Analytic Study And Numerical Simulation On Optical Solitons Interaction

The propagation of the light wave within dispersive nonlinear medium maintains highly stable, with neither the wave form nor the wave speed changing, in the formation of soliton, under the balance between group dispersion and nonlinearity. According to such characteristic, optical soliton works as an effective information carrier to perform the long-haul and ultra-large-capacity communication system. However, when solitons inputted into the medium are not separated enough, the mutual interaction of adjacent solitons would leads to the aberration of the sequence of solitons and serious distortion of the pulse sequence. Therefore, study on the soliton interaction in nonlinear dynamics system based on the nonlinear Schr?dinger-typed equations plays a crucial role towards the realizati on of the soliton-based optical communication system.The theory of optical soliton is based on the Nonlinear Schr?dinger Equation(NLS) mathematically, which describes the electromagnetic wave propagation in dispersive nonlinear medium. The master dissertation is devoted to study the soliton interaction by solving the NLS equation in both analytic and numerical method.Firstly, Hirota bilinear method is performed to solve the high-order NLS equation analytically to obtain the one-soliton and two-soliton solutions. Also, the coupled NLS equation is solved to get the analytic two-soliton solution. Afterwards, Matlab computer program is compiled to conduct a symbolic computation analysis on the propagation of single soliton and the soliton interaction, obtaini ng intensity profiles and evolution of solitons expressed via one-soliton and two-soliton solutions. Of physical and optical interests, relevant properties of solitons and its interaction with different sets of parameters have been analyzed and graphically discussed. Furthermore, the asymptotic analysis is conducted to investigate coefficient constraints and demonstrated elastic and inelastic interactions respectively.Secondly, on basis of the solution of standard NLS equation by inverse scattering method, split-step Fourier method is conducted to perform numerical simulation on high-order NLS equation by compiling Matlab program, to obtain the temporal and spectral evolution of fundamental soliton, second-order soliton and three-order soliton. From physical and optical perspective, relevant properties of solitons with different parameters have been analyzed and graphically discussed. Also, by solving perturbed NLS equation in two-soliton and three-soliton solutions, two-soliton, three-soliton and two high-order solitons interactions are numerically simulated, to investigate the influence of initial relative separation, phase and amplitude ratio separately.