| Self-focusing, especially small-scale self-focusing, is one of key factors limiting the performance and output power of high-power laser systems. As a special kind of small-scale self-focusing, hot-image effect often damages certain optical components in high-power laser systems accidentally even if the systems operating at the intensity level below so-called safety light intensity. So investigating the evolution of hot-image effect and seeking for an active and effective approach to restrain hot-image effect are of far reaching importance. Based on the diffraction theory model of hot-image, the evolution of hot-image effect as well as how to restrain hot-image effect was numerically investigated in this dissertation. The main contents are as follows.(1) The corresponding theories of hot-image were briefly discussed. Start with the Maxwell equations, the nonlinear paraxial wave equation describing the propagations of intense laser beams was derived; based on B-T theory, the evolution of small-scale self-focusing effect was analyzed; several kinds of numerical simulation methods were discussed, and the transmission matrix method and the Split-Step-Fourier-Transform were treated in detail; the diffraction theory model of hot-image was also discussed.(2) The evolutions of hot-images in the case of thick nonlinear medium were investigated. The dependences of the intensity and location of hot-image such as modulation coefficient (including amplitude modulation and phase modulation), the distance between scatterer and the front surface of medium, the scatterer size, the intensity of incident beam and so on were detailed analyzed, respectively. Moreover, the case of the scatters located in the surface of nonlinear medium was also investigated. Then the investigations were extended to the case of medium with gain and loss.(3) Hot-images from multi-scatterers were numerically simulated. Multi-scatterers located in the same plane and different planes were studied, respectively. The surrounding scatterers how to influence the hot-image effect of a certain scatterer was numerically specified. The simulations of hot-image from scatterers arranged in array were also presented.(4) The methods for restraining hot-image effect were studied. By comparing with other approaches, we selected the spatial filter method to restrain hot-image effect. Based on B-T theory, and considering the restrain effect of spatial filter on the frequency spectrum, an expression describing the pinhole diameter corresponding to the fastest growing frequency was derived. The restrain effect of spatial filter with different pinhole diameters on hot-image were numerically simulated based on the diffraction model of hot-image. The results showed that satisfying restrain effect on hot-image can obtained by choosing appropriate parameters if the pinhole diameters were small than the theoretical one.
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