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We explain the Lorentz resonances in plasmonic crystals that consist of 2Dnano dielectric inclusions as the interaction between resonant materialproperties and geometric resonances of electrostatic nature. One example ofsuch plasmonic crystals are graphene nanosheets that are periodically arrangedwithin a non-magnetic bulk dielectric. We identify local geometric resonanceson the length scale of the small scale period. From a materials perspective,the graphene surface exhibits a dispersive surface conductance captured by theDrude model. Together these phenomena conspire to generate Lorentz resonancesat frequencies controlled by the surface geometry and the surface conductance.The Lorentz resonances found in the frequency response of the effectivedielectric tensor of the bulk metamaterial is shown to be given by an explicitformula, in which material properties and geometric resonances are decoupled.This formula is rigorous and obtained directly from corrector fields describinglocal electrostatic fields inside the heterogeneous structure. Our analyticalfindings can serve as an efficient computational tool to describe the generalfrequency dependence of periodic optical devices. As a concrete example, weinvestigate two prototypical geometries composed of nanotubes and nanoribbons.

Lorentz Resonance in the Homogenization of Plasmonic Crystals