The radial smoothing scheme based on optical Kerr effect was proposed to quickly improve the irradiance uniformity of the laser beam. In order to analyze the moving characteristics of speckles on target plane, the transverse moving model has been established based on the concept of equivalent focal length. The analytical expression for the radial moving speed of the speckles in radial smoothing (RS) has been derived, and the moving characteristics have further been analyzed. Results indicate that, the focal spot tends to be larger when the radial moving speed increases. With a temporal shape of triangular wave, the pump laser generates a constant radial moving speed and achieves better smoothing effect. Due to the difficulty in obtaining the triangular pump laser in picoseconds level, the temporal shape of Gaussian wave was further optimized to obtain the greater speed while maintaining the same beam smoothing performance in the RS scheme. To further improve the smoothing performance of the radial smoothing scheme, the hybrid dispersion grating scheme is introduced to achieve the multidirectional smoothing. By introducing the hybrid dispersion grating to the radial smoothing scheme, the final beam smoothing performance is much better than either of them.
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