Effect of a semi-infinite substrate on the internal electric field intensity distribution of a monolayer of periodically arrayed dielectric spheres

We have investigated the effect of a semi-infinite substrate on the eigenstates of two-dimensional periodically arrayed dielectric spheres on the basis of the internal electric field intensity distributions. The internal field intensity distributions clearly represent the features of each eigenstate, compared with transmission spectra and external near-field intensity distributions. A substrate with low dielectric constant hardly affects the optical properties of monolayer spheres. However, when the dielectric constant of the substrate exceeds a certain threshold, the field intensity of eigenstates drastically reduces. This behavior can be explained by energy dissipation into the substrate by opening of diffraction channels. Therefore, dips in transmission spectra become broader by interaction with the monolayer spheres and the substrate.