Ring resonator gap determination design rule and parameter extraction method for sub-GHz resolution whole C-band Si3N4 integrated spectrometer

A panoramic ultra-high resolution photonic integrated circuit spectrometer is under development by the authors. The architecture comprises a tunable ring resonator stage and an AWG stage. The resolution defines the bandwidth of the ring resonator determined by the cross-coupled power and hence the gap between the access and ring waveguides. The AWG channel frequency spacing determines the required free-spectral range (FSR) and hence the perimeter of the ring resonator. The specified < 1GHz resolution combined with a FSR of 50 GHz render accurate simulation difficult obstructing the design process. In this report, a simplified design rule to determine the minimum gap between straight access waveguides and a circular ring waveguide is proposed. Realistic assumptions such as existence of local bisymmetry and adiabatic mode evolution throughout the coupling region permit a simple mode solver to determine the relationship between the cross-coupled power and the minimum gap size. A parameter extraction method is also formulated for add-drop rings equipped with two nominally identical couplers that disentangles the loss and coupling ring parameters from intensity-only transmission measurements. The proposed rule is applied to the design of ring resonators fabricated on a Si₃N₄ platform. The parameter extraction method is used to analyze the measured characterization data of the ring resonators. The results show good agreement between the design rule and parameters extracted from the measured data (measurement shows maximum deviation of ~43 nm from the design rule estimation) and provide experimental confirmation of the technological viability of the ring resonators required by the spectrometer.