Resonant coupling of dielectric optical waveguides via rectangular microcavities: the coupled guided mode perspective

Placed between two waveguides that serve as input and output ports, a wide segment of a third high contrast multimode dielectric waveguide can constitute the cavity in an integrated optical microresonator. We consider these devices in a spatial 2D setting by means of a bidirectional coupled mode theory (CMT) based on the guided fixed-frequency modes of the two port waveguides and the cavity segment. Combined with the numerically computed reflectivity of the cavity facets, the CMT equations can be solved for the power transmission of the resonators, in good agreement with rigorous mode expansion simulations. The CMT model allows to virtually detach the cavity from the port waveguides. Resonant configurations can thus be found as singularities in the matrix denominator of the CMT equations. Inspired by the field shape and the quality of some of the resonances, a more detailed look at the cavity facets reveals an effect of almost total reflection for specific slab mode superpositions. Both results together show that a slab waveguide mode solver is in principle sufficient for an approximate identification and classification of the resonances in the rectangular cavities. Several numerical examples illustrate the design procedure.