A multiple-interference model to describe double-grating waveguide structures is presented. It is based on the multiple-interference model for single-grating waveguide structures previously established by Friesem and co-workers [J. Opt. Soc. Am. A 14, 2985 (1997)]. We show that double grating waveguide structures, in particular, as well as the usual single-grating waveguide structures can be completely described by our model and that explicit dependences of the resonant conditions on the wavelength, the angle, and the polarization of the incident light as well as on system parameters such as refractive indices, layer thickness, grating depths, and grating period can be given. This multiple-interference model elucidates the resonance behavior of single- and double-grating waveguide structures and predicts reflection and transmission resonance bandwidths in analogy to those of the classic Fabry–Perot interferometer. One can explain and understand the periodicity of resonances by interpreting grating waveguide structures as inverted Fabry–Perot interferometers. Comparison with exact numerical calculations and verification by experimental investigations prove the model to be a powerful tool for design purposes and to provide a deep understanding of the observed resonance phenomena.

© 2004 Optical Society of America

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