First-principles homogenization theory for periodic metamaterials

We derive from first principles an accurate homogenized description of periodic metamaterials made of magnetodielectric inclusions, highlighting and overcoming relevant limitations of standard homogenization methods. We obtain closed-form expressions for the effective constitutive parameters, pointing out the relevance of inherent spatial dispersion effects, present even in the long-wavelength limit. Our results clarify the limitations of quasi-static homogenization models, restore the physical meaning of homogenized metamaterial parameters and outline the reasons behind magnetoelectric coupling effects that may arise also in the case of center-symmetric inclusions.

[1]  S. Ornes.  Metamaterials , 2013, Proceedings of the National Academy of Sciences.

[2]  Xing-Xiang Liu,et al.  Homogenization of quasi-isotropic metamaterials composed by dense arrays of magnetodielectric spheres , 2011 .

[3]  A. Alú.  Restoring the physical meaning of metamaterial constitutive parameters , 2010, 1012.1353.

[4]  Gennady Shvets,et al.  Current-driven metamaterial homogenization , 2010 .

[5]  Yuri S. Kivshar,et al.  Substrate-induced bianisotropy in metamaterials , 2010, 1006.1159.

[6]  D. Smith,et al.  Analytic expressions for the constitutive parameters of magnetoelectric metamaterials. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  C. Simovski,et al.  Material parameters of metamaterials (a Review) , 2009 .

[8]  M. Silveirinha,et al.  Nonlocal homogenization of an array of cubic particles made of resonant rings , 2009 .

[9]  Edward F. Kuester,et al.  Extracting the bulk effective parameters of a metamaterial via the scattering from a single planar array of particles , 2009 .

[10]  Pavel A. Belov,et al.  Spatial dispersion in lattices of split ring resonators with permeability near zero , 2008 .

[11]  N. Engheta,et al.  Transmission-line analysis of epsilon -near-zero-filled narrow channels. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  C. Soukoulis,et al.  Strong diamagnetic response in split-ring-resonator metamaterials: Numerical study and two-loop model , 2008 .

[13]  Mário G. Silveirinha,et al.  Generalized Lorentz-Lorenz formulas for microstructured materials , 2007 .

[14]  C. Simovski.  Bloch material parameters of magneto-dielectric metamaterials and the concept of Bloch lattices , 2007 .

[15]  R. Shore,et al.  Traveling waves on two‐ and three‐dimensional periodic arrays of lossless scatterers , 2007 .

[16]  N. Engheta,et al.  Optical 'shorting wires'. , 2007, Optics express.

[17]  Sergei A. Tretyakov,et al.  Local constitutive parameters of metamaterials from an effective-medium perspective , 2007 .

[18]  N. Engheta,et al.  Nanoinsulators and nanoconnectors for optical nanocircuits , 2007, cond-mat/0703600.

[19]  Jensen Li,et al.  Non-local effective medium of metamaterial , 2007, cond-mat/0701332.

[20]  M. Silveirinha.  Metamaterial homogenization approach with application to the characterization of microstructured composites with negative parameters , 2006, cond-mat/0611461.

[21]  Nader Engheta,et al.  Tunneling of electromagnetic energy through subwavelength channels and bends using epsilon-near-zero materials. , 2006, Physical review letters.

[22]  N. Engheta,et al.  Design of matched zero-index metamaterials using nonmagnetic inclusions in epsilon-near-zero media , 2006, cond-mat/0609675.

[23]  N. Engheta,et al.  Three-dimensional nanotransmission lines at optical frequencies: A recipe for broadband negative-refraction optical metamaterials , 2006, cond-mat/0609625.

[24]  N. Engheta,et al.  Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern , 2006, cond-mat/0609220.

[25]  David R. Smith,et al.  Electromagnetic parameter retrieval from inhomogeneous metamaterials. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[26]  P. Belov,et al.  Homogenization of electromagnetic crystals formed by uniaxial resonant scatterers. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  Richard W Ziolkowski,et al.  Propagation in and scattering from a matched metamaterial having a zero index of refraction. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[28]  N. Engheta,et al.  Polarizabilities and effective parameters for collections of spherical nanoparticles formed by pairs of concentric double-negative, single-negative, and∕or double-positive metamaterial layers , 2004, physics/0410011.

[29]  C. Holloway,et al.  A double negative (DNG) composite medium composed of magnetodielectric spherical particles embedded in a matrix , 2003 .

[30]  Gérard Tayeb,et al.  The richness of the dispersion relation of electromagnetic bandgap materials , 2003 .

[31]  P. A. Belov,et al.  A condition imposed on the electromagnetic polarizability of a bianisotropic lossless scatterer , 2003 .

[32]  D. Smith,et al.  Resonant and antiresonant frequency dependence of the effective parameters of metamaterials. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[33]  R. Baughman,et al.  Linear and nonlinear wave propagation in negative refraction metamaterials , 2003 .

[34]  P. Belov,et al.  Backward wave region and negative material parameters of a structure formed by lattices of wires and split-ring resonators , 2002, IEEE Antennas and Propagation Society International Symposium. Digest. Held in conjunction with: USNC/CNC/URSI North American Radio Sci. Meeting (Cat. No.03CH37450).

[35]  S. Tretyakov,et al.  Strong spatial dispersion in wire media in the very large wavelength limit , 2002, cond-mat/0211204.

[36]  Sailing He,et al.  Frequency range and explicit expressions for negative permittivity and permeability for an isotropic medium formed by a lattice of perfectly conducting /Ω particles , 2002, physics/0210049.

[37]  J. Pendry,et al.  Magnetic activity at infrared frequencies in structured metallic photonic crystals , 2002 .

[38]  G. Milton.  The Theory of Composites , 2002 .

[39]  Francisco Medina,et al.  Role of bianisotropy in negative permeability and left-handed metamaterials , 2002 .

[40]  A. Glisson,et al.  Electromagnetic mixing formulas and applications , 2000, IEEE Antennas and Propagation Magazine.

[41]  Vladimir M. Shalaev,et al.  Electromagnetic properties of small-particle composites , 1996 .

[42]  A. Yaghjian,et al.  Electric dyadic Green's functions in the source region , 1980, Proceedings of the IEEE.

[43]  M. Musgrave,et al.  Spatial Dispersion in Crystal Optics and the Theory of Excitons , 1968 .

[44]  Xing-Xiang Liu,et al.  Limitations and potentials of metamaterial lenses , 2011 .

[45]  H. Hazan,et al.  First Principles , 2011, For the University.

[46]  R. Collin.  Field theory of guided waves , 1960 .

[47]  P. P. Ewald.  Die Berechnung optischer und elektrostatischer Gitterpotentiale , 1921 .