Analytical study of the whispering-gallery mode in two-dimensional microgear cavity using coupled-mode theory

The microgear is a microdisk resonator surrounded by a circular grating. The circular grating increases the modal selectivity of the cavity. In this paper, a two-dimensional (2-D) analytical method that describes the whispering-gallery mode (WGM) in a microgear resonator is presented. The model based on coupled mode theory needs the normalization of the WGM. In the past, some normalizations have been proposed, they all assume the mode to be bound, which is not true as WGMs are leaky modes. A new normalization with no approximation is presented. The numerical integration of the model is compared to 2-D finite-difference time-domain computations. It shows accurate computations of the resonant wavelength with lower numerical complexity. The method can be generalized to any deformation of the microdisk. (c) 2005 Optical Society of America.