Nonparaxial propagation of a rectangular multi-Gaussian Schell-model beam

According to the vectorial Rayleigh-Sommerfeld diffraction integral formulas, analytical expressions for the elements of 3×3 cross-spectral density matrix of polarized Rectangular Multi-Gaussian Schell-Model (RMGSM) beam's nonparaxial propagation in free space are derived, and the paraxial analytical expression has also been presented as a special case of nonparaxial propagation. Its statistical properties, including the distributions of spectral density, spectral degree of coherence, and spectral degree of polarization of nonparaxial RMGSM beam are numerically demonstrated. Results reveal that the statistical properties of RMGSM beam's nonparaxial propagation in free space are closely related to the initial beam's transverse width σ and correlation widths δx and δy. These characteristics of RMGSM beam might be useful in optical material surface processing, imaging, and free space optical communication.