  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.
