Huygens-Fresnel wavefront tracing in non-uniform media

TL;DR

This paper introduces a novel numerical wavefront tracing method based on Huygens-Fresnel principle for modeling wave propagation in non-uniform media, including diffraction and refraction effects, with preliminary results demonstrating its effectiveness.

Contribution

The paper presents a new wavefront tracing technique that models wave propagation in complex media, incorporating diffraction and refraction, and discusses potential extensions to more complex media.

Findings

Successfully modeled diffraction around obstacles

Accurately simulated refraction in varying media

Demonstrated extension to anisotropic and absorbing media

Abstract

We present preliminary results on a novel numerical method describing wave propagation in non-uniform media. Following Huygens-Fresnel' principle, we model the wavefront as an array of point sources that emit wavelets, which interfere. We then identify a set of new points where the electric field has equal phase. In fact, without losing generality, we find zeros of the electric field, by means of the bisection method. This obviously corresponds to a specific phase-advance, but is easily generalized, e.g. by phase-shifting all sources. The points found form the new wavefront. One of the advantages of the method is that it includes diffraction. Two examples provided are diffraction around an obstacle and the finite waist of a focused Gaussian beam. Refraction is also successfully modeled, both in slowly-varying media as well as in the presence of discontinuities. The calculations were performed in two dimensions, but can be easily extended to three dimensions. We also discuss the extension to anisotropic, birefringent, absorbing media.