Dielectric equilateral triangle microresonators: integral equations and semiclassical physics approaches

Abstract

We investigate in detail the resonant properties of a two-dimensional dielectric cavity with an equilateral triangle shape, using a numerical integral equations approach and a semiclassical approach. The homogeneous Muller boundary equations are used to calculate the resonant modes of a dielectric triangle in a wide range of frequencies. It is shown that the modes of dielectric triangles localized on families of periodic orbits can be well described in terms of a semiclassical superscar model. Special attention is given to the families of resonances based on the inscribed triangle periodic orbit.