Nonparaxial propagation of a partially coherent four-petal Gaussian beam in free space

Based on the generalized Rayleigh-Sommerfeld diffraction integral, the equations of nonparaxial propagation, far field propagation and paraxial propagation of a partially coherent four-petal Gaussian beam in free space are obtained. The results show that the far field propagation and paraxial propagation can be regarded as special cases of nonparaxial propagation. The normalized intensity and degree of coherence of a nonparaxial partially coherent four-petal Gaussian beam are illustrated and analyzed using numerical example.