Study of the microgear resonators using the Floquet-Bloch formalism

The microgear cavity is a microdisk surrounded by a circular Bragg grating. It is well known for its high Q Whispering Gallery Mode (WGM) and its modal selectivity. Microgears are often simulated thanks to two-dimensional (2-D) Finite-Difference Time-Domain (FDTD) computations which are limited by their cartesian grid and experience a high numerical complexity. In this paper, a fast and accurate 2-D method describing the WGM in a microgear dielectric resonators is presented. The model is based on the Floquet Bloch formalism. The field is described analytically within the disk and outside the grating. The field within the grating is calculated with a finite difference formalism in polar coordinates. The resonant wavelength and quality factor can be deduced from the eigenvalue problem. Our method has been compared to the Coupled Mode Theory and to 2-D FDTD computations, it proves to be more accurate and much faster than both methods (few seconds versus few hours for FDTD). Moreover, we have demonstrated a polarization effect of the microgear. Finally, our model can be applied to different structures. Micro-flowers and microgear surrounded by multi-layer Bragg reflector are investigated.