We report simultaneous logic XOR gate for carrier-suppressed return-to-zero differential phase-shift keying (CSRZ-DPSK) and format conversion from CSRZ-DPSK to return-to-zero differential phase-shift keying (RZ-DPSK) by exploiting non-degenerate four-wave mixing (FWM) in a highly nonlinear fiber (HNLF). We derive analytical solutions to complex amplitudes under non-depletion approximation to show the principle of operation and verify the CSRZ-DPSK logic XOR gate and format conversion by theoretical analyses. Three converted idlers are obtained by three non-degenerate FWM processes. All-optical 40 Gbit/s simultaneous multicasting CSRZ-DPSK logic XOR gate and CSRZ-DPSK to RZ-DPSK format conversion are successfully demonstrated in the experiment.
©2009 Optical Society of America
Future high-speed large-capacity optical networks require all-optical signal processing to manipulate data information exclusively in the optical domain for the purpose of avoiding inefficient optical-electrical-optical (OEO) conversion [1, 2]. All-optical logic gate and format conversion are crucial functions for all-optical signal processing. The former is useful for addressing, header recognition, data encoding, and parity checking, while the latter helps to interface different optical networks employing different modulation formats according to the network scales and applications. In the recent years, various advanced modulation formats including phase-shift keying (PSK) have emerged to be attractive for optical transport networks, such as non-return-to-zero differential phase-shift keying (NRZ-DPSK), return-to-zero differential phase-shift keying (RZ-DPSK), carrier-suppressed return-to-zero differential phase-shift keying (CSRZ-DPSK), etc . It is highly desirable to perform logic gate and format conversion for advanced modulation formats. Previously, semiconductor optical amplifier (SOA) was used to carry out logic XOR gate for RZ-DPSK signals [4–6] or format conversion from on-off keying (OOK) to PSK . Fiber-based logic gate and format conversion were also widely demonstrated showing impressive operation performance [8–15]. Another promising candidate known as periodically poled lithium niobate (PPLN) waveguide was also employed to realize logic XOR operation for NRZ-DPSK/RZ-DPSK signals  or format conversion from NRZ-DPSK to RZ-DPSK/CSRZ-DPSK based on cascaded second-order nonlinearities [17, 18]. However, so far all-optical logic gate and format conversion for CSRZ-DPSK signals have not yet been reported. In addition, either logic gate or format conversion in the previous demonstrations was always performed separately [4–18]. It is of interest if we can also carry out these functions at the same time. For example, at the network nodes, it probably needs to simultaneously perform: (1) wavelength conversion to avoid channel contention; (2) logic gate to address and switch; (3) format conversion to connect different networks adopting different modulation formats. In such case, multi-functional operations combining both CSRZ-DPSK logic XOR gate and CSRZ-DPSK to RZ-DPSK format conversion could be promising. In this paper, by using non-degenerate four-wave mixing (FWM) in a highly nonlinear fiber (HNLF), we propose and demonstrate all-optical 40 Gbit/s simultaneous multicasting logic XOR gate for CSRZ-DPSK signals and format conversion from CSRZ-DPSK to RZ-DPSK.
2. Principle of operation and theoretical results
Figure 1 illustrates the operation principle for the proposed FWM-based CSRZ-DPSK logic XOR gate and CSRZ-DPSK to RZ-DPSK format conversion. For input CSRZ-DPSK signal A (ωSA), CSRZ-DPSK signal B (ωSB), and CW pump (ωP), note that three non-degenerate FWM processes occur simultaneously in an HNLF, generating three new idler waves as depicted in Fig. 1 (Idler 1: ω i1=ωSA+ωSB-ωP, Idler 2: ω i2=ωSA+ωP-ωSB, Idler 3: ω i3=ωSB+ωP-ωSA). Under the non-depletion approximation, we can derive the analytical solutions to the complex amplitudes of three idlers (A i1, A i2, A i3) respectively written by 
where Aj and Pj(j=SA0, SB0, P0) are the complex amplitudes and optical powers of input CSRZ-DPSK signal A, CSRZ-DPSK signal B, and CW pump, respectively. γ is the nonlinear coefficient. Δk 1, Δk 2 and Δk 3 are the phase mismatch of three non-degenerate FWM processes. L is the length of HNLF. According to Eqs. (1a)–(1c), we can further deduce following complex amplitude (A) and optical phase (ϕ) relationships expressed as
Based on Eqs. (2a)–(2c), the linear relationship between converted idlers and two input signals enables logic XOR operation for CSRZ-DPSK signals taking into account the optical phase periodicity of 2π. It is expected that all three converted idlers take the logic XOR results of two CSRZ-DPSK signals. Figure 2 depicts the schematic illustration of CSRZ-DPSK logic XOR gate. Compared to RZ-DPSK, CSRZ-DPSK introduces additional periodic phase alternation between ‘0’ and ‘π’ in adjacent bit periods. It is noted that all three idlers are generated from the non-degenerate FWM nonlinear interactions involving two CSRZ-DPSK signals. As expected from Eqs. (2a)–(2c), it is interesting to find that the periodic phase variation between ‘0’ and ‘π’ in CSRZ-DPSK signals is counteracted in the converted idlers, corresponding to RZ-DPSK modulation format. As a result, it is possible to perform FWM-based simultaneous multicasting CSRZ-DPSK logic XOR gate and CSRZ-DPSK to RZ-DPSK format conversion. In general, a one-bit-delay fiber delay interferometer (FDI) is employed to demodulate DPSK. It should be noted that the demodulation outputs from FDI also satisfy the logic XOR function as shown in Fig. 2 which can therefore be utilized for the experimental verification of CSRZ-DPSK logic XOR gate. Inset of Fig. 2 shows a schematic diagram of a 40G FDI used in the later experiment. The 40G FDI is formed by two 3 dB optical couplers and two fiber arms with a length difference of 5.2 mm, leading to a relative time delay of 25 ps (Δt), i.e. one-bit-delay for 40 Gbit/s data stream. The operating temperature of the lower arm is controlled by a temperature controlling block (TCB) to properly adjust the phase shift (Δφ). Such a passive 40G FDI can demodulate 40 Gbit/s CSRZ-DPSK signals and RZ-DPSK idlers. Remarkably, for CSRZ-DPSK and RZ-DPSK carrying the same data information, logically inverted demodulation outputs can be obtained from 40G FDI due to the periodic phase alternation (‘0’, ‘π’) characteristic of CSRZ-DPSK.
To verify the proposed FWM-based CSRZ-DPSK logic XOR gate and CSRZ-DPSK to RZ-DPSK format conversion, we present the theoretical results obtained from Eqs. (1a)–(1c) as shown in Fig. 3. 40 Gbit/s pseudo-random binary sequence (PRBS) CSRZ-DPSK signal A and signal B are considered. As depicted in Fig. 3, CSRZ-DPSK signal A and signal B have periodic phase alternation between ‘0’ and ‘π’ in successive bits, while such feature is lost in the three channel converted idlers taking RZ-DPSK format. It is found that the three channel idlers take the logic XOR results of input signal A and signal B. In addition, as can be clearly seen from Fig. 3, the destructive demodulation outputs of three channel RZ-DPSK idlers also take the logic XOR results of the destructive demodulation outputs of CSRZ-DPSK signal A and CSRZ-DPSK signal B. The obtained theoretical results substantiate the proposed FWM-based CSRZ-DPSK logic XOR operation and CSRZ-DPSK to RZ-DPSK format conversion.
3. Experimental setup
Figure 4 shows the experimental setup for FWM-based 40 Gbit/s multicasting CSRZ-DPSK logic XOR gate and CSRZ-DPSK to RZ-DPSK format conversion. Two tunable lasers (TLs), two cascaded Mach-Zehnder modulators (MZMs) driven by a bit pattern generator (BPG), and an erbium-doped fiber amplifier (EDFA) are used to generate two 40 Gbit/s PRBS CSRZ-DPSK signals (A, B). A wavelength division multiplexer (WDM) is utilized to separate signal A and signal B which are then relatively delayed integral bit periods compared to each other using an optical tunable delay line (ODL). CSRZ-DPSK signal A and signal B, together with a continuous-wave (CW) pump provided by an external cavity laser (ECL), are combined with an optical coupler (OC2), amplified by a high-power erbium-doped fiber amplifier (HP-EDFA), and then launched into HNLF to participate in the non-degenerate FWM nonlinear interactions. The polarization controllers (PCs) are used to adjust polarization states to optimize the FWM effect in the HNLF. The HP-EDFA offers a small-signal gain of 40 dB and a saturation output power of 30 dBm. The adopted HNLF in the experiment has a length of 135 m, a nonlinear coefficient of 20 (W·km)-1, a zero dispersion wavelength (ZDW) of 1552.0 nm, a dispersion slope of 0.031 ps/nm 2/km, an effective area of 11 µm 2, and a fiber loss of 0.51 dB/km. The optical spectra and temporal waveforms are respectively observed by an optical spectrum analyzer (OSA, Anritsu MS9710C) with the highest spectral resolution of 0.05 nm and a communications signal analyzer (CSA, Tektronix 8000B). The tunable filter (TF) with a Gaussian shape and 3 dB bandwidth of ~1nm and variable optical attenuator (VOA) are employed to select the converted idler waves and control the optical powers fed into OSA and CSA.
4. Experimental results and discussions
Figure 5 depicts the typical measured optical spectra for FWM-based 40 Gbit/s multicasting CSRZ-DPSK logic XOR gate and CSRZ-DPSK to RZ-DPSK format conversion. Signal A, signal B and CW pump are set at 1546.6, 1549.1 and 1558.4 nm, respectively. Three channel idler waves are generated from three non-degenerate FWM processes with idler 1 at 1537.4 nm, idler 2 at 1555.8 nm, and idler 3 at 1561.0 nm. The insets of Fig. 5 show the enlarged optical spectra for two CSRZ-DPSK signals and three channel new generated idler waves. From the spectra shown in Fig. 5, the powers of output signal A, signal B, CW pump, and three channel idler1~idler3 are measured to be about -10.64, -7.06, 5.67, -27.26, -24.86, and -25.78 dBm, respectively. The conversion efficiencies simply defined by the power ratio of output idlers to the output signal A, are estimated to be around -16.62 dB (idler 1), -14.22 dB (idler 2), and -15.14 dB (idler 3). It is expected to improve the efficiency by using longer HNLF with larger nonlinear coefficient, increasing the pump power, and properly suppressing the stimulated Brillouin scattering (SBS) effect. We can also assess the optical signal-to-noise ratio (OSNR) from the spectrum depicted in Fig. 5. The OSNR of three channel idler1~idler3 are measured to be approximately 25.89, 14.31, and 10.34 dB, respectively. The OSNR degradation of the converted idlers is mainly caused by the amplified spontaneous emission (ASE) noise originating from the EDFAs. It is possible to further suppress the ASE noise and improve OSNR simply by using narrowband filters after EDFAs.
To further confirm the proposed FWM-based 40 Gbit/s multicasting CSRZ-DPSK logic XOR gate and CSRZ-DPSK to RZ-DPSK format conversion, we observe the temporal waveforms for different optical waves. Figure 6 displays the observed temporal waveforms and eye diagrams of the destructive demodulation outputs from the 40G FDI. 40-bit sequences are presented. It can be clearly seen that all three channel demodulated idlers carry the logic XOR results of demodulated signal A and B. The waveforms for two CSRZ-DPSK signals and three RZ-DPSK idlers are plotted in Fig. 7 in which the optical phase information is explicitly marked according to the demodulation outputs depicted in Fig. 6. It is found from Fig. 7 that all three RZ-DPSK idler waves carry the logic XOR results of two CSRZ-DPSK signals. It is noted that the obtained experimental results are in good agreement with the theoretical results as shown in Fig. 3. As a consequence, it can be concluded from Fig. 3 and Figs. 5–7 that FWM-based all-optical 40 Gbit/s simultaneous multicasting CSRZ-DPSK logic XOR operation and CSRZ-DPSK to RZ-DPSK format conversion are successfully implemented in the experiment. As noticed from Figs. 6 and 7, the performance of three channel generated idlers is degraded which can be briefly explained as follows. (1) The quality of input CSRZ-DPSK signal source is degraded with obvious amplitude fluctuations as shown in Fig. 7. This amplitude fluctuation not only brings low extinction ratio but also causes noisy mark-level after DPSK demodulation. This limitation coming from the input signal source directly causes the performance degradation to the three channel generated idlers. (2) The ASE noise originating from EDFAs also introduces noisy mark-level to extend. In spite of the performance degradation, the obtained experimental results including temporal waveforms and eye diagrams indicate the successful implementation of FWM-based CSRZ-DPSK logic XOR gate and CSRZ-DPSK to RZ-DPSK format conversion. Remarkably, FWM has the distinct advantages in optical signal processing such as ultrafast nonlinear optical response and negligible spontaneous emission noise. Thus the performance degradation comes from the experimental conditions but not the FWM itself. It is expected to effectively improve the operation performance by adopting input signal sources with higher quality and reducing the ASE noise via narrowband filtering after EDFAs.
With future improvement, the proposed FWM-based simultaneous multicasting CSRZ-DPSK logic XOR operation and CSRZ-DPSK to RZ-DPSK format conversion can operate at much higher speed (160 Gbit/s, 320 Gbit/s and above) owing to the ultrafast nonlinear optical response characteristic of FWM. In addition, the proposed logic XOR gate is also available for binary phase-shift keying (BPSK) signals. It is also possible to perform multicasting three-input CSRZ-DPSK logic XOR gate by use of non-degenerate FWM in an HNLF. As a side consideration, it is easy to further extend the multicasting operation with multiple (>3) output channels by employing multiple (>2) CW pumps . To optimize the performance with multiple (>3) outputs, it is beneficial to suppress the unwanted components generated by spurious FWM shown in Fig. 5 . These potential FWM-based ultrafast all-optical signal processing applications are attractive for high-speed optical communications networks.
We propose and investigate a novel approach to perform simultaneous CSRZ-DPSK logic XOR gate and CSRZ-DPSK to RZ-DPSK format conversion by using non-degenerate FWM in an HNLF. Approximate analytical solutions are deduced under non-depletion approximation to clearly describe the operation principle. The obtained theoretical results and experimental results indicate the successful implementation of FWM-based all-optical 40 Gbit/s simultaneous CSRZ-DPSK logic XOR operation and CSRZ-DPSK to RZ-DPSK format conversion.
This work was supported by the Natural Science Foundation of Hubei Province of China under Grant No. 2008CDB313 and National Natural Science Foundation of China under Grant No. 60577006.
References and links
1. D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, and D. C. Rogers, “Nonlinear optics for high-speed digital information processing,” Science 286, 1523–1528 (1999). [CrossRef] [PubMed]
2. M. Saruwatari, “All-optical signal processing for terabit/second optical transmission,” IEEE J. Sel. Top. Quantum Electron. 6, 1363–1374 (2000). [CrossRef]
3. P. J. Winzer and R.-J. Essiambre, “Advanced modulation formats for high-capacity optical transport networks,” J. Lightwave Technol. 24, 4711–4728 (2006). [CrossRef]
4. K. Chan, C. K. Chan, L. K. Chen, and F. Tong, “Demonstration of 20-Gb/s all-optical XOR gate by four-wave mixing in semiconductor optical amplifier with RZ-DPSK modulated inputs,” IEEE Photon. Technol. Lett. 16, 897–899 (2004). [CrossRef]
5. C. Kang, J. Dorrer, and Leuthold, “All-optical XOR operation of 40 Gbit/s phase-shift-keyed data using four-wave mixing in semiconductor optical amplifier,” Electron. Lett. 40, 496–498 (2004). [CrossRef]
6. N. Deng, K. Chan, C. K. Chan, and L. K. Chen, “An all-optical XOR logic gate for high-speed RZ-DPSK signals by FWM in semiconductor optical amplifier,” IEEE J. Sel. Top. Quantum Electron. 12, 702–707 (2006). [CrossRef]
7. K. Mishina, S. M. Nissanka, A. Maruta, S. Mitani, K. Ishida, K. Shimizu, T. Hatta, and K. Kitayama, “All-optical modulation format conversion from NRZ-OOK to RZ-QPSK using parallel SOA-MZI OOK/BPSK converters,” Opt. Express 15, 7774–7785 (2007). [CrossRef] [PubMed]
9. J. Wang, Q. Sun, J. Sun, and X. Zhang, “Experimental demonstration on 40 Gbit/s all-optical multicasting logic XOR gate for NRZ-DPSK signals using four-wave mixing in highly nonlinear fiber,” Opt. Commun. 282, 2615–2619 (2009). [CrossRef]
10. C. H. Kwok and C. Lin, “Polarization-insensitive all-optical NRZ-to-RZ format conversion by spectral filtering of a cross phase modulation broadened signal spectrum,” IEEE J. Sel. Top. Quantum Electron. 12, 451–458 (2006). [CrossRef]
11. B. P. P. Kuo, P. C. Chui, and K. Wong, “All-optical tunable delay with NRZ-to-RZ format conversion capability based on optical Kerr switch and pulse pre-chirping,” J. Lightwave Technol. 26, 3770–3775 (2008). [CrossRef]
12. S. Arahira, H. Murai, and K. Fujii, “All-optical modulation-format convertor employing polarization-rotation-type nonlinear optical fiber loop mirror,” IEEE Photon. Technol. Lett. 20, 1530–1532 (2008). [CrossRef]
13. G. W. Lu, K. S. Abedin, and T. Miyazaki, “All-optical RZ-DPSK WDM to RZ-DQPSK phase multiplexing using four-wave mixing in highly nonlinear fiber,” IEEE Photon. Technol. Lett. 19, 1699–1701 (2007). [CrossRef]
14. K. Mishina, S. Kitagawa, and A. Maruta, “All-optical modulation format conversion from on-off-keying to multiple-level phase-shift-keying based on nonlinearity in optical fiber,” Opt. Express 15, 8444–8453 (2007). [CrossRef] [PubMed]
15. W. Astar, C.-C. Wei, Y.-J. Chen, J. Chen, and G. Carter, “Polarization-insensitive, 40 Gb/s wavelength and RZ-OOK-to-RZ-BPSK modulation format conversion by XPM in a highly nonlinear PCF,” Opt. Express 16, 12039–12049 (2008). [CrossRef] [PubMed]
16. J. Wang, J. Sun, X. Zhang, D. Huang, and M. M. Fejer, “Ultrafast all-optical three-input Boolean XOR operation for differential phase-shift keying signals using periodically poled lithium niobate,” Opt. Lett. 33, 1419–1421 (2008). [CrossRef] [PubMed]
17. J. Wang, J. Sun, X. Zhang, and D. Huang, “Proposal for PPLN-based all-optical NRZ-to-CSRZ, RZ-to-CSRZ, NRZ-DPSK-to-CSRZ-DPSK, and RZ-DPSK-to-CSRZ-DPSK format conversions,” IEEE Photon. Technol. Lett. 20, 1039–1041 (2008). [CrossRef]
18. J. Wang, J. Sun, X. Zhang, D. Liu, and D. Huang, “Proposal and simulation for all-optical format conversion between differential phase-shift keying signals based on cascaded second-order nonlinearities,” Opt. Commun. 281, 5019–5024 (2008). [CrossRef]
19. X. M. Liu, “Four-wave mixing self-stability based on photonic crystal fiber and its applications on erbium-doped fiber lasers,” Opt. Commun. 260, 554–559 (2006). [CrossRef]
20. G. W. Lu, K. S. Abedin, and T. Miyazaki, “DPSK multicast using multiple-pump FWM in Bismuths highly nonlinear fiber with high multicast efficiency,” Opt. Express 16, 21964–21970 (2008). [CrossRef] [PubMed]
21. F. A. Callegari, J. M. Chavez Boggio, and H. L. Fragnito, “Spurious four-wave mixing in two-pump fiber-optic parametric amplifiers,” IEEE Photon. Technol. Lett. 16, 434–436 (2004). [CrossRef]