Enhancement of local field by a two-dimensional array of dielectric spheres placed on a substrate

We consider a two-dimensional periodic array of dielectric spheres placed on a flat substrate and calculate its response to an incident electromagnetic wave. A remarkable feature of this system is the presence of electromagnetic resonance modes, which are shown to be closely related to the localized modes of a dielectric slab. When the resonance mode is excited, the local field near the sphere and consequently various electromagnetic quantities are enhanced. Enhancement factor of the Raman spectrum by adsorbed molecules is calculated and an optical bistability at a low laser power is predicted.