1.       Introduction

 Recently, there is an increasing interest among researchers in the replacement of electrons with photons due to several advantages such as low crosstalk, high speed and bandwidth, parallel signal processing etc. Hence optical switching and interconnections will be the best alternative for the coming generation. The important aspects of all-optical computing are the possibility to integrate a large number of devices in a small chip and the possibility to cascade a large number of devices. Till now so many all data encoding techniques have been reported to design multiplier circuit such as polarization encoding, phase encoding, intensity encoding etc., [1,2]. But it is very difficult to maintain the specific state of polarization of the polarization encoded data, phase of the phase encoded data, and threshold intensities of the intensity encoded data in long haul communication system, and therefore, all these proposed schemes lead to bit error problems [3]. In this article, the authors propose a new method of implementing two-bit-binary multiplication operation using frequency encoded data. The advantage of frequency encoded data is that, frequency is the fundamental character of a signal and it does not alter in reflection, refraction, absorption [4] etc., during transmission and therefore communication is almost bit error free [4].

 2.       Theory 

2.1.  Semiconductor Optical Amplifier

The increasing data traffic and the advantages of fiber optics for data transmission are the basic reasons behind the interest in the development of optical components, especially those capable to process the signals in the optical domain without the need of cumbersome opto-electro-optical conversions. Such a component, with central interest in fiber communications is the Semiconductor Optical Amplifier (SOA) and it is shown in (Figure 1).

The reason behind the growing interest in SOAs is their ability to amplify and process optical signals in a wide range of bit rates at modest bias power requirements and in a tiny volume [5]. (Figure 1) depicts the basic structure of a SOA. The incoming optical beam is coupled into the active waveguide of the SOA. The free carrier population in the active region is inverted by electrical pumping providing optical gain. Thus, the optical beam is amplified during the propagation along the active waveguide and emerges from the opposite facet of the chip. SOAs are compact, electrically pumped and have a large optical bandwidth. Moreover, the semiconductor technology offers a wide flexibility in the choice of the gain peak wavelength by just appropriately choosing the material composition of the active layer. Another key advantage is that these devices can be integrated with other active or passive optical components to generate more complex functionalities. Finally, they are potentially cheap, according to the mature technology and economics of scale. The SOA is of two types: Fabry-Perot amplifier shown in (Figure 2) and travelling wave amplifier shown in (Figure 3).

In Fabry-Perot amplifier the light entering active region is reflected several times from cleaved face and is amplified as it leaves the cavity. The travelling wave amplifier is an active medium without reflective facets. So that the input signal is amplified by a single passage through active region.

3.       Optical Multiplier

For the past several years, scientists have been trying to use the advantages in optics in data and signal processing because of its high speed, bandwidth, response time, and low noise etc. over electronics. All-optical combinational & sequential logic circuits and many other such devices are already developed. The prime motive in optical computation is to achieve the super-fast computation which is totally controlled by all-optical techniques. The multiplier is a basic requirement in a data processing [5]. It multiplies the N*M bit. Here, the binary logic state ‘1’ and state ‘0’ are encoded by the optical beams of frequency ‘v2’ and ‘v1’, respectively. Let two two-bit binary numbers are A = (A1A0) and B = (B1B0). Their multiplication gives the result Y = ‘S3S2S1S0’. The optical multiplier is designed by using all optical AND and Optical HALF Adder.

3.1.  Optical and Gate

The all-optical AND gate is one of the fundamental logic gates because it is able to perform the bit-level functions such as address recognition, packet-header modification, and data-integrity verification. The optical and gate consists of add drop mux, SOA and WDM. The channels of WDM are varied to perform AND operation [6].

3.2.  Optical XOR Gate

The all-optical XOR gate is a key technology to implement primary systems for binary address and header recognition, binary addition and counting, decision and comparison, encoding and encryption, and pattern matching.

3.3.  Optical Half Adder

The optical half adder adds two input bits and generates a carry and sum, which are the two outputs of a half adder shown in (Figure 4).

The input variables of a half adder are called the augend and addend bits. The output variables are the sum and carry and its corresponding truth table is shown in (Table 1).

3.4.  Two Bit Binary Multiplier

The all optical circuit for implementing the frequency encoded multiplication operation is shown in (Figure 5).

It is consisting of four all optical AND logic gates and two half adders. Input data of AND1 is A0, B0; for AND2 is A0, B1; for AND3 is A1, B0; for AND4 is A1, B1. The output of AND1 gives Least Significant Bit (LSB) ‘S0’ of the multiplication. Output of the AND2 and AND3 are used as the input of HA1.Sum of HA1 is transmitted to ‘S1’and carry is added with the output of AND3 by means of HA2 which finally gives ‘S2’ and carry ‘S3’.

Where,

S0=AB; S1= (A0B1) XOR (A1 B0); S2= (A1B1) XOR (Carry); S3= Carry;

The optical two-bit binary data multiplier has sixteen cases for different states. Some of the input combinations and corresponding output spectrums are given below. Here, there are two different types of input beams. To represent the logic state 1 v2 is used. To represent the logic state 0 v1 is used. This shows the output spectrum of the input ‘1000’. The result of output spectrum is ‘0000’ and it is shown in (Table 2).

And its corresponding output is shown in (Figure 6).

4.       Results 

A Binary Multiplier is a digital circuit used in digital electronics to multiply two binary numbers and provide the result as output. The method used to multiply two binary numbers is similar for multiplying decimal numbers which is based on calculating partial product, shifting them and adding them together. Similar approach is used to multiply two binary numbers. Long multiplicand is multiplied by 0 or 1 which is much easier than decimal multiplication as product by 0 or 1 is 0 or same number respectively. The two numbers A1A0 and B1B0 are multiplied together to produce a 4-bit output S3S2S1S0. The optical two-bit binary multiplier is shown in (Figure 6).

5.       Conclusion

The whole process is all an optical one, and the operational speed depends on the switching time of the SOA. The proposed optical binary data multiplier is designed using the all optical AND gate and all optical half adder and it is successfully simulated using Opti system. The results thus obtained satisfy the truth table. Realization of the all optical logic gates will provide not only increased speed and capacity of telecommunication systems, but also various functionalities including optical packet switching, add/drop, decision making, bit extraction, regenerating, and basic or complex optical computing. Since all the conversion techniques are based on frequency encoding/decoding technique, it is free from bit error problems which exist in conventional encoding/decoding techniques.

Figure 1: Structure of Semiconductor Optical Amplifier.

Figure 3: Gain Vs Wavelength of Fabry-Perot And Travelling Wave Amplifier.

Figure 4: Optical HALF Adder.

Figure 5: Optical two-bit binary multiplier.

Figure 6: Optical Two-Bit Binary Multiplier.

Table 1: Truth table of Optical HALF Adder.

Table 2: Truth Table of Multiplier.

1.       Ahmed JU, Awwal AAS (1991) Polarization-encoded optical shadow casting: an efficient multiplier design. Microwave Opt Technol Lett 4: 328-331.

2.       Moniem TA, Rabou NA, Sayed EM (2008) Parallel Shift Register and binary multiplier using optical hard components. Opt Eng 47: 035201.

3.       Gayen DK, Chattopadhyay T, Pal RK, Roy JN (2010) All-optical Multiplication with the help of semiconductor optical Amplifier-assisted sagnac switch. J Comput Electron 9: 57–67.

4.       Garai SK (2011) A novel all optical frequency encoded method to develop arithmetic and logic unit (ALU) using semiconductor optical amplifiers. IEEE J Lightwave technology 29: 3506-3514.

5.       Schubert C, Schmidt C, Ferber S, Luwig R, Weber HG (2003) Error free all optical add drop multiplexing at 160 Gbit/s. Electron letter 39:1074-1076.

6.       Fu S, Zhong WD, Shum P, Wu C, Zhou JQ (2007) Nonlinear polarization rotation in semiconductor optical amplifiers with linear polarization maintenance. IEEE Photonics technology letter 19: 191-193.