Rigorous model for the design of ultra-high Q-factor resonant cavities

A rigorous mathematical method to simulate an ultra-high Q-factor 1D PhC ring resonator (1D PhCRR) is proposed. The integration of a 1D PhC in a ring cavity resonator allows an enhancement of the Q-factor of a single ring resonator up to 109 or more, without enlarging the device footprint, with an improvement of at least two orders of magnitude in comparison with the values obtained without the grating. Rigorous modelling and simulations of such ultra high-Q resonant cavities are very challenging, because of the structure complexity, due to the large device footprint and the requirements for an accurate spectral analysis. Conventional numerical methods, such as Finite Element Method (FEM) and Finite Difference Time Domain (FDTD) require very long simulation time and huge computing resource. Therefore, a general mathematical method, able to reduce the computing time, assuring accurate solutions, and investigating the effect of the grating in the coupling region, is a real need. Several configurations of 1D PhCRRs have been investigated. An ultra-high Q-factor (> 109) for a 1D PhCRR in Si3N4 technology with a footprint of 64 mm2 has been calculated. Similar performance makes the 1D PhC ring resonator suitable for several applications, such as optical gyroscopes for space environment and ultra-sensitive biosensors.