Fast analysis for the focusing of a laser beam with amplitude modulation and phase fluctuation through an aperture lens

Based on the treatment that a rectangular function can be expanded into an approximate sum of complex Gaussian functions with finite numbers, the analytical expression for the focusing intensity distribution of a laser beam with amplitude modulation (AM) and phase fluctuation (PF) through an aperture lens is derived. The typical numerical examples are given and compared with those obtained from numerically integral calculation. The results show that our method can significantly improve the numerical calculation efficiency.