| In recent years, nonlocal spatial optical solitons in nonlocal nonlinear media have become the subject of intense studies, and it has been theoretically and experimentally demonstrated that the nonlocal spatial optical solitons have more rich phenomena and potential applications comparable to the local solitons. The propagation of optical beams in the nonlocal nonlinear media is modelled by the nonlocal nonlinear Schrodinger equation (NNLSE).In this thesis, the propagation properties of spatial optical solitons and their interactions in the focusing media with a Gaussian-shaped response for different degrees of nonlocality are explored by numerical method.Firstly, an iteration algorithm based on the split-step Fourier method is presented to obtain the solutions of the solitons,and profiles of the spatial optical solitons for different degrees of nonlocality are numerically obtained. It shows that in spite of the degree of nonlocality, stable solitons can always exist, but they exhibit different properties for different degrees of nonlocality. The profiles of the solitons undergo a gradual and continuous transition from a Gaussian function in the strongly nonlocal case into a hyperbolic secant function in the local case; the stronger the nonlocality is, the more the critical power is; although despite the degree of nonlocality, the soliton phase always increases with the propagation distance, yet the rate of the phase shift decreases as the nonlocality decreases.Secondly,we study the influence of the degree of the media nonlocality to the solitons interactions.lt is found that the degree of nonlocality has different critical values for different relative phases of the solitons, beyond which the interaction becomes insensitive to the relative phase.The main acievement of this thesis is the thorough research for the first time by numerical method on properties of the spatial optical solitons and their interactions for different degrees of nonlocality, and the explanation of the corresponding physical origin for the results.There are four chapters in this thesis. In Chapter 1, the recent developments about the research of the optical beams propagating in the nonolocal nonlinear media are summarized. In Chapter 2, the iteration algorithm to obtain the solutions of the solitons for different degrees of nonlocahty is introduced in detail. In Chapter 3, discussed is the propagation properties and the stability of the spatial optical solitons for different degrees of nonlocality. In Chapter 4, it is concerned with the effects on the interactions of the solitons made by the change of the degree of nonlocality. |
