Wave-matching method for mode analysis of dielectric waveguides

Frequently the cross-section of a longitudinally homogeneous dielectric waveguide may be decomposed into rectangles with constant permittivity. For points inside these rectangles the wave equation for modal fields is solved analytically by expanding into functions with harmonic or exponential dependence on the transverse coordinates. Minimization of a least-squares expression for the remaining misfit on the boundary lines allows us to determine propagation constants and fields for guided modes. Semivectorial calculations for two sets of rib waveguides and the centre sections of a directional coupler and an MMI device show very good agreement with results found in the literature.