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Comparative study of all-optical INVERTER and BUFFER gates using MZI structure

In the paper, one input optical gates i.e., INVERTER and BUFFER have been designed using some basic assumption to analyze with the help of Semiconductor Optical Amplifier based Mach–Zehnder Interferometer structure. The results are optimized by iterative process. The proposed design of optical gates presents low complexity, high scalability and more feasible to evaluate through digital Boolean analyzation. The digital Boolean analyzation is analyzed by some basic Boolean rules and assumptions whichmakes the designmore digital so that it can be compatible for more than one input optical gates also. Optical Gate is designed to get constructive and destructive interference for pump and probe as they are injected into SOA simultaneously. The phasemodulation is converted into intensity modulation which gives a Boolean result. The paper is optimized by Eye diagram, Q factor, wavelength spectrum and frequency chirp for both the gates. The comparative results of extinction ratio for both the gates have also been discussed. The design is supported by theoretical analysis, simulation tool (Optsim) and Boolean explanation. The proposed designs are constructed with same pattern which supports the same Boolean analysis.


Introduction
An optical fiber communication system is similar to any other communication system. The commercial demand for higher capacity transmission is needed to introduce a new information service and broadband service. The increase demand of bandwidth and cost are interconnected. Optical technology has succeeded in reducing the cost of bandwidth to improve the novel set of applications of bandwidth, making it more useful in behavioral pattern. The survival and improvement of optical fiber communication is based on the development of laser, amplifiers, photo detectors, switches, optical gates, optical circuits and optical devices etc. Last few decades, the research is going on to provide optical signal processing which include optical logic gates, memory elements, power limiters and pulse shapers, differential amplifiers, and A/D converters etc. All-optical logic gates are in category of ultra-fast switching device that can perform a Boolean operation in compact integration circuit [1][2][3]. Moreover, all optical logic gates response to light in non-linear manner to perform an optical computing where one optical data stream controls another data stream. In optical communication systems, an optical logic operation plays an essential roll to perform the optical signal processing. Now days, most of the research are diverted in the area for growing high speed optical networks. Therefore, it is essential to design an all-optical gate to avoid power consumption in opto-electronics conversion. The research is going in the field of optical logic gates is to demonstrate, ultra-highspeed optical signal processing. Many approaches have been implemented to design an optical logic gates by introducing SOA [4,5] in waveguide, either in line or in design of MZI to produce phase modulation. Design of optical logic gates in which SOA is used, has advantage of simple implementation with large bandwidth and highpower efficiency. SOA is a single mode waveguide structure with small size, so it is easy to integrate to produce subsequent systems which are essential in optical communication [6]. For optical logic operation, a nonlinear effect is required which is introduced by SOA, making it as an excellent choice for optical switches. At low power level switching speed of SOA depends on driving power that offers potential for fast switching in picoseconds using pico-joules energy. Recent optical digital system operation is also based on digital logic design [7]. Now, to setup this technology it is important to develop basic Boolean function such as optical gates which can operate at high speed. These logic elements include the traditional Boolean logic functions operating optically such as INVERTER, BUFFER, OR, AND, NOR, XOR, NAND etc. [8,9] and circuits such as parity checker, all-optical adder, shift registers and memory elements [10][11][12][13].
Many research papers have investigated one input NOT gate with the help of different schemes [14][15][16]. In the paper, we have done comparative study of one input gates i.e., BUFFER and INVERTER [17,18] with the help of two SOAs in MZI structure that made it possible to use its nonlinearity for gates. The study is also analyzed by the new optical Boolean synthesis. The switching operation of INVERTER helps to construct two inputs NOR gate as well as n-input NOR gate. Same as switching operation of Buffer helps to construct two inputs OR gate as well as n-input OR gate. The design result and analysis was supported by the opti-sim simulator and theoretical analysis.

Proposed model and principle
The proposed model of INVERTER/BUFFER gates, as in Figure 1 consists of a symmetrical Mach-Zehnder Interferometer (MZI) where the two SOAs are placed in series with multiplexer at the upper and lower arm of MZI. In the simulated design, the optical data (0100000 1001000001001) and string of (11111111111111111111)/ (00000000000000000000) which is pump signal are fed in the upper and lower arms of multiplexers through CW laser to perform Boolean INVERTER/BUFFER operation. Mode lock laser (MLL) is used to generate a string of (11111111111111111111)/(01000001001000001001) which acts as a probe signal is fed into the upper arm of first 3 dB coupler. The phase shift of π/2 is produced between upper and lower arm of probe pulse traveling through it, as it is fed into the first 3 dB coupler. Pump and probe at different wavelengths are injected into SOA, so that it may operate under the gain saturated condition. As XGM occurs in SOA, available optical gain will be distributed between pump and probe wavelengths according to their photon densities. Thereby, the probe is compressed, giving the inverse effect on the gain, available to the pump wavelength. Therefore, the outputs of SOA1 and SOA2 for INVERTER/ BUFFER gates with respect to the probe signal are (10111110110111110110)/(00000000000000000000) and (00000000000000000000)/(01000001001000001001) respectively. After passing through SOAs these saturated signals are fed into the second 3dB coupler, again the phase shift of π/2 is created on the probe pulse. Due to the phase modulation in MZI structure with second 3dB couplers, the total phase shift i.e., π/2 (introducer by first coupler) added to π/2 (introduced by second coupler) equals to π (at T-port) for probe signal. Therefore, if outputs of SOAs are same, it is canceled, and no pulse appears at the T-port. If it is different, then it still appears as T-port giving the INVERTER/BUFFER operation as (01000001001000001001)/(01000001001000001001).

Theoretical analysis
In the proposed model, of the given design the path length (L) of two arms of interferometer is same and both signals present the same wavelength (λ). As θ 1 and θ 2 is a phase difference created by both the arms then, total phase difference created by both the arms of MZI is Δθ that can be described by where, n 1 and n 2 are refractive index of both the arms of MZI. As in design, the first 3dB coupler of 50:50 coupling ratio for which ϵ 0.5can be calculated with the scattering matrix or propagation matrix as in [19] is given by If I 1 and I 2 are intensity of light at the input terminal of MZI, which is output of Mode lock laser and MUX 1 and MUX 2 is intensity of light after passing through first 3dB coupler then, After passing through SOA, due to XGM, the MLL pulse is compressed, giving the inverse effect on the gain, available to the CWL pulse. This will create the phase change in MLL pulse, so the propagation matrix is given as [20] The transfer matrix of an MZI can be defined as Since the second 3 dB coupler has same coupling factor, so at the output of MZI can be calculated as As there is no signal in input 1 so, the output power at T-port and R-port is given as P T-port T port .T port* sin 2 Δθ 2 P 1 (7) P R-port R port .R port* cos 2 Δθ 2 P 1 (8) where, P 1 is power at input terminal-1. From this equation we can conclude that, At Δθ = 180°Power of T-port has maximum intensity of light and R-port has minimum. To create the optical logic gates with good performance, it is always required that for logic 0, we have to create a proper phase difference of π so that pulse is totally canceled and no power should occur at the output terminal.

Boolean analysis
As in digital gates, we expect the same output from the alloptical logic gates shown in Table 1. The proposed one input gates are based on XGM in SOA and XPM in MZI configuration. The design of two input gates with four case studies was mentioned in [21] Boolean analysis for the proposed gates is given as Condition-1-Due to cross gain modulation (XGM) in SOA.
There will be two Rules Rule-1-If Input probe traveling through MLL i.e., I probe = 0, then after passing through SOA it is multiplied to corresponding pump signal i.e., I pump.
Rule-2-If Input probe traveling through MLL i.e., I probe = 1, then after passing through SOA it is added to corresponding pump signal i.e., I pump .
Condition-2-Due to cross phase modulation (XPM) in MZI configuration. There will be two Rules Rule-1-After passing through SOAs, if data are same, then it will be canceled, and the output will be '0' at T-port. Rule-2-After passing through SOAs, if data are different, then it will be added, and the output will be '1' at T-port.
At the upper arm of INVERTER gate Input one from CW laser, acts as a pump multiplexed with string of ones, generated from MLL laser acting as probe signal, therefore Output of upper arm multiplexer is (I 1 I 2 ) CWL .
( 1 1 1 2 )   At the upper arm of BUFFER gate Input data, I from CW laser, acts as a pump multiplexed with same Input I, generated from MLL laser acting as probe signal, therefore Output of upper arm multiplexer is (I 1 I 2 ) CWL · (I 1 I 2 ) MLL = (0 1). (0 1) Output of SOA1 is = {(0.0). (1 + 1)} as condition-1 Rule-1&2, = {0.0} At the lower arm of BUFFER gate string of ones from CW laser, acts as a pump multiplexed with Input I, generated from MLL laser acting as probe signal, therefore

Specification and method
The proposed design of optical gates presented in Figure 1, of pump signal 10 Gb/s, with peak power of 0.05 W of continuous wave. Binary sequence of 1550 nm with chirp factor 0.5 A driven by raised cosine RZ pulse is generated through PRBS. Mach-Zehnder modulator is used to modulate the signal with point per bit 2 5 -1. Pump signal peak power, generated through CW laser is 0.015 × 10 −4 W and probe signal peak power, generated through ML laser is 1 × 10 −3 W with same PRBS at 1555 nm. Modulated Gaussian pulse, chirped with 0.5 factors driven by raised cosine RZ pulse launched into multiplexer through 3 dB coupler. After passing through both the arms of interferometer, both the arms data are merged through second 3 dB coupler at T-port to achieve the required gate output.   filter is used to filter the probe pulse giving the extinction ratio 18.71 dB where the maximum Q-factor lies between −4 × 10 −11 and 4 × 10 −11 s. This shows the significant effect of noise with decision point at zero decision offset which is 20 dB. 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. It was developed to address the need for a practical and accurate way of measuring the system margin and defined as linear unit of SNR for decision circuit Figure 3(c) shows the wavelength spectrum, which indicates that the highest power pulse occurs at 1555 nm with 5.9 × 10 −5 W. Other two pulses of lower power are resultant of four waves mixing which are filtered by Lorentzian filter at the output. When probe and pump pass through SOA, then due to XGM, there is a phase modulation which gives raises an instantaneous change in refractive index. This creates a variation in optical frequency with time given in Figure 3(d). Figure 4(a) shows the variation of ER at different data wavelengths for three different bitrates i.e., 9.0, 10.0 and 11.0 Gb/s. The extinction ratio for RZ modulation format at 9.0 Gb/s is higher than 11.0 Gb/s by 3.0 dB at 1550 nm pump wavelength as for higher bit rate resultant output is degraded. Maximum extinction ratio 19.25 dB is found at 1550 nm for 9.0 Gb/s. Figure 4(b) shows the eye pattern with color code with respect to decision time and decision level. The highest intensity of light is shown in red and lowest with pink. Depending upon the pulse generation, these data are defined as pump and probe signals. The output of both multiplexers and SOAs are shown in Figure 5(d)-(g). Figure 5(h) shows the output of BUFFER gate results at transmission port. In Figure 6(a) and (b) show the eye diagram and Q-factor filtered by Gaussian filter at T-port with extinction ratio 30.0 dB where the maximum Q-factor lies between −1.5 × 10 −11 and 1.5 × 10 −11 s. In eye diagram, the effect of pattern dependence is due to the laser properties as dispersion, nonlinearity, or certain noise. This problem with eye exhibiting pattern dependence is impossible to fit as a simple Gaussian distribution to either the mark or space level. Eye diagram of the received signal is important because it represents a direct measure of a system performance deprivation caused by transmission deficiency and environmental change. Figure 6(c) shows the wavelength spectrum, which indicates that the probe pulse power occurs at 1555 nm with 10.0 × 10 −8 W. Wavelength spectrum at the output T-port is due to the four-wave mixing (FWM) which is analogous to intermodal distortion occurring at output signal. Other pulse at 1550 nm is a resultant of pump power which is filtered at the output. During the modulation process in SOA a time dependent phase change lead to a variation in optical frequency of the pulse at each instant given in Figure 6(d).

Decisions
Extinction ratio for RZ modulation format at 10.0 Gb/s is compared in Figure 8, for Inverter and Buffer. It is seen that the extinction ratio of Buffer is higher than Inverter for the pump wavelength in the range of 1550-1553 nm because in Inverter when string of ones from clock wave laser passes through SOA, it is not totally suppressed but still some fraction of light is left out which gives the inferior extinction ratio than Buffer.

Scope of the work
Tremendous developments in all-optical semiconductor optical amplifier-based Mach-Zehnder Interferometer gates have been achieved in the last decade. Advance research and technological innovations have improved the design of all optical gates. Nowadays, it has become necessary 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. Gates that can be controlled optically are basic elements for high speed signal processing which can avoid optoelectronic conversion in communication systems. In future, all-optical logic gates are the key elements for optical signal processing such as, data encryption, address recognition and label swapping etc. The designs aim to achieve the goal through simulation and Boolean analysis in terms of gates to provide simple design rule. Still there is a vast scope to develop the memory element with the help of semiconductor optical amplifier-based Mach-Zehnder Interferometer structure. Therefore, there is broad scope for the future work in the field of all-optical digital circuit.

Conclusions
In the paper, we demonstrated the basic design perform alloptical INVERTER/BUFFER gates. The purpose is to get the output pulse at same wavelength for comparative study. And also develop a common Boolean rule for all-optical logic gates at same output pulse as in digital gates. Extinction ratio is a key parameter to optimize the gate operation to get a similar result as in Digital gates. In digital gates we define the gate operation if zero i.e., less than threshold voltage and one i.e., above threshold voltage. In optical gates zero, is significance of no light pulse and one is presence of light pulse. Therefore explaining optical gates with extinction ratio will make it easy to analyze and compare with digital gates. Furthermore, as we go for a higher linewidth enhancement factor, it limits the Extinction ratio to optimize the gate performance.
Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.