Modeling of the origin of photonic bands in the arrayed dielectric and metallic spheres

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1.We have derived the model Hamiltonian to be called the photonic Anderson model, in which the coupling constant between a localized photonic state and an outer plane-wave state is obtained. The model Hamiltonian leads to an optical response of a spherical dielectric system which agrees quite well with the numerical calculation.2.We derived the formula of the density of states of photons of photonic crystals with a flat surface, which takes account of the finite lifetime of photonic states arising from the leakage of the photonic energy to the exterior region. By using the formula, the calculated photon emission spectrum from an electron traveling near the surface of photonic crystal is analyzed and is shown to be due to the excitation of leaky photonic bands in it.3.The system called uniformly distributed photonic scatterers is proposed, in which a group of dielectric cylinders are distributed randomly with a sole restriction that the mutual spacing of cylinders is not smaller than a certain minimal value. It is shown that this system has a clear-cut and robust frequency region where the density of states of photons vanishes almost completely. The device application making use of this peculiar system is proposed.