Whispering gallery modes in hexagonal microcavities

We investigated the whispering gallery modes (WGMs) of cavities with a hexagonal cross section. We found two different modes, namely, perturbed and quasi-WGMs, of which the former exhibits a $Q$ of greater than ${10}^{7}$ when the corner radii are large and $1.8\ifmmode\times\else\texttimes\fi{}{10}^{4}$ when the corners are sharp. 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.