Theory for Gaussian beam diffraction in 2D inhomogeneous medium, based on the eikonal form of complex geometrical optics

Abstract

A simple and effective method to describe Gaussian beams propagation and diffraction in arbitrary smoothly inhomogeneous 2D medium has been developed based on the eikonal form of complex geometrical optics. The method assumes the eikonal equation can be solved in paraxial approximation in curvilinear frame of references, connected with the central ray. The Riccati-type ordinary differential equation is derived for complex parameter characterizing the Gaussian beam width and phase front curvature. The same parameter was proved to define both the modulus and the argument of the complex amplitude. As a result, the problem of the Gaussian beam diffraction in inhomogeneous media has been reduced to the solution of the ordinary differential equation of the first order, which can be readily calculated numerically for arbitrary profile of dielectric permittivity.