Applicability of vector potentials with a single non-zero component for waves in uniaxially anisotropic media

Abstract

In this paper we derive conditions under which the electromagnetic field of a wave propagating in a uniaxial medium may be expressed with the aid of two vector potentials which are parallel to the optic axis. Unlike the coordinates of the electric field vector which are usually coupled owing to anisotropy, such single-component vector potentials form a pair of independent scalar field quantities. We prove that if the optic axis is in the transverse plane then the ordinary refractive index must be constant along that plane in order for the vector potential description to be applicable, but there is no restriction for the extraordinary refractive index or the dielectric interface. It is also shown that if the optic axis is in the longitudinal direction then the vector potential description can be used either in materials where the ordinary refractive index is constant in each region or in circularly symmetric fibres where the ordinary and extraordinary refractive indices have circular symmetry, being constant along the dielectric interface(s), or in slab waveguides, where the ordinary and extraordinary refractive index must be constant on the boundary of the slab.