Statistical properties of a nonparaxial Gaussian Schell-model beam in a uniaxial crystal.

Nonparaxial propagation theory of coherent beams in a uniaxial crystal is extended to the partially coherent case. An analytical formula for the 3×3 cross-spectral density matrix of a nonparaxial Gaussian Schell-model (GSM) beam propagating in a uniaxial crystal orthogonal to the optical axis is derived. Statistical properties, such as the spectral intensity and the degree of polarization, of a nonparaxial GSM beam in a uniaxial crystal are studied numerically. It is found that the statistical properties of a nonparaxial GSM beam are closely determined by its initial beam parameters and the parameters of the crystal. Uniaxial crystal can be used to modulate the spectral density and degree of polarization of a nonparaxial partially coherent beam. Our results may be useful in some applications, such as optical trapping and nonlinear optics, where a light beam with special beam profile and polarization is required.