Resonant scattering of electromagnetic waves by a lossy periodic dielectric waveguide

The problem of the excitation of guided modes in planar dielectric waveguides with periodically modulated surfaces is considered. In particular, the form of the radiation pattern of a lossy waveguide, the width and the position of the central angle of the radiation pattern as a function of the surface modulation depth are studied. A special numerical-analytical method for the calculation of the intensities of guided modes has been developed. In the case of a small modulation depth, this method makes use the expansion of the solutions of Maxwell equations into the Laurent series near the scattering matrix pole.