This paper presents a series solution for electromagnetic wave propagation in a medium in which the dielectric constant is given by ε=ε0-ε2(z)r2., without recourse to the WKB approximation. The results have been put in a form suitable for numerical computation. Explicit expression has been obtained for the irradiance distribution in the paraxial region, when the incident wave front is plane gaussian. These investigations are applicable to propagation of laser beams in self-focusing fibers/rods.
M. S. SODHA, A. K. GHATAK, and I. C. GOYAL, "Series Solution for Electromagnetic Wave Propagation in Radially and Axially Nonuniform Media: Geometrical-Optics Approximation," J. Opt. Soc. Am. 62, 963-966 (1972)