Three-dimensional coupled mode method for simulation of coupler and filter structures

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Abstract
A method based on coupled mode theory for numerical simulation of three-dimensional structures is presented. It can be applied to all coupling structures for which the interaction with radiation modes is unimportant and distortions of the fields due to waveguide curvature are small. It treats the device cross section by a two-dimensional finite-difference algorithm, thus avoiding the limitations and errors made by the effective index approximation. The coupled mode equations are solved. including the cross power terms, which are important for designing couplers and filters. The method permits the design of couplers with arbitrary 2-D cross sections, including the feeding branches. Examples for calculations of planar rib waveguide couplers and buried vertical couplers are given, together with design rules for couplers as arbitrary power dividers. A wavelength filter structured as a meander coupler was simulated, and good agreement with the experimental data was achieved. In spite of the two-dimensional cross-section treatment, the method is in most cases even faster than the standard beam propagation method with a one-dimensional effective index profile