Quasi-optical treatment of electromagnetic Gaussian beams in inhomogeneous and anisotropic plasmas

The main effect of the Gaussian behavior of an electromagnetic beam consists in a waist formation in focal regions, where the ordinary geometric optics would collapse. The characteristic features of Gaussian beams, both when they interact with the components of transmission lines and when they propagate through inhomogeneous and anisotropic media (as happens, for instance, in the case of diagnostic or heating experiments in magnetoactive plasmas of fusion interest), are of crucial relevance for many technical and scientific purposes. The present paper is devoted to the analysis of the propagation of Gaussian beams, showing in particular that a properly formulated eikonal equation contains all the elements required by a correct ray tracing procedure, basically amounting to a first-order description of the beam diffraction. Simple methods are proposed, apt to follow numerically the beam evolution for a quite general choice of refractive media and of wave launching conditions. Numerical results are presented for Gaussian beam propagation in vacuum, in isotropic and anisotropic media, and compared (evidencing significant deviations) to the corresponding ones in the optical case.