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Coupled mode modeling in guided-wave photonics: A variational, hybrid analytical-numerical approach

A general variant of coupled-mode-theory for frequency domain guided wave problems in integrated optics is discussed. Starting point is a physically reasonable field template, that typically consists of a few known, most relevant modes of the optical channels in the structure, superimposed with coefficient functions of the respective - in principle arbitrary - propagation coordinates. Discretization of these unknown functions into 1-D finite elements leads to an approximation of the optical field in terms of a linear superposition of structure-adapted, more or less localized modal elements. By variational restriction of a functional representation of the full 2-D/3-D vectorial first order frequency domain Maxwell equations (with transparent influx boundary conditions for inhomogeneous exterior), one can then reduce the problem to a small- to moderate-sized system of linear equations. 2-D examples for a crossing of dielectric waveguides and a grating-assisted rectangular resonator illustrate the performance of the approach.