Homogenization of metamaterials using full-wave simulations

We present a full-wave homogenization method to determine the effective material parameters of metamaterials by considering a spherical piece of metamaterial. We use a T-matrix approach that is accelerated by a multilevel fast multipole method that is stable at low frequencies. To determine the T-matrix of one inclusion in the metamaterial a Method of Moments surface integral equation is used that is also accelerated using another multilevel fast multipole method that is stable at low frequencies. We also derive a new closed-form expression to extract the effective material parameters from the T-matrix of the spherical piece of material. Examples verify the accuracy and limitations of the method. We show results for metamaterials comprising more than 40,000 particles.