Abstract
In this paper, a general version of coupled-mode theory for frequency-domain scattering problems in integrated
optics is proposed. As a prerequisite, a physically reasonable field template is required, that typically combines
modes of the optical channels in the structure with coefficient functions of in principle arbitrary coordinates.
Upon 1-D discretizations of these amplitude functions into finite elements, a Galerkin procedure reduces the problem
to a system of linear equations in the element coefficients, where given input amplitudes are included. Smooth
approximate solutions are obtained by solving the system in a least squares sense. The versatility of the approach
is illustrated by means of a series of 2-D examples, including a perpendicular crossing of waveguides, and a
grating-assisted rectangular resonator. As an Appendix, we show that, alternatively, a similar procedure can be
derived by variational means, i.e., by restricting a suitable functional representation of the full 2-D/3-D
vectorial scattering problem (with transparent influx boundary conditions for inhomogeneous exterior) to the
respective field templates.
© 2007 IEEE
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