Wideband and Narrowband Circuit Models for Fano-Shape Guided-Mode Resonance

In this paper, we propose two different types of circuit models for Fano-shape guided-mode resonance (GMR) in waveguide gratings. Both the models constitute a resonant tank circuit together with a direct non-resonant channel between the incident and scattered light. One neglects the frequency dependence of the direct non-resonant channel and is only more accurate in the immediate vicinity of the Fano-type resonance. The other accounts for the frequency dependence of the direct non-resonant channel and thus remains accurate within a wider range of frequencies. The former being referred to as the narrow-band model is extremely accurate, insofar as the isolated GMR is of interest within a narrow band spectrum. The latter being referred to as the wide-band model, on the other hand, is of interest when the GMR partly blends with the Fabry-Perot resonance supported by the direct channel between the incident and scattered light. An interesting case of low-frequency GMR is also reported, which can also be well captured by our circuit models. Having derived simple circuits for the physical phenomenon at hand, the concept of energy amplitude in the narrow-band circuit model is also introduced, and thus, the dynamics of the circuit is explained by differential equations that parallels the temporal coupled-mode theory for GMR in waveguide gratings. The proposed models are validated by using the rigorous coupled-wave analysis. These models may be useful in guiding the design of waveguide grating devices that make the use of GMR in various applications.