Huygens-Fresnel wavefront tracing

We present initial results from a novel numerical method describing wave propagation in slowly non-uniform media. Following Huygens-Fresnel's 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, then the process is reiterated. 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.