Slovick, B. A., Yu, Z. G., & Krishnamurthy, S. (2014). Generalized effective-medium theory for metamaterials. Physical Review B (Condensed Matter and Materials Physics), 89(15), 155118.
We present an effective-medium model for calculating the frequency-dependent effective permittivity ε(ω) and permeability μ(ω) 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 ε(ω) and μ(ω), in agreement with numerical finite-element calculations.