Variational analysis for photonic molecules: application to photonic benzene waveguides

A type of artificial molecule, called the photonic molecule, is investigated. It consists of coupled-defect atoms in photonic crystals. We theoretically present a method to determine the frequency of each resonant mode for the photonic molecule. Within the major band gap, the photonic molecule confines the resonant modes that are closely analogous to the ground-state molecular orbitals of an analogous chemical molecule and the corresponding electromagnetic spectrum is also isomorphous to the electric energy levels. By employing the variational theory, the constraint determining the resonant coupling is formulated, which is consistent with the results of both the scattering matrix method and the group analysis. In addition, a type of photonic waveguide is proposed for the two-dimensional system that manipulates the mechanism of photon hopping between photonic benzene and offers an optical feature of twin waveguiding bandwidths.