Nonlinear optimization technique for the homogenization of metamaterials from scattering parameters

We propose a novel numerical method for extracting the effective medium parameters of metamaterial structures. The reference scattering parameters of a metamaterial structure are provided as the target goal of a nonlinear optimization algorithm. The algorithm internally executes electromagnetic simulations of a homogeneous medium for identical excitations, and varies the relative permittivity and permeability values until the scattering parameters of that medium match the reference scattering values. A specific example for homogenizing a row of silver nanorods in visible wavelengths is presented, which highlights the limitations of relying solely on the scattering parameters.