Analysis of Thin-Film Waveguide with a Rectangular Groove Structure of Finite Extent

Abstract

A mode-matching method in the sense of least squares is proposed to analyze diffraction problems of thin-film waveguides with a rectangular groove structure of finite extent. Two diffraction problems are treated. The first problem is related to that of the grating coupler. The plane wave is incident on the surface of the core region from the cover region of the thin-film waveguide under the Bragg condition in the first problem. The second problem is related to those of the distributed feedback and Bragg reflection lasers. In the second problem, the lowest order guided mode is incident into the periodic part through the unperturbed part of the waveguide under the Bragg condition. The approximate scattered fields of each region of the waveguide are described by the superposition of plane waves with band-limited spectra. These approximate wave functions are determined by the minimization of the mean-square boundary residual. This method results in simultaneous integral equations of the Fredholm type of the s...