Abstract
We present a formulation for deriving effective medium properties of infinitely periodic two-dimensional metamaterial lattice structures beyond the conventional static and quasi-static limits. We utilize the multipole expansions, where the polarization currents associated with the supported Bloch modes are expressed via the electric dipole, magnetic dipole, and electric quadrupole moments per unit length. We then propose a method to calculate the Bloch modes based on the lattice geometry and individual unit element structure. The results revert to well-known formulas in the traditional quasistatic limit and are useful for the homogenization of nanorod-type metamaterials which are frequently used in optical applications.
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