Simultaneous reshaping of optically time-division-multiplexed RZ-OOK and RZ-DPSK signals by a fiber-based regenerator is numerically demonstrated. The regenerator utilizes the four-wave mixing (FWM) in a highly nonlinear fiber. A parametric amplifier configuration without wavelength conversion of the signal is assumed, in which ultra-fast saturation of the FWM interaction gives stabilization of signal amplitude with the signal phase principally maintained. The regenerator greatly improves the performance of OOK tributaries. Although the regenerator does not have the function of phase regeneration, it improves the DPSK signal quality when the signal power is relatively low where the amplitude noise is significant. Influence of the pump phase modulation on the regenerator performance is also examined.
© 2006 Optical Society of America
In future photonic networks, a variety of optical signals having different modulation formats will be transmitted along the same optical fiber. In some cases, differently modulated signals with the same carrier wavelength will be multiplexed in the time domain as shown in Fig. 1. One such example is found in optical label switching networks where optical packets composed of differently modulated serial label and payload data are transmitted. In Ref. [1–3], combination of differential-phase-shift keying (DPSK) encoded labels and on-off keying (OOK) payload data was proposed and its usefulness for label swapping operation was demonstrated.
To extend transmission distance for such hybrid modulation signals without electronic regeneration, optical regenerators capable of simultaneous regeneration of different signal types will be highly desired. Although most of the all-optical regenerators studied so far have been designed to regenerate OOK signals without attention to preservation of signal phase, some recent works aim to realize phase regenerative or phase transparent signal regeneration [4–9].
In this paper, reshaping by a fiber-based regenerator of hybrid signals consisting of return-to-zero (RZ) OOK and RZ-DPSK signals that are optically time division multiplexed is numerically studied. The fiber-based regenerator using ultra-fast saturation of the four-wave mixing (FWM) interaction can suppress amplitude noise of OOK and DPSK signals while the phase information carried by the signal is well, although not perfectly, preserved. The issue of performance degradation in such regenerators caused by pump phase modulation is also discussed.
2. All-optical regenerator (limiter) using FWM in a fiber
Figure 2 shows the fiber-based optical limiter acting as an amplitude regenerator analyzed in this paper. It principally consists of a pump source, a highly nonlinear fiber (HNLF), and an optical bandpass filter (OBPF), which is similar to typical parametric amplifiers. The incoming signal experiences FWM interaction in the HNLF and is extracted by the OBPF without wavelength conversion, where the amplitude stabilization comes from the ultra-fast saturation of the FWM interaction . Although higher-order FWM components can be used for the purpose of 2R (reamplifying and reshaping) regeneration , the parametric amplifier configuration is adopted here because the pump-to-signal phase-noise translation is minimal in this configuration even when a single pump is used. For the purpose of DPSK reshaping, furthermore, the use of higher-order FWM components is inadequate because the phase fluctuation contained in the input signal will be amplified and, even worse, the binary phase information is totally destroyed by the even-order higher-order FWM interactions. In the parametric amplifier configuration, however, the zero-level noise cannot be removed. In order to obtain a true 2R function by removing the zero-level noise, we need to insert a saturable absorber (SA) as shown in Fig. 2. The SA may be omitted if only a few regenerators are to be cascaded. In the numerical study in this paper, the SA is assumed to have a power transmission coefficient of the form 
where T 0, P in(t), and P s are unsaturated transmissivity, input instantaneous signal power, and saturation power, respectively. Such a SA can be realized by ion-irradiated semiconductor quantum wells. A response time as short as 5 ps was reported . Although the transient dynamics of the device should be considered for precise characterization, it is neglected here for simplification of the analysis. T 0 and P s are 0.2 and 40mW, respectively, in the numerical simulation in this paper.
It is noted that the regenerator shown in Fig. 2 acts as an amplitude regenerator while the phase information is not regenerated. Nevertheless, the regenerator can improve the performance of PSK signal transmission if the amplitude noise dominates the signal degradation under the operation at low signal powers. This is particularly true when balanced detection is not used in the receiver. The nonlinear phase noise caused by the translation from amplitude to phase noise via the transmission-line nonlinearity (the Gordon-Mollenauer effect ) in long-distance systems may also be reduced by the suppression of amplitude noise . Cubical growth of the phase-noise variance as distance is expected to be mitigated to linear growth.
Phase regeneration can be realized by the use of phase sensitive amplifiers (PSAs), which can suppress phase noise of any origin of binary PSK signals [5, 9, 16]. PSAs, however, are very difficult to realize in the real world because optical pump sources whose carrier phase is locked to the signal phase should be provided in the PSA. They, in addition, are not compatible with regeneration of multi-level PSK signals such as quadrature PSK.
3. Influence of pump phase modulation on the regenerator performance
To achieve appreciable FWM interaction in fibers, one has to increase the power of the pump wave to a level larger than, typically, tens of milliwatts. At these power levels, however, continuous-wave (CW) pump cannot penetrate into the fiber because of the backward stimulated Brillouin scattering (SBS). A commonly-employed method to reduce SBS is to apply phase modulation to the CW pump. Although the pump phase modulation is not directly translated to phase modulation on the signal in the parametric amplifier configuration, the resulting frequency modulation of the pump leads to gain modulation [17, 18]. This is a serious problem in realizing high-gain parametric amplifiers especially using a single pump wave. This section examines the influence of the pump-phase modulation on the performance of the FWM-based regenerator in parametric amplifier configuration.
In the ideal condition that the fiber loss is neglected and the polarization effects are ignored, the small-signal power gain of the parametric amplifier using a single pump is given analytically by 
where γ, P 0, and g are the nonlinear coefficient of the fiber, pump power, and gain coefficient, respectively. The gain coefficient is given in terms of the even-order dispersion coefficients at the pump frequency as
where ω is the difference between signal and pump angular frequencies. In Eq. (3) dispersion coefficients up to the fourth order are included.
Figure 3 shows an example of the parametric amplifier gain given by Eq. (2) for different pump powers. Length, nonlinearity, and dispersion coefficients of the HNLF are 1.5km, γ=16.2/W/km, β 2=-0.23 ps2/km, and β 4= -5x10-55 s4/m. When the peak gain is high as in usual parametric amplifier applications, the gain is not flat but varies significantly with the frequency difference between signal and pump. This is the cause of the detrimental gain modulation when the pump phase is modulated [17, 18]. The gain modulation is largest at inflexion points of the gain curve. In the regenerator application discussed here, we do not need to have large gain. The pump power, therefore, can be much lower, which leads to much smaller gain variation with the signal-pump frequency difference. The influence of pump-phase modulation is thus much smaller.
The discussion above is based on the small-signal gain, given by Eq. (2), without considering pump depletion. When we consider depleted-pump cases, which are relevant to the regenerator (limiter) applications, full numerical simulation of the modified nonlinear Schrödinger equation is needed. Figure 4 shows numerical results of the parametric gain for different signal powers input to the HNLF for a pump power of 30mW. The fiber loss is again neglected to confirm agreement of the gain curve with that obtained analytically for small input power (0.1mW). The parametric gain begins to saturate at a input signal power as small as a few milliwatts. Although some gain excursion as the pump frequency moves appears in the gain-saturated regime, the gain variation is still small as compared with that in large-gain parametric amplifiers. Figure 5 shows an example of the numerically obtained power transfer function of the regenerator for a CW input signal. Length and nonlinear coefficient of the HNLF are the same as those used in the calculation of Fig. 3. Dispersion slope, γp-γs,γs-γ0 (γp, γs, and γ0 are the pump, signal, and zero-dispersion wavelengths, respectively), and pump power are 0.03ps/nm2/km, 3nm, 3nm, and 30mW, respectively. Loss of the HNLF, 0.5dB/km, is considered. Random binary phase modulation (0~π rad) at a speed of 2.5Gb/s with 10-90% rise/fall time of 30ps is imposed on the pump. The solid curve in Fig. 5 is the averaged output power, which clearly shows saturation of the FWM interaction. Dashed curves are the maximum and minimum instantaneous output powers that occur at instances corresponding to the phase transition of the pump modulation. The instantaneous variation of the output power is shown to be small. In actual implementation, the influence of the pump phase modulation will be further smaller because the magnitude and steepness of the phase modulation can be smaller than those assumed here for the suppression of SBS by the relatively weak pump power ~ 30mW.
4. Simultaneous reshaping of RZ-OOK and RZ-DPSK signal
As a numerical demonstration of the regenerator’s ability to reshape OOK and DPSK signals simultaneously, we simulate long-distance transmission of bit-interleaved short-pulse RZ-OOK and RZ-DPSK signals periodically reshaped by the regenerators. Four 10Gb/s tributary channels, two of which are modulated in RZ-OOK format and the other two of which are modulated in RZ-DPSK format, are assumed to be optically bit-interleaved multiplexed to form a 40Gb/s pulse train. Each pulse in the train has an initial width of 7ps. Figure 6 shows an example of optical eye pattern of the multiplexed 40Gb/s signal. Ch.1 and 3 (ch.2 and 4) are modulated in OOK (DPSK) format. The transmission system is a quasi-linear highly-dispersed pulse transmission system, where each amplifier span (80km) consists of equal lengths of a standard single mode fiber (SMF) and a reversed dispersion fiber (RDF) with zero span-averaged dispersion. Dispersion, nonlinearity, and loss of SMF (RDF) are 17 (-17) ps/nm/km, 1.3 (4.5) /W/km, and 0.22 (0.27) dB/km, respectively. The in-line amplifiers have a noise figure of 5dB. At the receiver the signal is optically demultiplexed with rectangular-shaped ideal gates of width 25ps after passing an optical bandpass filter with bandwidth 150GHz. For DPSK tributaries, the signal is balanced-detected after a delayed interferometer with a 100ps delay. Cutoff frequency of the electrical low-pass filter is 7.5GHz for both OOK and DPSK tributaries. For the FWM-based signal regenerators, a preamplifier is placed in front of the SA, which amplifies the signal to a level that saturates the FWM interaction in the HNLF. Bandwidth of the OBPF after the HNLF is 150GHz.
Figures 7(a) and 7(b) are examples of eye patterns for OOK and DPSK tributaries, respectively, after the electrical low pass filter. The signal quality is quantified by the eye-opening (EO) degradation defined by -10 log[ERPT/(ETPR)], where E R(T) is the eye opening at the receiver (transmitter) and P R(T) is the average signal power at the receiver (transmitter). The decision time is optimized in a bit slot. It is noted that the eye opening E R(T) for DPSK tributaries are evaluated on the eye pattern after the demodulator as shown in Fig. 7(b).
Figure 8 is the maximum transmission distance, which is defined as the distance beyond which the EO degradation is larger than 2dB, versus the averaged signal power for the multiplexed 40Gb/s pulse train Pave. Averaged signal powers for OOK and DPSK tributaries are Pave/6 and Pave/3, respectively. Figure 8 shows that RZ-DPSK transmission outperforms RZ-OOK transmission when regenerators are not used. When regenerators are inserted every 6 spans (480km), the performance of RZ-OOK signals is significantly improved for signal powers in the range 0<Pave <4dBm. The regenerators also improve RZ-DPSK performance. The extent of the improvement for DPSK signals, however, is smaller than that for OOK signals because the phase information is not regenerated but only maintained. The improvement for the DPSK signals is seen for smaller signal power, Pave<1dBm, where the amplitude noise diminishes the eye opening when regenerators are not used. For larger signal power, Pave>2dBm, the DPSK transmission performance is mainly determined by the phase noise. In the transmission system assumed in this paper, the phase noise at high signal powers largely comes not from the Gordon-Mollenauer effect but from intrachannel FWM that directly induces phase noise without mediation of amplitude noise. In this case, the reduction of phase noise by the suppression of amplitude noise is not appreciable.
Figure 9 shows an example of optical eye pattern of the signal reshaped by the regenerator. Transmission distance and the signal power are the same as those in Fig. 6. Regenerators are inserted every six spans. Eye opening is shown to be improved by the regenerators as compared with the eye pattern given in Fig. 6. Figures 10(a) and 10(b) show electrical eye patterns of demultiplexed tributaries corresponding to ch.1 (OOK) and ch.2 (DPSK), respectively,
Figure 11 is the EO degradation versus transmission distance for (a) OOK and (b) DPSK tributaries for a fixed signal power of Pave =1dBm. Regenerators are inserted every 1,3,6, or 9 spans. For OOK signals, lager performance improvement is obtained for more frequent insertion of regenerators. For DPSK signals, on the other hand, frequent insertion of regenerators is harmful because small but finite extra phase noise is added to the signal at each regenerator. This indicates that the main benefit of the fiber-based regenerator analyzed in this paper is in the improvement of OOK transmission performance. As for DPSK signals moderate or marginal improvement is obtained unless the regenerators are inserted too frequently. An important feature of the regenerator is that the phase information of the signal is not destroyed. The regenerator can be used in systems in which both OOK and DPSK signals are simultaneously transmitted. The regenerators extend reach of OOK signals which is usually smaller than DPSK signals.
Simultaneous reshaping by a fiber-based all-optical 2R regenerator of RZ-OOK and RZ-DPSK signals that are bit-interleave multiplexed was numerically demonstrated. The regenerator significantly improves the signal quality of OOK tributaries. For DPSK tributaries, phase information is not destroyed by the regenerator and their performance is improved for low signal powers where amplitude noise degrades the signal quality.
Influence of the pump phase modulation on the operation of the FWM-based regenerator was also examined.
This work is supported by the National Institute of Information and Communications Technology (NICT) and by the Japan Society for the Promotion of Science (JSPS) Grant-in-aid for scientific research S13852010.
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