Designs of all-optical NOR gates using SOA based MZI

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Designs of all-optical NOR gates using SOA based MZI Pallavi Singh ∗ , D.K. Tripathi, H.K. Dixit Department of Electronics and Communication, University of Allahabad, Allahabad 211002, India

a r t i c l e

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Article history: Received 20 June 2013 Accepted 10 February 2014 Available online xxx Keywords: Semiconductor optical amplifier based Mach–Zehnder interferometer (SOA-MZI) Cross gain modulation (XGM) Cross phase modulation (XPM) Four wave mixing (FWM)

a b s t r a c t The paper investigates the non-linear behavior of semiconductor optical amplifier with Mach–Zehnder interferometer (SOA-MZI) configuration which makes it to work as a logic gate. The two designs of NOR gate based on SOA-MZI have been verified. The basic principal of both designs are same. The summation of data pulses have been taken and inverted to perform a NOR operation. In the design, the first 3 dB coupler creates a phase difference of ␲/2 in clock pulse and data pulse while passing through two interferometer arms. The clock and data pulses pass through SOA which attenuates the clock pulse wherever the data pulse is present. After passing through second 3 dB coupler a phase difference of ␲/2 is again created. Therefore, if the clock pulse is in the same phase will be added and if it is out of phase, will be canceled. The designs have been investigated at different bit-rates to achieve higher extinction ratio (ER), Q-factor and bit-error rate (BER) for different pump currents of SOA. © 2014 Elsevier GmbH. All rights reserved.

1. Introduction In the field of optical signal processing, it is desired to realize all-optical computers using digital optical elements to increase the speed of next generation photonic transmission systems. For all-optical functions wavelength conversion, multiplexing, clock recovery, regeneration and bit pattern recognition are needed. Nowadays, it has become necessity to build all-optical logic gates that can be controlled optically, on the same platform so that it may be easily integrated on a photonic chip. The competitors of optical gates are digital gates which are small, compact and easy in integration. But if we go for a speed all-optical gates are leading as it can reach up to THz and also provide a higher bandwidth. Gates that can be controlled optically are basic elements for high speed signal processing which can avoid optoelectronic conversion in communication system. In future all-optical logic gates are the key elements for optical signal processing such as data encryption, address recognition and label swapping. Recently, various schemes have been explored to make possible all-optical logic gates such as XOR, OR, NOR, AND and NAND. Basically all-optical logic gates are designed in two ways, without SOA [1–4] and with SOA [5–14]. Again the gates are divided based on interferometer techniques such as Sagnac/Terahertz optical Asymmetric De-multiplexer (TOAD) [5], Ultrafast Nonlinear

∗ Corresponding author. E-mail addresses: [email protected] (P. Singh), [email protected] (D.K. Tripathi), [email protected] (H.K. Dixit).

Interferometer (UNI) [6–8], Michelson Interferometer (MI) [9], Delay Interferometer (DI) [10] and SOA based Mach–Zehnder interferometer (SOA-MZI) [11–14] which exploit the ultra fast non-linear property of SOA. Such gates can provide a wavelength conversion with high power efficiency, large conversion range and high optical signal to noise ratio (OSNR) for the converted signal. Among the schemes stated above the SOA based MZI is most promising candidate due to its attractive features of low energy requirement, low latency, and high stability with compact and simple design that makes it easy to integrate for mass production. Gates using SOA are designed on the basis of nonlinearity effect in SOA i.e. cross gain modulation (XGM) [5–7,9–14] cross phase modulation (XPM) [5,9,11–14] and four wave mixing (FWM) [7,8] as these occur due to the stimulated emission in SOA during the amplification process. Cross gain modulation (XGM) occurs due to gain saturation in SOA. The simplest approach of XGM is shown in Fig. 1. When light of two different wavelengths, clock and data pulses pass through SOA where it is operated under the gain saturation condition, the total available gain is distributed between the two wavelengths of clock and data pulses. The distribution of gain depends on their relative photon densities. After passing through SOA, if the photon density of data pulse is more than the clock pulse then the gain of data pulse increases and simultaneously the clock pulse attenuates. For cross phase modulation (XPM) the refractive index of SOA active region is not constant but it depends on the carrier densities. This implies the phase and gain of the optical wave propagating through SOA is coupled. If more than one signal is injected into a SOA, there will be XPM between the two signals.

http://dx.doi.org/10.1016/j.ijleo.2014.02.032 0030-4026/© 2014 Elsevier GmbH. All rights reserved.

Please cite this article in press as: P. Singh, et al., Designs of all-optical NOR gates using SOA based MZI, Optik - Int. J. Light Electron Opt. (2014), http://dx.doi.org/10.1016/j.ijleo.2014.02.032

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Fig. 1. Effect of XGM on clock and data pulse in SOA.

Fig. 3. (a) Design-1 for NOR gate. (b) Design-2 for NOR gate.

Fig. 2. Mach–Zehnder interferometer.

Four wave mixing (FWM) is a process where optical signals at different wavelengths merge to produce new signals at other wavelengths. It is generated by the intensity-dependent refractive index of silica medium. The change in refractive index produces a phase shift within a channel which generates a new signal at different frequencies. Mach–Zehnder interferometer is a suitable device for high speed all optical demultiplexing. It operates on the principal of phase change, caused by the ray of light propagating through 3 dB coupler. As shown in Fig. 2, the ray of light passes through upper arm of 3 dB coupler producing a phase difference of ␲/2 between the light propagating through upper and lower arm of MZI. After passing through next 3 dB coupler, a phase difference of ␲/2 is again created. So, the total phase difference will become ␲ at T-port and the ray of light is canceled. At R-port the ray of light will be in the same phase, therefore it is added. The paper aim to achieve the goal through logical explanation of two designs of NOR gates based on SOA-MZI. Thus, it would be useful to investigate in extensive as well as systematic manner, as to how simple and standard SOA-MZI architecture can be exploited as an NOR gate at 10 Gb/s, extending the number of inputs up to ninteger. The obtained results are helpful to design other all-optical logic gates. The performance of two designs of NOR gate are compared in terms of extinction ratio (ER), bit-error rate (BER) and quality factor (Q-factor) at different bit rates to achieve an improved results. In addition, the novel approach is to extend the number of inputs by using (n × 1) MUX in order to realize all-optical n-input NOR gate as in design-1. The performance of 10 Gb/s NOR gates was presented for RZ signals. 2. Proposed model and operation principal

the inverter [12]. Fig. 3(a) design-1 shows two data pulse A (00000100000010000011) and B (11111100000010000000) which are mixed through multiplexer (11111100000010000011) and then propagates through upper arm of first 3 dB coupler to perform the NOR operation. Clock pulse passes through the lower arm of first 3 dB coupler. After passing through first 3 dB coupler, the data pulse propagating through the upper arm of MZI, is leading by phase difference of ␲/2 than the data pulse propagating through lower arm. Similarly, the clock pulse propagating through lower arm of MZI will be leading by phase difference of ␲/2 than the clock pulse propagating through upper arm. After passing through SOA, both the pulses are saturated. Wherever, data pulse is present, it attenuates the clock pulse and if data pulse is absent, clock pulse is present. When these saturated pulses pass through next 3 dB coupler again the phase difference of ␲/2 is created and the total phase difference will become ␲ for data pulse at T-port. Therefore, the data pulse will be canceled at T-port and only clock pulse performing the NOR operation is present (00000011111101111100). At the reflected port, the total phase difference will become ␲ for clock pulse and hence clock pulse is canceled only data pulse is present. In design-1 no filter is required at the T-port. The design-1 can be extended for more than two inputs. In Fig. 3(b) design-2 we push data A through multiplexer (MUX) and data B through upper arm of first 3 dB coupler. After passing through upper and lower arm of interferometer both pulses are added, then inverted to get NOR result, as discussed earlier. Here, since clock and data pulses are mixed at T-port, filter is needed to extract the clock pulse. Logical explanations for both the designs are given below. Design-1 If two inputs A and B occur, then NOR operation, NOR = (A + B)



(1)

where ‘+’ signifies Optical MUX, which adds data. A = 0, B = 0 ⇒ (A + B) = 0 ⇒ (A + B) = 1 

A = 0, B = 1 ⇒ (A + B) = 1 ⇒ (A + B) = 0 

A = 1, B = 0 ⇒ (A + B) = 1 ⇒ (A + B) = 0 

A = 1, B = 1 ⇒ (A + B) = 1 ⇒ (A + B) = 0

(3) (4) (5)

If n number of inputs occur, where n is an integer then N is nth input. If A = 0, B = 0,. . ., N = 0; ⇒ (A + B + · · · + N) = 0;

The result of NOR operation is given in Table 1. The basic principal to design all-optical NOR gate is same as in

(2)



⇒ (A + B + · · · + N) = 1.

(6) (7)

If any one of the data is ‘1’ then (A + B + · · · + N) = 1

Table 1 Truth table for NOR logic operation.



Data A

Data B

NOR

0 0 1 1

0 1 0 1

1 0 0 0

⇒ (A + B + · · · + N) = 0;

(8) (9)

Hence NOR operation for N input NOR = (A + B + · · · + N)

(10)

For design-2 for two signals

Please cite this article in press as: P. Singh, et al., Designs of all-optical NOR gates using SOA based MZI, Optik - Int. J. Light Electron Opt. (2014), http://dx.doi.org/10.1016/j.ijleo.2014.02.032

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Fig. 4. (a) Shows two Data A and B with NOR results for design-1 and design-2. (b) Wavelength spectrum at T-port of design-1. (c) Wavelength spectrum at T-port of design-2.

NOR = (A + B) + (A + B) – by basic theorem of Boolean algebra (x + x) = x = (A + B)

(11)

3. Results and discussion The simulation for implementation of all-optical NOR gates are shown in Fig. 3. The data stream of 10 Gb/s bit rate is taken to prove the principal of NOR gate operation. A 10 GHz external cavity mode lock laser (MLL) operating at 1.0 × 10−3 W at 1555 nm Gaussian pulse of 1.0 ps is used as a clock pulse. Probe pulse was formed by 10 Gb/s, 27 -1 pseudo random bit sequence (PRBS) with 0.05 W at 1550 nm. Return to zero (RZ) modulation is used to drive a raised cosine pulse. The SOA is biased at 0.7 mA to achieve an XGM. The length, width and depth are 5.0 × 10−4 , 3.0 × 10−6 and 1.5 × 10−7 m respectively. The confinement factor and line width enhancement factor are set at 0.3 and 5.0 respectively. In the Fig. 4(a) the result of NOR gate have been performed for two designs. In both designs, the output at T-port is broadened. Due to the nonlinear index of refraction in silica medium the wings of the pulse travel faster than the peak. Therefore, the pulses are stretched on the leading edge and compressed on the tailing edge. Thus, the leading edge of the pulse acquires a “red shift” and the tailing edge acquires a “blue shift”. Fig. 4(b) design-1 shows that the data pulse is −3 dBm as it is canceled at T-port and clock pulse is −35 dBm. Fig. 4(c) desin-2 shows both data pulse and clock pulses are present with power −38 dBm and −40 dBm respectively. We can get the result by filtering the data pulse. Extinction ratio is defined as the ratio of minimum power of one’s to maximum power of zero’s at T-port.

 ER = 10 log10

1 Pminimum 0 Pmaximum

 dB at T-Port

(12)

Fig. 5. (a) Shows extinction ratio, (b) Q-factor and (c) BER of design-1 and design-2. Legend of three Bit-rates are red – 12 × 109 , green – 10 × 109 and blue – 8 × 109 . (For interpretation of the references to color in figure legend, the reader is referred to the web version of the article.)

0 1 where Pmimimum is minimum power of 1’s and Pmaximum is maximum power of 0’s at T-port. For both the designs, the ER is 15.67 dB and 15.18 dB respectively. The bit error rate (BER) of a fiber link is the most significant measure of the accuracy of the link in transporting the binary data from transmitter to receiver. Signal is degraded due to dispersion, nonlinearities and noise therefore detector may make mistakes to detect binary “1” as “0” and binary “0” as “1”. Typical benchmarks for the BER are rates of 10−9 and 10−12 for 10 Gb/s system.



1 BER = erfc 4



1 − level √ 21



 + erfc

0 − level √ 20

 (13)

where level =

0 1 − 1 0 0 + 1

where 1 , 0 and level are the signals at the decision points for bit 1, 0 and threshold level. And  1 and  0 are standard deviation at 1 and 0 bit. At 10 Gb/s for pump current 0.7 mA the design-1 gives BER 2.3 × 10−9 and design-2 gives 4.3 × 10−12 . For the lower bit rate, improved result is obtained. The Q-factor is very useful parameter as it is evaluated from the eye diagram. It is also common in communication system to refer Q-factor in linear unit. Q =

1 − 0 1 − 0

(14)

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As shown in Fig. 4, Q factor is 5.86 dB at BER = 10−9 for design-1 and Q factor is 6.87 dB at BER = 10−12 for design-2 (Fig. 5). 4. Conclusion In the paper, the designs of all-optical NOR gates using SOA-MZI structures have successfully demonstrated. The given designs are optimized by adjusting the pump current and bit rate in SOA-MZI in order to obtain maximum ER, Q-factor and BER. The schemes have great merits to generate output pulse with high ER which enables NOR operation at the speed of over 10 Gb/s. The design-1 can extend to perform the NOR operation for more than two inputs. In future, the research will be directed to other optical gates. References [1] Y.-D. Wu, All-optical logic gates by using multibranch waveguide structure with localized optical nonlinearity, IEEE J. Sel. Top. Quantum Electron. 11 (2005) 307–312. [2] D.M.F. Lai, C.H. Kwok, T.I. Yuk, K. Wong, Picosecond all-optical logic gates (XOR, OR, NOT, and AND) in a fiber optical parametric amplifier, in: OFC/NFOEC, 2008, pp. 1–3. [3] M. Rakib Uddin, J.S. Cho, Y.H. Won, All-optical NOR and NOT gates at 10 Gb/s based on gain modulation in Fabry–Perot laser diode, in: Proceedings of COIN, 2008, pp. 1–2. [4] A. Bogoni, L. Potı‘, R. Proietti, G. Meloni, F. Ponzini, P. Ghelfi, Regenerative and reconfigurable all-optical logic gates for ultra-fast applications, Electron. Lett. 41 (2005) 435–456.

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Please cite this article in press as: P. Singh, et al., Designs of all-optical NOR gates using SOA based MZI, Optik - Int. J. Light Electron Opt. (2014), http://dx.doi.org/10.1016/j.ijleo.2014.02.032