Generalized effective-medium theory for metamaterials. Slovick, B. A., Yu, Z. G., & Krishnamurthy, S. Physical Review B, 89(15):155118, April, 2014.
Generalized effective-medium theory for metamaterials [link]Paper  doi  abstract   bibtex   
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.
@article{slovick_generalized_2014,
	title = {Generalized effective-medium theory for metamaterials},
	volume = {89},
	url = {http://link.aps.org/doi/10.1103/PhysRevB.89.155118},
	doi = {10.1103/PhysRevB.89.155118},
	abstract = {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.},
	number = {15},
	urldate = {2014-10-04TZ},
	journal = {Physical Review B},
	author = {Slovick, Brian A. and Yu, Zhi Gang and Krishnamurthy, Srini},
	month = apr,
	year = {2014},
	pages = {155118}
}

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