Analysis of optical waveguide junctions by means of an integral equation method

Using a slab waveguide model we analyze the problem of waveguide mode transmission and reflection that occurs at the junctions of dielectric optical waveguide due to lateral offset, angular tilt, and gap between the guides, and deformations of the end faces. the analysis first develops a set of integral equations for the unknown equivalent electric and magnetic surface currents over the end faces. the integral equations are discretized through partitioning of the boundaries of both ends into small elements, and their solutions are expanded in a Neumann series, which makes it possible to obtain the solutions iteratively. Using reciprocity and mode orthogonality properties appropriately, the mode coupling coefficients are obtained. After discussing the relation between partition number of the boundaries and convergence of solutions, and the satisfaction of energy relations, we give numerical examples for the reflection and transmission coefficients of guided modes, the radiation losses and the radiation power patterns, choosing end shapes and their locations as the parameters.