Modeling of grating assisted standing wave microresonators for filter applications in integrated optics

A wide, multimode segment of a dielectric optical waveguide, enclosed by Bragg reflectors and evanescently coupled to adjacent port waveguides, can constitute the cavity in an integrated optical microresonator. It turns out that the device can be described adequately in terms of an approximate coupled mode theory model which involves only a few guided modes as basis fields. By reasoning along the coupled mode model, we motivate a simple design strategy for the resonator device. Rigorous two dimensional mode expansion simulations are applied to verify the predictions of the approximate model. The results exemplify the specific spectral response of the standing wave resonators. As refinements we discuss the single resonance of a device with nonsymmetrically detuned Bragg reflectors, and the cascading of two Fabry-Perot cavities, where the coupling across an intermediate shorter grating region establishes a power transfer characteristic that is suitable for an add-drop filter.