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We investigated the whispering gallery modes of cavities with a hexagonalcross-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. Westudied the dependence of Q on the curvature radius of the polygonal cavitiesand found that the coupling between the two modes determines the Q of thecavity. In addition we fabricated a cavity by employing laser heated pedestalgrowth and demonstrated a high Q.

Whispering gallery modes in hexagonal microcavities fabricated by crystal growth