Propagation of Correlation Singularities of a Partially Coherent Laguerre–Gaussian Electromagnetic Beam in a Uniaxial Crystal

Abstract

The correlation singularities of a partially coherent Laguerre–Gaussian (LG) electromagnetic beam in a uniaxial crystal is shown to possess interesting evolution behavior. The analytical formula for the cross-spectral density matrix of a partially coherent LG electromagnetic beam propagating in a uniaxial crystal orthogonal to the optical axis is derived. It is found that the correlation singularities of a partially coherent LG electromagnetic beam in a uniaxial crystal is closely determined by the spatial coherence and mode orders of the beam, and the refractive indexes of the crystal. For a partially coherent LG electromagnetic beam, the correlation singularities can propagate further in a uniaxial crystal than that in isotropic medium. For a fully coherent LG electromagnetic beam, in isotropic medium the central correlation singularities and circular edge dislocations persist upon propagation; in a uniaxial crystal the circular edge dislocations become imperfect, and the central correlation singularities with topological charges $l \ne 1$ split up into correlation singularities with topological charges equaling 1.