Evolution properties of multi-Gaussian Schell model beams propagating in uniaxial crystal orthogonal to the optical axis

An analytical formula for the multi-Gaussian Schell model is derived for the beam propagating in a uniaxial crystal orthogonal to the optical axis. The propagation properties of multi-Gaussian Schell model beams in a uniaxial crystal orthogonal to the optical axis is investigated by using the analytical formula. Some results are illustrated by numerical examples related to the propagation properties of multi-Gaussian Schell model beams. It is found that the propagation properties of the multi-Gaussian Schell model beams are very different from the propagation properties in the free space. They are closely related to the initial coherence and the ratio of the extraordinary and ordinary refractive indices. The results provide a way for studying the propagation properties of the multi-Gaussian Schell model beams in the uniaxial crystal orthogonal to the optical axis.