Fully deterministic analysis on photonic whispering-gallery modes of irregular polygonal microcavities with testing in hexagons

Polygonal microcavities supporting whispering-gallery modes (WGMs) are widely investigated for optoelectronic applications. Recently, polygonal microcavities with reduced symmetry of various types have been realized in a large number of materials, while the corresponding theoretical analysis of WGMs was either absent or done only for individual cavity shapes. We perform a systematic analysis of irregular polygonal microcavities in general, allowing us to obtain deterministic conclusions on WGMs for all possible parameters of all types of shape irregularities from a set of analytical equations and inequalities. We test the theory with several typical irregular hexagonal microcavities that were experimentally reported, and we discuss the loss mechanism verified by wave optics simulations. The results provide a powerful analyzing tool for experimentalists working on irregular polygonal microcavities, and they constitute a significant extension to the scope of WGM theory.