Optical properties of photonic crystals composed of metal-coated spheres

We consider the optical properties of photonic crystals composed of metal-coated dielectric spheres. The calculations are performed using the multiple-scattering theory as well as a model of coupled dipole resonators that gives an intuitive understanding of band dispersions. The low frequency dispersions are found to originate from the hybridization of the dipolar resonance with the free-space propagating electromagnetic modes. We derived a wave-vector dependent effective-medium theory that can describe the low frequency resonating behavior very well. Within this new formulation, the effective constitutive parameters become k-dependent. In contrast to the standard Maxwell-Garnett type effective medium theory, which gives a gap near the resonances, the wave-vector dependent effective-medium theory can give the dispersion of the resonance bands. The very robust directional band gap between the second and the third band in the face-centered-cubic metallo-dielectric photonic crystals is found to originate from the dipole resonance of the coated spheres. The directional gap of the simple cubic structure also originates from the dipole resonance and the coupling to higher order resonances leads to an absolute gap.