Analytical approach to the transmission of a Gaussian beam into a biaxial crystal

Abstract

We study the transmission of a linearly polarised three-dimensional Gaussian beam through a plane interface between an isotropic medium and a biaxially anisotropic crystal for the case in which the interface normal is along one of the principal axes of the crystal. To that end, we use recently developed exact solutions for the transmitted field inside a biaxial crystal to derive an analytical expression for the transmitted field in the paraxial approximation for the case in which the incident wave is a linearly polarised non-truncated Gaussian beam with its main propagation direction along the interface normal. We express the non-truncated transmitted beam inside the biaxial crystal in a form similar to that for a scalar Gaussian beam that propagates in a homogeneous, isotropic medium. For a truncated incident Gaussian beam we derive a simplified integral representation for the transmitted field that is valid also in the limit as the biaxial crystal reduces to a uniaxial or an isotropic medium.