Menyuk, “Bit-pattern-dependent polarization rotation in first-order PMD-compensated WDM systems,” Opt. Commun. 257(1), 191–196 (2006).
[CrossRef]

Spälter, S.

S. L. Jansen, D. van den Borne, P. M. Krummrich, S. Spälter, G.-D. Khoe, and H. de Waardt, “Long-haul DWDM transmission systems employing optical phase conjugation,” IEEE Sel. Top. Quantum Electron. 12(4), 505–520 (2006).
[CrossRef]

Tabacchiera, M.

Torrengo, E.

S. J. Savory, G. Gavioli, E. Torrengo, and P. Poggiolini, “Impact of interchannel nonlinearities on a split-step intrachannel nonlinear equalizer,” IEEE Photon. Technol. Lett. 22(10), 673–675 (2010).
[CrossRef]

van den Borne, D.

S. L. Jansen, D. van den Borne, P. M. Krummrich, S. Spälter, G.-D. Khoe, and H. de Waardt, “Long-haul DWDM transmission systems employing optical phase conjugation,” IEEE Sel. Top. Quantum Electron. 12(4), 505–520 (2006).
[CrossRef]

Vinegoni, C.

C. Vinegoni, M. Wegmuller, B. Huttner, and N. Gisin, “Measurement of nonlinear polarization rotation in a highly birefringent optical fibre using a Faraday mirror,” J. Opt. A, Pure Appl. Opt. 2(4), 314–318 (2000).
[CrossRef]

Watanabe, S.

S. Watanabe, S. Kaneko, and T. Chikama, “Long-haul fiber transmission using optical phase conjugation,” Opt. Fiber Technol. 2(2), 169–178 (1996).
[CrossRef]

Wegmuller, M.

C. Vinegoni, M. Wegmuller, B. Huttner, and N. Gisin, “Measurement of nonlinear polarization rotation in a highly birefringent optical fibre using a Faraday mirror,” J. Opt. A, Pure Appl. Opt. 2(4), 314–318 (2000).
[CrossRef]

Willner, A. E.

R. Khosravani, Y. W. Song, Y. Xie, L.-S. Yan, A. E. Willner, and C. R. Menyuk, “Bit-pattern-dependent polarization rotation in first-order PMD-compensated WDM systems,” Opt. Commun. 257(1), 191–196 (2006).
[CrossRef]

Xia, T. J.

T. J. Xia, “Optical channel capacity – From Mb/s to Tb/s and beyond,” Opt. Fiber Technol. 17(5), 328–334 (2011).
[CrossRef]

Xie, C.

Xie, Y.

R. Khosravani, Y. W. Song, Y. Xie, L.-S. Yan, A. E. Willner, and C. R. Menyuk, “Bit-pattern-dependent polarization rotation in first-order PMD-compensated WDM systems,” Opt. Commun. 257(1), 191–196 (2006).
[CrossRef]

Yan, L.-S.

R. Khosravani, Y. W. Song, Y. Xie, L.-S. Yan, A. E. Willner, and C. R. Menyuk, “Bit-pattern-dependent polarization rotation in first-order PMD-compensated WDM systems,” Opt. Commun. 257(1), 191–196 (2006).
[CrossRef]

Electron. Lett. (1)

F. Curti, B. Daino, Q. Mao, F. Matera, and C. G. Someda, “Concatenation of polarisation dispersion in single-mode fibres,” Electron. Lett. 25(4), 290–292 (1989).
[CrossRef]

Fiber Integr. Opt. (1)

P. Minzioni, “Nonlinearity compensation in a fiber-optic link by optical phase conjugation,” Fiber Integr. Opt. 28(3), 179–209 (2009).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

S. J. Savory, G. Gavioli, E. Torrengo, and P. Poggiolini, “Impact of interchannel nonlinearities on a split-step intrachannel nonlinear equalizer,” IEEE Photon. Technol. Lett. 22(10), 673–675 (2010).
[CrossRef]

M. D. Pelusi, “WDM signal all-optical precompensation of Kerr nonlinearity in dispersion-managed fibers,” IEEE Photon. Technol. Lett. 25(1), 71–74 (2013).
[CrossRef]

B. C. Collings and L. Boivin, “Nonlinear polarization evolution induced by cross-phase modulation and its impact on transmission systems,” IEEE Photon. Technol. Lett. 12(11), 1582–1584 (2000).
[CrossRef]

IEEE Sel. Top. Quantum Electron. (1)

S. L. Jansen, D. van den Borne, P. M. Krummrich, S. Spälter, G.-D. Khoe, and H. de Waardt, “Long-haul DWDM transmission systems employing optical phase conjugation,” IEEE Sel. Top. Quantum Electron. 12(4), 505–520 (2006).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. A, Pure Appl. Opt. (1)

C. Vinegoni, M. Wegmuller, B. Huttner, and N. Gisin, “Measurement of nonlinear polarization rotation in a highly birefringent optical fibre using a Faraday mirror,” J. Opt. A, Pure Appl. Opt. 2(4), 314–318 (2000).
[CrossRef]

Opt. Commun. (2)

M. Martinelli, “A universal compensator for polarization changes induced by birefringence on a retracing beam,” Opt. Commun. 72(6), 341–344 (1989).
[CrossRef]

R. Khosravani, Y. W. Song, Y. Xie, L.-S. Yan, A. E. Willner, and C. R. Menyuk, “Bit-pattern-dependent polarization rotation in first-order PMD-compensated WDM systems,” Opt. Commun. 257(1), 191–196 (2006).
[CrossRef]

Opt. Express (5)

Opt. Fiber Technol. (2)

T. J. Xia, “Optical channel capacity – From Mb/s to Tb/s and beyond,” Opt. Fiber Technol. 17(5), 328–334 (2011).
[CrossRef]

S. Watanabe, S. Kaneko, and T. Chikama, “Long-haul fiber transmission using optical phase conjugation,” Opt. Fiber Technol. 2(2), 169–178 (1996).
[CrossRef]

Opt. Lett. (1)

Other (2)

L. Marazzi, P. Parolari, P. Martelli, R. Siano, P. Boffi, M. Ferrario, A. Righetti, M. Martinelli, V. Pusino, P. Minzioni, I. Cristiani, V. Degiorgio, C. Langrock, and M. M. Fejer, “Real-time 100-Gb/s POLMUX RZ-DQPSK transmission over uncompensated 500 km of SSMF by optical phase conjugation,” in Proc OFC/NFOEC 2009, paper JWA44 (2009).
[CrossRef]

W. Yan, Z. Tao, L. Dou, L. Li, S. Oda, T. Tanimura, T. Hoshida, and J. C. Rasmussen, “Low complexity digital perturbation back-propagation,” in Proc. ECOC 2011, paper Tu.3.A.2, 2011.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

(a) Schematic of dispersion-managed link with pre-compensation of fiber nonlinearity for PolMux signals by Tx-OPC. (b) Experimental set-up of Tx-OPC with nonlinear pre-distortion in SSMF before fiber loop OPC. (c) Optical spectra of fiber loop output for either 1 × or 3 × 80 Gb/s PolMux input signal at total applied PNL of 80 and 281 mW, respectively, and ≈1551 nm wavelength to generate phase conjugate at ≈1559 nm by FWM pumped by a CW laser. (Inset) First span input after EDFA for both with, and (blue lines) without Tx-OPC. (d) Set-ups of the 100 GHz spaced WDM 3 × 40 Gbaud RZ DPSK signal source, and the (e) direct detection receiver with a polarizer for polarization demultiplexing.

Fig. 2
Fig. 2

Transmission performance for 40 Gbaud RZ-DPSK signal in 10 span DM-link (solid lines, filled points) with nonlinearity compensation by Tx-OPC, and (dashed lines, empty points) without Tx-OPC. Output BER versus Pin for (colored curves) single polarization 40 Gb/s signal, and (black curves) 80 Gb/s PolMux signal for (triangle points) x and (circles) y polarization channels. The diamond and box points are PolMux 3 × 80 Gb/s WDM centre channel (Ch. 2) x and y polarization channels, respectively.

Fig. 3
Fig. 3

1 × 80 Gb/s PolMux signal transmission in 10 span link with Pin = 10 mW. (a) 40 Gbaud signal eye diagrams at photoreceiver output, and optical spectra after polarization demultiplexing of x polarization channel, and (b) minimum BER versus received optical power for (solid lines, filled points) with Tx-OPC at optimum PNL, and (dashed lines, empty points) without Tx-OPC, in the case of (black lines) fiber link transmission, and (colored lines) B2B with fiber link removed, for (triangle points) x and (circle points) y polarization channels.

Fig. 4
Fig. 4

PolMux 3 × 80 Gb/s RZ DPSK signal output from 10 span DM-link for (solid lines) with Tx-OPC at PNL = 276 mW, and (b) without Tx-OPC. (a) Optical spectra after polarization demultiplexing, and center channel (Ch. 2) 40 Gb/s eye diagrams from Rx, and (b) output BER for (triangle points) x and (circle points) y polarization channels.

Fig. 5
Fig. 5

1 x 80 Gb/s PolMux signal BER measured at fixed received power after 10-span DM-fiber link for PolMux input signal to either (solid lines) Tx-OPC, or (dashed lines) pre-GVD module at the Tx for (triangle points) x and (circle points) y polarization channels, showing the improved BER by Tx-OPC despite the added pre-distortion nonlinearity

Fig. 6
Fig. 6

1 × 80 Gb/s PolMux signal transmission in 10 span DM-fiber link with Tx-OPC inserted (black lines) after PolMux circuit for dual polarization channel input, or (colored lines) before PolMux circuit for single polarization channel input. (a) (solid lines, filled data points) Minimum BER versus Pin and (dashed lines, open data points) corresponding UNL for PNL normalized to (N·Pin·Leff·M*/(M·LNL), and (b) BER versus normalized PNL at fixed Pin = 10 mW. Triangle and circle points are for x and y polarization channels, respectively.

Fig. 7
Fig. 7

Output BER measured at fixed received power versus the product Pin × N/M for 1 × 80 Gb/s PolMux signal transmission in (black lines) 10 span and (colored lines) single span fiber link for (solid lines) with and (dashes) without Tx-OPC of PolMux input signal, showing the similar performance for comparable 〈ϕT. Triangle and circle points are for the x and y polarization channels, respectively.

Metrics