Nonparaxial propagation of elliptical Gaussian vortex beams in uniaxial crystal orthogonal to the optical axis

Analytical expressions for the three components of nonparaxial propagation of a polarized elliptical Gaussian vortex beam in uniaxial crystal orthogonal to the optical axis are derived. Intensity and phase distributions of the three components of a polarized elliptical Gaussian vortex beam propagating in a uniaxial crystal orthogonal to the optical axis are illustrated by numerical examples. The influences of the initial beam’s parameters and the parameters of the uniaxial crystal on the evolution of the beam’s intensity and phase distributions in the uniaxial crystal are examined in detail. Results show that the statistical properties of an elliptical Gaussian vortex beam nonparaxially propagating in uniaxial crystal orthogonal to the optical axis are closely determined by the initial beam’s parameters and the parameters of the crystal. The beam waist width ω0 not only affects the size of the beam profile in uniaxial crystal but also determines the nonparaxial effect of an elliptical Gaussian vortex beam. The profile of an elliptical Gaussian vortex beam in the uniaxial crystal becomes twisted and tilted, whether the elliptical factor α is greater or smaller than unity. The beam profile is tilted to the left in positive crystal. In contrast, it is inclined to the right in negative crystal. The results indicate that uniaxial crystal provides a convenient method to modulate the intensity and phase distributions of an elliptical Gaussian vortex beam, which is beneficial to optical manipulation of microscopic particles and nonlinear optics involving a specific beam profile and phase.