An analytical approach is used to describe the dispersion of phase resonances occurring between waveguide cavity modes in compound transmission gratings. The strongly enhanced evanescent fields associated with the phase resonances are used to derive an approximate closed-form equation for the dispersion of phase resonances. The equation that is derived predicts the dependence of the frequencies and dispersion of the phase resonances on structural feature sizes, material parameters, and the momentum of the phase resonance. This analytical description is compared to results obtained by using a rigorous coupled wave algorithm. This equation allows one to design a compound transmission grating that supports phase resonances with particular properties, such as resonant frequencies and momenta. Applications of the phase resonances to high-finesse electromagnetic filters and corrugated surface antennas are discussed.
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Mandel et al. (2013) studied this question.
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