Evolution properties of a Laguerre-Gaussian correlated Schell-model beam propagating in uniaxial crystals orthogonal to the optical axis.

Analytical expressions for the cross-spectral density function and the second-order moments of a Laguerre-Gaussian correlated Schell-model (LGCSM) beam propagating in uniaxial crystals orthogonal to the optical axis are derived. Based on the formulas derived, we study the propagation properties, such as beam irradiance, beam diameters, and the spectral degree of coherence, of a LGCSM beam inside uniaxial crystals in detail. The effect of the initial beam parameters (mode order and spatial coherence length) and the parameters of the uniaxial crystals on the evolution properties of a LGCSM beam is revealed through numerical examples. The uniaxial crystals provide one way to modulate the properties of a LGCSM beam.