Thin-film waveguide with a periodic groove structure of finite extent

Abstract

A mode-matching method in the sense of least squares is used to analyze thin-film waveguides with a periodic groove structure of finite extent. Two diffraction problems are treated. The first is that of a grating coupler for plane-wave incidence and for which the Bragg condition is satisfied. In the second problem a guided mode is incident upon the periodic part through the unperturbed part of a waveguide, and the Bragg condition is satisfied. The approximate scattered fields of each region of the waveguide are described by a superposition of plane waves with band-limited spectra. These approximate wavefunctions are determined by the minimization of the mean-square boundary residual resulting in simultaneous Fredholm-type integral equations of the second kind for these spectra. Results based on the first-order approximate solutions of the integral equations are presented.