SPMC path integral method applied to electromagnetic wave propagation in transversely inhomogeneous media

A stationary phase Monte Carlo (SPMC) approach based on the path integral formulation of the electromagnetic (EM) wave equation is applied to the computation of EM wave propagation in transversely inhomogeneous media having an arbitrary smoothly varying index of refraction profile. This method is developed to compute the fields in such a medium where the observation point is many, perhaps several hundred, wavelengths from the source. The Helmholtz equation is first transformed into its equivalent time-dependent Schrodinger equation with the direction of propagation taking the place of the time coordinate. The solution to the Schrodinger equation is then expressed in terms of Feynman´s propagator. A SPMC filter, which results in a stable SPMC output with respect to various Monte Carlo parameters and thus overcomes the difficulties previously associated with the multidimensional SPMC method, is designed to evaluate the propagator.<>