Abstract
We investigated the whispering gallery modes of cavities with a hexagonal cross-section. We found two different modes, namely perturbed and quasi-WGMs, of which the former exhibits the higher Q when the corner radius is large. We studied the dependence of Q on the curvature radius of the polygonal cavities and found that the coupling between the two modes determines the Q of the cavity. In addition we fabricated a cavity by employing laser heated pedestal growth and demonstrated a high Q.
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