We experimentally demonstrate that mid-link optical phase conjugation (OPC) effectively compensates fiber nonlinearity in coherent optical OFDM super-channels. The OPC was produced by pump × subcarrier degenerate four-wave-mixing in a 1-km highly nonlinear fiber. The nonlinear threshold for the 10 × 80-km 604.7-Gb/s 16-QAM test system was increased by 4.8 dB. The performance at the optimum power was only improved by 0.2 dB because the OPC module produces a 1.6 dB penalty for the back-to-back system. FWM theory shows that the ‘noise’ processes of OPC modules utilizing χ3 nonlinearities could be reduced by increasing the pump power, which will improve back-to-back performance with the OPC module.
©2012 Optical Society of America
With the ever-increasing demand for bandwidth, it is critical that the capacity of optical networks is increased . Coherent systems are now able to compensate for linear impairments such as chromatic dispersion (CD) and polarization-mode dispersion (PMD). However, fiber nonlinearity limits the maximum power that systems can operate at; thus, higher optical signal-to-noise ratios (OSNR) cannot be achieved by increasing the power without using fiber nonlinearity compensation . Most recent nonlinearity compensation research has focused on using digital techniques such as backpropagation (BP) [3, 4]. However, the computational power required for BP is very high, which makes BP difficult to implement using real-time digital signal processing (DSP) . In addition, using BP for multiple wavelength channels is even more difficult because the computational effort increases with the total bandwidth of the signal .
Optical phase conjugation (OPC) was shown to be capable of compensating for fiber nonlinearity in 1983 . By conjugating the signal near the mid-point of the link, the fiber nonlinearity products generated in the second half of the link mitigate the fiber nonlinearity products generated in the first half . This method is often referred to as mid-span spectral inversion (MSSI). A single OPC module can conjugate multiple wavelength channels ; therefore, MSSI can compensate for fiber nonlinearity in wavelength division multiplexed (WDM) systems . Recently, OPC has also been demonstrated for polarization multiplexed systems ; MSSI was proposed for coherent optical orthogonal frequency division multiplexed (CO-OFDM) systems . An analytical study using FWM theory has shown that MSSI can increase the nonlinearity-limited performance of CO-OFDM systems .
At OECC2012 , we experimentally demonstrated fiber nonlinearity compensation using MSSI for a CO-OFDM super-channel. The nonlinear threshold of a 604.7 Gb/s single-polarization CO-OFDM signal was increased by 4.8 dB for a 10 × 80-km link. However, the system performance at the optimal launch power was only improved by 0.2 dB. In this paper, I-Q imbalance compensation is used to further improve the results from . Additionally, we show that non-degenerate four-wave-mixing (FWM) and amplified spontaneous emission (ASE) generated in the OPC module limit the back-to-back performance of MSSI systems. FWM theory shows that this limit can be improved by increasing the power of the pump laser.
2. Experimental setup
Figure 1(a) shows the transmitter and receiver configurations. At the transmitter, a 14.4-GHz comb is generated by modulating the output of a 193.1-THz external cavity laser (ECL) with two phase modulators connected in series. A Finisar Waveshaper flattens the comb’s spectrum and selects 11 spectral lines. A 27.5-Gb/s OFDM signal is generated with a 10-GSample/s 2-channel Tektronix arbitrary waveform generator (AWG). The OFDM symbols were generated with a 158-point inverse discrete Fourier transform (IDFT): 112 subcarriers were modulated with 16-QAM, all other subcarriers were zeroed and a 5-point cyclic prefix (CP) was inserted after the IDFT. The OFDM signal is modulated onto all eleven comb lines using a single Sumitomo complex Mach-Zehnder modulator (C-MZM). The multi-band optical signal is then divided into two paths; one path is frequency shifted by 7.2-GHz using a Covega C-MZM and amplified before the shifted and unshifted signal paths are combined, forming a 22-channel continuous super-channel with an optical bandwidth of 158.7-GHz, carrying 604.7 Gb/s in a single polarization. A 163-sample OFDM symbol gives an integer-OFDM-symbol delay between the unshifted and shifted signals. At the receiver, another Waveshaper selects a portion of the super-channel. The selected signal is fed into a coherent receiver, built with a Kylia optical hybrid and U2T balanced photodiodes. A second ECL is used as the local oscillator. An Agilent DSO-X 92804A real-time sampling oscilloscope digitizes the signal at 40 GS/s. The offline equalizer consists of: a resampler, an I-Q imbalance compensator , a frequency offset compensator, a standard OFDM 1-tap equalizer, and a decision-directed symbol phase estimator. In the system without MSSI, digital chromatic dispersion (CD) compensation precedes the 1-tap equalizer. For the system with MSSI, the complex signal is constructed from I – jQ, rather than I + jQ to undo the OPC.
Figure 1(b) shows the optical link, including the OPC module. The link for the system without MSSI comprises 10 × 80-km spans of standard single-mode fiber (S-SMF). Erbium doped fiber amplifiers (EDFA) are used to set the launch power into each S-SMF span. For the MSSI system, the OPC module is placed after the fifth span, preceded by a 60-km dispersion compensation module (DCM). The DCM improves the nonlinearity compensation [11, 14]. The signal is amplified and filtered by a 200-GHz demultiplexer centered at 193.1 THz (from a Siemens TransXpress system), which removes the out-of-band ASE. A polarization controller is used to align the polarizations of the signal and pump. A third ECL (193.4 THz) is used as the pump for OPC. The pump and signal are combined with a 90/10 coupler (the 90 port is used for the pump) and passed into a 1008-m long OFS HNLF. The HNLF has a nonlinear coefficient, γ, of 11.5 W−1km−1, CD of −0.05 ps.nm−1.km−1 at 1550 nm, CD slope of 0.02 ps.nm−2.km and a total loss of 0.97 dB. Figure 1(c) shows the output of the HNLF. The pump and the original signal are removed with a second 200-GHz demultiplexer centered at 193.7 THz. The signal is then transmitted through another five spans.
Figure 2 shows the spectrum of the super-channel at the receiver. The entire super-channel is very flat for the system without MSSI (Fig. 2(a)). However, with MSSI (Fig. 2(b)), the outermost channels are attenuated relative to the central channels. This roll-off will degrade the performance of the edge channels, especially at ASE-limited powers. The roll-off is due to the 200-GHz demultiplexers.
3. Impairments induced by OPC using χ3 nonlinearity
The OPC module uses a HNLF and a pump laser to achieve phase conjugation and wavelength conversion using the χ3 nonlinearity in the HNLF. Degenerate FWM between the pump and the signal produces the conjugated signal, S(opc); this is shown in blue in Fig. 3 . The total power of the conjugated signal is given by :
The numerous subcarriers in an OFDM signal will also produce other FWM products as they propagate through the HNLF. The most significant of these are the FWM products generated by mixing between the subcarriers themselves, not involving the pump (yellow in Fig. 3), FWM(sc), and the non-degenerate FWM products between any two subcarriers and the pump (green in Fig. 3), FWM(sps). After the HNLF, the power of FWM(sc) and FWM(sps) are approximately given by:
The power of FWM(sps) can be comparable to the power of S(opc) as shown in Fig. 1(c). Therefore, it is important to have a sufficiently wide guard-band between the signal and the pump to prevent S(opc) from falling on top of FWM(sps). Although FWM(sc) and FWM(sps) do not fall within the frequency band of S(opc), they will interact with the pump to produce new products that fall on S(opc). These products are shown in purple in Fig. 3. Because FWM(sc) and FWM(sps) are not present at the start of the HNLF, but are generated along the HNLF, calculations to predict the power of any secondary FWM products resulting from FWM(sc) and FWM(sps) must consider the variation in power along the HNLF of FWM(sc) and FWM(sps). If the HNLF is approximated to be lossless and dispersionless, then the power in the secondary FWM products that fall at the S(opc) frequency is approximately given by:
These equations show that the FWM products that cause distortion are proportional to the power of the signal cubed, whereas the power of the conjugated signal is only linearly proportional to the power of the signal. Therefore, the signal power into the HNLF should be limited. This theory also explains the observations in  for optical parametric amplifiers. However, an EDFA will then be required to amplify S(opc) after the HNLF, which will produce ASE proportional to its gain. Thus, there is an optimal input signal power that will maximize the back-to-back performance with an OPC module. A more detailed analysis of the impairments of the OPC module will be presented in a later paper.
To find the optimum signal power, we performed a back to back experiment. The power of the pump was 16 dBm, which is the maximum output power of our ECL. Figure 4 shows the average signal quality, Q, of the middle three OFDM channels, against the input power of the signal into the HNLF. The optimal input power into the HNLF is between 1 and 3 dBm. The back-to-back performance without the OPC module is shown for comparison. The minimum Q penalty due to the OPC module is 1.6 dB. The performance is better than that presented in  because I-Q imbalance compensation was added to the equalization algorithm at the receiver. This penalty can be further reduced by increasing the power of the pump . For the remainder of this paper, the signal power into the HNLF is set to 2 dBm.
4. Transmission results
Figure 5 plots the received Q against the launch power into the S-SMF spans, with MSSI (●) and without MSSI (▲). The Q was averaged over the 22 individual channels. The dashed lines represent the maximum Q that was achieved in a back-to-back configuration with and without MSSI. MSSI increased the nonlinearity threshold by 4.8 dB, from 4.9 dBm to 9.7 dBm. Because of the lower back-to-back limit of the MSSI system, as discussed in the Section 3, the Q at the optimal power was only increased by 0.2 dB, which is within the variation between the channels. The distortions produced in the link are reduced by MSSI; however, this is counter-balanced by the distortions produced in the OPC. If the distortions in the OPC module were reduced, the higher nonlinearity limit of the MSSI system would produce an increase in peak Q, which will extend system reach by allowing more spans or longer spans.
There is an additional performance degradation associated with using MSSI at launch powers below 3 dBm. To investigate this further, the BER for each individual sub-channel is plotted against the sub-channel index in Fig. 6 at: (a) 3 dBm – the optimal power without MSSI; and (b) 6 dBm – the optimal power with MSSI. Figure 6(a) shows the BER with and without MSSI is flat across the central sub-channels. However, the BER for the sub-channels at the edge of the super-channel have significantly higher BER for the MSSI system. The roll-off of the demultiplexers used in the OPC module caused the power in the edge sub-channels to be lower, relative to the central channels, after OPC. Therefore, the edge sub-channels will be launched into the second half of the link at a lower power than the sub-channels in the center of the band. This makes them more susceptible to the ASE produced by the EDFAs in the second half of the link.
Figure 6(b) shows the BER of all sub-channels, except sub-channel 22, is below the FEC limit of 3.8 × 10−3 for the MSSI system. The average BER of the super-channel is 2.0 × 10−3. If MSSI is not used, all sub-channels are well above the FEC limit. This shows that MSSI has significantly reduced the degradation induced by fiber nonlinearity.
We have experimentally demonstrated that MSSI is effective for fiber nonlinearity compensation in OFDM super-channels. MSSI improved the nonlinear threshold of a 604.7-Gb/s 16-QAM single-polarization CO-OFDM super-channel by 4.8 dB over the tested 10 × 80-km link. A polarization independent OPC module have been demonstrated ; such a setup would also allow polarization multiplexed systems. Polarization multiplexing would allow the super-channel to carry more than 1 Tb/s. Since the signal’s bandwidth would be unchanged, the improvement should be similar for low-PMD fibers. The signal bandwidth was 158.7 GHz wide and was passed through a 200-GHz demultiplexer; therefore, the signal is suitable for a 200-GHz WDM grid.
Although fiber nonlinearity was compensated effectively, the OPC module used did reduce the back-to-back performance of the system by 1.6 dB, from 19.9 dB to 18.3 dB. FWM theory suggests that the back-to-back performance of the MSSI system could be improved by increasing the pump power. The addition of I-Q imbalance compensation improved back-to-back performance by 0.9 dB and 0.8 dB for without MSSI and with MSSI respectively compared with the results presented in OECC2012 .
This work is supported the Australian Research Council’s (ARC) Centre of Excellence for Ultrahigh bandwidth Devices for Optical Systems, CUDOS (project CE110001018).
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