Abstract
The Floquet-Bloch theory is used to develop a theory for grating-assisted directional couplers which predicts the coupled power and coupling lengths and is applicable to lossy waveguides. This theory views grating-assisted directional couplers as conceptually similar to conventional synchronous (nongrating) couplers. In the Floquet-Bloch analysis of the directional coupler, it is necessary to include both proper and improper space harmonics. The determination of which space harmonics are improper is critical to the understanding of the coupler performance. The choice of the improper space harmonics used for the analysis of the coupler is different from that used in contemporary papers.
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