Backscattering in Silicon Microring Resonators: A Quantitative Analysis

Silicon microring resonators very often exhibit resonance splitting due to backscattering. This effect is hard to model in a quantitative and predictive way. This paper presents a behavioral circuit model for ring resonators that quantitatively explains the wide variations in resonance splitting observed in experiments. The model is based on an in-depth analysis of the contributions to backscattering by both the ring waveguides and the coupling sections, and it accurately explains the origin of asymmetric resonance splitting. Backscattering transforms unidirectional ring resonators into bidirectional circuits by coupling the clockwise and counter-clockwise circulating modes.In highQ rings this will induce visible resonance splitting, but due to the stochastic nature of backscattering this splitting is different for each resonance. Our model, based on temporal coupled mode theory, and the associated fitting method are both accurate and robust, and can also, for the first time, explain asymmetrically split resonances. The cause of asymmetric resonance splitting is identified as the backcoupling in the coupling sections. This is experimentally confirmed, and we further analyze the dependency on gap and coupling length. Moreover, the wide variations in resonance splitting of one spectrum is also analyzed and successfully explained by our circuit model that incorporates most linear parasitic effects in the ring resonator. This analysis uncovers multi-cavity interference within the ring as the source of this variation. O R IG IN A L PA P E R Backscattering in Silicon Microring Resonators: A Quantitative Analysis Ang Li1,2, Thomas Van Vaerenbergh1,2,3, Peter De Heyn3 ,Peter Bienstman1,2, and Wim Bogaerts1,2,4