Nonparaxial analysis in the propagation of a cylindrical vector Laguerre–Gaussian beam in a uniaxial crystal orthogonal to the optical axis

Analytical expressions for the three components of the nonparaxial propagation of cylindrical vector Laguerre–Gaussian beams with two cases in a uniaxial crystal orthogonal to the optical axis are derived, respectively. The distributions of the intensities and the degrees of the polarization of cylindrical vector Laguerre–Gaussian beams with two cases propagating in a uniaxial crystal orthogonal to the optical axis are demonstrated by numerical examples. The beam profiles of the x- and y-components with the second case are somewhat similar to those of the x- and y-components with the first case rotating π/2. However, the beam profile of the longitudinal component with the second case is completely different from that of the longitudinal component with the first case. The degrees of the polarization of cylindrical vector Laguerre–Gaussian beams with the two cases take on different distribution. The uniaxial crystal can modulate the distributions of the intensity and the degree of the polarization for a cylindrical vector Laguerre–Gaussian beam, which is beneficial to the optical trapping and nonlinear optics involving in the special beam profile.