1. Introduction

Differential phase-shift-keying (DPSK) data signal exhibits remarkable transmission performance owing to its high tolerance to nonlinear impairments in optical fibers. For direct-detection of DPSK signal, a demodulator is required to convert the phase modulation to intensity modulation before the signal is fed to a balanced or a single-ended detector. Balanced detection grants DPSK format a ~3-dB lower requirement on optical signal-to-noise ratio (OSNR) compared to amplitude shift-keying format at a given bit-error rate (BER), while single-ended detection of DPSK is favored for its simplicity and low cost. DPSK demodulator is also useful in generating optical duobinary (DB) format [1], bypassing the bandwidth limitation of electronic devices. The demodulation of DSPK signals has been achieved by different approaches. Examples include the use of a delay interferometer (DI) based on fiber [2] or silicon-on-insulator (SOI) [3], a birefringent fiber loop [4], a fiber Bragg grating (FBG) [5], a stimulated-Brillouin-scattering-based optical filter [6] and a silicon microring resonator [7]. Among them, DI is the most commonly used structure.

For a conventional DI, the delay is usually fixed for DPSK demodulation at a given bit-rate. However, DI with a tunable delay is useful for various applications. It allows DPSK demodulation at variable bit-rates to meet the need for dynamic bandwidth allocation. Another scenario is in the optimization of delay time to increase the chromatic dispersion tolerance of the system [8]. In addition, an optically time-division-multiplexed (OTDM) DPSK data stream can use a delay-tunable demodulator to perform multibit delay demodulation, where a fine tuning of the delay time is also required to control the detrimental bit-delay mismatch [9]. Apart from DPSK demodulation, cascaded DIs with different delays can be used to perform real-time optical fast Fourier transform to demultiplex an optical OFDM signal [10].

Previously, DI with a tunable delay from 0 to 200 ps has been demonstrated using a tunable differential-group-delay element [11]. For a larger tunable range, the combination of wavelength conversion and dispersion is ready to be used. Based on this method, we have recently demonstrated DPSK demodulation with widely continuous bit-rate tunability using a delay asymmetric nonlinear loop mirror (DANLM) [12,13]. In the DANLM, the wavelength conversion is based on four-wave mixing (FWM) in a 64-m photonic crystal fiber (PCF), while a 10-ps/nm dispersion is provided by a 600-m single mode fiber (SMF). The bulkiness of the DANLM can be a concern in some applications. For miniaturization, a silicon waveguide [14] can be used to replace the nonlinear PCF, while a chirped FBG (CFBG) offers a means to provide tens of ps/nm dispersion over a short fiber segment. Unfortunately, the CFBG cannot be used in a loop structure since it operates in a reflection manner. To overcome this problem, we propose a straight-line structure that incorporates the CFBG and verify the operation of variable bit-rate demodulation [15]. In this paper, we explain the role of two FWM processes in the structure as similar to phase sensitive amplification based on cascaded FWM. We further demonstrate that in addition to achieving bit-rate variable demodulation, a 0-phase or π-phase shift can be introduced to switch the demodulated signal into an optical DB or alternate mark inversion (AMI) format. The precise phase control may also be useful for OFDM demultiplexing [10]. NRZ/RZ-DB/AMI signals at 10 Gb/s and 5 Gb/s are successfully generated and the performances are characterized by BER measurements.

2. Operation principle

Figure 1 illustrates the scheme of DPSK demodulation based on cascaded FWM. The principle is similar to that of phase sensitive amplification [16]. The first FWM generates idler 1 which is then automatically phase-locked to the signal and the pump. The phase of idler 1 is determined by the signal phase and pump phase as${\varphi }_{I1}(t)=2{\varphi }_p-{\varphi }_s(t)$. Since the pump is CW with a linewidth of ~100 kHz (Agilent HP 8168F), it is not necessary to consider its phase variation over time compared to the phase-modulated signal. After a delay time T is introduced between the signal and idler 1, the second FWM is initiated to amplify or to attenuate the idler through the interference between idler 1 and idler 2. The amplification or attenuation is determined by the phase difference between the signal, the pump, and idler 1 in the second FWM,

 

Fig. 1 Principle of DPSK demodulation based on cascaded FWM. S: signal; P: pump; I: idler.

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The delay time T is generated based on a combination of wavelength conversion and dispersion. For a given dispersion coefficient, T is determined by the wavelength shift between the signal and idler 1, which is adjustable by tuning the pump wavelength. If T is set to one bit period of a DPSK signal, the idler power after the cascaded FWM processes will depend on the phase difference between two neighboring bits in the data sequence, converting the phase modulation to intensity modulation. In our setup, the delay time T is introduced in a CFBG with a 20-ps/nm dispersion. By tuning the pump wavelength of FWM, one-bit delay can always be generated for DPSK signals at variable bit-rates to achieve the demodulation. Moreover, additional 0-phase or π-phase shift can be introduced between the signal and idler 1, thus switching the output between DB and AMI formats that appear respectively at the constructive and destructive ports of a conventional fixed-delay DI. The wavelength resolution of our CW pump is 0.001 nm, corresponding to a minimum phase shift of ~0.05π for a 20-ps/nm dispersion. To introduce a π-phase shift, the pump wavelength should be shifted by 0.02 nm to yield a 0.04-nm shift of the idler wavelength.

3. Experimental results and discussion

Figure 2 shows the experimental setup of our bit-rate variable DPSK demodulator. The FWM-based wavelength conversion is performed in a 41-m PCF. The PCF is placed between two polarization controllers to overcome polarization change caused by the PCF birefringence. Following the PCF, a CFBG provides a flattened dispersion of 20 ps/nm and a reflectance of 99% over the range of 1535 to 1565 nm. An optical circulator and a bandpass filter with a 3-dB bandwidth of 0.6 nm are used to extract the idler output.

 

Fig. 2 Setup of the bit-rate variable demodulator. TL: tunable laser; PM: phase modulator; MZM: Mach-Zehnder modulator; EDFA: erbium-doped fiber amplifier; PC: polarization controller; BPF: optical bandpass filter; PCF: photonic crystal fiber; CFBG: chirped fiber Bragg grating; BER: bit error rate.

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The DPSK transmitter consists of a tunable laser, a phase modulator driven by a PRBS (2³¹-1), and a Mach-Zehnder modulator (MZM) driven by a clock. When NRZ-DPSK signal is used as the input, the MZM is turned off. The DPSK signal is combined with a wavelength tunable CW pump before they are amplified by an EDFA to a total power of ~26 dBm. The first stage of FWM takes place when the signal and the pump propagate through the PCF towards the CFBG. After the reflection from the CFBG, the pump, the signal, and the generated idler 1 will travel through the PCF again in the opposite direction. Owing to the high reflectance of the CFBG, the optical power loss results mainly from the splice between the PCF and the CFBG. The loss is ~2.5 dB in our setup such that the second stage of FWM is still effective. Idler 1 experiences a tunable delay with reference to the signal in the CFBG according to its wavelength, which is controlled by the CW pump wavelength. When the delay is set to one bit period of the corresponding data rate, the phase difference between two neighboring bits of the DPSK signal will determine an amplification or attenuation of idler 1, resulting in DPSK demodulation at variable bit-rates.

To verify the demodulation principle, Fig. 3 shows the eye diagrams and spectra of the idlers obtained from 10-Gb/s RZ-DPSK signal measured at three different positions in the setup, indicated as A, B, and C in Fig. 2. These are the idlers obtained after the first stage of FWM, behind the CFBG, and after the second stage of FWM, respectively. At points A and B, both the eye diagrams and the spectra agree with those of a DPSK signal without demodulation [17], implying that demodulation is achieved neither by a single FWM process nor by the filtering of the CFBG. Only after two stages of FWM, the phase modulation is converted to intensity modulation. By slightly tuning the CW pump wavelength, an additional phase shift of 0 or π can be introduced to generate an output in DB format or AMI format, respectively, as shown in Figs. 3(c) and 3(d).

 

Fig. 3 Eye diagrams and optical spectra of the idlers centered at 1555 nm. (a) after the first FWM, (b) behind the CFBG, (c) after the second FWM with 0-phase shift, and (d) after the second FWM with π-phase shift. The measurement positions correspond to points A, B, and C in Fig. 2. Inset: incomplete depletion of idler 1.

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It is worth mentioning that the splicing loss between the PCF and the CFBG results in a difference of the signal powers in the two stages of FWM, possibly leading to incomplete depletion of idler 1 and hence a degraded extinction ratio (ER) of the demodulated signal, as shown in the inset of Fig. 3. We experimentally find that the ER can be improved by changing the signal-to-pump power ratio to a positive value of ~3 dB, unlike the usual case where the ratio is negative to keep the signal weaker than the pump. With the adjustment, the residual power of bit 0 in idler 1 is reduced, as shown in the other two eye diagrams in Fig. 3. One also notices a finite signal distortion of AMI format compared to DB format. It can be explained by the discrete control of phase shift resulted from discrete wavelength tuning of the pump laser. When the phase shift is aligned to be 0 for the DB format, it may be difficult to tune it exactly to π to generate AMI format. The problem can be mitigated using a smaller dispersion to provide a finer tuning at a given tuning resolution of the pump wavelength.

To demodulate DPSK signals at different bit rates, we tune the wavelength of the CW pump to introduce a proper delay between the signal and idler 1. Figures 4(a) and 4(b) show the experimental FWM spectra in the demodulations of 10-Gb/s and 5-Gb/s signals, respectively. The FWM efficiency, defined as the power ratio of the generated idler to the input signal, is ~-22 dB. For 10-Gb/s signal, the wavelength shift between the signal and idler is 5 nm, thus providing a 100-ps delay with the 20-ps/nm dispersion in the CFBG. For 5-Gb/s signal, a 10-nm wavelength shift provides a 200-ps delay.

 

Fig. 4 FWM spectra in the demodulation of (a) 10 Gb/s and (b) 5 Gb/s signals.

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For NRZ-DPSK signals, the demodulated signals are shown in Fig. 5 , including 10-Gb/s DB, 10-Gb/s AMI, 5-Gb/s DB and 5-Gb/s AMI as indicated in (a)-(d). For all cases, clear eyes are obtained, demonstrating the capability of our demodulator to operate at widely variable bit rates. For comparison, the eye diagrams of demodulated 10-Gb/s NRZ-DPSK signals obtained from a standard fiber-based Mach-Zehnder DI [18] with a fixed-delay of ~100 ps are also shown in Figs. 5(e) and 5(f). The BERs of the six signals measured with a 10-GHz single-ended photodetector are shown in Fig. 5(g). In general, the NRZ-AMI format has a higher receiver sensitivity compared to NRZ-DB format due to a difference in the pulse shape caused by transient phase modulation at the rising edge and falling edge. For 10-Gb/s NRZ-DPSK signal, the standard DI exhibits 2.5 and 2.8 dB improvement in the receiver sensitivities over our bit-rate variable demodulator for DB and AMI formats, respectively. The difference can be explained by the occurrence of ASE noise in the EDFA and signal degradation in FWM in the bit-rate variable scheme. The additional 0.3 dB degradation of AMI may result from the discrete phase tuning as mentioned above. The results of RZ-DPSK signals with a duty cycle of ~50% are also shown in Figs. 6(a) - 6(g). For the standard DI, DB and AMI formats show almost identical receiver sensitivities. For variable bit-rate demodulation, however, RZ-AMI has a smaller tolerance to discrete phase tuning compared to NRZ-AMI, resulting in an additional degradation of 0.7 dB with reference to RZ-DB.

 

Fig. 5 Demodulated NRZ-DPSK signals. Bit-rate variable demodulator: (a) 10-Gb/s DB, (b) 10-Gb/s AMI, (c) 5-Gb/s DB, (d) 5-Gb/s AMI; Standard DI: (e) 10-Gb/s DB, (f) 10-Gb/s AMI; and (g) BER measurement of the demodulated signals.

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Fig. 6 Demodulated RZ-DPSK signals. Bit-rate variable demodulator: (a) 10-Gb/s DB, (b) 10-Gb/s AMI, (c) 5-Gb/s DB, (d) 5-Gb/s AMI; Standard DI: (e) 10-Gb/s DB, (f) 10-Gb/s AMI; and (g) BER measurement of the demodulated signals.

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For further miniaturization of our setup, integrated devices can be used to replace the fiber components. A chirped vertical grating based on SOI technology has been demonstrated in [19], providing a 7.0 × 10⁵ ps/nm/km dispersion with an acceptable level of reflectance. Combining with a silicon nano-waveguide [14], both the functionalities of wavelength conversion and dispersion can be possibly integrated into a tiny silicon chip.

4. Conclusion

A bit-rate variable DPSK demodulator is demonstrated in a straight-line structure. The setup exploits a process similar to phase sensitive amplification using cascaded FWM in a 41-m PCF separated by a tunable optical delay. The delay is obtained from wavelength conversion followed by dispersion in a chirped fiber Bragg grating. By tuning the delay, NRZ-DPSK and RZ-DPSK signals at 10 Gb/s and 5 Gb/s are demodulated with error-free performances. The switching between DB and AMI formats is also achieved by the fine control of the delay.