Gaussian beams in anisotropic media

Abstract

It is shown that rigorous beam solutions of the Maxwell field equations in an anisotropic medium can be generated from known field solutions due to dipole or line source excitation by assigning a complex value to the source coordinates. The fields so obtained behave like Gaussian beams in the vicinity of the beam axis, but they provide a valid description also outside the paraxial region. The complex-source-point method, which eliminates the need for spectral decomposition of an impressed Gaussian profile, is developed for media with arbitrary anisotropy, with emphasis on asymptotic descriptions in the paraxial regime. Detailed consideration is then given to the special case of a uniaxially anisotropic medium, for which point and line source solutions are available in closed form; their asymptotic development provides confirmation of the formulas derived for the general case. Because the analytic continuation from real to complex source points can be performed directly on the high-frequency ray fields, the method converts ray solutions into beam solutions without the need of further calculation.