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

Subject of our investigation are resonance phenomena in optical cavities realized as defects in 1D gratings with piecewise constant refractive index distributions. Upon viewing the cavity as a passive open system with intrinsically leaky behavior due to the 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, or quasinormal-modes QNMs [1], [2]. The imaginary part of the frequency represents the energy decay, closely related to the Q-factor of the cavity [3]. Our aim is to predict the response of the structure to external excitation and/or parameter perturbations, solely based on the knowledge of profiles and eigenfrequencies of the QNMs supported by the cavity. Quasi-normal mode theory We consider a defect grating consisting of two Bragg reflectors (high index nSi, low index nSiO2, widths LSi and LSiO2) with one wider middle layer of high refractive index (defect). The grating is enclosed by semi-infinite media of index n0. This arrangement of layers represents a Fabry-Perot cavity with one transmission resonance in the middle of the bandgap of the reflector gratings. The cavity is described with a two-component formalism [1], for the (scalar) electric field E(x, t) and a conjugated variable Ê(x, t): E = (E, Ê)T = Time evolution operator and equation: ∂ 2 xx E, n