1. 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 [1]. 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 (AND, NAND, OR, XOR, XNOR, NOR) in optical domain [2–5]. 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 AND output while cross-gain modulation (XGM) generates the NOR output. These two channels are combined by a coupler to obtain the XNOR logic [7]. Berrettini et al set the NOR and 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 [1], but the logic gates are highly dependent on the polarization states of input signals.

In this paper, we propose arbitrary two-input logic gates (AND, NAND, OR, XOR, XNOR, NOR) based on single SOA and optical filtering. Two data signals with picosecond-pulse 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 AND, OR, XOR, and NOR. Finally, the logic XNOR and NAND 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.

2. Concept of two-input arbitrary Boolean logic

 

Fig. 1. the digital logic conceptual diagram and truth table for two-input logic gates

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As for two-input digital logic, there are six basic logic units, i.e., logic AND, OR, XOR, NAND, NOR, and XNOR. Figure 1 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 XNOR/NAND can be realized by combining logic NOR with logic AND/XOR, therefore arbitrary two-input logic gates can be obtained provided that four basic units, OR, AND, NOR, and XOR, were successfully implemented.

3. Operation principle

Previously, all optical adders [9]and multifunctional logic gates [10] were reported based on transient cross phase modulation (T-XPM) with picosecond-pulse injection. Enlightened by these schemes, we present arbitrary two-input Boolean logic based on single SOA and optical filtering. The schematic diagram is shown in Fig. 2(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_dj, j =1,2,3,4 . Because the frequency shift of the probe signal is highly dependent on the peak power of input power of both data signals, the OBF with different detuning can achieve different logic gates. Figure 2(b) shows the output peak power as a function of the filter detuning, where P₁₀ and P₁₁ represent only one data signal is present and both data signals are present, respectively. We assume that P₁₀=10mW and P₁₁=20mW. It is noted that the notch of curve P₁₁ represents the best logic XOR, where the extinction ratio (ER) is maximum. Similarly, the notch of curve P₁₀ represents the best logic AND, and the cross of P₁₁ and P₁₀ represents the best logic OR. The logic AND, XOR, and OR 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 AND gate. Similarly, the OBF can be adjusted to select the weaker blue-shift and reject the stronger blue-shift, resulting in an XOR 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 OR 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. 2. (a) Schematic diagram of two-input arbitrary logic gates, (b) output peak power curve as a function of the filter’s detuning.

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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 NOR, and the small detuning of the filter is useful to accelerate the amplitude recovery [11]. Therefore four parallel OBFs after the SOA with different detuning will achieve logic OR, AND, NOR and XOR. From logic principle, the logic XNOR/NAND is then achieved by mixing the channels of logic AND/XOR and NOR with proper power proportion. Since the NOR has an inverted polarity, the output data format is changed to dark-RZ (DRZ). The logic XNOR and NAND 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 2.5ps with peak power of 10mW and both are modulated at 10Gb/s. The wavelengths of data signal and probe are 1563nm and 1554nm, respectively. The probe power is 0.2mW. 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 1 and other parameters can be found in Ref. [9].

Table .1. Parameter List

View Table

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 1.1nm, the best XOR result is shown in Fig. 3(c). The right column of Fig. 3 is the corresponding eye diagrams. We can see that the XOR result has a full width half maximum (FWHM) of 20ps and the ER is about 12.4dB. When the OBF1 is blue shifted by 1.4nm, the best result for logic OR is achieved, as shown in Fig. 3(d). We notice that the ER is 25dB and the FWHM is about 16ps. When the OBF2 is blue shifted by 1.7nm, the output waveform shows a logic AND function, as shown in Fig. 3(e). The eye diagram shows that the ER is 8.9dB and the FWHM is 16ps.

 

Fig. 3. simulation results for arbitrary two-input logic gates, (a) and (b) are input data signals, (c)–(h) are logic XOR, OR, AND, NOR, XNOR, and NAND respectively.

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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 1.1nm, 1.4nm, 1.7nm, and 0.14nm, respectively

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When the OBF3 is blue-shifted by 0.14nm, the best logic NOR is shown in Fig. 3(f). The output waveform is changed to DRZ format. The NOR gate has an ER of 10.3dB and a FWHM of 24ps. In the simulation, the power of logic AND is amplified by 27dB and then combined with logic NOR. The mixed waveform is shown in Fig. 3(g), which reveals the logic XNOR. The ER is 10.1dB and the FWHM is 22ps. Similarly, when the power of logic XOR is amplified by 23dB and combined with logic NOR, the mixed waveform reveals logic NAND, as shown in Fig 3(h). The output ER is 9.2dB and the FWHM is 25ps. From the eye diagrams of logic XNOR and NAND, we can see some ripples on the level “1” because the FWHM of two mixed channels does not match completely. In fact, the FWHM of logic NOR is determined by inherent SOA gain dynamics, which has a typical value of ~25ps. It is shown that a bandwidth of 40GHz is the optimal choice for logic NOR. Whereas, the FWHM of logic gates due to T-XPM effect is determined by OBF bandwidth. The larger the bandwidth is, the shorter the FWHM will be [9]. Therefore, the waveforms of logic XNOR and NAND 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 XOR, OR, and AND where the OBF is blue shifted by 1.1nm, 1.4nm, and 1.7nm, 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 NOR when the OBF is blue shifted by 0.14nm. 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 spontaneous-spontaneous beat noise. These may be described in terms of the corresponding variance of the Equivalent Photo Current (EPC) [12]

where N_th is the thermal noise spectral density, B_e and B_o 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 P_sp (t). Finally, the total noise variance becomes

Assuming that the noise distributions are Gaussian, the minimum BER may be approximated with

Where the Q value is defined as

Where i _s,0, i _s,1, σ ² _tot,0, and σ ² _tot,1 are the EPCs and the total noise variances corresponding to the “0” and “1” 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 AND, XOR and OR has a power penalty of 5.2dB, 8.8dB and 11dB at BER of 10^-9. At the same peak power level, the original input signal has much lower received power due to its very small duty cycle. The FWHM of the original input signal is 2.5ps, whereas it is about 16ps for the logic gates of RZ format, so large penalty is introduced. The logic AND, XOR and OR have a mark density of 0.25, 0.5 and 0.75 if the original signal has a mark density of 0.5. Therefore, the average received power of logic OR should be highest for equal pulse energies. Since logic NOR, XNOR and NAND are DRZ formats, the average received power is much higher than the pulse of RZ format. For example, the power penalty at BER=10^-9 for logic NOR, XNOR, and NAND is 17dB, 20.5dB, and 19.5dB, respectively.

 

Fig. 5. BER measurement for all logic gates

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Figure 6 shows the Q-factor of all logic gates when the probe wavelength varies from 1544nm to 1560nm. One can see that all the Q-factors are larger than 6, revealing a BER less than 10^-9. As a whole, the best Q-factor appears at 1552nm and 1554nm. 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 11dB, and the average ER is about 8.5dB. As a whole, the best ER appears at 1552nm and 1554nm as well. From both Fig. 6 and Fig. 7, we can infer that the probe wavelength can be chosen near 1552nm and 1554nm to obtain the logic of optimum performance.

 

Fig. 6. Q factor as a function of the probe wavelength.

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Fig. 7. Extinction ratio as a function of the probe wavelength.

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7. Conclusion

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., AND, NOR, OR, and XOR. Finally, the logic XNOR/NAND is achieved by combining two channels of logic AND/XOR and logic NOR. 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 16nm. The whole logic performance is optimum when the probe wavelength is chosen near 1552nm and 1554nm.

This work was partially supported by the National High Technology Developing Program of China (Grant No. 2006AA03Z0414).