Negative refractive index, perfect lenses and checkerboards: Trapping and imaging effects in folded optical spaces

Sébastien Guenneau; S. Anantha Ramakrishna

doi:10.1016/j.crhy.2009.04.002

Negative refractive index, perfect lenses and checkerboards: Trapping and imaging effects in folded optical spaces
[Réfraction négative, lentilles parfaites et échiquiers : piégeage et imagerie dans des espaces optiques repliés]

Sébastien Guenneau ¹ ; S. Anantha Ramakrishna ^2,³

¹ Department of Mathematical Sciences, University of Liverpool, Liverpool L69 3BX, United Kingdom
² Department of Physics, Indian Institute of Technology, Kanpur 208016, India
³ Indian Institute of Science Education and Research, Mohali, Transit Campus, MGSIPA Complex, Sector 26, Chandigarh 160019, India

Comptes Rendus. Physique, Volume 10 (2009) no. 5, pp. 352-378.

Résumé
Abstract

Les métamatériaux, structures diélectriques et métalliques dont la périodicité est inférieure à la longueur d'onde, ouvrent de nouveaux horizons dans le contrôle de la lumière par le truchement de la réfraction négative, où la lumière prend un mauvais tour. Leur brique élementaire est constitutée d'une part d'un résonateur de type anneau fendu qui conduit la perméabilité à prendre des valeurs négatives, et d'autre part d'une barre métallique qui joue un rôle similaire pour la permittivité. A l'échelle macroscopique, ils prennent la forme de lentilles plates, cylindriques et sphériques (dont celle éponyme imaginée par Victor Veselago en 1968 et dont John Pendry démontre qu'elle est parfaite en l'an 2000), ou d'échiquiers et de solides platoniques qui piègent la lumière en leur sein.

Newly discovered metamaterials have opened new vistas for better control of light via negative refraction, whereby light refracts in the “wrong” manner. These are dielectric and metallic composite materials structured at subwavelength lengthscales. Their building blocks consist of local resonators such as conducting thin bars and split rings driving the material parameters such as the dielectric permittivity and magnetic permeability to negative (complex) values. Combined together, these structural elements can bring about a (complex valued) negative effective refractive index for the Snell–Descartes law and result in negative refraction of radiation. Negative refractive index materials can support a host of surface plasmon states for both polarizations of light. This makes possible unique effects such as imaging with subwavelength image resolution through the Pendry–Veselago slab lens. Other geometries have also been investigated, such as cylindrical or spherical lenses that enable a magnification of images with subwavelength resolution. Superlenses of three-fold (equilateral triangle), four-fold (square) and six-fold (hexagonal) geometry allow for multiple images, respectively two, three, and five. Generalization to rectangular and triangular checkerboards consisting of alternating cells of positive and negative refractive index represents a very singular situation in which the density of modes diverges at the corners, with an infinity of images. Sine-cosecant anisotropic heterogeneous square and triangular checkerboards can be respectively mapped onto three-dimensional cubic and icosahedral corner lenses consisting of alternating positive and negative refractive regions. All such systems with corners between negative and positive refractive media display very singular behavior with the local density of states becoming infinitely large at the corner, in the limit of no dissipation. We investigate all of these, using the unifying viewpoint of transformation optics.

Publié le : 2009-06-01

DOI : 10.1016/j.crhy.2009.04.002

Keywords: Surface modes, Negative refraction, Lenses, Resonators, Geometric transforms
Mot clés : Modes de surface, Réfraction négative, Lentilles, Résonateurs, Transformations géométriques

Affiliations des auteurs :

Sébastien Guenneau ¹ ; S. Anantha Ramakrishna ^{2, 3}

¹ Department of Mathematical Sciences, University of Liverpool, Liverpool L69 3BX, United Kingdom
² Department of Physics, Indian Institute of Technology, Kanpur 208016, India
³ Indian Institute of Science Education and Research, Mohali, Transit Campus, MGSIPA Complex, Sector 26, Chandigarh 160019, India

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     title = {Negative refractive index, perfect lenses and checkerboards: {Trapping} and imaging effects in folded optical spaces},
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     pages = {352--378},
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Sébastien Guenneau; S. Anantha Ramakrishna. Negative refractive index, perfect lenses and checkerboards: Trapping and imaging effects in folded optical spaces. Comptes Rendus. Physique, Volume 10 (2009) no. 5, pp. 352-378. doi : 10.1016/j.crhy.2009.04.002. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2009.04.002/

Bibliographie
Cité par

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

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

[3] R.C. McPhedran; N.A. Nicorovici; G.W. Milton Optical and dielectric properties of partially resonant composites, Phys. Rev. B, Volume 49 (1994), p. 8479

[4] J.B. Pendry; S.A. Ramakrishna Focussing light using negative refraction, J. Phys.: Condens. Matter., Volume 15 (2003), pp. 6345-6364

[5] S. Guenneau; A.C. Vutha; S.A. Ramakrishna Negative refraction in 2D checkerboards by mirror anti-symmetry and 3D corner lenses, New J. Phys., Volume 7 (2005), p. 164

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

[7] G.W. Milton; N.A. Nicorovici On the cloaking effects associated with anomalous localized resonance, Proc. R. London A, Volume 462 (2006), p. 3027

[8] J.B. Pendry Perfect cylindrical lenses, Opt. Express, Volume 11 (2003) no. 7, pp. 755-760

[9] S.A. Ramakrishna; T.M. Grzegorczyk Physics and Applications of Negative Refractive Index Materials, CRC Press, Boca Raton, 2009

[10] D.R. Smith; D. Schurig; M. Rosenbluth; S. Schultz; S.A. Ramakrishna; J.B. Pendry Limitations on subdiffraction imaging with a negative refractive index slab, Appl. Phys. Lett., Volume 82 (2003) no. 10, p. 1506

[11] S.A. Ramakrishna; J.B. Pendry The asymmetric lossy near-perfect lens, J. Mod. Opt., Volume 49 (2002) no. 10, pp. 1747-1762

[12] N. Fang; H. Lee; C. Sun; X. Zhang Sub-diffraction-limited optical imaging with a silver superlens, Science, Volume 308 (2005), p. 534

[13] S.A. Ramakrishna; J.B. Pendry; M.C.K. Wiltshire; W.J. Stewart Imaging the near field, J. Mod. Opt., Volume 50 (2003), p. 1419

[14] Z. Jacob; L. Alekseyev; E. Narimanov Optical hyperlens: far-field imaging beyond the diffraction limit, Opt. Express, Volume 14 (2006) no. 18, pp. 8247-8256

[15] A. Salandrino; N. Engheta Far-field subdiffraction optical microscopy using metamaterial crystals: theory and simulations, Phys. Rev. B, Volume 74 (2006) no. 7, p. 751031

[16] D.R. Smith; D. Schurig Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors, Phys. Rev. Lett., Volume 90 (2003), p. 077405

[17] Z. Liu; H. Lee; Y. Xiong; C. Sun; X. Zhang Far-field optical hyperlens magnifying sub-diffraction-limited objects, Science, Volume 315 (2007) no. 5819, p. 1686

[18] I. Smolyaninov; Y.-J. Hung; C. Davis Magnifying superlens in the visible frequency range, Science, Volume 315 (2007) no. 5819, p. 1699

[19] G. Shvets; S. Trendafilov; J. Pendry; A. Sarychev Guiding, focusing, and sensing on the subwavelength scale using metallic wire arrays, Phys. Rev. Lett., Volume 99 (2007), p. 053903

[20] J.B. Pendry; A.J. Holden; D.J. Robbins; W.J. Stewart Magnetism from conductors and enhanced nonlinear phenomena, IEEE Trans. Microwave Theory Tech., Volume 47 (1999), p. 2075

[21] A.B. Movchan; S. Guenneau Split-ring resonators and localized modes, Phys. Rev. B, Volume 70 (2004), p. 125116

[22] S.A. Ramakrishna; O.J.F. Martin Resolving the wave vector in negative refractive index media, Opt. Lett., Volume 30 (2005) no. 19, p. 2626

[23] Y.F. Chen; P. Fischer; F.W. Wise Negative refraction at optical frequencies in nonmagnetic two component molecular media, Phys. Rev. Lett., Volume 95 (2005), p. 067402

[24] J. Skaar On resolving the refractive index and the wave vector, Opt. Lett., Volume 31 (2006), pp. 3372-3374

[25] S.A. Ramakrishna Comment on ‘Negative refraction at optical frequencies in nonmagnetic two component molecular media’, Phys. Rev. Lett., Volume 98 (2007), p. 059701

[26] A. Lakhtakia; J.B. Geddes; T.G. Mackay When does the choice of the refractive index of a linear, homogeneous, isotropic, active, dielectric medium matter?, Opt. Express, Volume 15 (2007), pp. 17709-17714

[27] J. Seidel; F. Grafström; L. Eng Stimulated emission of surface plasmons at the interface between a silver film and an optically pumped dye solution, Phys. Rev. Lett., Volume 94 (2005), p. 177401

[28] M.P. Silverman And Yet It Moves, Cambridge Univ. Press, New York, NY, USA, 1993 (pp. 151–163)

[29] V.U. Nazarov; Y.C. Chang Resolving the wave vector and the refractive index from the coefficient of reflectance, Opt. Lett., Volume 32 (2007), pp. 2939-2941

[30] J.B. Pendry; A.J. Holden; D.J. Robbins; W.J. Stewart Low frequency plasmons in thin-wire structures, J. Phys.: Condens. Matter, Volume 10 (1998), pp. 4785-4809

[31] D.R. Smith; W.J. Padilla; V.C. Vier; S.C. Nemat-Nasser; S. Schultz Composite medium with simultaneously negative permeability and permittivity, Phys. Rev. Lett., Volume 84 (2000), p. 4184

[32] S.A. Ramakrishna; A. Lakhtakia Spectral shifts in the properties of a periodic multilayered stack due to isotropic chiral layers, J. Opt. A: Pure Appl. Opt., Volume 11 (2009), p. 074001

[33] S. Guenneau, F. Zolla, Homogenization of three-dimensional finite chiral photonic crystals, Physica B, | DOI

[34] G.W. Milton; J.R. Willis On modifications of Newton's second law and linear continuum elastodynamics, Proc. R. Soc. London A, Volume 463 (2007), pp. 855-880

[35] F. Hao; P. Nordlander Efficient dielectric function for FDTD simulation of the optical properties of silver and gold nanoparticles, Chem. Phys. Lett., Volume 446 (2007), p. 115

[36] J.A. Buck Fundamentals of Optical Fibers, John Wiley & Sons, Hoboken, NJ, USA, 2004 http://www.cvilaser.com (Also see for data sheets)

[37] T.M. Grzegorczyk; M. Nikku; X. Chen; B.-I. Wu; J.A. Kong Refraction laws for anisotropic media and their applications to left-handed metamaterials, IEEE Trans. Microwave Theory Tech., Volume 53 (2005), pp. 1443-1450

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

[39] G. Guida; D. Maystre; G. Tayeb; P. Vincent Electromagnetic modeling of three-dimensional photonic crystals, J. Elec. Waves Appl., Volume 12 (1998), pp. 1153-1179

[40] D. Felbacq; G. Bouchitte Homogenization of a set of parallel fibers, Waves Rand. Med., Volume 7 (1997), p. 245

[41] C.G. Poulton; S. Guenneau; A.B. Movchan Non-commuting limits and effective properties for electromagnetism in conical incidence, Phys. Rev. B, Volume 69 (2004), p. 195112

[42] K.D. Cherednichenko; V.P. Smyshlyaev; V.V. Zhikov Non-local homogenized limits for composite media with highly anisotropic periodic fibers, Proc. R. Soc. Edinburgh A, Volume 136 (2006), p. 87

[43] J.B. Pendry; L. Martin-Moreno; F.J. Garcia-Vidal Mimicking surface plasmons with structured surfaces, Science, Volume 305 (2004), p. 847

[44] T.J. Yen; W.J. Padilla; N. Fang; D.C. Vier; D.R. Smith; J.B. Pendry; D.N. Basov; X. Zhang Terahertz magnetic response from artificial materials, Science, Volume 303 (2004), p. 1494

[45] S. Linden; C. Enkrich; M. Wegener; J. Zhou; T. Koschny; C.M. Soukoulis Magnetic response of metamaterials at 100 terahertz, Science, Volume 306 (2004), pp. 1351-1353

[46] S. O'Brien; J.B. Pendry Magnetic activity at infrared frequencies in structured metallic photonic crystals, J. Phys.: Condens. Matter, Volume 14 (2002), pp. 6383-6394

[47] S. O'Brien; T. McPeake; S.A. Ramakrishna; J.B. Pendry Near-infrared photonic band gaps and nonlinear effects in negative magnetic metamaterials, Phys. Rev. B, Volume 69 (2004), p. 241101

[48] J. Zhou; Th. Kloschny; M. Kafesaki; E.N. Economou; J.B. Pendry; C.M. Soukoulis Saturation of the mangetic response of split-ring resonators at optical frequencies, Phys. Rev. Lett., Volume 95 (2005), p. 223902

[49] G. Dolling; C. Enkrich; M. Wegener; C.M. Soukoulis; S. Linden Low-loss negative-index metamaterial at telecommunication wavelengths, Opt. Lett., Volume 31 (2006), pp. 1800-1802

[50] B. Kante; A. de Lustrac; J.M. Lourtioz; F. Gadot Engineering resonances in infrared metamaterials, Opt. Express, Volume 16 (2008) no. 10, pp. 6774-6784

[51] R. Marques; F. Mesa; J. Martel; F. Medina Comparative analysis of edge and broadside-coupled split ring resonators for metamaterial design – theory and experiments, IEEE Trans. Antennas Propag., Volume 51 (2003) no. 10, pp. 2572-2581 Part 1 (2004)

[52] M. Shamonin; E. Shamonina; V. Kalinin; L. Solymar Resonant frequencies of a split-ring resonator: Analytical solutions and numerical simulations, Microwave Opt. Technol. Lett., Volume 44 (2005) no. 2, pp. 133-136

[53] M.W. Klein; C. Enkrich; M. Wegener; C.M. Soukoulis; S. Linden Single-slit split-ring resonators at optical frequencies: limits of size scaling, Opt. Lett., Volume 31 (2006), pp. 1259-1261

[54] V.M. Shalaev; W. Cai; U.K. Chettiar; H. Yuan; A.K. Sarychev; V.P. Drachev; A.V. Kildishev Negative index of refraction in optical metamaterials, Opt. Lett., Volume 30 (2005), pp. 3356-3358

[55] S. Zhang; W. Fan; N.C. Panoiu; K.J. Malloy; R.M. Osgood; S.R.J. Brueck Experimental demonstration of near-infrared negative-index metamaterials, Phys. Rev. Lett., Volume 95 (2005), p. 137404

[56] A. Alù; A. Salandrino; N. Engheta Negative effective permeability and left-handed materials at optical frequencies, Opt. Express, Volume 14 (2006), pp. 1557-1567

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

[58] S. Guenneau; B. Gralak Métamatériaux pour une lentille parfaite, La Recherche, Volume 401 (2006), pp. 58-61

[59] J.B. Pendry; S. Ramakrishna Near-field lenses in two dimensions, J. Phys.: Condens. Matter, Volume 14 (2002) no. 36, p. 8463

[60] G.W. Milton; N.A. Nicorovici; R.C. McPhedran; V.A. Podolskiy A proof of superlensing in the quasistatic regime, and limitations of superlenses in this regime due to anomalous localized resonance, Proc. R. Soc. London A, Volume 461 (2005), pp. 3999-4034

[61] S.A. Ramakrishna; J.B. Pendry Spherical perfect lens: Solutions of Maxwell's equations for spherical geometry, Phys. Rev. B, Volume 69 (2004), p. 115115

[62] A.J. Ward; J.B. Pendry Refraction and geometry in Maxwell's equations, J. Modern Opt., Volume 43 (1996) no. 4, pp. 773-793

[63] S. Guenneau; B. Gralak; J.B. Pendry Perfect corner reflector, Opt. Lett., Volume 30 (2005), p. 1204

[64] F. Zolla; G. Renversez; A. Nicolet; B. Kuhlmey; S. Guenneau; D. Felbacq Foundations of Photonic Crystal Fibres, ICP Press, London, 2005

[65] J.B. Pendry; D. Schurig; D.R. Smith Controlling electromagnetic fields, Science, Volume 312 (2006), p. 1780

[66] U. Leonhardt; T.G. Philbin General relativity in electrical engineering, New J. Phys., Volume 8 (2006), p. 247

[67] A. Nicolet; F. Zolla; Y. Ould Agha; S. Guenneau Geometrical transformations and equivalent materials in computational electromagnetism, Int. J. Comput. Math. Electrical Electronic Eng. COMPEL, Volume 27 (2008), pp. 806-819

[68] A.V. Kildishev; V.M. Shalaev Engineering space for light via transformation optics, Opt. Lett., Volume 33 (2008) no. 1, pp. 43-45

[69] M. Tsang; D. Psaltis Magnifying perfect lens and superlens design by coordinate transformation, Phys. Rev. B, Volume 77 (2008) no. 3, p. 035122

[70] D. Schurig; J.B. Pendry; D.R. Smith Transformation-designed optical elements, Opt. Express, Volume 15 (2007) no. 22, pp. 14772-14778

[71] D. Schurig; J.B. Pendry; D.R. Smith Calculation of material properties and ray tracing in transformation media, Opt. Express, Volume 14 (2006), pp. 9794-9804

[72] P.R. Mc Isaac Symmetry-induced modal characteristics of uniform waveguides – II: Theory, IEEE Trans. Microwave Theory Tech., Volume 23 (1975), p. 429

[73] A.N. Lagarkov; V.N. Kissel Near-perfect imaging in a focusing system based on a left-handed-material plate, Phys. Rev. Lett., Volume 92 (2004), p. 077401

[74] J.J. Chen; T.M. Grzegorczyk; B.-I. Wu; J.A. Kong Imaging properties of finite-size left-handed material slabs, Phys. Rev. E, Volume 74 (2006), p. 046615

[75] M. Born; E. Wolf Principles of Optics, Cambridge University Press, Cambridge, UK, 1999

[76] J.B. Pendry Negative refraction, Contemp. Phys., Volume 45 (2004), p. 191

[77] T.W. Ebbesen; H.J. Lezec; T. Thio; P.A. Wolff Extraordinary optical transmission through subwavelength hole arrays, Nature, Volume 391 (1998), pp. 667-669

[78] S. Chakrabarti; S.A. Ramakrishna; S. Guenneau Finite checkerboards of dissipative negative refractive index, Opt. Express, Volume 14 (2006), p. 12950

[79] S.A. Ramakrishna; S. Guenneau; S. Enoch; G. Tayeb Light confinement through negative refraction in photonic crystal and metamaterial checkerboards, Phys. Rev. A, Volume 75 (2007), p. 063830

[80] S.A. Ramakrishna Physics of negative refraction, Rep. Prog. Phys., Volume 68 (2005), p. 449

[81] J.M. Lourtioz; H. Benisty; V. Berger; J.M. Gerard; D. Maystre; A. Tchelnokov; D. Pagnoux Photonic Crystals: Towards Nanoscale Devices, Springer Verlag, Berlin, 2008

[82] X. Parazzoli; C.G. Greegor; K. Li; B.E.C. Kontenbah; M.H. Tanielan Experimental verification and simulation of negative index of refraction using Snell's law, Phys. Rev. Lett., Volume 90 (2003), p. 107401

[83] J. Zhu J; G.V. Eleftheriades Experimental verification of overcoming the diffraction limit with a volumetric Veselago–Pendry transmission-line lens, Phys. Rev. Lett., Volume 101 (2008) no. 1, p. 013902

[84] D. Schurig; D. Smith Negative index lens aberrations, Phys. Rev. E, Volume 70 (2004) no. 6, p. 65601

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

[86] E. Yablonovitch Inhibited spontaneous emission in solid-state physics and electronics, Phys. Rev. Lett., Volume 58 (1987), p. 2059

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

[88] C. Luo; S.G. Johnson; J.D. Joannopoulos; J.B. Pendry All-angle negative refraction without negative effective index, Phys. Rev. B, Volume 65 (2002), p. 201104

[89] T. Decoopman; G. Tayeb; S. Enoch; D. Maystre; B. Gralak Photonic crystal lens: From negative refraction and negative index to negative permittivity and permeability, Phys. Rev. Lett., Volume 97 (2006), p. 073905

[90] N. Fabre; L. Lalouat; B. Cluzel; X. Melenique; D. Lippens; F. de Fornel; O. Vanbesien Optical near-field microscopy of light focusing through a photonic crystal flat lens, Phys. Rev. Lett., Volume 101 (2008) no. 15, p. 073901

[91] Z.Y. Liu; X.X. Zhang; Y.W. Mao; Y.Y. Zhu; Z.Y. Yang; C.T. Chan; P. Sheng Locally resonant sonic materials, Science, Volume 289 (2000), p. 1734

[92] J. Li; C.T. Chan Double negative acoustic metamaterial, Phys. Rev. E, Volume 70 (2004), p. 055602

[93] G.W. Milton New metamaterials with macroscopic behavior outside that of continuum elastodynamics, New J. Phys., Volume 9 (2007), p. 359

[94] S. Guenneau; A.B. Movchan; G. Petursson; S.A. Ramakrishna Acoustic meta-materials for sound focussing and confinement, New J. Phys., Volume 9 (2007), p. 399

[95] M. Farhat; S. Guenneau; S. Enoch; G. Tayeb; A.B. Movchan; N.V. Movchan Analytical and numerical analysis of lensing effect for linear surface water waves through a square array of close to touching rigid square cylinders, Phys. Rev. E, Volume 77 (2008), p. 046308

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