| The spatial soliton is one of major research fields in nonlinear optics, and its existence is correlated with the dynamic balance between the linear and nonlinear effects of the interactions between optical fields and media. Plenty of research achievements have been made in the last 40 years. But all along, attentions were mainly paid to coherent solitons in both theoretical and experimental investigations. With the recent developments in material science and experimental technology, incoherent solitons excited with incoherent light sources were experimentally observed. The findings of incoherent solitons have changed our traditional understanding of soliton phenomena and led to many new research topics. It's hopeful that the application of incoherent solitons shall improve the development of soliton-based all optical communication systems.The aim of this thesis is to theoretically study the self-trapping behaviors of incoherent light beams in nonlinear media, including the dynamic evolution of incoherent solitons, incoherently coupled screening soliton pairs and incoherent bistable solitons, and the propagation characteristics of incoherent vector beams in free space.The paper is arranged as follows:(1) The self-trapping characteristics of one-dimensional and two- dimensional incoherent optical beams in logarithmically saturable photorefractive media are studied by means of the coherent density approach and the mutually coherent function approach, respectively, (a) The analytical expressions of Gaussian model incoherent solitons are obtained by resolving the nonlinear propagation equations for incoherent beams, (b) The propagating behaviors of the incoherent solitons are analyzed. It is shown that the solitons can propagate in a stationary or periodical way, depending on the initial beam conditions and the nonlinearity of the media, (c) The coherence length of incoherent soliton is given. Analysis shows that the coherence property of incoherent solitonevolves diversely under different propagation conditions, (d) The coherent density approach and the mutually coherent function approach seem to be different, but they are in fact equivalent to each other.(2) Incoherently coupled screening soliton pairs can be established in biased photorefractive media under steady-state conditions, each constituent of which is not only spatially incoherent with the other, but also with itself, (a) The properties of incoherently coupled soliton pairs in bright-bright, dark-dark and bright-dark configurations are studied with the coherent density approach, and the intensity expressions for these soliton pairs are given. The results show that the existence of coupled soliton pairs have nothing to do with the incoherence property of beams. However, the types of soliton pairs depend on the direction of external bias voltage, (b) The analytical solution of bright-dark soliton pair can be found when the intensity peaks of the two soliton constituents are approximately equal, (c) The propagation characteristics of coherent components that compose each constituent of coupled soliton pairs are discussed in detail. And their intensity distributions depend closely upon the incoherence property of beams.(3) Incoherent bistable solitons can exist in high-order nonlinear media, (a) Using the coherent density method, I obtain the analytical expression for the spatially incoherent bistable soliton and find that the incoherence of the beam doesn't affect the existence of the incoherent bistable soliton. The widths of the two stable state solitons are the same, but their intensity peaks are different, (b) The high-order nonlinearity determines the existence and the intensity peak of the bistable soliton. The cut-off wavelength, the minimum width of incoherent beam and the nonlinearity of medium required for the existence of bistable soliton are found, (c) The incoherent bistable soliton is rigorously proven to keep propagating steadily against perturbation. It is also proven that the...
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