Generalized effective-medium theory for metamaterials

Abstract

We present an effective-medium model for calculating the frequency-dependent effective permittivity $\ensuremath{\epsilon}(\ensuremath{\omega})$ and permeability $\ensuremath{\mu}(\ensuremath{\omega})$ of metamaterial composites containing spherical particles with arbitrary permittivity and permeability. The model is derived from the zero-scattering condition within the dipole approximation, but does not invoke any additional long-wavelength approximations. As a result, it captures the effects of spatial dispersion and predicts a finite effective refractive index and antiresonances in $\ensuremath{\epsilon}(\ensuremath{\omega})$ and $\ensuremath{\mu}(\ensuremath{\omega})$, in agreement with numerical finite-element calculations.