Computation of Wave Fronts on a Disk I: Numerical Experiments

This paper discusses numerical experiments of wave front propagation on a flat disk and related results. In particular, notions of extremal rays and wave front caustics are introduced to investigate the dynamic behaviors of wave fronts under repeated reflection. These results are related to earlier work on caustics of ray systems. It is shown that wave fronts require a modified notion of caustic when considered under repeated reflection. We observe specific conditions for formation and annihilation of cusp singularities, self-tangencies and self-intersection of wave fronts.