Comprehensive mathematical modelling of ultra-high Q grating-assisted ring resonators

A comprehensive electromagnetic mathematical model of an ultra-high Q-factor 1D-PhC ring resonator (1D-PhCRR) is proposed. The 1D-PhCRR results by the integration of a 1D-PhC in a ring cavity and its operation is based on the slow-light effect, allowing an improvement of the Q-factor of at least three orders of magnitude in comparison with the values obtained for a ring resonator without the grating. Accurate modelling and simulation of such ultra-high-Q ring resonator require very long simulation time and huge computing resource by using the conventional numerical methods, as the finite element method and finite difference time domain, because of the structure complexity. Therefore, to overcome these bottlenecks, an accurate mathematical model has been developed, able to take into account the waveguide curvature and dispersion, and the effect of the grating in the coupling region, reducing also the computation time. An ultra-high Q-factor (>109) 1D-PhCRR in Si3N4 technology with a footprint of 16 mm2 has been simulated in relatively short computer time, using the model described in the paper. This performance makes the 1D-PhCRR suitable for several applications, such as filters, ultra-sensitive biosensors and integrated photonic-gyroscopes, for which ultra-high Q-factor sensitive element ensures a high resolution.