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Abstract
Whispering gallery mode microcavities have been widely explored because of high $Q$ factors and small mode volumes. Although small mode volumes are beneficial in sensors and nonlinear applications, recent studies suggest that large mode volumes are required for noise reduction in advanced applications. To enhance the mode volume, one possible method is to utilize the material inside the cavity. Herein, a radial gradient refractive index (GRIN) microresonator has an internal potential well and allows the mode field to shift inward. The GRIN resonator is formed by changing the radial refractive index $n(r)$, and can be produced by the mature ion-exchange process. By adjusting the process parameters, the internal potential well can be widened to generate large mode volumes. However, it takes a lot of time to optimize the process parameters of wide potential well resonators using commercial software. Therefore, in this paper, we propose a fast algorithm for radial GRIN microcavities. Using this algorithm, we optimize the diffusion and annealing times of the GRIN resonator to increase the mode volume to more than four times that of the WGM microcavity. COMSOL simulations also support the conclusion with no additional loss in the $Q$ factor.
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