Generation And Management Of Optical Self-Similar Waves In Inhomogeneous Graded-Index Waveguides

In recent years, self-similar wave has become an attractive subject of research. It can attract a lot of interest, because it plays an important role in all-optical devices and all-optical communication.In this dissertation, based on the nonlinear Schrodinger equation with variable coefficients, which can describe the transmission of optical wave in inhomogeneous graded-index waveguide, the generation and management of the bright and dark soliton-like self-similar waves in different waveguides are discussed. According to the exact optical self-similar solutions of the equation, we study in detail the evolutions of the bright and dark self-similar waves in different waveguides, respectively.The specific contents are as follows:(1) The research reviews of spatial solitons and self-similar waves are introduced, respectively. In addition, we illuminate the features of the self-similar wave.(2) The general theoretical model of spatial optical wave transmitting in nonlinear media is derived directly from the Maxwell equation. Based on the theoretical model, the specific transmission equation of spatial optical wave in inhomogeneous graded-index nonlinear waveguide, namely, the nonlinear Schrodinger equation with variable coefficients is obtained. And the exact bright and dark spatial soliton-like self-similar solutions of the equation are presented.(3) Based on the transmission equation in inhomogeneous graded-index nonlinear waveguide and the exact optical soliton-like self-similar solutions of the equation, we study in detail the evolutions of the self-similar waves in the Kerr nonlinear plane waveguide, the homogeneous graded-index waveguide, and the inhomogeneous graded-index waveguide with periodic distribution and with hyperbolic distribution respectively. The results show that the generation of the self-similar wave relates to the distribution of the linear and the nonlinear refractive index. The self-similar waves can be compressed and amplified in both the homogeneous system and the hyperbolic system. However, in the hyperbolic system, the transmission distance of self-similar waves could be more limited. In a periodic oscillation system, self-similar waves with a periodic oscillation can be generated and propagate stably.(4) Besides, we analyze the dynamical behaviors of the dark self-similar waves on a super-Gaussian background in inhomogeneous graded-index waveguide by numerical method. We mainly discuss the evolutions of dark spatial self-similar waves and the interaction scenarios of the neighboring dark self-similar waves in both self-defocusing waveguide and self-focusing waveguide, respectively. The results show that the dark self-similar wave can be compressed and amplified in self-defocusing waveguide. The neighboring dark self-similar waves can repel each other when the initial separation is small enough. In self-focusing waveguide, the dark self-similar wave can split into several bright beams which can be compressed and enlarged in the propagation. The neighboring dark self-similar waves can merge into one when the initial separation is small enough.