Nonparaxial propagation of a partially coherent four-petal Gaussian vortex beam

In the analysis of the nonparaxial propagation and far field propagation, the analytical propagation equations of a partially coherent four-petal Gaussian vortex beam have been derived based on the Rayleigh-Sommerfeld diffraction. The properties of nonparaxial propagation properties of a partially coherent four-petal Gaussian vortex beam have been obtained and analyzed using the numerical examples. And the influences of beam parameters on the average intensity of nonparaxial and far field propagation properties of partially coherent four-petal Gaussian vortex beam have been analyzed.