Commun. Comput. Phys., 11 (2012), pp. 489-507.

Multiscale Nanorod Metamaterials and Realizable Permittivity Tensors

G. Bouchitte 1*, C. Bourel 1

1 IMATH, University of Sud-Toulon-Var, 83957 La Garde cedex, France.

Received 17 December 2009; Accepted (in revised version) 11 August 2010
Available online 24 October 2011


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.

AMS subject classifications: 35B27, 35Q60, 35Q61, 78M35, 78M40

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Key words: Homogenization, photonic crystals, metamaterials, micro-resonators, effective tensors, non local effects.

*Corresponding author.
Email: (G. Bouchitte), (C. Bourel)

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