Evolution Properties Of A Laguerre-gaussian Correlated Schell-model Beam Propagating In Uniaxial Crystals Orthogonal To The Optical Axis

In the past decades, propagation and modulation of laser beams have been widely studied, and it is found that some better results will be given in many applications when reducing the coherence of a laser beam. Laguerre-Gaussian correlated Schell-model(LGCSM) beam is one of partially coherent beams with nonconventional correlation functions, which has more novel properties than traditional Gaussian Schell-model beams. LGCSM beams have been widely studied recently, including its experimental generation and propagation in different media such as in free space and turbulent atmosphere.On the other hand, crystals are widely used as anisotropic medium due to its unique spatial structure. Familiar devices based on transmission principles in crystals like wave plates, polarizers, compensators etc. has been developed. Moreover, the anisotropy of crystals has much influence on the properties of beam propagation, polarization and coherence. Thus, it is significant to investigate the propagation of a beam passing through crystals. The main works of this paper are as follows:1. The propagation of LGCSM in free space has been extended into uniaxial crystal cases. With the help of scalar diffraction method, the cross-spectral density(CSD) function and the Wigner distribution function are derived. Our results show that the anisotropy of crystals leads to the inconsistent propagation of orthogonal directions. Thus, beam irradiance has an elliptical hollow shape in the far field while the degree of coherence has multi ring-shape beamlets along one direction.2. We derived analytical expressions of second-order moments, M2 factors, beam diameters and the beam divergences of a LGCSM propagating in uniaxial crystals orthogonal to the optical axis with the help of Wigner distribution function. Our results indicate that the beam has simple astigmatism and the variances of beam diameters are proportional to refractive-index related coefficients. An advisable way to modulate LGCSM beams in uniaxial crystals is provided. Our results may also help the studies of other special correlated beams propagating in uniaxial crystals.