Circular integrated optical microresonators: Analytical methods and computational aspects

This chapter discusses an ab-initio frequency-domain model of circular microresonators, built on the physical notions that commonly enter the description of the resonator functioning in terms of interaction between fields in the circular cavity with the modes supported by the straight bus waveguides. Quantitative evaluation of this abstract model requires propagation constants associated with the cavity/bend segments, and scattering matrices, that represent the wave interaction in the coupler regions. These quantities are obtained by an analytical (2-D) or numerical (3-D) treatment of bent waveguides, along with spatial coupled mode theory (CMT) for the couplers. The required CMT formulation is described in detail. Also, quasianalytical approximations for fast and accurate computation of the resonator spectra are discussed. The formalism discussed in this chapter provides valuable insight in the functioning of the resonators, and it is suitable for practical device design.