Energy spectra for a photonic analog of multilayer graphene

We present a multiple-scattering method to study the dispersion of multilayer honeycomb arrays of metallic nanoparticles. Three types of stacking are considered. It is shown that the energy spectra for these multilayer photonic structures strongly depend on the distances between the layers, stacking number of layers, and the type of stacking, which are closely analogous to the electronic ones in multilayer graphene. The effects of interlayer coupling on the energy spectra have been demonstrated by exact numerical simulations. Thus, extensive applications of such a phenomenon to design optical devices are anticipated.