## Generalized Linear Dispersion Relation for Symmetrical Directional-coupler of Five-layer Waveguide

September 5, 2008 by rohedi

pattern-of-normal-modes-for-s3cebcm-and-v2955-and-the-power-transfer-between-the-two-waveguides

This paper presents generalization of the dispersion relation for analysis of optical power transfer of transverse-electric (TE) mode in five-layer of linear symmetrical directional-coupler, which consists of two equal waveguides as guiding layers with a gap material sandwiched between a semi-infinite clad and a substrate. The dispersion equation formulated by normalizing the intensity of normal modes which involve phase-shift due to the internal reflection at each boundary of neighboring layers corresponds to the standing-wave form, i.e, contains the terms of overlapping the normal modes in gap region, the evanescent waves into the superstate regions, and effective lateral width of the directional-coupler. This generalized dispersion equation can overcome disability of coupled–mode approximation when the two waveguides get too close, evenly it can also be used for designing a zero-gap coupler. Simulation of beam propagation and analysis of optical power transfer in the linear directional-coupler are also presented.

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