Propagation properties of flat-topped vortex hollow beam in uniaxial crystals orthogonal to the optical axis

The analytical expressions of a flat-topped vortex hollow beam propagating in uniaxial crystals orthogonal to the optical axis are obtained. The evolution properties of intensity and phase for flat-topped vortex hollow beam are discussed by using the numerical examples in detail. It is found that the beam order N, topological charge M and the ratio of refractive index ne/none/no of uniaxial crystals will influent the beam intensity and phase distributions.