Advances in Optical Technologies

Volume 2014, Article ID 754713, 6 pages

http://dx.doi.org/10.1155/2014/754713

## Performance of All-Optical XNOR Gate Based on Two-Photon Absorption in Semiconductor Optical Amplifiers

Department of Physics, Faculty of Science, University of Fayoum, Fayoum 63514, Egypt

Received 12 September 2014; Revised 4 December 2014; Accepted 5 December 2014; Published 31 December 2014

Academic Editor: José Luís Santos

Copyright © 2014 Amer Kotb. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

All-optical logic XNOR gate is realized by a series combination of XOR and INVERT gates. This Boolean function is realized by using Mach-Zehnder interferometers (MZIs) and exploiting the nonlinear effect of two-photon absorption (TPA) in semiconductor optical amplifiers (SOAs). The employed model takes into account the impact of amplified spontaneous emission (ASE), input pulse energy, pulsewidth, SOAs carrier lifetime, and linewidth enhancement factor (*α*-factor) on the gate’s output quality factor (*Q*-factor). The outcome of this study shows that the all-optical XNOR gate is indeed feasible with the proposed scheme at 250 Gb/s with both logical correctness and acceptable quality.

#### 1. Introduction

The development of all-optical logic technology is important for a wide range of applications in all optical networks, including high speed all-optical packet routing and optical encryption [1]. An important step in the development of all-optical logic technology, which includes key functionalities in fundamental and system-oriented level such as buffering, demultiplexing, clock recovery, packet processing, wavelength conversion, data regeneration, and optical encryption/decryption, is the demonstration of optical logic elements that can operate at ultrahigh speeds. All-optical logic gates based on several different schemes have been demonstrated and reported, including that based on dual semiconductor optical amplifier (SOA) Mach-Zehnder interferometer (MZI) [2, 3], semiconductor laser amplifier loop mirror (SLALM) [4], ultrafast nonlinear interferometer (UNI) [5], four-wave mixing (FWM) process in SOA [6], or cross-gain modulation (XGM) or cross-phase modulation (XPM) in nonlinear devices [7]. All-optical logic XNOR gate using SOA is described and demonstrated earlier [8–13]. However the main limitation imposed on most of these schemes is that they cannot keep conveniently pace with the upgrades of single channel data rates in the effort to satisfy the unceasing bandwidth demand [14]. Thus in this work, we propose to address this critical issue by exploiting two-photon absorption (TPA) in SOAs, which are placed in the two arms of MZI operated in probe-dual pump mode. According to relevant pump-probe experiments, when a data modulated pump beam of appropriate intensity is launched into a SOA, the phase induced through TPA on a weak probe signal can change as fast as 1 ps, which subsequently can enable ultrafast interferometric switching of the same order [15]. Pump-probe experiments have shown that phase change takes place in duration ~1 ps or less when the pump and probe signals are injected into a SOA [16, 17]. Still so far previous reports on all-optical logic gates based on TPA process have not treated the XNOR gate [18–22]. However ASE is a degradation factor of the SOA response [23, 24] and should be considered in order to obtain realistic and accurate results for the intended all-optical logic at the pursued ultrafast data rate. In this work, I continue, extend, complete, and generalize the relevant previous work based on TPA [18–22] by investigating the high-speed performance of the all-optical logic XNOR gate with the help of numerical simulation conducted at a repetition rate of ~250 Gb/s. Among these approaches, SOA is believed to be a key component for all-optical logic gates, because it has a stronger nonlinearity than optical fibers and it can be integrated more easily. However the speed of conventional bulk SOA operation is limited by the finite gain and phase recovery time of their temporal response. The study is carried out when the effect of the ASE is taken into account in the simulation analysis. The primary noise in this calculation (which lowers the quality factor (-factor)) in the absence of ASE noise is pattern effects resulting from long recovery times of gain and gain induced phase change. The ASE causes additional output noise through spontaneous-spontaneous beat noise and signal-spontaneous beat noise. In addition if one were to measure the error rate of the gate output, the dark current of the photodiode, shot noise and thermal noise need to be considered. The ASE-related noise depends on the spontaneous emission factor () of the amplifier [1]. The employed model takes into account the impact of pulse energy, pulsewidth, SOAs carrier lifetime, and linewidth enhancement factor (-factor) on the gate’s output -factor. The outcome of our study shows that the all-optical XNOR gate is indeed feasible with the proposed scheme at 250 Gb/s with both logical correctness and acceptable quality. The input intensities are high enough so that the two-photon induced phase change is larger than the regular gain induced phase change. The advantage of this model is the lower power consumption and higher power transmission than in [18–22].

#### 2. SOA-MZI Model

The operation of the SOA-MZI can be theoretically described by using a rate equation model as shown in [11–17].

The magnitude of the TPA-induced phase shift can be expressed as [18–22]
where is the TPA coefficient, is the linewidth enhancement factor due to TPA process, and is the effective length of SOA active region. The negative sign represents the observation that the TPA induced phase change is in an opposite direction from that for the gain-induced phase change [10]. The experimentally derived is ~4-5 and the quantity is ~20–35 cm/GW [10]. For a SOA having typical active region cross section 5 × 10^{−9} cm^{2} and effective length 2 mm, = 30 cm/GW and = 4. The peak phase change experienced by the probe would be around . This phase change is large enough for temporal interference of probe pulses traveling through the two arms of the MZI.

The carrier density induced phase change is given by where is the traditional linewidth enhancement factor and is the carrier heating alpha factor.

The data inputs are assumed to be Gaussian-shaped pulse streams with temporal profile [18–24]: where represents the th pulse in the data streams and can take the logical value “1” or “0” with equal probability, is the input pulse energy, is the bit period which is given by 1000/data rate, and is the pulsewidth (full width at half maximum).

#### 3. XNOR Model

##### 3.1. Operation Principle

In this study, XNOR gate is realized by a series combination of XOR and INVERT gates [8–10]. For XOR operation, two data signals A and B are injected into the SOAs incorporated in the upper and lower arms of MZI 1. A clock stream comprising continuous “1”s is introduced in the setup from the middle input port of the configuration, as shown in Figure 1. The data signals A and B, which are spectrally located at wavelengths and , respectively, induce via cross-phase modulation (XPM) a phase shift in the split components of the clock signal, at wavelength , in each SOA. Then the recombined clock signal at the output of MZI 1 carries the result of XOR operation between the binary content of data A and B. For proper signal discrimination wavelength must be chosen so that it is different from and , while and need not be different. Initially MZI 1 is balanced, and so when A = “0” and B = “0” the decomposed clock signal components traveling through the two MZI arms do not acquire any phase shift in the respective SOAs. Thus when they recombine at the output the result is “0.” However when A = “1”, B = “0”, the clock signal replica traveling through the upper arm together with signal A acquires due to XPM a phase change, while its counterpart traveling through the lower arm does not suffer any such change. This results in “1” at the output. The same happens when A = “0,” B = “1”. However when A = “1” and B = “1” the phase changes induced on the clock signal constituents traveling through both MZI arms are equal, hence the output is “0.” The INVERT operation is obtained similarly to XOR operation if one of the data inputs is replaced by a clock signal. Then in order to realize the XNOR operation, the XOR output from MZI 1 is launched into the upper arm of MZI 2. Concurrently a continuous wave (CW) beam and another clock signal are launched into the middle and bottom input ports, respectively, as shown in Figure 1. The effect of ASE on the performance of the XNOR gate is due to the contribution both from the XOR and INVERT operations.