Prediction of coupling length in a rectangular-core directional coupler: an accurate analysis

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Abstract
It is shown that, for rectangular-core directional couplers, Marcatili's widely used analysis [Bell Syst. Tech. J. 48, 2071 (1969)] predicts almost the same value of coupling length as that obtained by the simple slab-waveguide approximation. A more accurate analysis, which takes the effect of corner regions into account through first-order perturbation theory, shows that Marcatili's analysis may lead to inaccurate results for small values of depths of channel waveguides, which are the most practical directional couplers involving single-mode channel waveguides.