Propagation And Interacion On Ultrashort Optical Pulses In Optical Fiber

In the paper, we will investigate the transmission of ultrashort pulses in optical fiber. From the analytical point of view, with the aid of the numerical simulation, we will discuss the higher-order nonlinear Schrodinger equation in femtosecond regime and Ginzburg-Landau equation that describes ultrashort pulses in the presence of self-frequency shift, respectively. The main results are as follows:1. To present the basic model for the propagation of optical pulse -the nonlinear Schrodinger equation, the higher-order nonlinear Schrodinger equation, and the Ginzburg- Landau equation. Then the basic properties of the light and dark soliton, and interaction between neighboring soliton for the nonlinear Schrodinger equation are presented. Finally, the symmetric split-step Fourier methods is introduced.2. The N-soliton solutions for the integrable Hirota equation are presented by using the Darboux transformation method. As an example, the general one-soliton solution on a continuous wave background is given in its explicit form. Then, two exact analytic solutions that describe (i) modulation instability and (ii) bright pulse propagation on a continuous wave background are discussed in detail.3. The higher-order Ginzburg- Landau equation is considered, and the chirped solitary-like solution is presented. Then interaction between neighboring chirped solitary-like solution is investigated by numerical simulation method. At the same time, the shortest separation between neighboring solitons by unequal amplitude method is found.4. The dark soliton-like solution for the higher-order Ginzburg-Landau eqation and the requirement of existing dark soliton solution are presented by employing ansatz method. The stability of the solution is investigated numerically and theoretically. In addition, we also calculate the integrals of motion for the dark soliton-like solution, including the power, the momentum and the energy.