Experimental demonstration of XPM compensation for WDM ﬁbre transmission L. Zhu, F. Yaman and G. Li Distributed compensation for cross-phase modulation (XPM) by solving the coupled nonlinear Schro ¨dinger equations in digital back- ward propagation is demonstrated experimentally. The results show that XPM compensation provides signiﬁcant improvement over self- phase modulation compensation. Introduction: Coherent detection combined with digital signal proces- sing is emerging as one of the most promising techniques for long- haul ﬁbre transmission. One of the beneﬁts of coherent detection is that the complete information of the optical ﬁeld including amplitude and phase can be obtained, which enables the compensation of dis- persion and nonlinearity by digital backward propagation [1, 2]. Digital backward propagation (DBP) can be implemented by solving the total-ﬁeld nonlinear Schro ¨dinger equation (NLSE) or the coupled NLSEs. By solving the coupled NLSEs, cross-phase modulation (XPM) can be compensated while neglecting the effects of four-wave mixing (FWM). In comparison with XPM + FWM compensation by solving the total-ﬁeld NLSE, XPM compensation via coupled NLSEs requires a smaller computational load [3]. Moreover, XPM compen- sation does not need phase-locked local oscillators to reconstruct the total optical ﬁeld. Distributed nonlinearity and dispersion compensation by solving the total-ﬁeld NLSE has been experimentally demonstrated [4]. In this Letter, we experimentally demonstrate XPM compensation via coupled NLSEs for WDM transmission. Digital backward propagation: In a coherent wavelength-division mul- tiplexed (WDM) system, the total received ﬁeld can be expressed as E = ∑ N m=1 ˆ E m exp(i2mpDft ), where m ={1, 2, ··· , N } and N is the total number of channels, ˆ E m is the ﬁeld envelope detected by the coher- ent receiver for the mth channel, Df is the channel spacing. The total- ﬁeld NLSE for backward propagation is given by − ∂E ∂z + a 2 E + ib 2 2 ∂ 2 E ∂t 2 − ig|E| 2 E = 0 (1) where a is the ﬁbre loss, b 2 is the group velocity dispersion, and g is the nonlinearity parameter [5]. Equation (1) governs the total-ﬁeld backward propagation where dispersion, self-phase modulation (SPM), XPM and FWM are compensated. By expanding E in (1) and neglecting the terms for FWM, a set of coupled equations for backward propagation can be derived as [3] − ∂ ˆ E m ∂z + a 2 ˆ E m + 2mpDf b 2 ∂ ˆ E m ∂t + ib 2 2 ∂ 2 ˆ E m ∂t 2 − ig 2 ∑ N q=1 | ˆ E q | 2 −| ˆ E m | 2   ˆ E m = 0 (2) It is clear from (2) that changes in the relative phase among the channels do not affect the results of backward propagation. As a result, neglecting FWM alleviates the requirement of phase-locking among the local oscillators. Experimental setup: The experimental setup of the coherent trans- mission system is shown in Fig. 1. Three distributed-feedback lasers were used as the WDM carriers. Two QPSK modulators were driven by a pattern generator to modulate the central channel and two side chan- nels. Two RF delay lines were used to align the in-phase (I ) and quad- rature (Q) inputs of the QPSK modulators. The same data pattern with a pseudorandom bit sequence length of 2 23 2 1 was used to modulate all the channels. The data sequence of the central channel and the side chan- nels was decorrelated by an optical delay line. The symbol rate was chosen to be 6 Gsymbols/s so that all three WDM channels could ﬁt within the 24 GHz double-sided bandwidth of the real-time oscillo- scope. The channel spacing of the WDM channels was set to be 6.8 GHz which made the three WDM channels nearly orthogonal, resulting in the lowest linear crosstalk. QPSK modulator QPSK modulator pattern generator RF delay RF delay opt. delay AO switch AO switch loop control BPF NZDSF LO EDFA EDFA EDFA PC PD (I) 90° hybrid 50/50 50/50 50/50 PD (Q) PC VOA VOA PC PC PC ~D D real-time oscilloscope L R C Fig. 1 Experimental setup of QPSK transmission and coherent detection The WDM signal was launched into a recirculating loop controlled by two acousto-optic switches. The length of the nonzero dispersion shifted ﬁbre (NZ-DSF) spool in the loop was 80 km. The total launching power into the ﬁbre was 6 dBm. Variable optical attenuators (VOA) and polar- isation controllers (PC) were used to balance the power levels and align the polarisations of the three channels. The local oscillator was tuned to the central channel and mixed with the signal in a 908 hybrid. The I and Q components of the received signal were detected with two photodetec- tors. The real-time oscilloscope was used for analogue-to-digital conver- sion at 40 Gsamples/s and data acquisition. Results: The three WDM channels were demultiplexed using digital ﬁlters. Digital backward propagation was performed ofﬂine using the split-step Fourier method to solve the coupled NLSEs. Clock recovery, phase estimation and Q-value calculation were performed after compen- sation of ﬁbre impairments using DBP. The ﬁbre parameters were deter- mined by optimising the performance in the training experiments. The dispersion parameter was found to be 3.9 ps/nm/km by performing dis- persion compensation for 80 km transmission. The ﬁbre loss and non- linear parameter were found to be 0.2 dB/km and 1.4 /W/km by optimising the nonlinearity compensation after 800 km transmission. In DBP, the step size should be much smaller than the dispersion length L D =(b 2 Dn 2 ) −1 and nonlinear length L NL = L sp [gP T  Lsp 0 exp(−az)dz] −1 , where Dn is the total bandwidth, L SP is the span length, and P T is the total launching power. In this system, the dispersion and nonlinear length were 347 km and 675 km, respectively. The Q-value after 640 km transmission and DBP against step size was calcu- lated and shown in Fig. 2. There was no appreciable penalty when the step size was smaller than 80 km. Thus the step size was chosen to be 80 km which was the length of one ﬁbre span. 14 12 10 8 Q, dB 6 4 10 0 10 1 step size, km XPM compensation total-field NLSE 10 2 10 3 Fig. 2 Q-value against step size of digital backward propagation We used one local oscillator for coherent detection of all the three WDM channels. Therefore, the relative phase among all three channels has been preserved in our measurement. To verify that it is not necessary to preserve the relative phase for XPM compensation, we added random phase shifts (0.1p rad, 1.3p rad and 0.6p rad) to E 1 , E 2 and E 3 before solving the coupled NLSEs as expressed in (2). The random phase shifts made no difference to the resulting Q-values. To evaluate the effectiveness of XPM compensation, other compen- sation methods are included here for comparison. Fig. 3a shows the back-to-back constellation corresponding to a Q-value of 17.6 dB. The constellations after 800 km transmission and digital signal processing are shown in Figs. 3b – e. Fig. 3b is obtained after dispersion compen- sation only and the corresponding Q-value is 8.1 dB. Fig. 3c is obtained after SPM compensation by neglecting both FWM and XPM terms in the coupled NLSEs and the corresponding Q-value is 8.5 dB. The ELECTRONICS LETTERS 5th August 2010 Vol. 46 No. 16