Techniques to deal with Feshbach resonances are applied to describe resonant light scattering off one dimensional photonic crystal slabs. Accurate expressions for scattering amplitudes, free of any fitting parameter, are obtained for isolated as well as overlapping resonances. They relate the resonance properties to the properties of the optical structure and of the incident light. For the most common case of a piecewise constant dielectric function, the calculations can be carried out essentially analytically. After establishing the accuracy of this approach we demonstrate its potential in the analysis of the reflection coefficients for the diverse shapes of overlapping, interacting resonances.
The concept of Feshbach resonances developed for quantum mechanical scattering is applied in the analysis of classical light scattering off photonic crystal slabs. It is shown that this concept can be realized almost perfectly in these systems. As an application guided-mode resonances in the grating waveguide structure (GWS) are studied in detail. Using simple resonance dominance approximation the characteristic properties of isolated Feshbach resonances in light scattering are exhibited. Formation and interaction of overlapping resonances are investigated. The relevant parameters of the GWS are identified which control the shape of the reflectivity of interacting resonances as well as the enhancement of the electromagnetic field. The differences in the properties of TE and TM resonances is emphasized for both isolated and interacting resonances.
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