All Optical Half Adder Design Using Equations Governing XGM and FWM Effect in Semiconductor Optical Amplifier V. K. Srivastava, V. Priye Indian School of Mines University, Dhanbad srivastavavikrant@hotmail.com ABSTRACT In this paper Mechanism of XGM and FWM, in SOAs is taken into consideration to develop the logic of the half adder circuit. A Matlab simulation analysis based on cross gain modulation in a semiconductor optical amplifier is presented. This work shows the utilization of nonlinear properties of the semiconductor optical amplifier SOA in constructing optical logic gates. The various equations representative of the pump, probe and conjugate pulses in a SOA are first solved. The pulse behavior are analyzed and applied to realize behavior of alloptical various gate. This design is very economical and integration capable. The full design is easy to understand and one can approach to make chip. Error monitoring and error debugging in our design is easy than all other design reported yet. The various outputs can be manipulated in different manner by making change in inputs. The waveform proves the behavior of Half Adder circuit taken into consideration. Fully tested and verified output is presented in this paper. Keywords: Optical half adder, Optical Logic Gates, Semiconductor Optical Amplifier, cross gain modulation, four wave mixing. 1. Introduction Optical units have the advantage over electronic ones in situations where lightweight is critical, the environment is hazardous (for example inflammable), low power is important, and data is already in optical form. Therefore, all optical binary logic gates are expected to become a key technique in future communication networks. A binary half adder is a well known function in electronic gates and is a basis for enhanced complex processing circuits such as a full adder, a binary decoder, and a binary counter. The reference circuit for developing all optical binary half adder using SOA s has been take from [2]. As electronic circuits are anticipated to confront the speed limitation, efforts on the realization of all optical logic systems are eventually increasing. All optical binary half adders have been reported by using many optical designs such as terahertz optical asymmetric demultiplexers (TOAD) and ultra fast nonlinear interferometer. Comparing to techniques based on a fiber, wavelength conversion techniques based semiconductor optical amplifiers (SOA) are attractive because of their high gain, high saturation output power, wide gain bandwidth, compactness, and integratibility with other photonic devices. The cross gain modulation (XGM), one of several wavelength conversion techniques based on SOAs, is simple to implement and has shown impressive operation for a high bit rate. Moreover, the XGM shows a high conversion efficiency as well as insensitivity to the polarization of input signals. The cross gain modulated (XGM) gate is extremely simple to assemble. It is polarization insensitive because of polarization independent SOA gain, and it is very power efficient. It also turned out that the gate can be extremely fast, and, by 1998, bit rate capabilities of 100 Gb/s were reported. 396
In the present paper, nonlinear equations governing XGM in SOA is solved for two input signals that are combined in different manner to show a XOR and AND operation. Next, by combining the both XOR and AND logic an all optical half adder circuit is realized. The simulation is done on MATLAB platform. 2. Simulation Method In our approach the reference equations are taken from S Junqlang et al.(2001) and different parameters which are taken into consideration are tabulated below in table (1). (1) Where A 0 (0, t), input pump pulse amplitude at any end of SOA, A 0 (L, t), input pump pulse amplitude at any length L of SOA,L= length of SOA, t=time.rest parameters are defined in Table I. (2) Where A 1 (0, t), input probe pulse amplitude at any end of SOA, A 1 (L, t), input probe pulse amplitude at any length L of SOA, L= length of SOA, t=time.rest parameters are defined Table I. (3) Where A 2 (0, t), input conjugate pulse amplitude at any end of SOA, A 2 (L, t), input conjugate pulse amplitude at any length L of SOA, L= length of SOA, t=time.rest parameters are defined in Table I. (4) Where, The amplification function h and coupling coefficient (2001). ij are defined in S Junqlang et al. 397
2. Result and Discussion Table 1: Parameters used in simulation work Parameters Symbol Values Unit Length of the amplifier L 450 µ m Small signal gain g 1.54*10 m 1 Carrier lifetime s 300 ps Nonlinear gain compression t 0.13 w 1 for carrier heating Non linear gain compression for spectral hole burning shb 0.07 w 1 Traditional linewidth 5.0 enhancement factor Temperature linewidth T 3.0 enhancement factor Linewidth enhancement factor for spectral hole burning shb 0.1 Time for carrier carrier 1 50 fs scattering Time for carrier photon h 700 fs scattering Fig 1 shows the general concept of an optical half adder based on the XGM. In an XOR (Ā B + A ) gate, Boolean A is obtained by using signal A as a probe beam and signal B as a pump beam in SOA 1. Also, Boolean Ā B is obtained by using signal B as a probe beam and signal A as a pump beam in SOA 2. By adding two outputs from SOA 1 and SOA 2, Boolean (Ā B + A ) (logic XOR) can be obtained. In an AND (A.B) gate, Boolean is firstly obtained by using signal B as a pump beam and clock signal as a probe beam in SOA 3. By passing signal A as a probe beam and as a pump beam through SOA 4, Boolean A.B is acquired. The combination of the XOR and AND gates as SUM and CARRY gives the operation of a half adder. The following waveforms shown below are the results of simulation. 4 398
2.1 Half Adder Circuit using SOA s Figure 1: XOR and AND Gate using SOA s At first All optical XOR gate is designed. Basic digital XOR gate is shown in Fig. 1 and its truth table is shown in truth table 2 given below. Fig. 2 represents basic logic XOR gate structure using two SOAs. With proper manipulation of pump and probe signal the truth table is verified. The Fig. 6 shows an XOR output with input A=[1 1 0 1 1 1 0 1],and B=[1 0 1 0 1 0 1 0].For these pulse of inputs the generated output is [0 1 1 1 0 1 1 1].This verifies the truth table of XOR gate. Truth table 2: Truth Table of XOR Gate A B Y 0 0 0 0 1 1 1 0 1 1 1 0 Xor output (for input b=[1 0 1 0 1 0 1 0] and a=[1 1 0 1 1 1 0 1]) Figure 2: Input pump B of SOA 1=[1 0 1 0 1 0 1 0] 399
Figure 3: Input probe A of SOA 1=[1 1 0 1 1 1 0 1] Figure 4: Input pump A of SOA 2=[1 1 0 1 1 1 0 1] Figure 5: Input probe B of SOA 2=[1 0 1 0] Figure 6: Final XOR output =[0 1 1 1 0 1 1 1] In Figure 2, shown above Input pump B of SOA 1 is taken as B=[1 0 1 0 1 0 1 0]. In Fig 3, Input probe A of SOA 1 is taken as A=[1 1 0 1 1 1 0 1]. In Fig 4, Input pump A of SOA 2 is taken as A=[1 1 0 1 1 1 0 1]. In Fig 5, Input probe B of SOA 2 is taken as A= [1 0 1 0 1 0 1 0]. Fig 6, represents XOR Output= [0 1 1 1 0 1 1 1]. This clearly describes that if the inputs (A,B) as (0,1) or (1,0) are applied to SOA as shown in Fig 1 in case of XOR logic, it results a high output and for the rest combination outputs are logic 0, which is the characteristics of XOR Gate. 400
Next a logic for AND gate is designed. Fig. 1 shows that in an AND (AB) gate, Boolean is firstly obtained by using signal B as a pump beam and clock signal as a probe beam in SOA 1. Next, by passing signal A as a probe beam and as a pump beam through SOA 2, Boolean AB is acquired. Column AB of the above Truth table 3 indicates logic behavior of AND gate. The full design needs two SOAs. At first the input A=[0 1 1 0 0 1 1 0],and B=[1 0 1 1 1 0 1 1] are applied in SOA 4 and SOA 3 respectively. Clock is taken as [1 1 1 1 1 1 1 1].For these pulse of inputs the generated output is [0 0 1 0 0 0 1 0].This verifies the truth table of AND gate. Truth table for AND Logic can be given as Truth table 3: Truth Table of AND Gate A B AB 0 0 0 0 1 0 1 0 0 1 1 1 AND output for input b=[1 0 1 1 1 0 1 1], a=[0 1 1 0 0 1 1 0], clock=[1 1 1 1 1 1 1 1]) Figure 7: Input pump B=[1 0 1 1 1 0 1 1], Input clock=[1 1 1 1 1 1 1 1] and Input probe A=[0 1 1 0 0 1 1 0] Figure 8: Final output of AND=[0 0 1 0 0 0 1 0] 401
In Fig 7, Input pump B of SOA 1 is taken as B=[1 0 1 1 1 0 1 1], Input probe A of SOA 1 is taken as A=[0 1 1 0 0 1 1 0] and Input clock signal is taken as clock=[1 1 1 1 1 1 1 1]. Fig 8, represents XOR Output=[0 0 1 0 0 0 1 0]. This clearly describes that if the inputs (A,B) as (0,0) or (1,0) or (0 1) are applied to SOA as shown in Fig 1 in case of AND logic, it results a low output and for the combination (1,1) output is logic 1, which is the characteristics of AND Gate. 4. Conclusion We have successfully demonstrated an all optical binary Half Adder circuit using cross gain modulation (XGM) effect in individual SOAs. The designed circuit is easily integrable on a single chip to make a compact and stable logic device which can be further used for other signal processing application. 5. References 1. J. H. Kim, Y. T. Byun, Y. M. Jhon, S. Lee, D. H. Woo, and S. H. Kim, All optical half adder using Semiconductor Optical Amplifier based devices, Opt. Commun. 218 (2003),pp 345 349. 2. Sang Hun Kim1, Jae Hun Kim, Jae Won Choi1, Chang Wan Son, Young Tae Byun, Young Min Jhon, Seok Lee, Deok Ha Woo, and Sun Ho Kim, All optical half adder using cross gain modulation in semiconductor optical amplifiers, Optics Express. Opt. Vol. 14(2006), No. 22 3. A. J. Poustie, K. J. Blow, A. E. Kelly, and R. J. Manning, All optical binary half adder,, (1998), pp 22 26. 4. D. Tsiokos, E. Kehayas, K. Vyrsokinos, T. Houbavlis, L. Stampoulidis, G. T. Kanellos, N. Pleros, G. Guekos, and H. Avramopoulos, 10 Gb/s all optical half adder with interferometric SOA gates, IEEE Photon. Technol. Lett. 16 (2004)., pp 284 286. 5. B. K. Kang, J. H. Kim, Y. T. Byun, S. Lee, Y. M. Jhon, D. H. Woo, J. S. Yang, S. H. Kim, Y. H. Park and B. G. Yu, All optical AND gate using probe and pump signals as the multiple binary points in cross phase modulation, Jpn. J. Appl. Phys. 41 (2002), pp 568 570 6. S. Lee, J. Park, K. Lee, D. Eom, S. Lee, and J. H. Kim, All optical exclusive NOR logic gate using Mach Zender Interferometer, Jpn. J. Appl. Phys. 41 (2002)., pp 1155 1157 7. H. Lee, H. Yoon, Y. Kim, and J. Jeong, Theoretical study of frequency chirping and extinction ratio of wavelength converted optical signals by XGM and XPM using SOA s, IEEE J. Quantum Electron. 35 (1999). pp 1213 1219 402
8. T. Durhuus, B. Mikkelsen, C. Joergensen, S. L. Danielsen, and K. E. Stubkjaer, All Optical Wavelength Conversion by Semiconductor Optical Amplifiers, J. Lightwave Technol. 14 (1996), pp 942 954. 9. K. E. Stubkjaer, Semiconductor Optical Amplifier Based All Optical Gates for High Speed Optical Processing, IEEE J. Sel. Top. Quantum Electron 6 (2000), pp 1428 1435 10. X. Jin, T. Keating, and S. L. Chuang, Theory and Experiment of High Speed Cross Gain Modulation in Semiconductor Lasers, IEEE J. Quantum Electron. 36 (2000), pp 1485 1493 11. X. Zhang, Y. Wang, J. Sun, D. Liu, and D. Huang, All optical AND gate at 10 Gbit/s based on cascaded single port couple SOAs, Opt. Express 12 (2004), pp 361 366. 12. J. H. Kim, Y. M. Jhon, Y. T. Byun, S. Lee, D. H. Woo and S. H. Kim, All optical XOR gate using semiconductor optical amplifiers without additional input beam, IEEE Photon. Technol. Lett. 14 (2002), pp 1436 1438 13. J. H. Kim, B. C. Kim, Y. T. Byun, Y. M. Jhon, S. Lee, D. H. Woo and S. H. Kim, Alloptical AND gate using cross gain modulation in semiconductor optical amplifiers, Jpn. J. Appl. Phys. 43 (2004)., pp 608 610 14. S. H. Kim, J. H. Kim, J. W. Choi, Y. T. Byun, Y. M. Jhon, S. Lee, D. H. Woo, and S. H. Kim, All optical NAND Gate using cross gain modulation in Semiconductor Optical Amplifiers, IEE Electron. Lett. 41, pp 1027 1028. 15. A. D. Ellis, A. E. Kelly, D. Nesset, D. Pitcher, D. G. Moodie, and R. Kashyap, Error free 100 Gb/s wavelength conversion using grating assisted cross gain modulation in a 2 mm long semiconductor amplifier, Electron. Lett., vol. 34 1998, pp 1958 1959. 16. K. L. Hall and K.A. Rauschenbach, Fiber optics and optical communications 100 Gb/s bitwise logic, Opt Lett., vol. 23, no. 16, (1998), pp 1271 1273 17. S Junqlang et al., Analytical solution of Four wave mixing between picosecond opticalpulses in semiconductor optical amplifiers with cross gain modulation and probedepletion, Microwave and Optical technology Letters, Vol. 28, No. 1 (2001), pp 78 82. 403