By means of Collins' diffraction integral formula in the paraxial approximation, the analytical expressions for linearly polarized and azimuthally polarized Bessel-Gauss beams through any axisymmetric optical system that can be described by an ABCD ray transfer matrix are given. For example, the transformation characteristics of these two kinds of Bessel-Gauss beams through an optical system with a lens are compared by numerical calculation. The results are analyzed and discussed. [References: 12]
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