Towards the optimization of dielectric branching waveguides: the effect of longitudinal variations in the branching angle

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Abstract
Mathematical models that describe mode propagation in planar Y-branch waveguides indicate there is a region in the branch where mode conversion occurs, provided asymmetry exists in the waveguide geometry or refractive index profile. Since the mode conversion is influenced by the degree of asymmetry and by the branching angle, the Y-branch can be designed to act as a power divider or as a mode splitter. The problem of identifying constant width Y-branch structures where longitudinal variations in the branching angle are introduced to optimize the power division or mode-splitting properties of a branching waveguide is considered. This constrained optimization is performed using forward dynamic programming and a compatible method of mode propagation analysis, the step approximation technique. The propagation characteristics of the optimized waveguide structure are compared to those of conventional constant-slope waveguides.