A numerical investigation of wave interactions in dielectric waveguides with periodic surface corrugations

The modal properties of planar multilayered waveguides with a rectangular surface corrugation are investigated. A rigorous full Floquet numerical analysis is performed for the fundamental TE mode of the infinite periodic structure. The algorithm is based on a boundary element solution of the integral wave equation in the grating region. A generalized transverse resonance-type matrix equation is sought that matches all continuity, periodicity, and boundary conditions. The resonant solutions of this characteristic equation represent all the surface and leaky waves supported by the structure. The exact dispersion characteristics, as well as the amplitudes of the space harmonics are computed and discussed in connection with radiation losses and coupling mechanisms near resonant Bragg conditions. In particular, a specific double-heterostructure GaAs/AlGaAs waveguide geometry is examined in detail.>