A proposal for two-input arbitrary Boolean logic gates using single semiconductor optical amplifier by picosecond pulse injection

A proposal for two-input arbitrary Boolean logic gates using single semiconductor optical amplifier by picosecond pulse injection Jianji Dong,,* Xinliang Zhang, and Dexiu Huang Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology, Wuhan, 430074, China Centre for Photonic Systems, Department of Engineering, University of Cambridge, Cambridge, CB3 0FA, UK * Corresponding author: jjdong@mail.hust.edu.cn Abstract: We propose theoretically two-input arbitrary Boolean logic (N,,, X, XN, N) using single semiconductor optical amplifier (SOA) assisted by several detuning optical filters. The probe spectrum is broadened by picosecond pulse injection in the SOA, and four consequent optical Gaussian filters are used to select different frequency components to acquire logic N,,, X, respectively. Then two additional logic gates, XN and N, are realized by combining two logic channels. The power penalty, Q-factor, and extinction ratio are measured for all logic gates. It is shown that the output logic with dark return-to-zero (RZ) format has a large power penalty. The Q-factor is larger than 6 and the extinction ratio is larger than 6.3dB for all logic gates within 6nm wavelength range. 009 Optical Society of America OCIS codes: (5980) Semiconductor optical amplifier; (00.4660) Optical logic. References and links. K. Vahala, R. Paiella, and G. Hunziker, "Ultrafast WDM logic," J. Sel. Top. Quantum Electron. 3, 698 (997).. T. Houbavlis, K. Zoiros, A. Hatziefremidis, H. Avramopoulos, L. Occhi, G. Guekos, S. Hansmann, H. Burkhard, and R. Dall'Ara, "0Gbit/s all-optical Boolean X with SOA fibre Sagnac gate," Electron. Lett. 35, 650-65 (999). 3. S. H. Kim, J. H. Kim, B. G. Yu, Y. T. Byun, Y. M. Jeon, S. Lee, and D. H. Woo, "All-optical N gate using cross-gain modulation in semiconductor optical amplifiers," Electron. Lett. 4, 07-08 (005). 4. X. Zhang, Y. Wang, J. Sun, D. Liu, and D. Huang, "All-optical gate at 0 Gbit/s based on cascaded single-port-couple SOAs," Opt. Express, 36-366 (004), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe--3-36. 5. J. Dong, X. Zhang, J. Xu, and D. Huang, "40 Gb/s all-optical logic N and gates using a semiconductor optical amplifier: Experimental demonstration and theoretical analysis," Opt. Commun. 8, 70-75 (008). 6. Z. Li and G. Li, "Ultrahigh-speed reconfigurable logic gates based on four-wave mixing in a semiconductor optical amplifier," IEEE Photon. Technol. Lett. 8, 34-343 (006). 7. S. Kumar and A. E. Willner, "Simultaneous four-wave mixing and cross-gain modulation for implementing an all-optical XN logic gate using a single SOA," Opt. Express 4, 509-5097 (006), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-4--509. 8. G. Berrettini, A. Simi, A. Malacarne, A. Bogoni, and L. Poti, "Ultrafast integrable and reconfigurable XN,, N, and NOT photonic logic gate," IEEE Photon. Technol. Lett. 8, 97-99 (006). 9. J. Dong, S. Fu, X. Zhang, P. Shum, L. Zhang, J. Xu, and D. Huang, "Single SOA based all-optical adder assisted by optical bandpass filter: Theoretical analysis and performance optimization," Opt. Commun. 70, 38-46 (007). 0. Z. Li, Y. Liu, S. Zhang, H. Ju, H. de Waardt, G. D. Khoe, H. J. S. Dorren, and D. Lenstra, "All-optical logic gates using semiconductor optical amplifier assisted by optical filter," Electron. Lett. 4, 397-399 (005).. Y. Liu, E. Tangdiongga, Z. Li, H. de Waardt, A. M. J. Koonen, G. D. Khoe, X. Shu, I. Bennion, and H. J. S. Dorren, "Error-Free 30-Gb/s All-Optical Wavelength Conversion Using a Single Semiconductor Optical Amplifier," J. Lightwave Technol. 5, 03-08 (007). #0483 - $5.00 USD Received 4 Dec 008; revised 3 Feb 009; accepted 6 Feb 009; published 7 Apr 009 (C) 009 OSA May 009 / Vol. 7, No. 0 / OPTICS EXPRESS 775

. J. Dong, X. Zhang, J. Xu, D. Huang, S. Fu, and P. Shum, "40 Gb/s all-optical NRZ to RZ format conversion using single SOA assisted by optical bandpass filter," Opt. Express 5, 907-94 (007), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-5-6-907. 3. N. A. Olsson, "Lightwave Systems with Optical Amplifiers," J. Lightwave Technol. 7, 07-08 (989).. Introduction In future communications networks, optical solutions to logic functionalities are expected to present an alternative to current electronic signal processing because of faster response []. However, the first optical logic functionalities in the networks are relatively simple, i.e. consisting of relatively few Boolean logic gates. To date, many schemes have been demonstrated to realize various logic functions (, N,, X, XN, N) in optical domain [-5]. However, the single logic implementation has very finite function in the network nodes. To extend the logic functions and make them smart and flexible, one may develop reconfigurable multifunctional logic gates by using an independent optical module. For example, Li et al demonstrated reconfigurable logic gates based on four-wave mixing (FWM) in the semiconductor optical amplifier (SOA) [6]. Kumar et al proposed that FWM generates the output while cross-gain modulation (XGM) generates the N output. These two channels are combined by a coupler to obtain the XN logic [7]. Berrettini et al set the N and outputs at the same wavelength to be filtered together [8], whereas the polarization states of the two signals should be orthogonal to minimize the coherent crosstalk. Vahala et al presented arbitrary Boolean logic based on FWM in the SOA [], but the logic gates are highly dependent on the polarization states of input signals. In this paper, we propose arbitrary two-input logic gates (, N,, X, XN, N) based on single SOA and optical filtering. Two data signals with picosecondpulse and a probe signal are injected into the SOA simultaneously to arouse cross phase modulation (XPM). The spectrum of the probe will be broadened, and designed optical filters are used to filter out different frequency components, which contain different logic output, such as logic,, X, and N. Finally, the logic XN and N are achieved by combining two logic channels. The bit-error rate (BER), Q-factor, and extinction ratio (ER) are measured for all logic gates. Our scheme is simple and flexible for arbitrary logic switching, which can be used to the advanced complex logic circuits.. Concept of two-input arbitrary Boolean logic Fig.. the digital logic conceptual diagram and truth table for two-input logic gates As for two-input digital logic, there are six basic logic units, i.e., logic,, X, N, N, and XN. Figure shows a simple digital logic conceptual diagram and logic truth table for two-input logic gates. From the truth table, it is noted that the logic XN/N can be realized by combining logic N with logic /X, therefore arbitrary two-input logic gates can be obtained provided that four basic units,,, N, and X, were successfully implemented. 3. Operation principle Previously, all optical adders [9]and multifunctional logic gates [0] were reported based on transient cross phase modulation (T-XPM) with picosecond-pulse injection. Enlightened by #0483 - $5.00 USD Received 4 Dec 008; revised 3 Feb 009; accepted 6 Feb 009; published 7 Apr 009 (C) 009 OSA May 009 / Vol. 7, No. 0 / OPTICS EXPRESS 776

these schemes, we present arbitrary two-input Boolean logic based on single SOA and optical filtering. The schematic diagram is shown in Fig. (a). Two input data signals to be processed (Data A and Data B) and a probe signal are launched into the nonlinear SOA to cause cross phase modulation. Then the probe signal has some frequency shifts. Data A and Date B are assumed to have equal peak power with return-to-zero (RZ) format. The subsequent four optical bandpass filters (OBFs) are used to extract different sideband spectrum with its central wavelength λ, j=,,3,4. Because the frequency shift of the probe signal is highly dj dependent on the peak power of input power of both data signals, the OBF with different detuning can achieve different logic gates. Figure (b) shows the output peak power as a function of the filter detuning, where P 0 and P represent only one data signal is present and both data signals are present, respectively. We assume that P 0 =0mW and P =0mW. It is noted that the notch of curve P represents the best logic X, where the extinction ratio (ER) is maximum. Similarly, the notch of curve P 0 represents the best logic, and the cross of P and P 0 represents the best logic. The logic, X, and are based on T-XPM, so the output logic gates remain RZ formats. These logic gates can be explained from the viewpoint of spectrum shifts. If both data signals are launched simultaneously, the modulated probe will receive a much stronger spectral blue-shift compared to where only one pulse is present. The OBF can be used to select this stronger blue-shift while reject the weaker blue-shift. Thus, at the output of the OBF, a pulse from the probe will be generated in the presence of both data signals, resulting in an gate. Similarly, the OBF can be adjusted to select the weaker blue-shift and reject the stronger blue-shift, resulting in an X gate. When the OBF is adjusted to the middle area of weak blue-shift and strong blue-shift, a pulse from the probe will be generated by either two data signals or a single signal injection, resulting in an gate. In order to enhance the T-XPM effect, the data signals should be ultrashort pulse (several picoseconds) because the probe signal will generate large chirps and large frequency shifts by the picosecond-pulse injection. Fig.. (a) Schematic diagram of two-input arbitrary logic gates, (b) output peak power curve as a function of the filter s detuning. If the OBF has relatively small detuning to the probe signal, then the XGM is dominant to make the output pulse inverted. Thus, the output gate turns to be logic N, and the small detuning of the filter is useful to accelerate the amplitude recovery []. Therefore four parallel OBFs after the SOA with different detuning will achieve logic,, N and X. From logic principle, the logic XN/N is then achieved by mixing the channels of logic /X and N with proper power proportion. Since the N has an inverted polarity, the output data format is changed to dark-rz (DRZ). The logic XN and N are DRZ formats as well. 4. Results and discussion When the SOA operates with pulses shorter than a few picoseconds, the intraband effects, such as spectrum hole burning (SHB) and carrier heating (CH), become important. Therefore we adopt the ultrafast SOA model by considering the intraband mechanism [9]. It is assumed that both data signals have a pulsewidth of.5ps with peak power of 0mW and both are #0483 - $5.00 USD Received 4 Dec 008; revised 3 Feb 009; accepted 6 Feb 009; published 7 Apr 009 (C) 009 OSA May 009 / Vol. 7, No. 0 / OPTICS EXPRESS 777

modulated at 0Gb/s. The wavelengths of data signal and probe are 563nm and 554nm, respectively. The probe power is 0.mW. The SOA is biased at 500mA to enhance the T- XPM effect. The consequent OBFs are Gaussian. Some essential parameters of the simulation are listed in Table and other parameters can be found in Ref. [9]. Table. Parameter List Parameter Value Parameter Value Linewidth enhancement factorα 5 Filter bandwidth for T-XPM 30GHz N CH-induced parameterα Filter bandwidth for N 40GHz CH SHB gain suppression factorε 0. W - Injected current I 500mA SHB CH gain suppression factorε 0.4W - Extinction ratio of input signals 30dB CH Figure 3 shows the simulation results for arbitrary two-input logic gates, where the bit sequences of data A and data B are shown in Fig 3(a) and (b). When the OBF4 is blue-shifted by.nm, the best X result is shown in Fig. 3(c). The right column of Fig. 3 is the corresponding eye diagrams. We can see that the X result has a full width half maximum () of 0ps and the ER is about.4db. When the OBF is blue shifted by.4nm, the best result for logic is achieved, as shown in Fig. 3(d). We notice that the ER is 5dB and the is about 6ps. When the OBF is blue shifted by.7nm, the output waveform shows a logic function, as shown in Fig. 3(e). The eye diagram shows that the ER is 8.9dB and the is 6ps. Normalized power (a.u.) (a) (b) (c) (d) (e) Data A Data B X ER=.4dB ER=5dB ER=8.9dB.5ps.5ps 0ps 6ps 6ps 4ps (f) N ER=0.3dB (g) XN ps ER=0.dB 5ps (h) N ER=9.dB 0 0 00 400 600 800 000 50 00 Time (ps) Fig. 3. simulation results for arbitrary two-input logic gates, (a) and (b) are input data signals, (c)-(h) are logic X,,, N, XN, and N respectively. Optical spectrum (dbm) 40 0 0-0 (a) Probe signal, before OBF -0 (b) Blue shift.nm Logic X -00 (c) Blue shift.4nm Logic -00 (d) Blue shift.7nm Logic -00 0-0 (e) Blue shift 0.4nm Logic N -00-3 -.5 - -.5 - - 0 Wavelength (nm) Fig. 4. Output optical spectra, (a) the output spectrum of probe signal after SOA, (b)-(d) are the output spectra when the OBF has a detuning of.nm,.4nm,.7nm, and 0.4nm, respectively When the OBF3 is blue-shifted by 0.4nm, the best logic N is shown in Fig. 3(f). The output waveform is changed to DRZ format. The N gate has an ER of 0.3dB and a of 4ps. In the simulation, the power of logic is amplified by 7dB and then combined with logic N. The mixed waveform is shown in Fig. 3(g), which reveals the logic XN. The ER is 0.dB and the is ps. Similarly, when the power of logic X is amplified by 3dB and combined with logic N, the mixed waveform reveals logic N, as shown in Fig 3(h). The output ER is 9.dB and the is 5ps. From the eye diagrams of logic XN and N, we can see some ripples on the level because the of two mixed channels does not match completely. In fact, the of logic N #0483 - $5.00 USD Received 4 Dec 008; revised 3 Feb 009; accepted 6 Feb 009; published 7 Apr 009 (C) 009 OSA May 009 / Vol. 7, No. 0 / OPTICS EXPRESS 778

is determined by inherent SOA gain dynamics, which has a typical value of ~5ps. It is shown that a bandwidth of 40GHz is the optimal choice for logic N. Whereas, the of logic gates due to T-XPM effect is determined by OBF bandwidth. The larger the bandwidth is, the shorter the will be [9]. Therefore, the waveforms of logic XN and N can be optimized by adjusting the OBF bandwidth. In our simulation, we choose a bandwidth of 30GHz for T-XPM-based logic gates. The optical spectra of output logic signals are correspondingly shown in Fig. 4. The probe signal after the SOA is shown in Fig. 4(a). We can see that the probe spectrum is broadened and some sideband frequencies are generated due to T-XPM effect. Figure 4(b)-(d) show the output spectra of logic X,, and where the OBF is blue shifted by.nm,.4nm, and.7nm, respectively. The OBF is used to select the sideband frequency of probe signal and suppress the probe carrier, so the T-XPM effect is dominant. Figure 4(e) shows the output spectrum of logic N when the OBF is blue shifted by 0.4nm. We can see the OBF does not suppress the probe carrier completely. Hence the XGM effect has main contributions. Ref. [9] suggested that our logic scheme has a limited operation speed less than 40Gb/s. In order to investigate the output performance, a simple model for calculating the BER in a direct detection system is used. The BER measurement system consists of an ideal photodiode, an electrical low-pass filter, and a sampling/decision circuits. There are five contributions to the noise accumulation on the photodiode, i.e., thermal noise, shot noise, shot noise from spontaneous emission, signal-spontaneous beat noise, and spontaneousspontaneous beat noise. These may be described in terms of the corresponding variance of the Equivalent Photo Current (EPC) [] σ = N B () th th th e σ = eb i () s shot e s σ = eb i (3) sp shot e sp Be σ s sp = 4isisp (4) B o B o B σ e sp sp isp Be Bo = (5) where N is the thermal noise spectral density, B and B are the bandwidth of the electrical filter and optical filter, e is the elementary charge, and i s is the EPC of the input signal power P ( ) in t, i sp is the EPC of the spontaneous noise power Psp ( t ). Finally, the total noise variance becomes σ = σ + σ + σ + σ + σ (6) e tot th s shot sp shot s sp sp sp Assuming that the noise distributions are Gaussian, the minimum BER may be approximated with exp( Q / ) BER= (7) π Q Where the Q value is defined as is, is,0 Q= (8) σ + σ Where i s,0, i s,, σ, and tot,0 tot,0 tot, o σ tot, are the EPCs and the total noise variances corresponding to the 0 and levels of the signal, respectively. Based on the BER model mentioned above, the simulated BER curves for all logic gates are shown in Fig. 5. We notice that the logic, X and has a power penalty of 5.dB, 8.8dB and db at BER of 0-9. At the same peak power level, the original input signal has much lower received power due to its very small duty cycle. The of the #0483 - $5.00 USD Received 4 Dec 008; revised 3 Feb 009; accepted 6 Feb 009; published 7 Apr 009 (C) 009 OSA May 009 / Vol. 7, No. 0 / OPTICS EXPRESS 779

original input signal is.5ps, whereas it is about 6ps for the logic gates of RZ format, so large penalty is introduced. The logic, X and have a mark density of 0.5, and 0.75 if the original signal has a mark density of. Therefore, the average received power of logic should be highest for equal pulse energies. Since logic N, XN and N are DRZ formats, the average received power is much higher than the pulse of RZ format. For example, the power penalty at BER=0-9 for logic N, XN, and N is 7dB, db, and 9.5dB, respectively. log (BER) -3-4 -5-6 -7-8 -9-0 - data A/B X N XN N - -45-35 -30-5 -0-5 -0 Received power (dbm) Fig. 5. BER measurement for all logic gates Figure 6 shows the Q-factor of all logic gates when the probe wavelength varies from 544nm to 560nm. One can see that all the Q-factors are larger than 6, revealing a BER less than 0-9. As a whole, the best Q-factor appears at 55nm and 554nm. Figure 7 shows the output ER variation with the probe wavelength. One can see that the ER has a large floating scope from 6.3dB to db, and the average ER is about 8.5dB. As a whole, the best ER appears at 55nm and 554nm as well. From both Fig. 6 and Fig. 7, we can infer that the probe wavelength can be chosen near 55nm and 554nm to obtain the logic of optimum performance. Q factor 30 5 0 5 N N XN X Extionction ratio (db) 4 0 8 X N N XN 0 544 546 548 550 55 554 556 558 560 Probe wavelength (nm) Fig. 6. Q factor as a function of the probe wavelength. 7. Conclusion 6 544 546 548 550 55 554 556 558 560 Probe wavelength (nm) Fig. 7. Extinction ratio as a function of the probe wavelength. Multifunctional all-optical logic gates are expected to be useful in optical network nodes because of flexibility and smartness. In this paper, we propose and theoretically demonstrate arbitrary two-input logic gates based on single SOA and optical filtering. There are two data signals with picosecond pulse and a probe light launched into the SOA to cause XPM and XGM effect. Four OBFs with different detuning will achieve four logic gates, i.e.,, N,, and X. Finally, the logic XN/N is achieved by combining two channels of logic /X and logic N. The BER measurements, Q-factor, and ER for all logic gates are calculated. It is shown that the logic with DRZ format has a large power penalty. All the logic gates have a Q-factor larger than 6 and an ER over 6.3dB in a wavelength span of 6nm. The whole logic performance is optimum when the probe wavelength is chosen near 55nm and 554nm. This work was partially supported by the National High Technology Developing Program of China (Grant No. 006AA03Z044). #0483 - $5.00 USD Received 4 Dec 008; revised 3 Feb 009; accepted 6 Feb 009; published 7 Apr 009 (C) 009 OSA May 009 / Vol. 7, No. 0 / OPTICS EXPRESS 7730