Rigorous analysis of an embedded optical waveguide

Rigorous analysis of an embedded optical waveguide is tried by applying the mode-matching method, which is based on the Rayleigh expansion theorem and the mode -matching technique, by which the boundary conditions are matched in the sense of least squares. In conclusion, a high degree of accuracy is realised, and detailed propagation characteristics are obtained not only on the dispersion relation but also on the field distribution, comparing with the results by Marcatili´s approximate method. The problem of single-mode transmission in the embedded waveguide is also discussed.