Comptes Rendus
no. 6
Metamaterials: from microwaves to the visible region
[Métamatériaux : des microondes au domaine visible]
Daniel Maystre1  ; Stefan Enoch1 ; Boris Gralak1 ; Gérard Tayeb1
1 Institut Fresnel, unité mixte de recherche CNRS 6133, faculté des sciences et techniques de St Jérôme, case 161, 13397 Marseille cedex 20, France
Comptes Rendus. Physique, Volume 6 (2005) no. 6, pp. 693-701.

Dans un récent article, J.B. Pendry [J.B. Pendry, Negative refraction makes a perfect lens, Phys. Rev. Lett. 86 (2000) 3966–3969] a mentionné la possibilité d'élaborer des lentilles parfaites en utilisant une couche plane de matériau main gauche dont les permittivité et perméabilité relatives sont égales à −1. Dans sa démonstration, Pendry montre l'importance capitale des ondes évanescentes dans cette propriété, ces ondes subissant une amplification dans le matériau main gauche. Dans cet article, nous donnons d'abord une démonstration électromagnétique rigoureuse du résultat énoncé par Pendry. Nous relevons qu'en fait, l'expression intégrale du champ diverge dans une certaine région de l'espace. Cette remarque ne démontre évidemment pas que la lentille parfaite n'existe pas. Nous donnons donc une démontration théorique simple qu'un métamatériau possédant une permittivité et une perméabilité relatives égales à −1 ne peut exister, même à une seule fréquence. Toutefois, en prenant en compte la nature hétérogène d'un métamatériau, on peut montrer qu'un matériau capable de focaliser la lumière plus efficacement qu'un dispositif classique (mais non parfaitement) peut exister. Finalement, nous montrons qu'une couche planaire d'un cristal photonique diélectrique peut lui aussi focaliser la lumière, une propriété qui pourrait se révéler cruciale pour la construction de superlentilles dans les domaines visible et microonde.

In a recent paper, J.B. Pendry [J.B. Pendry, Negative refraction makes a perfect lens, Phys. Rev. Lett. 86 (2000) 3966–3969] has mentioned the possibility of making perfect lenses using a slab of left-handed material with relative permeability and permittivity equal to −1. He gave a demonstration of the vital influence of the evanescent waves in this process, arguing that these waves are amplified inside the slab. In the present paper, we first try to give a rigorous electromagnetic demonstration of Pendry's statement, and we show that in fact the integral expression of the field in a region of space diverges. Since this divergence does not prove that the perfect lens does not exist, we then give a very simple theoretical demonstration that a homogeneous material with both relative permittivity and permeability equal to −1 cannot exist, even for a unique frequency. However, thanks to the heterogeneous nature of a metamaterial, it is shown that a material able to focus light more efficiently than current devices (but not perfectly) could exist. Finally, it is shown that a plane slab of dielectric photonic crystal can also focus light, a property which could be crucial for construction of superlenses in the visible and infrared regions.

Publié le :
DOI : 10.1016/j.crhy.2005.06.005
Keywords: Metamaterials, Left-handed materials, Negative refraction, Superlens, Electromagnetic theory, Photonic crystals
Mot clés : Métamatériaux, Matériaux main gauche, Réfraction négative, Superlentille, Théorie électromagnétique, Cristaux photoniques
Daniel Maystre 1 ; Stefan Enoch 1 ; Boris Gralak 1 ; Gérard Tayeb 1

1 Institut Fresnel, unité mixte de recherche CNRS 6133, faculté des sciences et techniques de St Jérôme, case 161, 13397 Marseille cedex 20, France 
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Daniel Maystre; Stefan Enoch; Boris Gralak; Gérard Tayeb. Metamaterials: from microwaves to the visible region. Comptes Rendus. Physique, Volume 6 (2005) no. 6, pp. 693-701. doi : 10.1016/j.crhy.2005.06.005. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2005.06.005/

[1] J.B. Pendry Negative refraction makes a perfect lens, Phys. Rev. Lett., Volume 86 (2000), pp. 3966-3969

[2] G.W. 't Hooft; J.B. Pendry Comment on Negative refraction makes a perfect lens, Phys. Rev. Lett., Volume 87 (2001), p. 249701

[3] J.M. Williams; J.B. Pendry Some problems with negative refraction, Phys. Rev. Lett., Volume 87 (2001), p. 249703

[4] D. Maystre Electromagnetic analysis of ultra-refraction and negative refraction, J. Modern Optics, Volume 50 (2003), pp. 1431-1444

[5] S. Enoch; G. Tayeb; P. Sabouroux; N. Guérin; P. Vincent A metamaterial for directive emission, Phys. Rev. Lett., Volume 89 (2002), p. 213902

[6] J.P. Dowling; C.M. Bowden Anomalous index of refraction in photonic bandgap material, J. Modern Optics, Volume 41 (1994), pp. 345-351

[7] R. Zengerle Light propagation in singly and doubly periodic planar waveguides, J. Modern Optics, Volume 34 (1987), pp. 1589-1617

[8] S.Y. Lin; V.M. Hietala; L. Wang; E.D. Jones Highly dispersive photonic band-gap prism, Opt. Lett., Volume 21 (1996), pp. 1771-1773

[9] H. Kosaka; T. Kawashima; A. Tomita; M. Notomi; T. Tamamura; T. Sato; S. Kawakami Superprism phenomena in photonic crystals, Phys. Rev. B, Volume 58 (1998), pp. 10096-10099

[10] C.M. Soukoulis Photonic Band-Gap Materials, Kluwer Academic, Dordrecht, 1996

[11] S. Enoch; G. Tayeb; D. Maystre Numerical evidence of ultrarefractive optics in photonic crystals, Optics Comm., Volume 161 (1999), pp. 171-176

[12] B. Gralak; S. Enoch; G. Tayeb Anomalous refractive properties of photonic crystals, J. Opt. Soc. Am. A, Volume 17 (2000), pp. 1012-1020

[13] V.G. Veselago The electrodynamics of substances with simultaneously negative value of ɛ and μ, Sov. Phys. Uspekhi, Volume 10 (1968), pp. 509-514

[14] P.M. Valanju; R.M. Walser; A.P. Valanju Wave refraction in negative-index media: always positive and very inhomogeneous, Phys. Rev. Lett., Volume 88 (2002), p. 187401-1-4

[15] R.W. Ziolkowski; E. Heyman Wave propagation in media having negative permittivity and permeability, Phys. Rev. E, Volume 64 (2001), p. 56625-1-15

[16] N. Garcia; M. Nieto-Vesperinas Left-handed materials do not make a perfect lens, Phys. Rev. Lett., Volume 88 (2002), p. 207403-1-4

[17] D. Maystre; S. Enoch Perfect lenses made with left-handed materials: Alice's mirror?, J. Opt. Soc. Amer. A, Volume 21 (2004), pp. 122-131

[18] J.B. Pendry; A.J. Holden; D.J. Robbins; W.J. Stewart Magnetism from conductors and enhanced nonlinear phenomena, IEEE Trans. Microwaves Theory Tech., Volume 47 (1999), pp. 2075-2084

[19] J.B. Pendry; A.J. Holden; W.J. Stewart; I. Youngs Extremely low frequency plasmon in metallic mesostructures, Phys. Rev. Lett., Volume 76 (1996), pp. 4773-4776

[20] R.A. Shelby; D.R. Smith; S. Schultz Experimental verification of a negative index of refraction, Science, Volume 292 (2001), pp. 77-79

[21] P.M. Morse; H. Feshbach Methods of Theoretical Physics, McGraw Hill Book Company, New York, 1953 (p. 823)

[22] M. Cadilhac Electromagnetic Theory of Gratings, Some Mathematical Aspects of the Grating Theory (R. Petit, ed.), Springer-Verlag, Berlin, 1980, pp. 53-62

[23] R. Courant; D. Hilbert Methods of Mathematical Physics, vol. 2, Interscience, New York, 1962

[24] D.W. Pohl; D. Courjon Near Field Optics, Kluwer Academic, Dordrecht, 1993

[25] D. Felbacq; G. Bouchitté Homogenization of a set of parallel fibres, Waves in Random Media, Volume 7 (1997), pp. 245-256

[26] M.C.K. Wiltshire; J.B. Pendry; I.R. Young; D.J. Larkman; D.J. Gilderdale; J.V. Hajnal Microstructured magnetic materials for RF flux guides in magnetic resonance imaging, Science, Volume 291 (2001), pp. 849-851

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