Ray theory for scattering by two-dimensional quasiperiodic plane finite arrays

Many scattering configurations of interest include finite portions with periodic or quasiperiodic features. Several recent investigations have dealt with this problem for the planar two-dimensional case and have developed high-frequency asymptotic solutions that include multibeam reflections obeying the Bragg condition and Bragg-modulated edge diffractions. These constituents have been interpreted as wave objects in a generalized geometrical theory of diffraction (GTD). The present investigation adds to these previous results and formalizes them into a ray theory. This allows the scattered fields due to a finite quasiperiodic array of obstacles, excited by an arbitrary incident field, to be constructed entirely by ray tracing. Scattered ray plots and caustics for various shapings of incident fields and array parameters illustrate the variety of phenomena associated with this class of scattering environments.