Evolution properties of partially coherent standard and elegant Hermite-Gaussian beams in uniaxial crystals

The propagation properties of a partially coherent elegant Hermite-Gaussian beam (EHGB) and a partially coherent standard Hermite-Gaussian beam (SHGB) in uniaxial crystals orthogonal to the optical axis are studied. The propagation expression for the cross-spectral density of the partially coherent EHGB and SHGB propagating in a uniaxial crystal is derived. With the help of the derived formula, some analyses are illustrated by numerical examples related to the evolution properties of the spectral density, the spectral degree of coherence, and the effective beam width of the partially coherent EHGB and SHGB in a uniaxial crystal. It is shown that propagation properties of the partially coherent EHGB and SHGB in an isotropic crystal are much different from the evolution properties in an anisotropic crystal. The evolution behavior of spectral density and the spectral degree of coherence depends on the parameters of the uniaxial crystals (the ratio of extraordinary and ordinary refractive indices), and beam parameters including the coherence length and the beam order, as well as the propagation distance.