Generalized effective-medium theory for metamaterials

We present an effective-medium model for calculating the frequency-dependent effective permittivity $$\epsilon${}($\omega${})$ and permeability $$\mu${}($\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 $$\epsilon${}($\omega${})$ and $$\mu${}($\omega${})$, in agreement with numerical finite-element calculations.