Propagation of a rectangular multi-gaussian schell-model vortex beam in uniaxial crystal

The cross-spectral density of a rectangular multi-Gaussian Schell-model vortex beam propagating in uniaxial crystal orthogonal to the optical axis has been derived, and the normalized intensity and effective beam widths are investigated by using numerical analysis. The results indicate that the rectangular multi-Gaussian Schell-model vortex beam propagating in uniaxial crystal will evolve from circular dark hollow beam into an elliptical flat-topped beam due to the influences of uniaxial crystal. The effective beam width Wx will gradually increase as the propagation distance z increase, and the beam with larger M and N1=N2 or smaller σ will have a larger effective beam width Wx at the same propagation distance.