The Research Of Surface Kinks And Defected Vortex Solitons

Spatical solitons exhibit unique properties, such as having fixed space shape, steady energy, etc. When spatial solitons propagate in nonlinear media, the nonlinear effects of the medium material and the diffraction effects produced by the solitons may achieve a balance. Thus, spatical solitons can play a considerablely important role in creating reconfigurable all-optical circuits where is guided and controlled by light itself. And the exploration and research of the properties of optical solitons have a powerful means.This thesis is focusing on the analysis and simulation of propagation dynamics of spatial solitons. The beam evolution is described by nonlinear Schrodinger equation. In our calculation, we use finite-difference method, fourth-order pseudospectral method, Split-Step Fourier methods, etc.The thesis includes mainly as following parts:1. Interface kink solitons in defocusing saturable nonlinear mediaIn the third chapter, we discuss the properties of semi-localized nonlinear optical modes supported by an interface separating a uniform defocusing saturable medium and an imprinted semi-infinite photonic lattice, including the existence and stability properties of optical kink solitons. The solutions of kink solitons can be found in the first gap and high gaps. After examining the stability properties of the stationary solu-tions (kink solitons), we found that out-of-phase kink solitons will be completely stable provided that lattice depth exceeds a critical value, moreover, saturable nonlinearity enhances the pedestal height and renormalized energy flow of kink solitons evidently. We also reveal that band gap structure and depth of semi-infinite lattice can influence the dynamics of kink solitons remarkably.2. Surface vector kink solitonsIn the fourth chapter, we will discuss the properties of surface vector kink solitons, including the existence domain and stability properties. The mutual trapping between two orthogonally polarized components results in the formation of vector states com-posed of well-known components in various forms, i.e., out-of-phase kinks, in-phase kinks, and surface gap solitons. Interestingly, due to the cross-phase modulation, a sur-face gap soliton with a negative propagation constant can be found as a component of the vector kink soliton. This is in contrast to the scalar surface gap soliton in the similar regime, where it can be found only for the positive propagation constant.3. Stability of higher-charged vortex solitons in defected radial latticesIn the fifth chapter, we study the dynamics of the fundamental radially symmetric solitons and vortex solitons in defected radial lattices. The defect scale can be utilized to control the energy flow of both types of solitons. Vortex solitons with various charges are stable in a region near the upper cutoffs of propagation constant. Although higher-charged vortices at higher energy flow suffer oscillatory instability, they can survive very long distances without visible distortions. Vortex solitons at lower or moderate en-ergy flow are completely stable under appropriate conditions. Especially, we revealed that the variation of topological charges slightly influences the existence and stability domains of vortex solitons. This property provides an effective way for the experimen-tal realization of vortex solitons with different charges in a optical setting with fixed parameters.