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Multiscale Nanorod Metamaterials and Realizable Permittivity Tensors

Published online by Cambridge University Press:  20 August 2015

G. Bouchitté  and
C. Bourel
G. Bouchitté*
Affiliation:
IMATH, University of Sud-Toulon-Var, 83957 La Garde cedex, France
C. Bourel*
Affiliation:
IMATH, University of Sud-Toulon-Var, 83957 La Garde cedex, France
*
Corresponding author.Email:bouchitte@univ-tln.fr
Email address:bourel@univ-tln.fr
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Abstract

Our aim is to evidence new 3D composite diffractive structures whose effective permittivity tensor can exhibit very large positive or negative real eigenvalues. We use a reiterated homogenization procedure in which the first step consists in considering a bounded obstacle made of periodically disposed parallel high conducting metallic fibers of finite length and very thin cross section. As shown in [2], the resulting constitutive law is non-local. Then by reproducing periodically the same kind of obstacle at small scale, we obtain a local effective law described by a permittivity tensor that we make explicit as a function of the frequency. Due to internal resonances, the eigenvalues of this tensor have real part that change of sign and are possibly very large within some range of frequencies. Numerical simulations are shown.

Keywords

35B2735Q6035Q6178M3578M40Homogenizationphotonic crystalsmetamaterialsmicro-resonatorseffective tensorsnon local effects
Type
Research Article
Information
Communications in Computational Physics , Volume 11 , Issue 2 , February 2012 , pp. 489 - 507
Copyright
Copyright © Global Science Press Limited 2012

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References

[1]Allaire, G., Homogenization and two-scale convergence, SIAM J. Math. Anal., 23 (1992), 1482–1518.Google Scholar
[2]Bouchitté, G. and Felbacq, D., Homogenization of a wire photonic crystal: the case of small volume fraction, SIAM J. Appl. Math., 66 (2006), 2061.Google Scholar
[3]Bouchitté, G. and Bourel, C., Homogenization of finite metallic fibers and 3D-effective permittivity tensor, Proc. SPIE San Diego, Metamaterials, 702914 (2008), DOI:10.1117/12.794935.Google Scholar
[4]O’Brien, S. and Pendry, J. B., Photonic band-gaps effects and magnetic activity in dielectric composites, J. Phys. Condens. Matter, 14 (2002), 4035–4044.Google Scholar
[5]Felbacq, D. and Bouchitté, G., Left handed media and homogenization of photonic crystals, Opt. Lett., 30 (2005), 10.CrossRefGoogle ScholarPubMed
[6]Felbacq, D. and Bouchitté, G., Homogenization of wire mesh photonic crystals embdedded in a medium with a negative permeability, Phys. Rev. Lett., 94 (2005), 183902.Google Scholar
[7]Pendry, J. B., Holden, A. J., Stewart, W. J. and Youngs, I., Extremely low frequency plasmons in metallic mesostructures, Phys. Rev. Lett., 76 (1996), 4773–4776.Google Scholar
[8]Bouchitté, G. and Felbacq, D., Homogenization of a set of parallel fibers, Waves Random Media, 7(2) (1997), 1–12.Google Scholar
[9]Bouchitté, G. and Felbacq, D., Homogenization near resonances and artificial magnetism from dielectrics, C. R. Math. Acad. Sci. Paris, 339 (2004), 377–382.Google Scholar
[10]Bouchitté, G., Bourel, C. and Felbacq, D., Homogenization of the 3D Maxwell system near resonances and artificial magnetism, C. R. Math. Acad. Sci. Paris, 347(9-10) (2009), 571–576.Google Scholar
[11]Nguetseng, G., A general convergence result for a functional related to the theory of homog-enization, SIAM J. Math. Anal., 20 (1989), 608–623.CrossRefGoogle Scholar
[12]Bouchitté, G., Felbacq, D. and Zolla, F., Bloch vector dependence of the plasma frequency in metallicphotonic crystals, Phys. Rev. E, 74 (2006), 056612.Google Scholar
[13]Bensoussan, A., Lions, J. L. and Papanicolaou, G., Asymptotic Analysis for Periodic Structures, Studies in Mathematics and its Applications, North-Holland Publishing Co. 1978.Google Scholar
[14]Chatelin, F., Spectral Approximation of Linear Operators, Academic Press, New York, 1983.Google Scholar
[15]Marshall, S. L., A periodic Green function for calculation of coloumbic lattice potentials, J. Phys. Condens. Matter, 12 (2000), 4575–4601.CrossRefGoogle Scholar
[16]Tartar, L., Compensated compactness and applications to partial differential equations, Nonlinear Analysis and Mechanics, Heriot-Watt Symposium, Vol. IV, pages 136–212, Pitman, Boston, Mass., 1979.Google Scholar