Theoretical Study On Propagation Of Optical Pulse In Optical Fiber

From the analytical point of view, with the aid of the numerical simulation, we investigate the propagation properties of optical pulses for the nonlinear Schrodinger equation in picosecond regime, the higher-order nonlinear Schrodinger equation in femtosecond regime, the nonlinear Schrodinger equation with varying gain/loss and frequency chirping in homogeneous optical fibers, and Ginzberg-Landau equation that describes ultrashort pulses in the presence of self-frequency shift, respectively. The main contents are as follows:(1) By employing the direct method, the soliton periodic amplification system in optical fiber link with loss is considered, and the adiabatic solution (slowly varying portion) and first-order correction (rapidly varying portion ) for a single soliton case are presented.(2) Under Hirota condition, by making use of the inverse scattering transform, the femtosecond dark N-soliton solution for the Hirota equation is obtained, and the dark one-and two-soliton solutions are presented in explicit forms. Interesting physical applications arise from the characteristics of the grey two-soliton solution. And we extend the model beyond the Hirota conditions and obtain the generalized dark solitary wave solutions for the general higher-order nonlinear Schrodinger equation. Also, by numerical method, the stability and interaction between the femtosecond dark solitary solutions are discussed in detail.(3) From the integrability point of view, the nonlinear Schrodinger equation and the coupled nonlinear Schrodinger equation with varying gain/loss and frequency chirping are considered, and the relevant soliton solutions are given by employing the Darboux transformation, and the properties are discussed in detail. The propagation of soliton and interaction for the periodic distributed amplification line are discussed in detail, and the explicit soliton solution on continuous wave (cw) background is presented, and two exact analytic solutions that describe the modulation instability and the soliton propagation on a cw background are in detail discussed, and inelastic interaction for the vector solitons is also investigated.(4) Finally, the Ginzberg-Landau equation is considered. By the ansatz method, the chirped femtosecond solitonlike solution is given, and the stability of the solutions are studied in detail by linear stability analysis with variation method. Also the long-distance stability of the ultrashort pulse and the interaction between the solutions are also discussed by numerical method.