[1] G. Bouchitté, C. Bourel, D. Felbacq : Homogenization of the 3D Maxwell system near resonances and artificial magnetism. (English, French summaries) C. R. Math. Acad. Sci. Paris 347 (2009), no. 9-10, 571-576.

Résumé : Il est maintenant bien connu que l'homogénéisation d'un réseau périodique de fibres diélectriques de forte permittivité peut conduire à une perméabilité effective négative sur certaines bandes de fréquences. Cependant ce résultat basé sur l'analyse d'un résonateur en dimension deux ne pouvait être justifiée sans l'hypothèse de polarisation du champ magnétique et en pratique seuls des obstacles cylindriques infinis pouvaient être considérés. Dans cette note nous proposons une extension complète au cas 3D basée sur une nouvelle notion de moyennisation du champ magnétique. Nous obtenons un problème spectral vectoriel sur la cellule unité qui décrit l'effet de résonance et conduit à un tenseur de perméabilité effective dont les parties réelles des valeurs propres changent de signe suivant la fréquence.

[2] G. Bouchitté, C. Bourel : Multiscale nanorods metamaterials and realisable permittivity tensors. Commun. Comput. Phys. (2012) Vol. 11, No. 2, pp. 489-507

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 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 explicit as a function of the frequency. Due to internal resonances, the eigenvalues of this tensor have real part changing of sign and possibly very large within some range of frequencies. Numerical simulations are shown.

[3] D. Felbacq, B. Guizal, G. Bouchitté, and C. Bourel : Resonant homogenization of a dielectric metamaterial Microwave and Optical Technology Letters 51, 2009, 2695 - 2701.

Abstract : We investigate numerically and theoretically the homoge- neous properties of a metamaterial made of nanorods with a high di- electric constant. The rods have inner resonances leading to an effective magnetic behavior. The influence of various parameters, such as the wavelength, the angle of incidence, and the filling ratio is quantified by means of rigorous numerical computations.

[4] D. Felbacq, B. Guizal, G. Bouchitté, and C. Bourel : Effective properties of membrane photonic crystals. Journal of Nanophotonics, Vol. 3, 031507 (20 February 2009)

Abstract : Wave propagation in thin nanostructured films in the low frequency regime was studied. By means of a two-scale analysis, the medium can be homogenized, i.e. described by effective electromagnetic parameters. The effective permeability and permittivity were obtained from a set of partial differential equations. A numerical approach based on the Fourier Modal Method was devised in order to solve these equations.

[5] G. Bouchitté, C. Bourel , D. Felbacq : Homogenization of 3D-dielectric Photonic Crystals and Artifcial Magnetism. Proceedings of Waves 09 , editeur(s): INRIA , Waves 2009, 15th-19th June, Pau (France), 2009, 396 - 397 .

[6] G. Bouchitté, C. Bourel : Reiterated Homogenization and 3D-negative Permittivity Tensors in Electromagnetism. Proceedings of Waves 09 , editeur(s): INRIA , Waves 2009, 15th-19th June, Pau (France), 2009, 392 - 393 .

[7] G. Bouchitté , C. Bourel , D. Felbacq , B. Guizal : Spatial dispersion in a wire mesh metamaterial. Proceedings of SPIE, vol. 7353 , editeur(s): The International Society for Optical Engineering , Metamaterials IV, Prague, Czech Republic, 2009, 81947627.2 - 81947627.7 .

[8] G. Bouchitté , C. Bourel , D. Felbacq , B. Guizal : Effective properties of resonant arrays of rods. Proc. SPIE 7404, 740409 (2009) , editeur(s): Smith, Geoffrey B.; Lakhtakia, Akhlesh; Lee, Cheng-Chung, Nanostructured Thin Films II, 2009 , 740409.1 - 740409.8 .

[9] G. Bouchitté, C. Bourel : Homogenization of finite metallic fibers and 3D-effective permittivity tensor. Proc. SPIE, Vol. 7029, 702914 (2008); doi:10.1117/12.794935