An adaptive delay control to maintain time-interleaving condition of multi-channel input signals of all-optical amplitude limiter based on saturation of four-wave mixing (FWM) in a nonlinear fiber is demonstrated. The delay control utilizes as a monitor signal the optical power after the nonlinear fiber at a wavelength that is affected by interchannel FWM in the fiber. When the scheme is applied to 2 x 10 Gbit/s return-to-zero differential phase-shift keying signals where the time separation between the input channels is intentionally changed randomly, the delay control works well and error free detection after transmission is obtained.
© 2011 OSA
Four-wave mixing (FWM) in fibers has found various applications in ultrahigh-speed all-optical signal processing. One of the promising signal processing is phase-preserving amplitude limiter based on saturation of FWM, which has a potential to enhance phase-modulated signals transmission by suppressing nonlinear phase noise [1–3]. As compared with other schemes for the phase-preserving amplitude limiter such as a modified nonlinear amplifying loop mirror (NALM) , the limiter based on saturation of FWM has a feature that additional functionalities such as wavelength conversion can be easily incorporated .
Most of fiber based limiters (or regenerators) studied so far only concern single channel operation. Thus, for the use in wavelength-division multiplexing (WDM) systems, the number of limiters required is proportional to the number of channels. Limiters that can process multi-channel signals in a nonlinear medium are desirable but quite challenging to realize. For the multi-channel regeneration, interchannel nonlinear crosstalks in nonlinear fiber have to be avoided while efficient nonlinear effect is needed in the regeneration process. Some techniques for fiber based multi-channel limiters and regenerators have been proposed. Some of the studies use dispersion management of the nonlinear fiber to suppress interchannel crosstalks, however, spectral efficiency is still inadequate [6–8]. Other studies proposed bidirectional configuration to avoid interchannel crosstalks, but the number of channels is limited [9,10]. Orthogonal polarization has also been proposed for interchannel crosstalk mitigation in additional to other methods [6,9], but the number of channels is also limited. Interchannel crosstalk mitigation by properly time-interleaved channels is another method introduced in [11–13]. Number of channels as large as six with using pulses having small duty ratios have been regenerated in . Although signal pulse widths should be shorter for larger number of channels to be simultaneously processed in this scheme, which is incompatible to today’s dense WDM systems where high spectral efficiency is one of the most important requirements, this scheme can still be a candidate for a multi-channel signal processor in high-speed all-optical systems.
Recently, we have demonstrated the time-interleaved multi-channels method for the FWM-based limiter in a single fiber for differential phase-shift keying (DPSK)  and on-off keying (OOK)  modulated signals. The limiter can process time-interleaved multi-channel signals simultaneously because FWM process in fiber is ultrafast and limited in space in the vicinity of input pulses. Thus, multi-channel signals can share a single pump and a nonlinear fiber if the signals are properly time-interleaved, which avoids crosstalks induced by cross-gain saturation (XGS) and interchannel FWM . However, this method requires adaptive delay control of signals for practical applications.
Several suitable techniques of adaptive delay control for the time-interleaved multi-channel limiter based on FWM have been discussed in , which are based on monitoring the time interleaving conditions and then controlling the delay time between the input channels. For monitoring, a possible method is measuring and detecting the radio-frequency (RF) component in detected input signals which appears when correct time interleaving is achieved. For example, for 2 × 10 Gbit/s channels operation, the RF component at 20 GHz should be measured and maximized by the delay control. This method, however, needs high-speed photo detectors and high-frequency electrical components which cover the aggregated signal speed (20GHz in the case of 2 x 10G bit/s operation). Other possible method for monitoring is to measure the output power after the FWM interaction in the HNLF at a wavelength that is affected by the interchannel FWM. This monitoring scheme does not require high-speed RF components. Delay time has to be adjusted to minimize the interchannel FWM power. Then, a fast and efficient delay controller needs to be applied to time-interleave channels before the FWM interaction in the limiter. A straightforward method is to demux and mux the channels with variable delay lines given to each of the channels between the demux and mux stages. Other choice of the channel selective time delay, without using delay lines and demultiplexing, will be to utilize a slow light technique .
In this paper, we demonstrate an adaptive delay control technique for the limiter based on saturation of FWM in a highly nonlinear fiber (HNLF) for 2 x 10 Gbit/s return-to-zero (RZ) DPSK signals. The optical power after the HNLF at a wavelength that is maximally affected by the interchannel FWM is monitored and then the time between the channels is adjusted using a variable delay line at the input of the limiter so that the monitored power is minimized. Simultaneous amplitude-noise suppression for the two channels is achieved in a situation where the relative time delay between the channels is randomly changed.
2. Experimental setup
Experimental setup of the DPSK signal transmission with the limiter and an adaptive delay control is illustrated in Fig. 1 . Two continuous-wave (CW) signals with wavelengths of 1555.5 nm (ch.1) and 1556.3 nm (ch.2) from distributed feedback (DFB) lasers are launched to two cascaded 10-GHz RF-driven chirp-free Mach-Zehnder modulators (MZMs) as pulse carvers. The first MZM is used to obtain 10-GHz 50% RZ pulses and the second MZM is used to further decrease the pulse width to ~30 ps, so that the signals can be properly time-interleaved in the limiter. Then, the phase of the signal is modulated with a 1024-bit length data pattern generated by a pulse pattern generator (PPG). After that, the signals are amplitude-modulated with a 7-GHz RF tone to simulate amplitude noise. The signals are then demultiplexed to respective channels.
In the path of ch.1, a transmission line, consisting of a 50-km single-mode fiber and a ~6-km dispersion compensating fiber (SMF + DCF), and a motorized variable delay line (DL) are inserted to simulate delay fluctuation between channels. The SMF and DCF are inserted so that the two channel signals are decorrelated in the limiter and an unintentional time delay between the channels is introduced in the measurement. Dispersion compensation in the SMF + DCF fiber is almost perfect. The delay fluctuation in the SMF + DCF is about ± 1 ps/second during this experiment, which is due to the change in temperature. The time delay of the variable delay line is varied at a speed of 4 ps/second from and to uniformly distributed random variables within 0 - 100 ps. The change of the time delay is programmed in LabVIEW. In the path of ch.2, a piezoelectric fiber stretcher (FS) and another motorized variable delay line are inserted for adaptive delay control operation. The details of the adaptive delay control operation will be explained in Section 4. Then, the signals are amplified to an optimum power for the limiting process and are multiplexed again. After that, the signals are combined with a CW pump. Wavelength and power of the pump are 1561 nm and 70 mW, respectively. The pump is phase-modulated with RF tones of 1 GHz and 100 MHz to suppress stimulated Brillouin scattering (SBS). Polarization of the signals and the pump are aligned to get maximum FWM efficiency. A circulator is inserted before the HNLF for SBS threshold measurement. The zero-dispersion wavelength, dispersion slope, nonlinearity, and length of the HNLF are 1556 nm, 0.026 ps/nm2/km, ~14 /W/km, and 1500 m, respectively. When the input signal power is increased to an appreciable level, the output signal power at the HNLF end saturates and amplitude fluctuation is suppressed.
At the output of the HNLF a 2.7-nm bandwidth optical bandpass filter (OBPF) is placed to extract the two signal channels with the pump rejected. In examining the performance of the system with or without the limiter, the signal is transmitted over a densely dispersion-managed fiber (DDMF) after the limiter. The DDMF consists of alternating normal- and anomalous-dispersion (~ ±3 ps/nm/km) nonzero dispersion-shifted fiber sections with zero average dispersion around the signal wavelength. Length of each fiber section is 2 km and the total length is 40 km. In this fiber, dispersive pulse broadening is limited, which enhances the translation from amplitude to phase fluctuations of the signal via the effect of self-phase modulation (SPM). After the DDMF, an attenuator (ATT) and a power meter (PM) are inserted to measure the received signal power. Then a pre-amplifier and a channel selection filter having a 0.6-nm bandwidth are inserted. After that, another ATT and a PM are added to monitor and maintain the signal power directed to a delay interferometer followed by a balanced photo-detector at a constant level.
3. Power-transfer characteristics of the limiter
Power transfer function curves of the limiter for single-channel and time-interleaved two-channel operations are shown in Fig. 2 . For this measurement, the SMF and DCF in the path of ch.1 shown in Fig. 1 are omitted for avoiding unintentional delay variations between the channels. Mark-level noise is not applied in this measurement. Curves with triangle and square symbols are the average powers of ch.1 and ch.2, respectively. Solid curves with empty symbols are obtained when the two channels are launched simultaneously and properly time-interleaved, while dotted curves with filled symbols are for single-channel operations. For the simultaneous two-channel operation, the input power of the other channel, i.e. unmeasured channel, is fixed at a constant value in the saturation regime. The power transfer characteristics of the time-interleaved two-channel operation are almost the same as the single-channel case, which indicates that the interchannel interaction is negligible. Strong saturation of output power at input powers around 10 mW is observed for both wavelength channels. Gain and saturation behaviors of ch.1 and ch.2 do not differ much as the wavelength difference between the channels is small (0.8nm) relative to the pump-signal separation. It is noted that the signal wavelengths in this experiment are located around the peak of the gain spectrum of the single-pump parametric amplifier .
Corresponding power transfer curves when channels are overlapped are shown by solid curves in Fig. 3 . Filled triangle and square symbols indicate transfer functions of ch.1 and ch.2, respectively. In this curves the input power of the other (unmeasured) channel is kept constant at its saturation input power. When compared with the time-interleaved case as shown in Fig. 2, we can see that the output powers of the overlapped signals are lower. This is because when the signals are overlapped, stronger pump depletion occurs and some of the signal power is used for generation of interchannel FWM products. In the same figure, we also show by dashed curves output powers of each of the overlapped channels when the input power of the other channel is varied while the input power of the measured channel is maintained at its optimum power for limiting operation. The output power is greatly reduced as the input power of the other channel is increased. This shows that strong crosstalk between channels is unavoidable when the two channels are overlapped.
Figure 4(a) and 4(c) show the optical eye patterns at the input and output, respectively, of the limiter when the two channels are time-interleaved. The signals are detected after the 2.7-nm filter for the rejection of the pump power after the HNLF. Bandwidth of detection is 30 GHz. The amplitude noise of the input signal is successfully suppressed by the limiter. The corresponding input and output eye patterns when the two channels are overlapped are shown in Fig. 4(b) and 4(d), respectively. The eye patterns show the sum of the power-waveforms of ch.1 and ch.2. Although the amplitude noise is seen to be suppressed as shown in Fig. 4(d), this does not mean that the noise on the signal in individual channel is suppressed. Figure 5(a) , 5(b) and 5(c), 5(d) are the input and output optical eye patterns, respectively, for the channel overlapping case after one of the two channels is selected by a 0.6-nm bandwidth OBPF. It is shown in Fig. 5(b) and 5(d) that the amplitude noise suppression for individual channels is not successful when the two channels are overlapped in the limiter.
4. Adaptive delay control
In the adaptive delay control for proper time interleaving of different channels, we monitor a power at a specific wavelength after the HNLF that is affected by the interchannel FWM. Figure 6 illustrates spectra measured at the output end of the HNLF when the two channels are simultaneously launched to the limiter at the optimum input power for the limiting process. The resolution of the spectrum analyzer is 0.1 nm. Solid curve shows output spectrum when the input signal pulses are time-interleaved, while dashed curve shows output spectrum when they are overlapped. The solid curve shows that small side bands appear at frequencies above and below the pump, signals, and idlers separated by Δf = f1 - f2, where f1 and f2 are the frequencies of ch.1 and ch.2, respectively. This means that tails of the pulses in ch.1 and ch.2 slightly overlap with each other even in the case of the optimal time interleaving. The side bands grow appreciably as shown by the dashed curve in Fig. 6 when the signal pulses maximally overlap at the entrance of the HNLF. The spectral power difference between the cases with and without pulse overlap becomes maximum at a wavelength ~1559.3 nm, which is shown by a shaded column shown in Fig. 6. We therefore extract the power of the spectral portion by a 0.6-nm OBPF and use it as a monitor for the time-interleaving condition.
The monitored power versus the relative time delay Δτ between channels is shown in Fig. 7 . In this measurement, the relative time delay is varied using the delay line in the path of ch.1, where the SMF + DCF is removed. It is shown that the power is high when the channels are overlapped (Δτ = 100 and 200 ps) and decreases as the channels become interleaved.
For the delay time monitoring, we insert a piezoelectric FS in the path of ch.2 and drive it with a small-amplitude dithering signal at 18 kHz. The monitored power then oscillates at this frequency and the amplitude of this frequency component, denoted as V, is detected by a lock-in amplifier (LIA). Then a LabVIEW program is used to control the delay time by varying the delay line inserted just after the FS to make sure that the channels are properly time-interleaved. The algorithm of the program is simple as shown in Fig. 8 : Δτ is changed by 1 ps every operating loop (200 ms) to keep V at zero, by which the monitored power P is minimized.
5. Performance investigation
Figure 9 shows bit error rates (BERs) as a function of received power for (a) ch.1 and (b) ch.2 when channels are properly time-interleaved. In this measurement, delay fluctuation from the variable delay line in the path of ch.1 is turned off and the SMF + DCF is removed. Back-to-back performance is measured after the mux stage. Total launched signal powers (the sum of ch.1 and ch.2) to the DDMF are 12, 13, and 14 dBm shown by circle, triangle, and square symbols, respectively. The figure shows that the performance without the limiter degrades as the signal power launched to the DDMF is increased. This is partly due to the enhanced translation from amplitude to phase fluctuations, or the enhanced nonlinear phase noise, and to the broadening of signal spectrum both in the DDMF when the signal power is increased. While for the performance with the limiter, it is almost unaffected by the change in the signal launched power, which shows the effectiveness of the limiter in suppressing amplitude noise. Note that there is a penalty about 3.5 dB for the signal transmission using the limiter as compared with the back-to-back case. This penalty is attributed to signal degradation in the transmission over the DDMF and also to generation of nonlinear phase noise and broadening of signal spectrum inside the HNLF in the limiter.
BER performance when the relative time delay between ch.1 and ch.2 is randomly changed is then measured. Time separation between ch.1 and ch.2 is intentionally changed by a speed of 4 ps/second from and to uniformly distribute random variables within 0 - 100 ps using the variable delay line in the path of ch.1. The SMF + DCF is also inserted to add some unintentional delay fluctuation, which is at most about ±1 ps/second during the measurement. Figure 10 shows BERs as a function of measured time for (a) ch.1 and (b) ch.2 when the limiter is operating in the system. Sum of the power of ch.1 and ch.2 launched to the DDMF is 12 dBm. Adaptive delay control is initially turned off and then, turned on during the measurement. The results show that BERs of ch.1 and ch.2 fluctuate from error free to BER ~10−2 when the delay control is turned off. On the other hand, when the delay control is turned on, BER below 10−9 is stably obtained for both channels. In this measurement, BER of ch.1 is a little worse than BER of ch.2, which is considered due to input signal degradation caused by the SMF + DCF inserted in the ch.1 input path. Corresponding BER performance when the limiter is removed from the system is shown in Fig. 11(a) and 11(b). The BERs are worse on the average than those in the system using the limiter with the adaptive delay control turned off. In the systems without the limiter, the BERs degrade when the pulses in ch.1 and ch.2 are overlapped in the DDMF. The causes of the performance degradation when the pulses are overlapped are considered to be the enhanced nonlinear phase noise mediated by cross-phase modulation  and generation of FWM products pumped by the pulses in ch.1 and ch.2.
An adaptive delay control technique for a multi-channel limiter based on saturation of FWM in a HNLF is demonstrated. The delay controller effectively handles delay fluctuation between two 10-Gbit/s DPSK signals with 0.8 nm spacing by speed of about 4 ps/second. Delay time between input signals is controlled by monitoring the change of an interchannel FWM power after the HNLF. In the control algorithm, 200 ms is consumed to renew the relative delay by 1 ps due to a slow processing speed of the conventional LabVIEW on a laptop computer, which limits the speed of delay variation adaptively controlled by this method to about 4 ps/second. The operation time can be significantly reduced by using faster control devices, which makes it possible to follow much faster delay variations.
For real applications in transmission systems, large number of channels should be able to be processed by the limiter, which is not an easy task. So far, we have demonstrated the multi-channel limiter for 3 channels x 10 Gbit/s  and discussed a suitable monitoring technique for adaptive delay control of 3-channel signals . For the time delay adjustment, the number of delay lines increases as the number of channels increases, which may be solved by using a wavelength-selective slow light technique .
Another issue when using large number of channels is the signal pulse width. A pulse compression stage before the limiter might be required to obtain short pulses for proper time-interleaving. It is noted that the pulse compression should be performed while the channels are demultiplexed because the pulse compression itself is a nonlinear processing so that simultaneous compression of asynchronous multi-channel pulses is difficult. The pulse compression prior to the limiter, therefore, will not be compatible with the configuration where the wavelength-selective delay control is performed without channel demultiplexing.
This work is supported in part by the Japan Society for the Promotion of Science Grant-in-Aid for Scientific Research (B) under Grant 20360171 and 23360171.
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