Skip to main content
SpringerLink
Log in

Metamaterials: A new direction in materials science

  • Published:
Glass Physics and Chemistry Aims and scope Submit manuscript

Abstract

A review is presented of materials science of metamaterials, i.e., the area of research that has been extensively developed over the last decade. Metamaterials are artificial materials consisting of structural elements, whose type and mutual arrangement can be specified during the fabrication. The development of metamaterials was associated initially with the idea of the design of electromagnetic media with a negative refractive index and, more recently, with the prospect for fabrication of superlenses, invisible objects, and other optical devices. As a result, there appeared a new branch of materials science and an intimately related new branch of optics—transformation optics. This review has discussed the main directions of research in this field and problems encountered in this way. It is noted that metamaterials cannot be designed without invoking the most modern tools for performing numerical simulation and that their implementation requires the use of high-level technologies. The idea of metamaterials is important not only for optics and electromagnetism but also for acoustics.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Born, M. and Wolf, E., Principles of Optics: Electromagnetic Theory of Propagation, Interference, and Diffraction of Light, London: Pergamon, 1959. Translated under the title Osnovy optiki, Moscow: Nauka, 1973.

    MATH  Google Scholar 

  2. Landau, L.D. and Lifshitz, E.M., Teoreticheskaya fizika, Volume 8: Elektrodinamika sploshnykh sred, Moscow: Nauka, 1982. Translated under the title Course of Theoretical Physics, Volume 8: Electrodynamics of Continuous Media, Oxford: Butterworth-Heinemann, 1984.

    Google Scholar 

  3. Veselago, V.T., The Electrodynamics of Substances with Simultaneously Negative Values of ɛ and μ, Usp. Fiz. Nauk, 1967, vol. 92, no. 3, pp. 517–526 [Sov. Phys. Usp. (Engl. transl.), 1968, vol. 10, no. 4, pp. 509–514].

    CAS  Google Scholar 

  4. Mandelshtam, L.I., Lectures on Certain Problems of the Theory of Oscillations, in Polnoe sobranie trudov (Complete Collection of Works), Moscow: Academy of Sciences of the Soviet Union, 1950, vol. 5, pp. 428–467 [in Russian].

    Google Scholar 

  5. Lamb, H., On Group-Velocity, Proc. London Math. Soc., 1904, vol. 1, pp. 473–479.

    Article  Google Scholar 

  6. Schuster, A., An Introduction to the Theory of Optics, London: Edward Arnold, 1904.

    MATH  Google Scholar 

  7. Mandelshtam, L.I., Group Velocity in the Crystal Lattice, Zh. Eksp. Teor. Fiz., 1945, vol. 15, no. 9, pp. 475–478.

    Google Scholar 

  8. Ramakrishna, S.A., Physics of Negative Refractive Index Materials, Rep. Prog. Phys., 2005, vol. 68, no. 2, pp. 449–521.

    Article  ADS  Google Scholar 

  9. Bliokh, K.Yu. and Bliokh, Yu.K., What Are the Left-Handed Media and What Is Interesting about Them? Usp. Fiz. Nauk, 2004, vol. 174, no. 4, pp. 439–447 [Phys.—Usp. (Engl. transl.), 2004, vol. 47, no. 4, pp. 393–400].

    Article  Google Scholar 

  10. Pendry, J.B., Negative Refraction Makes a Perfect Lens, Phys. Rev. Lett., 2000, vol. 85, no. 18, pp. 3966–3969.

    Article  ADS  PubMed  CAS  Google Scholar 

  11. Hooft, G.W.’t., Comment on “Negative Refraction Makes a Perfect Lens,” Phys. Rev. Lett., 2001, vol. 87, no. 24, article 249701 (1 page).

  12. Williams, J.M., Some Problems with Negative Refraction, Phys. Rev. Lett., 2001, vol. 87, no. 24, article 249703 (1 page).

  13. Garcia, N. and Nieto-Vesperinas, M., Left-Handed Materials Do not Make a Perfect Lens, Phys. Rev. Lett., 2002, vol. 88, no. 20, article 207403 (4 pages).

  14. Pendry, J., Replay, Phys. Rev. Lett., 2001, vol. 87, no. 24, article 249 702 (1 page).

  15. Pendry, J., Replay, Phys. Rev. Lett., 2001, vol. 87, no. 24, article 249 704 (1 page).

  16. Shen, J.T. and Platzman, P.M., Near Field Imaging with Negative Dielectric Constant Lenses, Appl. Phys. Lett., 2002, vol. 80, no. 18, pp. 3286–3288.

    Article  ADS  CAS  Google Scholar 

  17. Smith, D.R., Schurig, D., Rosenbluth, M., Schultz, S., Ramakrishna, S.A., and Pendry, J.B., Limitations on Subdiffraction Imaging with a Negative Refractive Index Slab, Appl. Phys. Lett., 2003, vol. 82, no. 10, pp. 1506–1508.

    Article  ADS  CAS  Google Scholar 

  18. Kolinko, P. and Smith, D., Numerical Study of Electromagnetic Waves Interacting with Negative Index Materials, Opt. Express, 2003, vol. 11, no. 7, pp. 640–648.

    Article  ADS  PubMed  Google Scholar 

  19. Cummer, S.A., Simulated Causal Subwavelength Focusing by a Negative Refractive Index Slab, Appl. Phys. Lett., 2003, vol. 82, no. 10, pp. 1503–1505.

    Article  ADS  CAS  Google Scholar 

  20. Rao, X.S. and Ong, C.K., Subwavelength Imaging by a Left-Handed Material Superlens, Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys., 2003, vol. 68, no. 6, article 067 601 (3 pages).

  21. Huang, X. and Zhou, L., Modulating Image Oscillations in Focusing by a Metamaterial Lens: Time-Dependent Green’s Function Approach, Phys. Rev. B: Condens. Matter, 2006, vol. 74, no. 4, article 045 123 (8 pages).

  22. Cubukcu, E., Aydin, K., Ozbay, E., Foteinopolou, S., and Soukoulis, C.M., Subwavelength Resolution in a Two-Dimensional Photonic-Crystal-Based Superlens, Phys. Rev. Lett., 2003, vol. 91, no. 20, article 207401 (4 pages).

  23. Grbic, A. and Eleftheriades, G.V., Overcoming the Diffraction Limit with a Planar Left-Handed Transmission-Line Lens, Phys. Rev. Lett., 2004, vol. 92, no. 11, article 117403 (4 pages).

  24. Tretyakov, S.A., Research on Negative Refraction and Backward-Wave Media: A Historical Perspective, in Collection of Papers of EPFL Latsis Symposium 2005 “Negative Refraction: Revisiting Electromagnetics from Microwaves to Optics,” Lausanne, Switzerland, 2005, pp. 30–35.

  25. Veselago, V., Braginsky, L., Shklover, V., and Hafner, C., Negative Refraction Index Materials, J. Comput. Theor. Nanosci., 2006, vol. 3, no. 2, pp. 1–30.

    Google Scholar 

  26. Kotthaus, J.P. and Jaccarino, V., Antiferromagnetic-Resonance Linewidths in MnF2, Phys. Rev. Lett., 1972, vol. 28, no. 25, pp. 1649–1652.

    Article  ADS  CAS  Google Scholar 

  27. Grunberg, P. and Metawe, F., Light Scattering from Bulk and Surface Spin Waves in EuO, Phys. Rev. Lett., 1977, vol. 39, no. 24, pp. 1561–1565.

    Article  ADS  Google Scholar 

  28. Sandercock, J.R. and Wettling, W., Light Scattering from Surface and Bulk Thermal Magnons in Iron and Nickel, J. Appl. Phys., 1979, vol. 50, no. B11, pp. 7784–7789.

    Article  ADS  CAS  Google Scholar 

  29. Camley, R.E. and Mills, D.L., Surface Polaritons on Uniaxial Antiferromagnets, Phys. Rev. B: Condens. Matter, 1982, vol. 26, no. 3, pp. 1280–1287.

    ADS  CAS  Google Scholar 

  30. Remer, L., Luthi, B., Sauer, H., Geick, R., and Camley, R.E., Nonreciprocal Optical Reflection of the Uniaxial Antiferromagnet MnF2, Phys. Rev. Lett., 1986, vol. 56, no. 25, pp. 2752–2754.

    Article  ADS  PubMed  CAS  Google Scholar 

  31. Dumelow, T., Camley, R.E., Abraha, K., and Tilley, D.R., Nonreciprocal Phase Behavior in Reflection of Electromagnetic Waves from Magnetic Materials, Phys. Rev. B: Condens. Matter, 1998, vol. 58, no 2, pp. 897–908.

    ADS  CAS  Google Scholar 

  32. Pendry, J.B. and O’Brien, S., Very-Low-Frequency Plasma, J. Phys.: Condens. Matter, 2002, vol. 14, no. 32, pp. 7409–7416.

    Article  ADS  CAS  Google Scholar 

  33. O’Brien, S., MacPeake, D., Ramakrishna, S.A., and Pendry, J.B., Near-Infrared Photonic Band Gaps and Nonlinear Effects in Negative Magnetic Metamaterials, Phys. Rev. B: Condens. Matter, 2004, vol. 69, no. 24, article 241101 (4 pages).

  34. Wiltshire, M.C.K., Pendry, J.B., Young, I.R, Larkman, D.J., Gilderdale, D.J., and Hajnal, J.V., Micro-structured Magnetic Materials for RF Flux Guides in Magnetic Resonance Imaging, Science (Washington), 2001, vol. 291, no. 5505, pp. 848–851.

    Article  ADS  Google Scholar 

  35. Wiltshire, M.C.K, Hajnal, J.V., Pendry, J.B., Edwards, D.J., and Stevens, C.J., Metamaterial Endoscope for Magnetic Field Transfer: Near Field Imaging with Magnetic Wires, Opt. Express, 2003, vol. 11, no. 7, pp. 709–715.

    Article  ADS  PubMed  Google Scholar 

  36. Pendry, J.B., Holden, A.J., Robbins, D.J., and Stewart, W.J., Magnetism from Conductors and Enhanced Nonlinear Phenomena, IEEE Trans. Microwave Theor. Tech., 1999, vol. 47, no. 11, pp. 2075–2084.

    Article  ADS  Google Scholar 

  37. Smith, D.R., Padilla, W.J., Vier, D.C., Nemat-Nasser, S.C., and Schultz, S., Composite Medium with Simultaneously Negative Permeability and Permittivity, Phys. Rev. Lett., 2000, vol. 84, no. 18, pp. 4184–4187.

    Article  ADS  PubMed  CAS  Google Scholar 

  38. Yen, T.J., Padilla, W.J., Fang, N., Vier, D.C., Smith, D.R., Pendry, J.B., Basov, D.N., and Zhang, X., Terahertz Magnetic Response from Artificial Materials, Science (Washington), 2004, vol. 303, no. 5663, pp. 1494–1496.

    Article  ADS  CAS  Google Scholar 

  39. Linden, S., Enkrich, C., Wegener, M., Zhou, J., Koschny, T., and Soukoulis, C.M., Magnetic Response of Metamaterials at 100 Terahertz, Science (Washington), 2004, vol. 306, no. 5700, pp. 1351–1353.

    Article  ADS  CAS  Google Scholar 

  40. Cai, W., Chettiar, U.K., Kildishev, A.V., and Shalaev, V.M., Optical Cloaking with Metamaterials, Nat. Photonics, 2004, vol. 1, pp. 224–227.

    Article  ADS  CAS  Google Scholar 

  41. Podolskiy, V.A., Sarychev, A.K., and Shalaev, V.M., Plasmon Modes in Metal Nanowires and Left-Handed Materials, J. Nonlinear Opt. Phys. Mater., 2002, vol. 11, no. 1, pp. 65–74.

    Article  ADS  Google Scholar 

  42. Kildishev, A.V., Cai, W., Chettiar, U.K., Yuan, H.K., Sarychev, A.K., Drachev, V.P., and Shalaev, V.M., Negative Refraction Index in Optics of Metal-Dielectric Composites, J. Opt. Soc. Am. B, 2006, vol. 23, no. 3, pp. 423–433.

    Article  ADS  CAS  Google Scholar 

  43. Pendry, J.B., Holden, A.J., Stewart, W.J., and Youngs, I., Extremely Low Frequency Plasmons in Metallic Mesostructures, Phys. Rev. Lett., 1996, vol. 76, no. 25, pp. 4773–4776.

    Article  ADS  PubMed  CAS  Google Scholar 

  44. Pendry, J.B., Holden, A.J., Robbins, D.J., and Steward, W.J., Low Frequency Plasmons in Thin-Wire Structures, J. Phys.: Condens. Matter, 1998, vol. 10, no. 22, pp. 4785–4809.

    Article  ADS  CAS  Google Scholar 

  45. Raether, H., Excitation of Plasmons and Interband Transitions by Electrons, Berlin: Springer, 1980.

    Google Scholar 

  46. Raether, H., Surface Plasmons on Smooth and Rough Surfaces and on Gratings, Berlin: Springer, 1988.

    Google Scholar 

  47. Wu, D., Fang, K., Sun, C., Zhang, X., Padilla, W.J., Basov, D.K., Smith, D.R., and Schultz, S., Terahertz Plasmonic High Pass Filter, Appl. Phys. Lett., 2003, vol. 83, no. 1, pp. 201–203.

    Article  ADS  CAS  Google Scholar 

  48. Marqués, R., Medina, F., and Rafli-El-Idrissi, R., Role of Bianisotropy in Negative Permeability and Left-Handed Metamaterials, Phys. Rev. B: Condens. Matter, 2002, vol. 65, no. 14, article 144440 (6 pages).

  49. Gay-Balmaz, P. and Martin, O.J.F., Electromagnetic Resonances in Individual and Coupled Split-Ring Resonators, J. Appl. Phys., 2002, vol. 92, no. 5, pp. 2929–2936.

    Article  ADS  CAS  Google Scholar 

  50. Shelby, R.A., Smith, D.R., and Schultz, S., Experimental Verification of a Negative Index of Refraction, Science (Washington), 2001, vol. 292, no. 5514, pp. 77–79.

    Article  ADS  CAS  Google Scholar 

  51. Parazzoli, C.G., Greegor, R., Li, K., Kontenbah, B.E.C., and Tanielian, M.H., Experimental Verification and Simulation of Negative Index of Refraction Using Snell’s Law, Phys. Rev. Lett., 2003, vol. 90, no. 10, article 107401 (4 pages).

  52. Li, K., McLean, S.J., Greegor, R.B., Parazzoli, C.G., and Tanielian, M.H., Free-Space Focused-Beam Characterization of Left-Handed Materials, Appl. Phys. Lett., 2003, vol. 82, no. 15, pp. 2535–2537.

    Article  ADS  CAS  Google Scholar 

  53. Gokkavas, M., Guven, K., Bulu, L., Aydin, K., Penciu, R.S., Kafesaki, M., Soukoulis, C.M., and Ozbay, E., Experimental Demonstration of a Left-Handed Metamaterial Operating at 100 GHz, Phys. Rev. B: Condens. Matter, 2006, vol. 73, no. 19, article 193104 (4 pages).

  54. Hsu, A.-C., Cheng, Y.-K., Chen, K.-K., Chern, J.-L., Wu, S.-C., Chen, C.-F., Chang, H., Lien, Y.-K., and Shy, J.-T., Far-Infrared Resonance in Split Ring Resonators, Jpn. J. Appl. Phys., 2004, vol. 43, no. 2A, pp. L176–L179.

    Article  ADS  CAS  Google Scholar 

  55. Enkrich, C., Wegener, M., Linden, S., Burger, S., Zschiedrich, L., Schmidt, F., Zhou, J.F., Koschny, T., and Soukoulis, C.M., Magnetic Metamaterials at Telecommunication and Visible Frequencies, Phys. Rev. Lett., 2005, vol. 95, no. 20, article 203901 (4 pages).

  56. Moser, H.O., Casse, B.D.F., Wilhelmi, O., and Saw, B.T., Terahertz Response of a Microfabricated Rod-Split-Ring Resonator Electromagnetic Metamaterial, Phys. Rev. Lett., 2005, vol. 94, no. 6, article 063901 (4 pages).

  57. Klar, T.A., Kildishev, A.V., Drachev, V.P., and Shalaev, V.M., Negative-Index Metamaterials: Going Optical, IEEE J. Selected Top. Quantum Electron., 2006, vol. 12, no. 6, pp. 1106–1115.

    Article  CAS  Google Scholar 

  58. Lagarkov, A.N. and Sarychev, A.K., Electromagnetic Properties of Composites Containing Elongated Conducting Inclusions, Phys. Rev. B: Condens. Matter, 1996, vol. 53, no. 10, pp. 6318–6336.

    ADS  CAS  Google Scholar 

  59. Podolskiy, V.A., Sarychev, A.K., and Shalaev, V.M., Plasmon Modes in Metal Nanowires and Left-Handed Materials, J. Nonlinear Opt. Phys. Mater., 2002, vol. 11, no. 1, pp. 65–74.

    Article  ADS  Google Scholar 

  60. Dolling, G., Enkrich, C., Wegener, M., Zhou, J.F., Soukoulis, C.M., and Linden, S., Cut-Wire Pairs and Plate Pairs as Magnetic Atoms for Optical Metamaterials, Opt. Lett., 2005, vol. 30, no. 23, pp. 3198–3200.

    Article  ADS  PubMed  CAS  Google Scholar 

  61. Panina, L.V., Grigorenko, A.N., and Makhnovskiy, D.P., Optomagnetic Composite Medium with Conducting Nanoelements, Phys. Rev. B: Condens. Matter, 2002, vol. 66, no. 15, article 155411 (17 pages).

  62. Podolskiy, V.A., Sarychev, A.K., and Shalaev, V.M., Plasmon Modes in Metal Nanowires and Left-Handed Materials, Opt. Express, 2003, vol. 11, no. 7, pp. 735–745.

    Article  ADS  PubMed  Google Scholar 

  63. Podolskiy, V.A., Sarychev, A.K., Narimanov, E.E., and Shalaev, V.M., Resonant Light Interaction with Plasmonic Nanowire Systems, J. Opt. A: Pure Appl. Opt., 2005, vol. 7, pp. S32–S37.

    Article  ADS  Google Scholar 

  64. Shalaev, V.M., Cai, W., Chettiar, U.K., Yuan, K.K., Sarychev, A.K., Drachev, V.P., and Kildishev, A.V., Negative Index of Refraction in Optical Metamaterials, Opt. Lett., 2005, vol. 30, no. 24, pp. 3356–3358.

    Article  ADS  PubMed  Google Scholar 

  65. Drachev, V.P., Cai, W., Chettiar, U.K., Yuan, K.K., Sarychev, A.K., Kildishev, A.V., Klimec, G., and Shalaev, V.M., Experimental Verification of an Optical Negative-Index Material, Laser Phys. Lett., 2006, vol. 3, no. 1, pp. 49–55.

    Article  ADS  Google Scholar 

  66. Smith, D.R., Schultz, S., Markoš, P., and Soukoulis, C.M., Determination of Effective Permittivity and Permeability of Metamaterials from Reflection and Transmission Coefficients, Phys. Rev. B: Condens. Matter, 2002, vol. 65, no. 19, article 195104 (5 pages).

  67. Grigorenko, A.N., Geim, A.K., Gleeson, H.F., Zhang, Y., Firsov, A.A., Khrushchev, I.Y., and Petrovic, J., Nanofabricated Media with Negative Perme ability at Visible Frequencies, Nature (London), 2005, vol. 438, no. 7066, pp. 335–338.

    Article  ADS  CAS  Google Scholar 

  68. Zhang, S., Fan, W., Malloy, K.J., Brueck, S.R.J., Panoiu, N.C, and Osgood, R.M., Near-Infrared Double Negative Metamaterials, Opt. Express, 2005, vol. 13, no. 13, pp. 4922–4930.

    Article  ADS  PubMed  Google Scholar 

  69. Zhang, S., Fan, W., Panoiu, N.C., Malloy, K.J., Osgood, R.M., and Brueck, S.R.J., Experimental Demonstration of Near-Infrared Negative-Index Materials, Phys. Rev. Lett., 2005, vol. 95, no. 13, article 137404 (4 pages).

  70. Zhang, S., Fan, W., Malloy, K.J., Brueck, S.R.J., Panoiu, N.C., and Osgood, R.M., Demonstration of Metal-Dielectric Negative-Index Metamaterials with Improved Performance at Optical Frequencies, J. Opt. Soc. Am. B, 2006, vol. 23, no. 3, pp. 434–438.

    Article  ADS  CAS  Google Scholar 

  71. Falcone, F., Lopetegi, T., Laso, M.A.G., Baena, J.D., Bonache, J., Beruete, M., Marques, R., Martin, F., and Sorolla, M., Babinet Principle Applied to the Design of Metasurfaces and Metamaterials, Phys. Rev. Lett., 2004, vol. 93, no. 19, article 197401 (4 pages).

  72. Dolling, G., Enkrich, C., Wegener, M., Soukoulis, C.M., and Linden, S., Low-Loss Negative-Index Metamaterial at Telecommunication Wavelengths, Opt. Lett., 2006, vol. 31, no. 12, pp. 1800–1802.

    Article  ADS  PubMed  CAS  Google Scholar 

  73. Dolling, G., Wegener, M., Soukoulis, C.M., and Linden, S., Negative-Index Metamaterial at 780 nm Wavelength, Opt. Lett., 2007, vol. 32, no. 1, pp. 53–55.

    Article  ADS  PubMed  CAS  Google Scholar 

  74. Dolling, G., Enkrich, C., Wegener, M., Soukoulis, C.M., and Linden, S., Simultaneous Negative Phase and Group Velocity of Light in a Metamaterial, Science (London), 2006, vol. 312, no. 5775, pp. 892–894.

    ADS  CAS  Google Scholar 

  75. Zhang, S., Fan, W., Panoiu, N.C., Malloy, K.J., Osgood, R.M., and Brueck, S.R.J., Optical Negative-Index Bulk Metamaterials Consisting of 2D Perforated Metal-Dielectric Stacks, Opt. Express, 2006, vol. 14, no. 15, pp. 6778–6787.

    Article  ADS  PubMed  Google Scholar 

  76. Valentine, J., Zhang, S., Zentgraf, T., Ulin-Avila, E., Genov, D.A., Bartal, G., and Zhang, X., Three-Dimensional Optical Metamaterial with a Negative Refractive Index, Nature (London), 2008, vol. 455, no. 7211, pp. 376–379.

    Article  ADS  CAS  Google Scholar 

  77. Navarro-Cia, M., Beruete, M., Sorolla, M., and Campillo, I., Negative Refraction in a Prism Made of Stacked Subwavelength Hole Arrays, Opt. Express, 2008, vol. 16, no. 2, pp. 560–566.

    Article  ADS  PubMed  CAS  Google Scholar 

  78. Lezec, H.J., Dionne, J.A., and Atwater, H.A., Negative Refraction at Visible Frequencies, Science (Washington), 2007, vol. 316, no. 5823, pp. 430–432.

    Article  ADS  CAS  Google Scholar 

  79. Koschny, T., Zhang, L., and Soukoulis, C.M., Isotropic Three-Dimensional Left-Handed Metamaterials, Phys. Rev. B: Condens. Matter, 2005, vol. 71, no. 12, article 121103 (4 pages).

  80. Andryieuski, A., Malureanu, R., and Lavrinenko, A., Nested Structures Approach in Designing an Isotropic Negative-Index Material for Infrared, J. Eur. Opt. Soc., Rapid Publ., 2009, vol. 4, article 09 003 (7 pages).

  81. Kussow, A.-G., Akyurtlu, A., Semichaevsky, A., and Angkawisittpan, N., MgB2-Based Negative Refraction Index Metamaterial at Visible Frequencies: Theoretical Analysis, Phys. Rev. B: Condens. Matter, 2007, vol. 76, no. 19, article 195123 (7 pages).

  82. Kussow, A.-G., Akyurtlu, A., and Angkawisittpan, N., Optically Isotropic Negative Index of Refraction Metamaterial, Phys. Status Solidi B, 2008, vol. 245, no. 5, pp. 992–997.

    Article  ADS  CAS  Google Scholar 

  83. Bohren, C.F. and Huffman, D.R., Absorption and Scattering of Light by Small Particles, New York: Wiley, 1983. Translated under the title Pogloshchenie i rasseyanie sveta malymi chastitsami, Moscow: Mir, 1986.

    Google Scholar 

  84. Yannopapas, V. and Moroz, A., Negative Refractive Index Metamaterials from Inherently Nonmagnetic Materials for Deep Infrared to Terahertz Frequency Ranges, J. Phys.: Condens. Matter, 2005, vol. 17, no. 25, pp. 3717–3734.

    Article  ADS  CAS  Google Scholar 

  85. Boltasseva, A. and Shalaev, V.M., Fabrication of Optical Negative-Index Metamaterials: Recent Advances and Outlook, Metamaterials, 2008, vol. 2, no. 1, pp. 1–17.

    Article  ADS  Google Scholar 

  86. Smolyaninov, I.I., Smolyaninova, V.N., Kildishev, A.V., and Shalaev, V.M., Anisotropic Metamaterials Emulated by Tapered Waveguides: Application to Optical Cloaking, Phys. Rev. Lett., 2009, vol. 102, no. 21, article 213901 (4 pages).

  87. Fante, R.L. and McCormack, M.T., Reflection Properties of the Salisbury Screen, IEEE Trans. Antenn. Propagation, 1988, vol. 36, no. 10, pp. 1443–1454.

    Article  ADS  Google Scholar 

  88. Ward, J., Towards Invisible Glass, Vacuum, 1972, vol. 22, no. 9, pp. 369–375.

    Article  CAS  Google Scholar 

  89. Alù, A. and Engheta, N., Achieving Transparency with Plasmonic and Metamaterial Coatings, Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys., 2005, vol. 72, no. 1, article 016 623 (9 pages).

  90. Leonhardt, U., Optical Conformal Mapping, Science (Washington), 2006, vol. 312, no. 5781, pp. 1777–1780.

    Article  MathSciNet  ADS  CAS  Google Scholar 

  91. Pendry, J.B., Schurig, D., and Smith, D.R., Controlling Electromagnetic Fields, Science (Washington), 2006, vol. 312, no. 5781, pp. 1780–1782.

    Article  MathSciNet  ADS  CAS  Google Scholar 

  92. Andreev, N.S., Scattering of Visible Light by Glasses Undergoing Phase Separation and Homogenization, J. Non-Cryst. Solids, 1978, vol. 30, no. 2, pp. 99–126.

    Article  ADS  CAS  Google Scholar 

  93. Walker, C.B. and Guinier, A., An X-Ray Investigation of Age Hardening in Alag, Acta Metall., 1953, vol. 1, no 5, pp. 568–577.

    Article  CAS  Google Scholar 

  94. Shatilov, A.V., Anomalous Scattering as the Case of Scattering from a System of Particles, Opt. Spektrosk., 1962, vol. 13, no. 5, pp. 728–733.

    CAS  Google Scholar 

  95. Goldstein, M., Theory of Scattering for Diffusion-Controlled Phase Separation, J. Appl. Phys., 1963, vol. 34, no. 7, pp. 1928–1934.

    Article  ADS  Google Scholar 

  96. Kerker, M., Invisible Bodies, J. Opt. Soc. Am., 1975, vol. 65, no. 4, pp. 376–379.

    Article  ADS  Google Scholar 

  97. Chew, H. and Kerker, M., Abnormally Low Electromagnetic Scattering Cross Sections, J. Opt. Soc. Am., 1976, vol. 66, no. 5, pp. 445–449.

    Article  ADS  Google Scholar 

  98. Kerker, M. and Blatchford, C.G., Elastic Scattering, Absorption, and Surface-Enhanced Raman Scattering by Concentric Spheres Comprised of a Metallic and a Dielectric Region, Phys. Rev. B: Condens. Matter, 1982, vol. 26, no. 8, pp. 4052–4063.

    ADS  CAS  Google Scholar 

  99. Aden, A.L. and Kerker, M., Scattering of Electromagnetic Waves from Two Concentric Spheres, J. Appl. Phys., 1951, vol. 22, no. 10, pp. 1242–1246.

    Article  MATH  MathSciNet  ADS  Google Scholar 

  100. Alù, A. and Engheta, N., Polarizabilities and Effective Parameters for Collections of Spherical Nanoparticles Formed by Pairs of Concentric Double-Negative, Single-Negative, and/or Double-Positive Metamaterial Layers, J. Appl. Phys., 2005, vol. 97, no. 9, article 094310 (12 pages).

  101. Alù, A. and Engheta, N., Erratum: “Polarizabilities and Effective Parameters for Collections of Spherical Nanoparticles Formed by Pairs of Concentric Double-Negative, Single-Negative, and/or Double-Positive Metamaterial Layers” [J. Appl. Phys., 2005, vol. 97, 094310], J. Appl. Phys., 2006, vol. 99, no. 6, article, 069901(E) (1 page).

  102. Zhou, X. and Hu, G., Design for Electromagnetic Wave Transparency with Metamaterials, Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys., 2006, vol. 74, no. 1, article 026607 (8 pages).

  103. Maxwell Garnett, J.C., Colours in Metal Glasses and in Metallic Films, Philos. Trans. R. Soc., Ser. A, 1904, vol. 203, pp. 385–420.

    Article  ADS  Google Scholar 

  104. Zhou, X. and Hu, G., Linear and Nonlinear Dielectric Properties of Particulate Composites at Finite Concentration, Appl. Math. Mech., 2006, vol. 27, no. 8, pp. 1021–1030.

    Article  MATH  Google Scholar 

  105. Alù, A. and Engheta, N., Plasmonic Materials in Transparency and Cloaking Problems: Mechanism, Robustness, and Physical Insights, Opt. Express, 2007, vol. 15, no. 6, pp. 3318–3332.

    Article  ADS  PubMed  Google Scholar 

  106. Alù, A. and Engheta, N., Cloaking and Transparency for Collection of Particles with Metamaterial and Plasmonic Covers, Opt. Express, 2007, vol. 15, no. 12, pp. 7578–7590.

    Article  ADS  PubMed  Google Scholar 

  107. Alù, A. and Engheta, N., Multifrequency Optical Invisibility Cloak with Layered Plasmonic Shells, Phys. Rev. Lett., 2008, vol. 100, no. 11, article 113901 (4 pages).

  108. Silveirinha, M.G., Alù, A., and Engheta, N., Parallel-Plate Metamaterials for Cloaking Structures, Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys., 2007, vol. 75, no. 3, article 036603 (16 pages).

  109. Nachman, A.I., Reconstructions from Boundary Measurements, Ann. Math., Ser. 2, 1988, vol. 128, no. 3, pp. 531–576.

    Article  MathSciNet  Google Scholar 

  110. Wolf, E. and Habashy, T., Invisible Bodies and Uniqueness of the Inverse Scattering Problem, J. Mod. Opt., 1993, vol. 40, no. 5, pp. 785–792.

    Article  ADS  Google Scholar 

  111. Leonhardt, U., Notes on Conformal Invisibility Devices, New J. Phys., 2006, vol. 8, article 118 (16 pages).

  112. Ochiai, T., Leonhardt, U., Nacher, J.C., A Novel Design of Dielectric Perfect Invisibility Devices, J. Math. Phys., 2008, vol. 49, no. 3, article 032903 (13 pages).

  113. Ward, A.J. and Pendry, J.B., Refraction and Geometry in Maxwell’s Equations, J. Mod. Opt., 1996, vol. 43, no. 4, pp. 773–793.

    MATH  MathSciNet  ADS  Google Scholar 

  114. Korn, G. and Korn, T., Mathematical Handbook for Scientists and Engineers, New York: McGraw-Hill, 1961. Translated under the title Spravochnik po matematike, Moscow: Nauka, 1978, pp. 186–188, Table 6.5-1.

    MATH  Google Scholar 

  115. Smith, D.R., Vier, D.C, Koschny, Th., and Soukoulis, C.M., Electromagnetic Parameter Retrieval from Inhomogeneous Metamaterials, Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys., 2005, vol. 71, no. 3, article 036617 (11 pages).

  116. Driscoll, T., Basov, D.N, Starr, A.F., Rye, P.M., Nemat-Nasser, S., Schurig, D., and Smith, D.R., Free-Space Microwave Focusing by a Negative-Index Gradient Lens, Appl. Phys. Lett., 2006, vol. 88, no. 8, article 081101 (3 pages).

  117. Greegor, R.B., Parazzoli, C.G., Nielsen, J.A., Thompson, M.A., Tanielian, M.H., and Smith, D.R., Simulation and Testing of a Graded Negative Index of Refraction Lens, Appl. Phys. Lett., 2005, vol. 87, no. 9, article 091114 (3 pages).

  118. Schurig, D., Mock, J.J., Justice, B.J., Cummer, S.A., Pendry, J.B., Starr, A.F., and Smith, D.R., Metamaterial Electromagnetic Cloak at Microwave Frequencies, Science (Washington), 2006, vol. 314, no. 5801, pp. 977–980.

    Article  ADS  CAS  Google Scholar 

  119. Rozanov, N.N., Invisibility: For and against, Priroda (Moscow), 2008, no. 6; http://elementy.ru/lib/430669.

  120. Dolin, L.S., On the Possibility of Comparing Three-Dimensional Electromagnetic Systems with Inhomogeneous Anisotropic Filling, Izv. Vyssh. Uchebn. Zaved., Radiofiz., 1961, vol. 4, no. 5, pp. 964–967.

    Google Scholar 

  121. Cummer, S.A., Popa, B.-L., Schurig, D., Smith, D.R., and Pendry, J., Full-Wave Simulations of Electromagnetic Cloaking Structures, Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys., 2006, vol. 74, no. 3, article 036621 (5 pages).

  122. Yan, M., Ruan, Z., and Qiu, M., Cylindrical Invisibility Cloak with Simplified Material Parameters Is Inherently Visible, Phys. Rev. Lett., 2007, vol. 99, no. 23, article 233901 (4 pages).

  123. Yan, M., Ruan, Z., and Qiu, M., Scattering Characteristics of Simplified Cylindrical Invisibility Cloaks, Opt. Express, 2007, vol. 15, no. 8, pp. 17772–17782.

    Article  ADS  PubMed  Google Scholar 

  124. Chen, X., Grzegorczyk, T.M., Wu, B.-L., Pacheco, J., and Kong, J.A., Robust Method to Retrieve the Constitutive Effective Parameters of Metamaterials, Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys., 2004, vol. 70, no. 1, article 016608 (7 pages).

  125. Cai, W., Chettiar, U.K., Kildishev, A.V., Shalaev, V.M., and Milton, G.W., Nonmagnetic Cloak with Minimized Scattering, Appl. Phys. Lett., 2007, vol. 91, no. 11, article 111105 (3 pages).

  126. Weder, R., A Rigorous Analysis of High-Order Electromagnetic Invisibility Cloaks, J. Phys. A: Math. Theor., 2008, vol. 41, no. 6, article 065207 (21 pages).

  127. Cai, W., Chettiar, U.K., Kildishev, A.V., and Shalaev, V.M., Design for Optical Cloaking with High-Order Transformations, Opt. Express, 2008, vol. 16, no. 8, pp. 5444–5452.

    Article  ADS  PubMed  Google Scholar 

  128. Collins, P. and McGuirk, J., A Novel Methodology for Deriving Improved Material Parameter Sets for Simplified Cylindrical Cloaks, J. Opt. A: Pure Appl. Opt., 2009, vol. 11, article 015104 (8 pages).

  129. Leonhardt, U. and Tyc, T., Broadband Invisibility by Non-Euclidean Cloaking, Science (Washington), 2009, vol. 323, no. 5910, pp. 110–112.

    Article  ADS  CAS  Google Scholar 

  130. Huang, Y., Feng, Y., and Jiang, T., Electromagnetic Cloaking by Layered Structure of Homogeneous Iso tropic Materials, Opt. Express, 2007, vol. 15, no. 18, pp. 11133–11141.

    Article  ADS  PubMed  Google Scholar 

  131. Qiu, C.-W., Hu, L., Xu, X., and Feng, Y., Spherical Cloaking with Homogeneous Isotropic Multilayered Structures, Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys., 2009, vol. 79, no. 4, article 047602 (4 pages).

  132. Sun, J., Zhou, J., and Kang, L., Homogenous Isotropic Invisible Cloak Based on Geometrical Optics, Opt. Express, 2008, vol. 16, no. 22, pp. 17768–17773.

    Article  ADS  PubMed  Google Scholar 

  133. Lai, Y., Chen, H., Zhang, Z.-Q., and Chan, C.T., Complementary Media Invisibility Cloak That Cloaks Objects at a Distance Outside the Cloaking Shell, Phys. Rev. Lett., 2009, vol. 102, no. 9, article 093901 (4 pages).

  134. Kante, B., Germain, D., and de Lustrac, A., Experimental Demonstration of a Nonmagnetic Metamaterial Cloak at Microwave Frequencies, Phys. Rev. B: Condens. Matter, 2009, vol. 80, no. 20, article 201104 (4 pages).

  135. Liu, X., Li, C., Yao, K., Meng, X., Feng, W., Wu, B., and Li, F., Experimental Verification of Broadband Invisibility Using a Cloak Based on Inductor-Capacitor Networks, Appl. Phys. Lett., 2009, vol. 95, no. 19, article 191107 (3 pages).

  136. Tretyakov, S., Alitalo, P., Luukkonen, O., and Simovski, C., Broadband Electromagnetic Cloaking of Long Cylindrical Objects, Phys. Rev. Lett., 2009, vol. 103, no. 10, article 103905 (4 pages).

  137. Smolyaninov, I.I., Hung, Y.J., and Davis, C.C., Two-Dimensional Metamaterial Structure Exhibiting Reduced Visibility at 500 nm, Opt. Lett., 2008, vol. 33, no. 12, pp. 1342–1344.

    Article  ADS  PubMed  CAS  Google Scholar 

  138. Li, J. and Pendry, J.B., Hiding Under the Carpet: A New Strategy for Cloaking, Phys. Rev. Lett., 2008, vol. 101, no. 20, article 203901 (4 pages).

  139. Liu, R., Ji, C., Mock, J.J., Chin, J.Y., Cui, T.J., and Smith, D.R., Broadband Ground-Plane Cloak, Science (Washington), 2009, vol. 323, no. 5912, pp. 366–369.

    Article  ADS  CAS  Google Scholar 

  140. Valentine, J., Li, J., Zentgraf, T., Bartal, G., and Zhang, X., An Optical Cloak Made of Dielectrics, Nat. Mater., 2009, vol. 8, no. 7, pp. 568–571.

    Article  ADS  PubMed  CAS  Google Scholar 

  141. Gabrielli, L.H., Cardenas, J., Poitras, C.B., and Lipson, M., Silicon Nanostructure Cloak Operating at Optical Frequencies, Nat. Photonics, 2009, vol. 3, no. 8, pp. 461–463.

    Article  ADS  CAS  Google Scholar 

  142. Lee, J.K., Blair, J., Tamma, V.A., Wu, Q., Rhee, S.J., Summers, C.J., and Park, W., Direct Visualization of Optical Frequency Invisibility Cloak Based on Silicon Nanorod Array, Opt. Express, 2009, vol. 17, no. 15, pp. 12922–12928.

    Article  ADS  PubMed  CAS  Google Scholar 

  143. Xu, X., Feng, Y., Hao, Y., Zhao, J., and Jiang, T., Infrared Carpet Cloak Designed with Uniform Silicon Grating Structure, Appl. Phys. Lett., 2009, vol. 95, no. 18, article 184102 (3 pages).

  144. Leonhardt, U. and Philbin, T.G., General Relativity in Electrical Engineering, New J. Phys., 2006, vol. 8, article 247 (18 pages).

  145. Schurig, D., Pendry, J.B., and Smith, D.R., Calculation of Material Properties and Ray Tracing in Transformation Media, Opt. Express, 2006, vol. 14, no. 21, pp. 9794–9802.

    Article  ADS  PubMed  CAS  Google Scholar 

  146. Chen, H. and Chan, C.T., Transformation Media That Rotate Electromagnetic Fields, Appl. Phys. Lett., 2007, vol. 90, no. 24, article 241105 (3 pages).

  147. Schurig, D., Pendry, J.B., and Smith, D.R., Transformation-Designed Optical Elements, Opt. Express, 2007, vol. 15, no. 22, pp. 14772–14782.

    Article  ADS  PubMed  CAS  Google Scholar 

  148. Chen, H., Liang, Z., Yao, P., Jiang, X., Ma, H., and Chan, C.T., Extending the Bandwidth of Electromagnetic Cloaks, Phys. Rev. B: Condens. Matter, 2007, vol. 76, no. 24, article 241104 (4 pages).

  149. Kildishev, A.V., Cai, W., Chettiar, U.K., and Shalaev, V.M., Transformation Optics: Approaching Broadband Electromagnetic Cloaking, New J. Phys., 2008, vol. 10, article 115029 (13 pages).

  150. Farhat, M., Guenneau, S., Movchan, A.B., and Enoch, S., Achieving Invisibility over a Finite Range of Frequencies, Opt. Express, 2008, vol. 16, no. 8, pp. 5656–5661.

    Article  ADS  PubMed  CAS  Google Scholar 

  151. Shalaev, V.M., Transforming Light, Science (Washington), 2008, vol. 322, no. 5900, pp. 384–386.

    Article  CAS  Google Scholar 

  152. Leonhardt, U. and Philbin, T.G., Transformation Optics and the Geometry of Light, Prog. Opt., 2009, vol. 53, pp. 69–152.

    Article  Google Scholar 

  153. Yan, W., Yan, M., Ruan, Z., and Qiu, M., Coordinate Transformations Make Perfect Invisibility Cloaks with Arbitrary Shape, New J. Phys., 2008, vol. 10, article 043040 (13 pages).

  154. You, Y., Kattawar, G.W., Zhai, P.-W., and Yang, P., Invisibility Cloaks for Irregular Particles Using Coordinate Transformations, Opt. Express, 2008, vol. 16, no. 9, pp. 6134–6145.

    Article  ADS  PubMed  Google Scholar 

  155. Jiang, W.X., Chin, J.Y., Li, Z., Cheng, Q., Liu, R., and Cui, T.J., Analytical Design of Conformally Invisible Cloaks for Arbitrarily Shaped Objects, Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys., 2008, vol. 77, no. 6, article 066 607 [6 pages).

  156. Wang, W., Lin, L., Yang, X., Cui, J., Du, C., and Luo, X., Design of Oblate Cylindrical Perfect Lens Using Coordinate Transformation, Opt. Express, 2008, vol. 16, no. 11, pp. 8094–8105.

    Article  ADS  PubMed  Google Scholar 

  157. Nicolet, A., Zolla, F., and Guenneau, S., Electromagnetic Analysis of Cylindrical Cloaks of an Arbitrary Cross Section, Opt. Lett., 2008, vol. 33, no. 14, pp. 1584–1586.

    Article  ADS  PubMed  Google Scholar 

  158. Rahm, M., Schurig, D., Roberts, D.A., Cummer, S.A., Smith, D.R., and Pendry, J.B., Design of Electromagnetic Cloaks and Concentrators Using Form-Invariant Coordinate Transformations of Maxwell’s Equations, Photonics Nanostruct., 2008, vol. 6, pp. 87–95.

    Article  ADS  Google Scholar 

  159. Li, C., Yao, K., and Li, F., Two-Dimensional Electromagnetic Cloaks with Non-Conformal Inner and Outer Boundaries, Opt. Express, 2008, vol. 16, no. 23, pp. 19366–19374.

    Article  MathSciNet  ADS  PubMed  Google Scholar 

  160. Wu, Q., Zhang, K., Meng, F., and Li, L.-W., Material Parameters Characterization for Arbitrary N-Sided Regular Polygonal Invisible Cloak, J. Phys. D: Appl. Phys., 2009, vol. 42, article 035408 (7 pages).

  161. Ma, H., Qu, S., Xu, Z., and Wang, J., The Open Cloak, Appl. Phys. Lett., 2009, vol. 94, no. 10, article 103501 (3 pages).

  162. Zhang, P., Jin, Y., and He, S., Cloaking an Object on a Dielectric Half-Space, Opt. Express, 2008, vol. 16, no. 5, pp. 3161–3166.

    Article  ADS  PubMed  Google Scholar 

  163. Rahm, M., Cummer, S.A., Schurig, D., Pendry, J.B., and Smith, D.R., Optical Design of Reflectionless Complex Media by Finite Embedded Coordinate Transformations, Phys. Rev. Lett., 2008, vol. 100, no. 6, article 063 903 (4 pages).

  164. Rahm, M., Roberts, D.A., Pendry, J.B., and Smith, D.R., Transformation-Optical Design of Adaptive Beam Bends and Beam Expanders, Opt. Express, 2008, vol. 16, no. 15, pp. 11555–11567.

    Article  ADS  PubMed  CAS  Google Scholar 

  165. Zhai, T., Zhou, Y., Zhou, J., and Liu, D., Polarization Controller Based on Embedded Optical Transformation, Opt. Express, 2009, vol. 17, no. 20, pp. 17206–17213.

    Article  ADS  PubMed  CAS  Google Scholar 

  166. Tyc, T. and Leonhardt, U., Transmutation of Singularities in Optical Instruments, New J. Phys., vol. 10, article 115038 (8 pages).

  167. Chen, H., Hou, V., Chen, S., Ao, X., Wen, W., and Chan, S.T., Design and Experimental Realization of a Broadband Transformation Media Field Rotator at Microwave Frequencies, Phys. Rev. Lett., 2009, vol. 102, no. 18, article 183903 (4 pages).

  168. Kundtz, N., Roberts, D.A., Allen, J., Cummer, S., and Smith, D.R., Optical Source Transformations, Opt. Express, 2008, vol. 16, no. 26, pp. 21215–21222.

    Article  ADS  PubMed  CAS  Google Scholar 

  169. Cummer, S.A., Kundtz, N., and Popa, B.-I., Electromagnetic Surface and Line Sources under Coordinate Transformations, Phys. Rev. A: At., Mol., Opt. Phys., 2009, vol. 80, no. 3, article 033820 (7 pages).

  170. Leonhardt, U. and Tyc, T., Superantenna Made of Transformation Media, New J. Phys., 2008, vol. 10, article 115026 (9 pages).

  171. Greenleaf, A., Kurylev, Y., Lassas, M., and Uhlmann, G., Invisibility and Inverse Problems, Bull. Am. Math. Soc., 2008, vol. 46, no. 1, pp. 55–97.

    Article  MathSciNet  Google Scholar 

  172. Cummer, S.A., Rahm, M., and Schurig, D., Material Parameters and Vector Scaling in Transformation Acoustics, New J. Phys., 2008, vol. 10, article 115025 (12 pages).

  173. Li, J. and Chan, C.T., Double-Negative Acoustic Metamaterial, Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys., 2004, vol. 70, no. 5, article 055602 (R) (4 pages).

  174. Lee, S.H., Park, C.M., Seo, Y.M., Wang, Z.G., and Kim, C.K., Composite Acoustic Medium with Simultaneously Negative Density and Modulus, Phys. Rev. Lett., 2010, vol. 104, no. 5, article 054301 (4 pages).

  175. Ambati, M., Fang, N., Sun, C., and Zhang, X., Surface Resonant States and Superlensing in Acoustic Metamaterials, Phys. Rev. B: Condens. Matter, 2007, vol. 75, no. 19, article 195447 (5 pages).

  176. Chen, H. and Chan, C.T., Acoustic Cloaking in Three Dimensions Using Acoustic Metamaterials, Appl. Phys. Lett., 2007, vol. 91, no. 18, article 183518 (3 pages).

  177. Zhang, S., Yin, L., and Fang, N., Focusing Ultrasound with an Acoustic Metamaterial Network, Phys. Rev. Lett., 2009, vol. 102, no. 19, article 194301 (4 pages).

  178. Li, J., Fok, L., Yin, X., Bartal, G., and Zhang, X., Experimental Demonstration of an Acoustic Magnifying Hyperlens, Nat. Mater., 2009, vol. 8, no. 12, pp. 931–934.

    Article  ADS  PubMed  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Scientific Research and Technological Institute of Optical Materials Science, All-Russia Science Center “S. I. Vavilov State Optical Institute,”, ul. Babushkina 36, St. Petersburg, 192171, Russia

    A. A. Zhilin & M. P. Shepilov

Authors
  1. A. A. Zhilin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. P. Shepilov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. P. Shepilov.

Additional information

Original Russian Text © A.A. Zhilin, M.P. Shepilov, 2010, published in Fizika i Khimiya Stekla.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhilin, A.A., Shepilov, M.P. Metamaterials: A new direction in materials science. Glass Phys Chem 36, 521–553 (2010). https://doi.org/10.1134/S1087659610050019

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1087659610050019

Key words

Search

Navigation