Open AccessSpatiotemporal coupled-mode theory of guided-mode resonant gratings
Author(s) -
Dmitry A. Bykov,
Leonid L. Doskolovich
Publication year - 2015
Publication title -
optics express
Language(s) - Uncategorized
Resource type - Journals
SCImago Journal Rank - 1.394
H-Index - 271
ISSN - 1094-4087
DOI - 10.1364/oe.23.019234
Subject(s) - coupled mode theory , optics , physics , grating , rigorous coupled wave analysis , guided mode resonance , fano resonance , reflection (computer programming) , fourier transform , coupling (piping) , diffraction grating , refractive index , computer science , quantum mechanics , plasmon , programming language , mechanical engineering , engineering
In this paper, we develop spatiotemporal coupled-mode theory to describe optical properties of guided-mode resonant gratings. We derive partial differential equations that describe both spatial and temporal evolution of the field inside the grating. These equations describe the coupling of two counter-propagating grating modes, revealing the structure's "dark" and "bright" resonances at normal incidence of light. Moreover, the proposed theory allows us to obtain a simple approximation of the transmission and reflection coefficients taking into account both light's frequency and angle of incidence. This approximation can be considered as the generalization of the Fano line-shape. The approximation is in good agreement with the rigorous computations based on the Fourier modal method. The results of the paper will be useful for design and analysis of guided-mode resonant filters and other photonic devices.