Lorentz resonance in the homogenization of plasmonic crystals

We explain the Lorentz resonances in plasmonic crystals that consist of two-dimensional nano-dielectric inclusions as interaction between resonant material properties and geometric electrostatic nature. One example such are graphene nanosheets periodically arranged within a non-magnetic bulk dielectric. identify local on length scale small-scale period. From materials perspective, surface exhibits dispersive conductance captured by Drude model. Together these phenomena conspire to generate at frequencies controlled geometry conductance. The found frequency response effective dielectric tensor metamaterial shown be given an explicit formula, which decoupled. This formula is rigorous obtained directly from corrector fields describing inside heterogeneous structure. Our analytical findings can serve efficient computational tool describe general dependence periodic optical devices. As concrete example, we investigate two prototypical geometries composed nanotubes nanoribbons.