The Study Of Self-Similar Property In Nonlinear Optical System

From the soliton being observed by J.S. Russell in shallow water waves in1834, solitons have been observed in many fields, such as nonlinear optics, plasma physics, fluid mechanics, Bose-Einstein condensation and superconductor physics. Solitons have attracted a lot of concern due to its property of propagating without spreading out and breaking up. These optical pulses which are formed by the exact balance between dispersion (diffraction) and nonlinearity, are called optical soliton. Optical solitons have attracted a lot of scientists not only in fundamentals research field but also in long distance optical fiber communicational fields due to its particle property and strong stability. Recently, as the development of the nonlinear optical material, people are gradually starting to concern the propagation of optical pulse in the fiber with distributed nonlinearity, dispersion and gain(loss). In this thesis, we studied the propagation property of self-similar optical pulses which was based on the exact self-similar soliton solution of the NLSE with distributed coefficients in the nonlinear media.The detailed contents can be concluded as follows:1、We introduced the concept and the developmental history of soliton, optical soliton and similariton, concluded the current situation of optical solitons and self-similar optical soliton in communication field in recent years and stated the significance of the study of the propagation of similaritons;2、We derived the theoretical model we studied, introduced several theoretical methods and the method of analyzing the stability of the solitons; 3、By means of the universal similarity transformation, the exact self-similar soliton solutions of CQNLSE with distributed coefficients have been obtained, and the propagation property of the similaritons have been studied in the CQ nonlinear media.4、We analysed the stability of exact self-similar soliton solutions and studied the interaction of multi-similaritons by using FFT method;5、We also discussed the tunneling effect of the similaritons in CQ nonlinear media. We found the similar optical pulses can not only tunnel through the barriers and wells, but also their pulse width can be controlled during the tunneling process.