Exact solutions for light scattering from dielectric-disk arrays

This paper reports the first stage of a study intended to shed light on our understanding of the connection between chaotic classical trajectories and scattering resonance distributions. We have numerically examined scalar-wave-equation solutions for light scattering from an array of three dielectric cylinders. Similar systems using hard disks as well as continuous repulsive potentials, which support classical chaos, have been studied before. Our dielectric cylinders have the advantage of allowing us to study the effect of caustics on the scattering while being a system simple enough to be solved exactly. Using a Greens-theorem approach, we have calculated differential and total cross sections in the relatively-long-wavelength regime (ka20) and compared them to previous results. We find interestingly large differences between the three-hard-disk case and our dielectric case: the dielectric scattering cross section displays considerably more structure. It may be possible to experimentally verify these results for our dielectric cylinders. Our paper includes an explanation of the major qualitative features exhibited by the cross sections.