Introduction

The problem of the propagation of electromagnetic, elastic or other waves in anisotropic media makes up a substantial part of wave physics. The main feature of inhomogeneous weakly anisotropic media is their capability of substantially transforming the polarization structure of vector fields. On entering an anisotropic medium, a transverse electromagnetic wave ceases to be polarizationally degenerate and experiences a substantial change of polarization. The Budden method, devised for smoothly inhomogeneous media, allows one to reduce substantially the order of that system: it becomes second-order and involves a pair of coupled first-order equations. That approach, called the quasi-isotropic approximation (QIA) of geometrical optics, is not constrained by plane-layered media, and applies to arbitrary 3D inhomogeneous media. The QIA hinges on the assumption that in the zeroth approximation the electromagnetic field has the same transverse structure as it would have in an isotropic medium.