Symmetry, degeneracy and optical confinement of modes in coupled microdisk resonators and photonic crystal cavities

Fast and highly accurate method based on the Muller contour integral equations and a trigonometric-trigonometric Galerkin discretization technique is presented for spectral design and fine-tuning of clusters of whispering-gallery (WG) mode microdisk resonators and photonic crystal (PC) defect cavities. It is shown that degeneracy and near-degeneracy of natural modes as well as modes optical confinement in coupled resonator clusters are significantly influenced by the symmetry of the structure. Photonic molecules with greatly enhanced quality factors are designed by exploiting the symmetry of the molecular geometry and tuning the inter-cavity coupling distances. Potential applications of the spectrally engineered coupled-resonator structures to low-threshold microdisk lasers, optical biosensors, and random powder lasers are discussed