Features of nonparaxial propagation of Gaussian and Bessel beams along the axis of the crystal

It is analytically and numerically shown that nonparaxial mode laser beams propagating along the axis of a crystal demonstrate the periodic change of intensity connected with an interference of ordinary and extraordinary beams. For Bessel beams the oscillation period inversely proportional to a square of spatial frequency of a laser beam and a difference of dielectric permittivity. For the linearly-polarized radiation there is a periodic redistribution of energy between two transversal components, and for beams with circular polarization energy is pumped from an initial beam into the vortex beam of the second order and vice-versa. The received dependence allows to select parameters of an incident beam with length of a crystal for full transformation to the vortex beam. For Gaussian beams similar periodic changes have nonlinear character. Laguerre-Gaussian laser modes with high radial order show a behavior close to Bessel beams on small distances. With increase of a distance the length of a period is increasing and the beam is astigmatically deforming.