On the nature of resonance splitting in coupled multiring optical resonators

The spectrum of resonance frequencies in so-called free-standing resonators, built with coupled ring or disk resonators is analytically and numerically investigated. The composite resonator which constitutes the core of numerous photonic devices such as channel dropping filters, dispersion compensators, laser mirrors, etc., determines the salient characteristics of the device, such as its passband width and free spectral range (FSR). The spectral characteristics of the resonances are determined by the refractive indices of the waveguides, the dimensions of the resonators, and the strength of coupling between them. Novel relationships between these parameters are described that result in the invariance of the splitting ratios and as a consequence maintain the passband characteristics of the associated devices. Waveguide attenuation affecting the Q factor of the composite resonators is found to have insignificant effect on their spectral characteristics.