Multi-wavelength regeneration free of inter-channel crosstalk is desirable for wavelength division multiplexing (WDM) systems, especially from the cost-effectiveness point of view. This paper presents the design rules of time-interleaved multi-wavelength 2R regeneration systems based on data-pump four wave mixing (FWM) effect, and several key factors, such as FWM bandwidth, wavelength assignment, and duty cycle, are comprehensively taken into account. The total data rate of time-interleaved WDM regeneration systems along with polarization multiplexing or bidirectional transmission are discussed, which are mainly determined by temporal overlap, spectral broadening and FWM bandwidth. As two examples, an eight-wavelength unidirectional regenerator using polarization multiplexing is designed by optimizing the fiber birefringence, and a six-wavelength bidirectional regenerator is demonstrated by experiment. Each is expected to have a total data rate of about 200Gb/s for the optical RZ-OOK signals, and the wavelength number is increased at the expense of spectral efficiency.
© 2014 Optical Society of America
To achieve more data capacity in fiber communication systems, researchers are pursuing either more signal channels or higher spectral efficiency for each channel. The former corresponds to multiplexing techniques such as wavelength division multiplexing (WDM)  and space division multiplexing (SDM) . The latter mainly corresponds to advanced modulation formats . The signal formats from OOK to QPSK/QAM have in turn been used in the fiber communication systems as well. At the same time, all-optical signal processing technologies, such as signal regeneration, format conversion, optical logic gates, optical sampling, are capable of overcoming the bandwidth limitation of optical-electronic-optical (OEO) conversion and then have potential applications to ultra-high speed communication systems . Among these functions, all-optical regeneration can compensate for the signal distortion induced by fiber dispersion, attenuation, nonlinearity, polarization mode dispersion and ASE noise . Clearly, from the cost-effectiveness point of view, the multi-wavelength regenerators just like EDFAs are always beneficial for WDM signals, regardless of the data format per wavelength.
The well-controlled all-optical regeneration can be obtained in fibers due to its pure and stable nonlinearity with ultrafast response time . The self-phase modulation (SPM)-based all-optical regenerator of OOK signals was originally proposed by Mamyshev  and further investigated extensively [7–10]. The 2R/3R regeneration can also be achieved by cross-phase modulation (XPM)  and four-wave mixing (FWM) [12–15]. And then, two- or four-wavelength regeneration based on SPM and FWM in a single highly nonlinear fiber (HNLF) was achieved by time-interleaving [16, 17], polarization multiplexing , bidirectional transmission  or the combination of these techniques [20–22]. We have made a throughout investigation on the three crosstalk suppression methods in  and demonstrate four-wavelength data-pump FWM based regeneration by using time-interleaving, bidirectional transmission and offset filtering in . Other techniques, such as dispersion management [25, 26], quasi-continuous filtering  or nonlinear optical loop mirrors (NOLM) with filtering  are also useful for multi-wavelength regeneration, but they often need multiple HNLF sections.
All-optical regeneration of advanced modulation formats is also developing recently. Initial schemes focused on phase-preserving amplitude regeneration  or phase regeneration based on format conversion and amplitude regeneration . The direct phase regeneration of DPSK signals were proposed by using NOLM  or phase-sensitive amplification , and the practical ‘black-box’ regeneration of DPSK signals was demonstrated later with injection-locking technique [33, 34]. Recently, the regeneration of multi-level signals is drawing more attentions. Multi-level nonlinear phase response can be provided by phase-sensitive amplifiers , and phase regeneration of QPSK was demonstrated . The regenerative performance for cascaded regenerative phase sensitive amplifiers has been investigated in [37, 38]. A novel scheme for multi-level amplitude regeneration based on NOLM is also proposed in . By comparison, few researches on multi-wavelength regeneration of advanced modulation formats have been published until now, except for a dual-channel regeneration scheme for DPSK signals based on phase-sensitive amplification . Clearly, the multi-wavelength regeneration of multi-level signals is much harder than that of OOK signals.
Nowadays, the multi-wavelength 2R/3R regenerators for RZ or NRZ OOK signals have not been applied to the practical WDM systems due to the limited wavelengths, let alone for the higher-order modulation signals, which are associated with amplitude and phase regeneration. The performance degradation of multi-wavelength regeneration mainly results from the inter-channel crosstalk induced by XPM and FWM. Some inter-channel crosstalk suppression methods for the RZ/NRZ OOK signals may as well be useful for other modulation formats. Therefore, we believe that it is valuable for a comprehensive investigation on the limiting factors of multi-wavelength regeneration, regardless of the data formats.
In this paper, the data-pump FWM-based multi-wavelength regeneration for RZ-OOK signals is taken into account. Compared with SPM-based regeneration, FWM-based regeneration possesses some unique properties in wavelength conversion and 3R regeneration . The resulting wavelength conversion has also some potential applications in wavelength routing  and phase conjugation  in spite of the different frequency spacing at the input and output in this case, which is probably desirable for flexible spectrum optical networks, just like liquid crystal on silicon (LCoS) technique .
This paper is organized as follows: Section 2 first presents the design rules of multi-wavelength regeneration for time-interleaved RZ signals, including FWM bandwidth, wavelength assignment, duty cycle, and so on. In this section, polarization multiplexing and bidirectional transmission are also discussed for further improving the regeneration capacity. As two applications of the design rules, the unidirectional (eight-wavelength) and bidirectional (six-wavelength) regeneration systems are respectively implemented by simulation and experiment in Section 2 and Section 3. Section 4 gives the conclusions.
2. Design rules of multi-wavelength regeneration for time-interleaved signalsEq. (1) into the well-known wave equations , the following coupled-mode equations are given by :Eq. (2), for the case of , otherwise ; if the coupled waves have the same polarization,, otherwise. The terms with , or and , are responsible for SPM or XPM, and the others are attributed to the FWM terms. The x- and y- polarization are aligned with the principal axis of the HNLF.
In the data-pump FWM along with single auxiliary optical wave, the degenerate FWM terms are desirable for multi-wavelength regeneration, which are related to the input (regenerating) and output (regenerated) waves and the auxiliary light, and the other FWM products as well as all XPM terms as the sources of crosstalk should be suppressed. Thus, the wavelength distribution of the input channels and the auxiliary wave should appropriately be chosen within the FWM bandwidth, dependent on the temporal and spectral properties of input pump signals.
2.1 FWM bandwidth and wavelength assignment
The number of regenerative channels can be analyzed according to the FWM bandwidth to a great extent. For the data-pump FWM process, the interaction between the pump wave (input signal) and the auxiliary (probe) light gives rise to the first-order idler wave as the regenerated signal. The corresponding phase-mismatching factor can be expressed as follows:Eq. (3) can also be written as:Fig. 1, in which the pump and auxiliary powers are respectively 20dBm and 14dBm, and the other parameters used in the paper are listed in Table 1. From Fig. 1(a), the frequency relationship of may also be illustrated by the y-axis as follows: for any given auxiliary light (dashed line), the idler powers (solid line) are determined by the pump frequencies (y = x line), and then the FWM bandwidth for the data-pump FWM case is defined by the pump frequency range according to the idler power and the receiver sensitivity. For example, when the auxiliary frequency is 192.1THz, the −10dB FWM bandwidth is, as shown in Fig. 1(b). In other words, the FWM bandwidth can be optimized by shifting the solid line, which means the change of auxiliary frequency. Thus, the total bandwidth of N input channels should not be larger than, that is,
On the other hand, the wavelength assignment should appropriately be designed for avoiding the spectral overlap between the higher-order FWM products and the first-order idlers as regenerated signals, that is,Fig. 2. The frequency spacing of the nth order idlers is (n + 1), in which is the frequency spacing of the input channels.
2.2 Duty cycle of time-interleaved signals
In principle, the time-interleaving scheme can effectively suppress the inter-channel crosstalk when the pulse width is less than for N time-interleaved channels, in which is the bit period of each channel, corresponding to the data rate and the duty cycle (DC). Actually, in the multi-wavelength regeneration, the duty cycle can further be optimized by means of the inter-modulation (IM) parameter:23].
Figure 3 shows the dependences of IM on DC for the different multi-wavelength cases with the pump frequency spacing of and the data rate of . From Fig. 3(a)-(e), the optimal DC range decreases with the increase of the time-interleaved wavelength number. It is shown by simulation that, the upper limit of optimal DC is approximately 0.5/N, almost independent of the data rate; in other words, the temporal overlap will occur when the pulse width is more than 0.5/N or so, which depends on the pulse broadening properties due to the dispersion and nonlinearity of fibers. On the other hand, for the different multi-wavelength cases, the lower limits of DC have small differences, which means that there exists a minimal pulse width free of crosstalk, or a largest spectral broadening acceptable for the regeneration scheme by spectral filtering. From Figs. 3(a)-3(c), and in Figs. 3(d)-3(e). Thus, for N time-interleaved signals, the optimal DC range at the data rate can be represented by:
Short pulse RZ signals should be obtained by using a pulse compression unit for multi-wavelength regeneration. According to Eq. (7), for aligned time-interleaved N-wavelength signals, the maximal pulse width and the time delay between the adjacent channels must be and , respectively. In other words, the time delay should be two times bigger than the pulse width to avoid the crosstalk. Thus, when , the temporal aligning tolerance of time-interleaved signals satisfies:
According to Eq. (7), the maximal data rate approaches to the value of for a given minimal pulse width and then the total date rate of regeneration can be obtained as follows:Fig. 4 and the slope of the lower DC limit can be determined by . Two time-interleaving cases with or without polarization multiplexing are given here, and the latter will be discussed in the following part.
From Eqs. (5) and (7), the number of regenerative channels is mainly determined by the combination of FWM bandwidth, wavelength assignment and duty cycle for a given data rate. The detailed design rules can be summarized as follows:
- i) The input pump signals should be chosen in the range of FWM bandwidth, which is determined by the auxiliary frequency and power as well as the fiber parameters.
- ii) The frequency spacing between the auxiliary and pump waves should be large enough to eliminate the impact of the higher-order FWM products on the regenerated channels, that is, the total bandwidth of input signals is no larger than .
- iii) For avoiding the interferences resulting from temporal overlap and spectral broadening, Eq. (7) should be satisfied for the data-pump FWM-based regeneration systems.
2.3 System upgrade using polarization multiplexing
For the time-interleaved optical signals with parallel states of polarization (SOPs), the temporal overlap between the signal pulses may produce strong XPM and FWM and then brings about the inter-channel crosstalk. However, if the SOPs are orthogonal to each other, the degenerate FWM between the pump signals can be suppressed and the nonlinear coefficient of the XPM terms is reduced to 1/3 according to Eq. (2). The XPM and non-degenerated FWM processes between two orthogonal states of polarization can be suppressed by introducing fiber birefringence related to and . Thus, the nonlinearity-induced spectral broadening or the resulting crosstalk is also decreased, i.e., polarization multiplexing can be used to upgrade the wavelength number of the regeneration systems by further suppressing the crosstalk. In other words, the minimal duty cycle of the time-interleaving channels can become smaller if the polarization multiplexing technique is utilized, and the double total date rate is expected.
As an example, a four-wavelength time-interleaving system with polarization multiplexing is taken into account and the SOPs of the odd and even channels are respectively aligned to two birefringent axes of the HNLF, as well as the 45° linearly polarized auxiliary light. In this case, the DC dependences of IM are plotted in Fig. 5, in which the power of the auxiliary light is 17dBm, the differential group delay (DGD) of the HNLF is 0 or 60ps/km, and the other parameters are the same as used in Fig. 3(c). From Fig. 5, the lower DC limit () is approximately reduced to an half of that in the presence of polarization multiplexing. However, the upper DC limit can further be optimized by choosing a proper DGD value for eliminating the non-degenerate FWM crosstalk between the regenerative channels [12, 21]. As shown in Fig. 5(b), the maximal DC is up to 0.25 for the DGD of 60ps/km, just as in the dual-wavelength case without polarization multiplexing, referring to Fig. 3(a). Thus, the maximal total date rate of the polarization multiplexing system is rewritten as follows:Fig. 4 shows the relation between the duty cycle and the bit rate using polarization multiplexing, and the total data rate for the four- or six-wavelength regeneration can be increased to 500Gb/s, which is five times that without polarization multiplexing.
The accuracy of polarization alignment can also be investigated by calculating the IM value. The results show that the accuracy of polarization alignment is dependent on the fiber birefringence and the duty cycle. For example, if polarization multiplexing is applied to the four-wavelength regeneration with the fiber DGD of 60ps/km and the duty cycle of 0.25, the azimuth deviation corresponding to 0.5dB IM is about 2°. Time and polarization alignment are more complicated for practical communication systems, especially for those of variable delay times or time-dependent polarizations, in which an intelligent tracking technique needs to be developed. For example, a smart polarization controller can lock the output polarization to a specific state and programmable optical delay arrays can adjust the time delays of multiple channels. Certainly, for polarization-insensitive regeneration schemes of time-interleaved signals, the polarization controllers aren’t needed .
2.4 Design of an eight-wavelength unidirectional regeneration system
According to the previous discussion, we designed a time-interleaved eight-wavelength unidirectional regeneration system, as shown in Fig. 6. The adjacent regenerating channels have a frequency spacing of 100GHz and their SOPs are orthogonal to each other. The DC of each channel is set to 0.1 for 10Gb/s 210-1 PRBS data, and the birefringent HNLF has a DGD of 60ps/km for effectively suppressing the crosstalk. The degradation of the optical RZ-OOK signals is emulated by introducing the amplitude fluctuation units after the different optical transmitters for data independency. The time-interleaved signals can be obtained by setting the different delay times. The pump powers of all channels are optimized for simultaneously reducing the amplitude noise on ‘one’ and ‘zero’ as possible. The OptiSystem simulations show that the Q improvement is approximately from 9 to 16 for all channels and the Q values of the input and output signals are also shown in Fig. 7. It is evident that the eight-wavelength regeneration system is capable of operating at the total data rate of 80Gb/s. In fact, according to Fig. 3(c) and Eq. (10), the total date rate of this system can be up to about 200Gb/s, with the bit rate of 25Gb/s per channel.
The spectral efficiency () after regeneration can be evaluated according to the total data rate, wavelength number and frequency spacing as follows:
3. Experiment of time-interleaved six-wavelength regeneration using bidirectional transmission
The regeneration capacity can further be increased by the bidirectional transmission technique, which can double the capacity in principle. In the bidirectional transmission, the crosstalk mainly comes from the nonlinear Rayleigh or Brouillon scattering and power leaking of the circulators [19, 49]. In particular, the crosstalk is not negligible when a regenerated channel has a superposition with a backward-propagating pump signal or auxiliary light. In this case, the offset filtering method can be used to improve the performance of the regenerated channel . As a result, the design of a bidirectional regenerator can be implemented by combining two unidirectional systems for simplicity.
In this paper, a time-interleaved six-wavelength regeneration using bidirectional transmission technique is demonstrated experimentally. In each transmission direction, the frequency spacing of the pump signals is , and the regenerated signals are produced by the degenerate FWM couplings with the different auxiliary light, as listed in Table 2. The regeneration system consists of a multi-wavelength signal generator, a channel control unit, the bidirectional all-optical regenerator and an optical receiver, as shown in Fig. 8.
The multi-wavelength signal generator generates a serial of PRBS pulses at six wavelengths by pulse compression technique for time interleaving . In our experiment, the optical RZ signals with the pulse width of 35ps are firstly obtained from the WDM optical transmitter twice-modulated by 10GHz clock and 231-1 PRBS data with 1/8 mark possibility, and then the optical pulses are compressed to 15ps by use of a phase modulator and a dispersion compensation fiber with the total dispersion of −113ps/nm. Finally, the DC is reduced to 0.15 for the bit rate of 10Gb/s, which is desirable for time interleaving of three wavelengths, just as in Fig. 3(b). The signal degradation is emulated by tuning the bias voltages of the modulators.
The channel control unit is used to achieve the degraded time-interleaved signals. The adjacent pump channels have a relative delay time of about 33.3ps and then are amplified by a high-power EDFA. The following de-multiplexers and multiplexers remove the outband ASE noise and synthesize the time-interleaved signals. At the same time, the data pattern correlation effect can also be avoided by introducing some bits’ delay using the optical delay lines and the fiber patch cords.
Then, the degraded time-interleaved signals (S1~S6), together with the auxiliary waves (A1 and A2), are coupled into the bidirectional regenerator with the auxiliary power of 14dBm. In the optical receiver, the regenerated signals (R1~R6) are selected by the tunable optical band pass filter (TOBPF, OTF-350, Santec, Japan) and then are converted into the electronic domain by an O/E detector after the variable optical attenuators (VOAs) and the EDFA as pre-amplifier. The waveform and performance of the regenerated signals are measured by the optical sampling oscilloscope (PSO-120, EXFO Corporation, Canada) and the digital serial analyzer (DSA8300, Tektronics, USA).
Figure 9 gives the FWM spectra measured at the 1% output ports of 1:99 optical splitters at two ends of the HNLF. By carefully tuning the EDFA gain and the attenuation of every channel, the pump powers of all channels are optimized to achieve a good regeneration performance. From Fig. 9, the reflection of the input pumps and the CW auxiliary waves are weak, and the pumps and idlers do not overlap in frequency domain. The FWM efficiencies for the forward channels are higher than those for the backward channels due to the different wavelength distributions. Certainly, the higher-order FWM products are also obvious in forward case, but they are separated from the regenerated idlers in the frequency domain. Thus, the bidirectional system can be divided into two unidirectional regenerators. Typical spectral broadening induced by SPM and XPM is also observed from Fig. 9, and the regenerated idlers have wider spectral lines than the input pumps.
The measured eye diagrams of the input and multi-channel regenerated signals the are given in Fig. 10 and the measured BER curves of six channels in single- and multi-wavelength cases are illustrated in Fig. 11. In the experiment, the central wavelength of the optical filter is slightly offset for the optimization of the regeneration performance. For multi-wavelength regeneration, the receiver sensitivities are respectively improved by 2dB, 1dB and 2.6dB for the forward channels R1~R3, and 2.4dB, 1.9dB and 1.5dB for the backward channels R4~R6. From Fig. 9, the FWM product resulting from A1, S1 and S3 has an influence on the performance of the regenerated channel R2 and leads to a smaller sensitivity improvement. The experimental data are in agreement with the simulation results, corresponding to the case with three wavelength regeneration, as shown in Fig. 3(b). According to the design rule mentioned above, the total date rate of the experimental system is about 200Gb/s, which is expected to increase to more than 400Gb/s by further applying polarization multiplexing.
We present the design rules of time-interleaved multi-wavelength 2R regeneration systems based on data-pump four wave mixing (FWM) scheme, mainly involved in FWM bandwidth, wavelength assignment, and duty cycle. The total date rate for the cases with or without polarization multiplexing is discussed by the OptiSystem simulation. It’s shown that the regenerative wavelength number or the total data rate is restricted by temporal overlap, spectral broadening and FWM bandwidth. By appropriately choosing the fiber birefringence, an eight-wavelength unidirectional regenerator is designed using polarization multiplexing and significant Q improvement is obtained for the optical RZ signals of 10Gb/s per channel. The calculation also shows that the regenerative wavelength number is increased at the expense of the spectral efficiency. A six-wavelength bidirectional regenerator is experimentally demonstrated and the receiver sensitivity improvements of all regenerated channels are more than 1dB. The regeneration systems given in Sections 2 and 3 are expected to have a total date rate of about 400Gb/s if all of three crosstalk suppression methods are applied to the regenerators.
This work is supported by the National 973 Program of China (2011CB301703), National 863 Program of China (2013AA014402) and Natural Science Foundation of China (61271166).
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