Based on the Snyder-Mitchell model that describes the paraxial beam propagating in strongly nonlocal nonlinear media and by constituting the trial solution with modulating the Gaussian beam by Ince polynomials in elliptic coordinate,the close forms of Ince-Gaussian beams have been accessed.

AbstractBy means of Collins diffraction integral formula in the paraxial approximation ,the analytical expression for azimuthally polarized Bessel-Gauss beam through any axisymmetric optical system that can be described by an ABCD ray transfer matrix is given in this paper.

This article makes theoretical analysis on the relationship and distinction between Bessel and Bessel-Gauss beams,the optical intensity distribution at any propagation plane of ideal Bessel beam and the Bessel-Gauss beam,and the effect of the beam waist and the cavity length L on the Bessel-Gauss beam were simulated.