Study On The Transmission Properties Of Femtosecond Optical Soliton In Optical Fiber

In the dissertation, based on the Kundu-Eckhaus equation with constantcoefficients and the Kundu-Eckhaus equation with variable coefficients which can beused to describe the propagation of the femtosecond soliton pulses in optical fiber, andby means of analytical method (Hirota bilinear method or similarity transformationmethod) and numerical method (the split-step Fourier method), the transmissioncharacteristic of the femtosecond soliton in optical fiber is investigated. The abovementioned results may be useful to provide some theoretical analysis for studying thereal optical soliton control systems or inhomogeneous fiber systems, and furtherrealizing optical soliton communication system with super long distance and superhigh capacity.The main contents are as follows:1) Based on the cubic-quintic nonlinear Schr dinger equation with Raman effect,i.e. the Kundu-Eckhaus equation, from the integrable point of view, adopting theHirota method, the exact one-soliton and two-soliton solutions has been obtained. Byemploying the exact solutions, propagation characteristics of solitons in optical fiberhave been investigated, including propagation characteristics of one-soliton and theinteraction between the solitons. Three interaction behaviors of the solitons have beendiscussed emphatically:(1) overtaking elastic interactions of the two solitons;(2)periodic attraction and repulsion of the bounded states of two solitons;(3) propagationin parallel of the two solitons. Meanwhile, using the split-step Fourier method, thevalidity of analytical solutions has been verified, and the interaction between thesolitons has been discussed further.2) Based on the Kundu-Eckhaus equation with variable coefficients, by anappropriate similarity transformation method, the exact one-soliton and two-solitonsolutions have been explicitly given. As an example, an exponential distributed fibercontrol system, nonlinearity management system and dispersion management systemhave been considered, and propagation characteristics of the exact soliton solutionsin the three nonuniform management systems have been investigated. Especially, thedynamics properties of the amplitude, pulse width and the central position of solitonwith transmission distance have been studied. These results have some guidingsignificance for soliton amplification, compression and control management, and can provide some theoretical analysis for carrying out optical soliton communicationexperiment.