Engineering the Electromagnetic Properties of Periodic Nanostructures Using Electrostatic Resonances

Electromagnetic properties of periodic two-dimensional subwavelength structures consisting of closely packed inclusions of materials with negative dielectric permittivity $ϵ$ in a dielectric host with positive ${ϵ}_h$ can be engineered using the concept of multiple electrostatic resonances. Fully electromagnetic solutions of Maxwell's equations reveal multiple wave propagation bands, with the wavelengths much longer than the nanostructure period. Some of these bands are described using the quasistatic theory of the effective dielectric permittivity ${ϵ}_{\mathrm{q}\mathrm{s}}$. Those bands exhibit multiple cutoffs and resonances which are found to be related to each other through a duality condition. An additional propagation band characterized by a negative magnetic permeability is found. Imaging with subwavelength resolution in that band is demonstrated.