  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.
