Nonparaxial propagation of a multi-Gaussian Schell-model beam

Abstract

Based on the vectorial Rayleigh–Sommerfeld diffraction integral formulas, analytical expressions for the elements of 3 × 3 cross-spectral density matrix of polarized multi-Gaussian Schell-model (MGSM) beam’s nonparaxial propagation in free space are derived, and used to investigate its propagation properties. As a special case of nonparaxial propagation, the paraxial case has also been considered by the reduced paraxial approximation expressions. The distributions of spectral density, spectral degree of coherence, and spectral degree of polarization of nonparaxial MGSM beam are illustrated by numerical examples. Results show that the statistical properties of MGSM beam’s nonparaxial propagation in free space are closely related to the initial beam’s correlation width related parameter and transverse width related parameter These characteristics of MGSM beam might find applications in laser scanning, optical trapping, and free space optical communication.