Extension of the ray equations of geometric optics to include diffraction effects

Abstract

The paper discusses an extension of the ray equations of geometric optics to include diffraction effects for a wave beam propagating in a dispersive anisotropic medium. The diffraction effects are introduced through a complex eikonal function, where the complex part describes the electric field profile of the beam. The ray equations are derived using a formalism that allows for a complex wave vector but yields trajectories of wave propagation in real space. The wavelength, width of the beam, and length scale over which the plasma parameters change are ordered 1: δ ⁻¹:δ ⁻², with δ being a small parameter. A consistent treatment of this ordering yields additional terms in the ray equations when compared with expressions in the literature, that arise from corrections to the dispersion relation. It is discussed to what accuracy the rays represent the flux of wave energy. An approximated set of equations that describe the propagation of a Gaussian beam is derived.