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.
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Huy et al. (2005) studied this question.
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