CALIFORNIA STATE UNIVERSITY, NORTHRIDGE Dispersion Managed Soliton A graduate project submitted in partial fulfillment of the requirements for the degree of Master of Science in Electrical Engineering By Murali Karthik Kothapalli December 2017 The Graduate Project of Murali Karthik Kothapalli is approved: Professor Xiaojun Geng Date Professor Jack Ou Date Professor Nagwa Bekir, Chair Date California State University, Northridge ii Acknowledgements The completion of this project would not have been possible without the continuous support and feedback from Dr. Nagwa Bekir, Dept. of Electrical and Computer Engg., and it was my pleasure working under her guidance. I would also like to express my gratitude to the committee members Dr. Geng Xiaojun and Dr. Jack Ou for their academic and moral support throughout the project. Last but not the least I would like to thank everyone who has directly or indirectly contributed in making the project a success. iii Table of Contents Signature Page……………………………………………………………….................................ii Acknowledgements……………………………………………………………………...….........iii List of Figures………………………………………………………………………...…………...v Abstract………………………………………………………………….…………………….....vii 1. Introduction to Optical Soliton……………………………………………………………..….1 1.1. Introduction to Optical Soliton………………………........................................................2 2. Evolution of an Optical Soliton: Mathematical Formulation…..................................................3 2.1. Evolution of Optical Soliton: Mathematical Formulation………………………………...3 2.2. Nonlinear Schrodinger Equation……………………………........................…………....3 2.3. Bright Solitons…………………………………………………………………………...4 3. Losses inside a Fiber……………………………………………………………..…………….7 3.1. Losses inside a Fiber……………………………………...……………………………....7 3.2. Group Velocity Dispersion……………………………...………………………………..7 3.3. Self-Phase Modulation……………………………………...……………….……………9 4. Communication Based on Soliton…………………………………………….……………...12 4.1. Communication Based on Soliton……………………………………………………….12 4.2. Transmission of Information Using Solitons…………………………….………………12 4.2.1. Initial Frequency Chirp…………………………………………..……………...12 4.3. Soliton Transmitters……………………………………...……………….……………..13 4.4. Interaction of Solitons…………………………………………………………………...15 5. Simulation and Results………………………………………………………..……………...18 5.1. System Design…………………………………………………………...……………...18 5.2. Results………………………………………………………………….…...…………...19 5.2.1. Group Velocity Dispersion Analysis………………………...……...……………19 5.2.2. Self-Phase Modulation Analysis…………………………...………...…………..27 5.2.3. BER (Bit Error Rate) Analysis……………………………...…………………… 30 5.2.4. GVD and SPM combined effect……………………………...……...…………...31 6. Conclusion iv List of Figures Figure 2.1: First order and Third order Soliton pulse for one soliton period………………………………………………..………………………………………….…5 Figure 2.2: Pulse evolution of a fundamental soliton for a distance range of 0 to 10 km………………………….…………………………………………………………..………….6 Figure 3.1: Frequency chirp introduced by SPM…………………........................……………...10 Figure 4.1: Figure shows the fraction of bit slot occupied by a Soliton……………………………………………………..………………………....…………..12 Figure 4.2: Evolution of a chirped input pulse into a fundamental soliton for N = 1 and C = 0.5………………………………………………………………………………………………...13 Figure 4.3: Figure shows a) Schematic b) Soliton pulse source…………………………………14 Figure 4.4: Soliton interaction for test values of relative amplitude, r and relative phase, 휃……16 Figure 5.1: Circuit Diagram to demonstrate soliton pulse propagation…………………....….....18 Figure 5.2: Layout parameters for the soliton system………………………………..…………..19 Figure 5.3: Optical fiber nonlinear properties in an optical fiber……..........................................20 Figure 5.4: Dispersion parameters in an optical fiber………………………………….………...20 Figure 5.5: Pulse broadening due to GVD for fiber length of 5 km…..........................................21 Figure 5.6: Pulse broadening due to GVD for fiber length of 10 km………………...………….21 Figure 5.7: Pulse broadening due to GVD for fiber length of 15 km…………………...……….22 Figure 5.8: Pulse broadening due to GVD for fiber length of 20 km…………………...……….22 Figure 5.9: Pulse broadening due to GVD for fiber length of 25 km…….……………......…….23 Figure 5.10: Pulse broadening due to GVD for fiber length of 30 km..........................................23 Figure 5.11: Pulse broadening due to GVD for fiber length of 35km…………………...………24 Figure 5.12: Pulse broadening due to GVD for fiber length of 40 km….……………...……......24 Figure 5.13: Pulse broadening due to GVD for fiber length of 50 km…………………..……....25 Figure 5.14: Full Width Half Maximum (FWHM) vs Fiber Length (Practically evaluated)…………………………………………………….......................................................26 v Figure 5.15: Full Width Half Maximum (FWHM) vs Fiber Length (Theoretically evaluated)……………………………………………………………………...…………………26 Figure 5.16: Effects of SPM for a fiber length of 15 km………………………..……………….28 Figure 5.17: Effects of SPM for a fiber length of 30 km………………………..……………….28 Figure 5.18: Effects of SPM for fiber length of 45 km…………………………..……………....29 Figure 5.19: Effects of SPM for fiber length of 60 km…………………………………..............29 Figure 5.20: min BER vs fiber length when only GVD is acting inside the fiber……………………………………………………………………………............................30 Figure 5.21: min BER vs fiber length when only SPM is acting inside the fiber……………………………………………………………………………............................31 Figure 5.22: Soliton in time domain after travelling 5 km……………………............................32 Figure 5.23: Soliton in time domain after travelling 15 km………………………......................32 Figure 5.24: Soliton in time domain after travelling 30 km…………………………………......33 Figure 5.25: Fiber Length vs Full Width Half Maximum when both SPM and GVD are acting…………………………………………………………………………………………......33 vi ABSTRACT Dispersion Managed Soliton By Murali Karthik Kothapalli Master of Science in Electrical Engineering This project demonstrates the design and performance analysis of an optical soliton in long distance communication systems. The soliton systems are stable and lossless, which are preserved throughout the length of the communication channel. These solitons do not spread along the link length and is reliable as compared to non-soliton communication systems. The soliton power levels are always maintained to a certain limit. The solitons are formed because of an interplay between the Group Velocity Dispersion and Self-Phase Modulation, which individually have depreciating effects on the propagating pulse. This report also demonstrated on how a sech pulse is converted to a soliton for propagation. When two solitons interact with each other during the propagation, they still would maintain their shape and power resulting in an elastic collision. vii 1. Introduction 1.1 Introduction to Optical Soliton: Optical fiber communication is a method by which we can transmit information using light pulses through an optical fiber. This method can be widely used in long-haul communications like telephone, Internet, Cable TV etc. The light travels as an electro- magnetic wave inside the optical fiber, which is modulated and serves as a carrier for carrying information. Optical fibers ae used instead of the electric cables like the copper wires, co-axial cables etc. This has changed the way of communication in telecommunication industry by providing low attenuation and interference. The light pulses travelling inside the fiber gradually broaden and peak power decreases with time and distance, and eventually overlap with other pulses and makes it impossible for the receiver input to distinguish between the pulses. This can be called as the Group Velocity Dispersion (GVD). Thus, dispersion can affect the transmission capacity and bandwidth. This dispersion can be a major problem for systems which need high bit rate and for long- distance communication systems. Optical Soliton which can cancel the dispersive effects offers a better solution for this problem. Optical solitons are solitary wave packets which can reinforce themselves to effectively balance the dispersive effects, also known as the GVD, with the nonlinear dispersive effects as it travels through the medium inside the optical fiber. Thus, optical soliton can retain its shape as it travels with time and constant velocity. The nonlinear dispersive effect also called as the Self Phase Modulation (resulting from Kerr nonlinearity) changes the frequency of the wave by causing a time-varying phase shift which directly is dependent on the intensity of the light pulse. Also, the refractive index is dependent on the intensity of the light pulse. The leading edge has a higher refractive index whereas the tail edge has the lower refractive index which eventually results in phase-shift. As we know the derivative of phase shift is frequency, any change in phase shift results in a frequency change. Thus, a soliton does not change its shape because this nonlinear property suppresses the broadening of the pulse eliminating the Group Velocity Dispersion and Inter Symbol Interference (ISI). For detailed description refer to Chapter-3. The concept of dispersion managed soliton has been a major area of research because it can be practically available in many optical communication devices and systems. In terms of nonlinear optical systems, there are two types of solitons: temporal solitons and spatial solitons both of which are the result of perfect balance