Resonance properties of optical all-dielectric metamaterials using two-dimensional multipole expansion

We examine the electromagnetic response of metamaterial unit elements consisting of dielectric rods embedded in a nonmagnetic background medium. We establish a theoretical framework in which the response is described through the electric and magnetic multipole moments that are simultaneously generated via the polarization currents that are excited upon the incidence of plane waves. The corresponding dipole and quadrupole polarizabilities are then calculated as a function of the Mie scattering coefficients, and their resonances are mapped for the case of dielectric cylindrical rods as a function of the geometry and the material parameters used. The results provide critical insight into the anisotropic response of two-dimensional rod-type metamaterials and can be used as a unified methodology in the calculation of exotic effective electromagnetic parameters involved in phenomena such as optical magnetism. DOI: 10.1103/PhysRevB.86.245108