Evolutions of random electromagnetic multi-Gaussian Schell-model vortex beams propagating in uniaxial crystals orthogonal to the optical axis

The analytical expressions of random electromagnetic multi-Gaussian Schell-model vortex beams propagating in uniaxial crystals orthogonal to the optical axis are derived. The effects of ratio of extraordinary index to ordinary index of uniaxial crystal on propagation properties of random electromagnetic multi-Gaussian Schell-model vortex beam are discussed by using numerical simulations. It is shown that the circular symmetry of random electromagnetic multi-Gaussian Schell-model vortex beam will translate into elliptical symmetry due to the influences of uniaxial crystal, and the beam propagation in uniaxial crystal with larger ratio of extraordinary index to ordinary index will evolve into an elliptical flat-topped beam with larger width along x-axis.