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Analysis of optical defect cavities in 1 D grating structures with quasi-normal mode theory

Subject of our investigation are resonance phenomena in optical cavities that are realized as defects in 1D grating with piecewise constant refractive index distribution. Upon viewing the cavity as a passive system with intrinsically leaky behaviour due to open boundaries where waves are permitted to leave the structure, the cavity can be characterized in terms of complex frequencies associated with unbounded field profiles (leaky modes, or quasi-normal-modes QNMs [1], [2]). The imaginary part of the frequency represents the energy decay, closely related to the Q-factor of the cavity. Our aim is to predict the response of the structure to external excitation and/or parameter perturbations, based on the profiles and eigenfrequencies of the QNMs supported by the cavity. Fig. 1 introduces a typical structure and shows a QNM field profile with the eigenfrequency next to the bandgap resonance (i.e. near the single peak of high transmission inside the forbidden frequency band of the periodic grating)..