Propagation and diffraction in uniaxially anisotropic regions. Part 1. Theory

Abstract
An analysis is made of the propagation and diffraction of electromagnetic waves in regions with uniaxial anisotropy, with special emphasis on the fields excited by arbitrarily prescribed sources. Two classes of problems are considered. In the first, the permittivity and permeability may both be anisotropic and may vary in the direction of the optic axis z; in addition, the cross-section transverse to z may be wholly or partially bounded by infinite, perfectly conducting, cylindrical surfaces of arbitrary cross-section, oriented parallel to z. It is shown that the fields may be decomposed into E and H modes relative to the direction of the optic axis, that the transverse dependence of a typical mode is as in an isotropically filled region, but that the anisotropy affects the longitudinal-propagation characteristics. Alternative formulations for the fields are given in terms of modal expansions, scalar potentials, and dyadic Green's functions. For media with piecewise constant properties, one may employ a co-ordinate scaling transformation which relates the given problem to similar ones in an isotropic region. In the second class of problems, the medium has constant anisotropic permittivity, and a cylindrical obstacle with arbitrary surface impedance is oriented perpendicular to the optic axis; the fields are now required to have no variation along the direction parallel to the surface. By co-ordinate scaling, one may again find an equivalent isotropic scattering problem in which, however, the obstacle contour is distorted. Applications of these procedures are given in Part 2 of the paper.

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