Theory of gyrotropic ring resonators with counterpropagating modes coupling

The Faraday effect in ring resonators leads to the resonance splitting of clockwise and counter-clockwise propagating modes. In this work we investigate how this resonance splitting influences the ring resonator's behavior if both modes are coupled by a sidewall corrugation of the resonator. Coupled mode theory is used to evaluate the transmission and reflection characteristics of a ring resonator coupled to a waveguide. Based on these evaluations, we characterize a novel ring resonator switch. The resonance of the corrugated gyrotropic resonator coupled to a waveguide can be switched off by the application of the external magnetic field. In this case, the resonance is not shifted, as what typically occurs at small perturbations, but suppressed.