Laguerre–Gauss and Bessel–Gauss beams in uniaxial crystals

Abstract

A simple correspondence between the paraxial propagation formulas along the optical axis of a uniaxial crystal and inside an isotropic medium is found in the case of beams with linearly polarized circularly symmetric boundary distributions. The electric fields of the ordinary and the extraordinary beams are related to the corresponding expressions in a medium with refractive index no and ne2/no, where no and ne are the ordinary and the extraordinary refractive indexes, respectively. Closed-form expressions for Laguerre–Gauss and Bessel–Gauss beams propagating through an anisotropic crystal are given.