Abstract

Using a ray-tracing approach, we calculate photorealistic images and simple movies of objects in a material with negative index of refraction. Our results show several surprising and drastic effects, for example reversal of apparent object velocity, extreme distortions of object shape, and even apparent loss of connectivity of simple objects. The material presented aims at giving both researchers and laymen an intuition and visual understanding for the unusual optical properties of negative-index materials.

© 2006 Optical Society of America

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  1. V. G. Veselago, “The Electrodynamics of Substances with Simultaneously Negative Values of ε and μ,” Sov. Phys. Usp. 10, 509 (1968).
    [Crossref]
  2. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from Conductors and Enhanced Nonlinear Phenomena,” IEEE Trans. MTT 47, 2075–2084 (1999).
    [Crossref]
  3. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental Verification of a Negative Index of Refraction,” Science 292, 77–79 (2001).
    [Crossref] [PubMed]
  4. T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz Magnetic Response from Artificial Materials,” Science 303, 1494–1496 (2004).
    [Crossref] [PubMed]
  5. D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and Negative Refractive Index,” Science 305, 788–792 (2004).
    [Crossref] [PubMed]
  6. S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic Response of Metamaterials at 100 Terahertz,” Science 306, 1351–1353 (2004).
    [Crossref] [PubMed]
  7. C. Enkrich, F. Perez-Willard, D. Gerthsen, J. F. Zhou, C. M. Soukoulis, M. Wegener, and S. Linden, “Focused-Ion-Beam Nanofabrication of Near-Infrared Magnetic Metamaterials,” Adv. Mater. 17, 2547–2549 (2005).
    [Crossref]
  8. C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic Metamaterials at Telecommunication and Visible Frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
    [Crossref] [PubMed]
  9. S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S.R. J. Brueck, “Midinfrared Resonant Magnetic Nanostructures Exhibiting a Negative Permeability,” Phys. Rev. Lett. 94, 037402 (2005).
    [Crossref] [PubMed]
  10. S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental Demonstration of Near-Infrared Negative-Index Metamaterials,” Phys. Rev. Lett. 95, 137404 (2005).
    [Crossref] [PubMed]
  11. G. Dolling, C. Enkrich, M. Wegener, J. Zhou, C.M. Soukoulis, and S. Linden, “Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials,” Opt. Lett 30, 3198–3200 (2005).
    [Crossref] [PubMed]
  12. V. M. Shalaev, W. Cai, U. Chettiar, H. K. Yuan, A.K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett 30, 3356–3358 (2005).
    [Crossref]
  13. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature 438, 335–338 (2005).
    [Crossref] [PubMed]
  14. J. F. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of Split-Ring Resonators at Optical Frequencies,” Phys. Rev. Lett. 95, 223902 (2005).
    [Crossref] [PubMed]
  15. A. Ishikawa, T. Tanaka, and S. Kawata, “Negative Magnetic Permeability in the Visible Light Region,” Phys. Rev. Lett. 95, 237401 (2005).
    [Crossref] [PubMed]
  16. M. W. Klein, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Single-slit split-ring resonators at optical frequencies: Limits of size scaling,” submitted to Opt. Lett., (2006).
    [Crossref]
  17. POV-Ray (Persistence of Vision Raytracer Pty. Ltd., 2006), http://www.povray.org/
  18. S. Linden, C. Enkrich, M. Klein, G. Dolling, N. Feth, and M. Wegener, “Metamaterials“ (2006), http://www.aph.uni-karlsruhe.de/ag/wegener/meta/meta.html
  19. Andrew S. Glassner, An Introduction to Ray Tracing (Morgan Kaufmann, 1989).
  20. J.B. Pendry, “Negative Refraction Makes a Perfect Lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
    [Crossref] [PubMed]

2006 (1)

M. W. Klein, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Single-slit split-ring resonators at optical frequencies: Limits of size scaling,” submitted to Opt. Lett., (2006).
[Crossref]

2005 (9)

C. Enkrich, F. Perez-Willard, D. Gerthsen, J. F. Zhou, C. M. Soukoulis, M. Wegener, and S. Linden, “Focused-Ion-Beam Nanofabrication of Near-Infrared Magnetic Metamaterials,” Adv. Mater. 17, 2547–2549 (2005).
[Crossref]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic Metamaterials at Telecommunication and Visible Frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[Crossref] [PubMed]

S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S.R. J. Brueck, “Midinfrared Resonant Magnetic Nanostructures Exhibiting a Negative Permeability,” Phys. Rev. Lett. 94, 037402 (2005).
[Crossref] [PubMed]

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental Demonstration of Near-Infrared Negative-Index Metamaterials,” Phys. Rev. Lett. 95, 137404 (2005).
[Crossref] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, J. Zhou, C.M. Soukoulis, and S. Linden, “Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials,” Opt. Lett 30, 3198–3200 (2005).
[Crossref] [PubMed]

V. M. Shalaev, W. Cai, U. Chettiar, H. K. Yuan, A.K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett 30, 3356–3358 (2005).
[Crossref]

N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature 438, 335–338 (2005).
[Crossref] [PubMed]

J. F. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of Split-Ring Resonators at Optical Frequencies,” Phys. Rev. Lett. 95, 223902 (2005).
[Crossref] [PubMed]

A. Ishikawa, T. Tanaka, and S. Kawata, “Negative Magnetic Permeability in the Visible Light Region,” Phys. Rev. Lett. 95, 237401 (2005).
[Crossref] [PubMed]

2004 (3)

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz Magnetic Response from Artificial Materials,” Science 303, 1494–1496 (2004).
[Crossref] [PubMed]

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and Negative Refractive Index,” Science 305, 788–792 (2004).
[Crossref] [PubMed]

S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic Response of Metamaterials at 100 Terahertz,” Science 306, 1351–1353 (2004).
[Crossref] [PubMed]

2001 (1)

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental Verification of a Negative Index of Refraction,” Science 292, 77–79 (2001).
[Crossref] [PubMed]

2000 (1)

J.B. Pendry, “Negative Refraction Makes a Perfect Lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[Crossref] [PubMed]

1999 (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from Conductors and Enhanced Nonlinear Phenomena,” IEEE Trans. MTT 47, 2075–2084 (1999).
[Crossref]

1968 (1)

V. G. Veselago, “The Electrodynamics of Substances with Simultaneously Negative Values of ε and μ,” Sov. Phys. Usp. 10, 509 (1968).
[Crossref]

Basov, D. N.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz Magnetic Response from Artificial Materials,” Science 303, 1494–1496 (2004).
[Crossref] [PubMed]

Brueck, S. R. J.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental Demonstration of Near-Infrared Negative-Index Metamaterials,” Phys. Rev. Lett. 95, 137404 (2005).
[Crossref] [PubMed]

Brueck, S.R. J.

S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S.R. J. Brueck, “Midinfrared Resonant Magnetic Nanostructures Exhibiting a Negative Permeability,” Phys. Rev. Lett. 94, 037402 (2005).
[Crossref] [PubMed]

Burger, S.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic Metamaterials at Telecommunication and Visible Frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[Crossref] [PubMed]

Cai, W.

V. M. Shalaev, W. Cai, U. Chettiar, H. K. Yuan, A.K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett 30, 3356–3358 (2005).
[Crossref]

Chettiar, U.

V. M. Shalaev, W. Cai, U. Chettiar, H. K. Yuan, A.K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett 30, 3356–3358 (2005).
[Crossref]

Dolling, G.

G. Dolling, C. Enkrich, M. Wegener, J. Zhou, C.M. Soukoulis, and S. Linden, “Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials,” Opt. Lett 30, 3198–3200 (2005).
[Crossref] [PubMed]

S. Linden, C. Enkrich, M. Klein, G. Dolling, N. Feth, and M. Wegener, “Metamaterials“ (2006), http://www.aph.uni-karlsruhe.de/ag/wegener/meta/meta.html

Drachev, V. P.

V. M. Shalaev, W. Cai, U. Chettiar, H. K. Yuan, A.K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett 30, 3356–3358 (2005).
[Crossref]

Economou, E. N.

J. F. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of Split-Ring Resonators at Optical Frequencies,” Phys. Rev. Lett. 95, 223902 (2005).
[Crossref] [PubMed]

Enkrich, C.

M. W. Klein, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Single-slit split-ring resonators at optical frequencies: Limits of size scaling,” submitted to Opt. Lett., (2006).
[Crossref]

G. Dolling, C. Enkrich, M. Wegener, J. Zhou, C.M. Soukoulis, and S. Linden, “Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials,” Opt. Lett 30, 3198–3200 (2005).
[Crossref] [PubMed]

C. Enkrich, F. Perez-Willard, D. Gerthsen, J. F. Zhou, C. M. Soukoulis, M. Wegener, and S. Linden, “Focused-Ion-Beam Nanofabrication of Near-Infrared Magnetic Metamaterials,” Adv. Mater. 17, 2547–2549 (2005).
[Crossref]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic Metamaterials at Telecommunication and Visible Frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[Crossref] [PubMed]

S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic Response of Metamaterials at 100 Terahertz,” Science 306, 1351–1353 (2004).
[Crossref] [PubMed]

S. Linden, C. Enkrich, M. Klein, G. Dolling, N. Feth, and M. Wegener, “Metamaterials“ (2006), http://www.aph.uni-karlsruhe.de/ag/wegener/meta/meta.html

Fan, W.

S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S.R. J. Brueck, “Midinfrared Resonant Magnetic Nanostructures Exhibiting a Negative Permeability,” Phys. Rev. Lett. 94, 037402 (2005).
[Crossref] [PubMed]

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental Demonstration of Near-Infrared Negative-Index Metamaterials,” Phys. Rev. Lett. 95, 137404 (2005).
[Crossref] [PubMed]

Fang, N.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz Magnetic Response from Artificial Materials,” Science 303, 1494–1496 (2004).
[Crossref] [PubMed]

Feth, N.

S. Linden, C. Enkrich, M. Klein, G. Dolling, N. Feth, and M. Wegener, “Metamaterials“ (2006), http://www.aph.uni-karlsruhe.de/ag/wegener/meta/meta.html

Firsov, A. A.

N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature 438, 335–338 (2005).
[Crossref] [PubMed]

Frauenglass, A.

S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S.R. J. Brueck, “Midinfrared Resonant Magnetic Nanostructures Exhibiting a Negative Permeability,” Phys. Rev. Lett. 94, 037402 (2005).
[Crossref] [PubMed]

Geim, A. K.

N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature 438, 335–338 (2005).
[Crossref] [PubMed]

Gerthsen, D.

C. Enkrich, F. Perez-Willard, D. Gerthsen, J. F. Zhou, C. M. Soukoulis, M. Wegener, and S. Linden, “Focused-Ion-Beam Nanofabrication of Near-Infrared Magnetic Metamaterials,” Adv. Mater. 17, 2547–2549 (2005).
[Crossref]

Glassner, Andrew S.

Andrew S. Glassner, An Introduction to Ray Tracing (Morgan Kaufmann, 1989).

Gleeson, H. F.

N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature 438, 335–338 (2005).
[Crossref] [PubMed]

Grigorenko, N.

N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature 438, 335–338 (2005).
[Crossref] [PubMed]

Holden, A. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from Conductors and Enhanced Nonlinear Phenomena,” IEEE Trans. MTT 47, 2075–2084 (1999).
[Crossref]

Ishikawa, A.

A. Ishikawa, T. Tanaka, and S. Kawata, “Negative Magnetic Permeability in the Visible Light Region,” Phys. Rev. Lett. 95, 237401 (2005).
[Crossref] [PubMed]

Kafesaki, M.

J. F. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of Split-Ring Resonators at Optical Frequencies,” Phys. Rev. Lett. 95, 223902 (2005).
[Crossref] [PubMed]

Kawata, S.

A. Ishikawa, T. Tanaka, and S. Kawata, “Negative Magnetic Permeability in the Visible Light Region,” Phys. Rev. Lett. 95, 237401 (2005).
[Crossref] [PubMed]

Khrushchev, I. Y.

N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature 438, 335–338 (2005).
[Crossref] [PubMed]

Kildishev, A. V.

V. M. Shalaev, W. Cai, U. Chettiar, H. K. Yuan, A.K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett 30, 3356–3358 (2005).
[Crossref]

Klein, M.

S. Linden, C. Enkrich, M. Klein, G. Dolling, N. Feth, and M. Wegener, “Metamaterials“ (2006), http://www.aph.uni-karlsruhe.de/ag/wegener/meta/meta.html

Klein, M. W.

M. W. Klein, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Single-slit split-ring resonators at optical frequencies: Limits of size scaling,” submitted to Opt. Lett., (2006).
[Crossref]

Koschny, T.

J. F. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of Split-Ring Resonators at Optical Frequencies,” Phys. Rev. Lett. 95, 223902 (2005).
[Crossref] [PubMed]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic Metamaterials at Telecommunication and Visible Frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[Crossref] [PubMed]

S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic Response of Metamaterials at 100 Terahertz,” Science 306, 1351–1353 (2004).
[Crossref] [PubMed]

Linden, S.

M. W. Klein, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Single-slit split-ring resonators at optical frequencies: Limits of size scaling,” submitted to Opt. Lett., (2006).
[Crossref]

C. Enkrich, F. Perez-Willard, D. Gerthsen, J. F. Zhou, C. M. Soukoulis, M. Wegener, and S. Linden, “Focused-Ion-Beam Nanofabrication of Near-Infrared Magnetic Metamaterials,” Adv. Mater. 17, 2547–2549 (2005).
[Crossref]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic Metamaterials at Telecommunication and Visible Frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[Crossref] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, J. Zhou, C.M. Soukoulis, and S. Linden, “Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials,” Opt. Lett 30, 3198–3200 (2005).
[Crossref] [PubMed]

S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic Response of Metamaterials at 100 Terahertz,” Science 306, 1351–1353 (2004).
[Crossref] [PubMed]

S. Linden, C. Enkrich, M. Klein, G. Dolling, N. Feth, and M. Wegener, “Metamaterials“ (2006), http://www.aph.uni-karlsruhe.de/ag/wegener/meta/meta.html

Malloy, K. J.

S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S.R. J. Brueck, “Midinfrared Resonant Magnetic Nanostructures Exhibiting a Negative Permeability,” Phys. Rev. Lett. 94, 037402 (2005).
[Crossref] [PubMed]

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental Demonstration of Near-Infrared Negative-Index Metamaterials,” Phys. Rev. Lett. 95, 137404 (2005).
[Crossref] [PubMed]

Minhas, B. K.

S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S.R. J. Brueck, “Midinfrared Resonant Magnetic Nanostructures Exhibiting a Negative Permeability,” Phys. Rev. Lett. 94, 037402 (2005).
[Crossref] [PubMed]

Osgood, R. M.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental Demonstration of Near-Infrared Negative-Index Metamaterials,” Phys. Rev. Lett. 95, 137404 (2005).
[Crossref] [PubMed]

Padilla, W. J.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz Magnetic Response from Artificial Materials,” Science 303, 1494–1496 (2004).
[Crossref] [PubMed]

Panoiu, N. C.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental Demonstration of Near-Infrared Negative-Index Metamaterials,” Phys. Rev. Lett. 95, 137404 (2005).
[Crossref] [PubMed]

Pendry, J. B.

J. F. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of Split-Ring Resonators at Optical Frequencies,” Phys. Rev. Lett. 95, 223902 (2005).
[Crossref] [PubMed]

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz Magnetic Response from Artificial Materials,” Science 303, 1494–1496 (2004).
[Crossref] [PubMed]

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and Negative Refractive Index,” Science 305, 788–792 (2004).
[Crossref] [PubMed]

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from Conductors and Enhanced Nonlinear Phenomena,” IEEE Trans. MTT 47, 2075–2084 (1999).
[Crossref]

Pendry, J.B.

J.B. Pendry, “Negative Refraction Makes a Perfect Lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[Crossref] [PubMed]

Perez-Willard, F.

C. Enkrich, F. Perez-Willard, D. Gerthsen, J. F. Zhou, C. M. Soukoulis, M. Wegener, and S. Linden, “Focused-Ion-Beam Nanofabrication of Near-Infrared Magnetic Metamaterials,” Adv. Mater. 17, 2547–2549 (2005).
[Crossref]

Petrovic, J.

N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature 438, 335–338 (2005).
[Crossref] [PubMed]

Robbins, D. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from Conductors and Enhanced Nonlinear Phenomena,” IEEE Trans. MTT 47, 2075–2084 (1999).
[Crossref]

Sarychev, A.K.

V. M. Shalaev, W. Cai, U. Chettiar, H. K. Yuan, A.K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett 30, 3356–3358 (2005).
[Crossref]

Schmidt, F.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic Metamaterials at Telecommunication and Visible Frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[Crossref] [PubMed]

Schultz, S.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental Verification of a Negative Index of Refraction,” Science 292, 77–79 (2001).
[Crossref] [PubMed]

Shalaev, V. M.

V. M. Shalaev, W. Cai, U. Chettiar, H. K. Yuan, A.K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett 30, 3356–3358 (2005).
[Crossref]

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental Verification of a Negative Index of Refraction,” Science 292, 77–79 (2001).
[Crossref] [PubMed]

Smith, D. R.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and Negative Refractive Index,” Science 305, 788–792 (2004).
[Crossref] [PubMed]

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz Magnetic Response from Artificial Materials,” Science 303, 1494–1496 (2004).
[Crossref] [PubMed]

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental Verification of a Negative Index of Refraction,” Science 292, 77–79 (2001).
[Crossref] [PubMed]

Soukoulis, C. M.

M. W. Klein, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Single-slit split-ring resonators at optical frequencies: Limits of size scaling,” submitted to Opt. Lett., (2006).
[Crossref]

J. F. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of Split-Ring Resonators at Optical Frequencies,” Phys. Rev. Lett. 95, 223902 (2005).
[Crossref] [PubMed]

C. Enkrich, F. Perez-Willard, D. Gerthsen, J. F. Zhou, C. M. Soukoulis, M. Wegener, and S. Linden, “Focused-Ion-Beam Nanofabrication of Near-Infrared Magnetic Metamaterials,” Adv. Mater. 17, 2547–2549 (2005).
[Crossref]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic Metamaterials at Telecommunication and Visible Frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[Crossref] [PubMed]

S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic Response of Metamaterials at 100 Terahertz,” Science 306, 1351–1353 (2004).
[Crossref] [PubMed]

Soukoulis, C.M.

G. Dolling, C. Enkrich, M. Wegener, J. Zhou, C.M. Soukoulis, and S. Linden, “Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials,” Opt. Lett 30, 3198–3200 (2005).
[Crossref] [PubMed]

Stewart, W. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from Conductors and Enhanced Nonlinear Phenomena,” IEEE Trans. MTT 47, 2075–2084 (1999).
[Crossref]

Tanaka, T.

A. Ishikawa, T. Tanaka, and S. Kawata, “Negative Magnetic Permeability in the Visible Light Region,” Phys. Rev. Lett. 95, 237401 (2005).
[Crossref] [PubMed]

Veselago, V. G.

V. G. Veselago, “The Electrodynamics of Substances with Simultaneously Negative Values of ε and μ,” Sov. Phys. Usp. 10, 509 (1968).
[Crossref]

Vier, D. C.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz Magnetic Response from Artificial Materials,” Science 303, 1494–1496 (2004).
[Crossref] [PubMed]

Wegener, M.

M. W. Klein, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Single-slit split-ring resonators at optical frequencies: Limits of size scaling,” submitted to Opt. Lett., (2006).
[Crossref]

C. Enkrich, F. Perez-Willard, D. Gerthsen, J. F. Zhou, C. M. Soukoulis, M. Wegener, and S. Linden, “Focused-Ion-Beam Nanofabrication of Near-Infrared Magnetic Metamaterials,” Adv. Mater. 17, 2547–2549 (2005).
[Crossref]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic Metamaterials at Telecommunication and Visible Frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[Crossref] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, J. Zhou, C.M. Soukoulis, and S. Linden, “Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials,” Opt. Lett 30, 3198–3200 (2005).
[Crossref] [PubMed]

S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic Response of Metamaterials at 100 Terahertz,” Science 306, 1351–1353 (2004).
[Crossref] [PubMed]

S. Linden, C. Enkrich, M. Klein, G. Dolling, N. Feth, and M. Wegener, “Metamaterials“ (2006), http://www.aph.uni-karlsruhe.de/ag/wegener/meta/meta.html

Wiltshire, M. C. K.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and Negative Refractive Index,” Science 305, 788–792 (2004).
[Crossref] [PubMed]

Yen, T. J.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz Magnetic Response from Artificial Materials,” Science 303, 1494–1496 (2004).
[Crossref] [PubMed]

Yuan, H. K.

V. M. Shalaev, W. Cai, U. Chettiar, H. K. Yuan, A.K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett 30, 3356–3358 (2005).
[Crossref]

Zhang, S.

S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S.R. J. Brueck, “Midinfrared Resonant Magnetic Nanostructures Exhibiting a Negative Permeability,” Phys. Rev. Lett. 94, 037402 (2005).
[Crossref] [PubMed]

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental Demonstration of Near-Infrared Negative-Index Metamaterials,” Phys. Rev. Lett. 95, 137404 (2005).
[Crossref] [PubMed]

Zhang, X.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz Magnetic Response from Artificial Materials,” Science 303, 1494–1496 (2004).
[Crossref] [PubMed]

Zhang, Y.

N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature 438, 335–338 (2005).
[Crossref] [PubMed]

Zhou, J.

G. Dolling, C. Enkrich, M. Wegener, J. Zhou, C.M. Soukoulis, and S. Linden, “Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials,” Opt. Lett 30, 3198–3200 (2005).
[Crossref] [PubMed]

Zhou, J. F.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic Metamaterials at Telecommunication and Visible Frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[Crossref] [PubMed]

C. Enkrich, F. Perez-Willard, D. Gerthsen, J. F. Zhou, C. M. Soukoulis, M. Wegener, and S. Linden, “Focused-Ion-Beam Nanofabrication of Near-Infrared Magnetic Metamaterials,” Adv. Mater. 17, 2547–2549 (2005).
[Crossref]

J. F. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of Split-Ring Resonators at Optical Frequencies,” Phys. Rev. Lett. 95, 223902 (2005).
[Crossref] [PubMed]

S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic Response of Metamaterials at 100 Terahertz,” Science 306, 1351–1353 (2004).
[Crossref] [PubMed]

Zschiedrich, L.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic Metamaterials at Telecommunication and Visible Frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[Crossref] [PubMed]

Adv. Mater. (1)

C. Enkrich, F. Perez-Willard, D. Gerthsen, J. F. Zhou, C. M. Soukoulis, M. Wegener, and S. Linden, “Focused-Ion-Beam Nanofabrication of Near-Infrared Magnetic Metamaterials,” Adv. Mater. 17, 2547–2549 (2005).
[Crossref]

IEEE Trans. MTT (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from Conductors and Enhanced Nonlinear Phenomena,” IEEE Trans. MTT 47, 2075–2084 (1999).
[Crossref]

Nature (1)

N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature 438, 335–338 (2005).
[Crossref] [PubMed]

Opt. Lett (2)

G. Dolling, C. Enkrich, M. Wegener, J. Zhou, C.M. Soukoulis, and S. Linden, “Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials,” Opt. Lett 30, 3198–3200 (2005).
[Crossref] [PubMed]

V. M. Shalaev, W. Cai, U. Chettiar, H. K. Yuan, A.K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett 30, 3356–3358 (2005).
[Crossref]

Phys. Rev. Lett. (6)

J.B. Pendry, “Negative Refraction Makes a Perfect Lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[Crossref] [PubMed]

J. F. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of Split-Ring Resonators at Optical Frequencies,” Phys. Rev. Lett. 95, 223902 (2005).
[Crossref] [PubMed]

A. Ishikawa, T. Tanaka, and S. Kawata, “Negative Magnetic Permeability in the Visible Light Region,” Phys. Rev. Lett. 95, 237401 (2005).
[Crossref] [PubMed]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic Metamaterials at Telecommunication and Visible Frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[Crossref] [PubMed]

S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S.R. J. Brueck, “Midinfrared Resonant Magnetic Nanostructures Exhibiting a Negative Permeability,” Phys. Rev. Lett. 94, 037402 (2005).
[Crossref] [PubMed]

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental Demonstration of Near-Infrared Negative-Index Metamaterials,” Phys. Rev. Lett. 95, 137404 (2005).
[Crossref] [PubMed]

Science (4)

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental Verification of a Negative Index of Refraction,” Science 292, 77–79 (2001).
[Crossref] [PubMed]

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz Magnetic Response from Artificial Materials,” Science 303, 1494–1496 (2004).
[Crossref] [PubMed]

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and Negative Refractive Index,” Science 305, 788–792 (2004).
[Crossref] [PubMed]

S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic Response of Metamaterials at 100 Terahertz,” Science 306, 1351–1353 (2004).
[Crossref] [PubMed]

Sov. Phys. Usp. (1)

V. G. Veselago, “The Electrodynamics of Substances with Simultaneously Negative Values of ε and μ,” Sov. Phys. Usp. 10, 509 (1968).
[Crossref]

submitted to Opt. Lett. (1)

M. W. Klein, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Single-slit split-ring resonators at optical frequencies: Limits of size scaling,” submitted to Opt. Lett., (2006).
[Crossref]

Other (3)

POV-Ray (Persistence of Vision Raytracer Pty. Ltd., 2006), http://www.povray.org/

S. Linden, C. Enkrich, M. Klein, G. Dolling, N. Feth, and M. Wegener, “Metamaterials“ (2006), http://www.aph.uni-karlsruhe.de/ag/wegener/meta/meta.html

Andrew S. Glassner, An Introduction to Ray Tracing (Morgan Kaufmann, 1989).

Supplementary Material (4)

» Media 1: AVI (1295 KB)     
» Media 2: AVI (1383 KB)     
» Media 3: AVI (1603 KB)     
» Media 4: AVI (2306 KB)     

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Figures (5)

Fig. 1.
Fig. 1.

(a) Calculated ray-tracing image of a metal rod in an empty drinking glass. (b) Same scenery, but the glass is filled with normal water, n =1.3 , leading to ordinary refraction. (c) The water is replaced by “water” with a fictitious refractive index of n = -1.3 .

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Fig. 2.
Fig. 2.

Illustration of the depth-dependent magnification factor s´/ s of an object with size s in a material with n = -1. The observer looks straight down onto the object (arrow). The observer-interface distance is a, the interface-object distance is a’. (a) a´ < a and (b) a´ > a.

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Fig. 3.
Fig. 3.

(a) Scheme of the movie scenery. The observer is at the cross and looks straight down. Four characteristic snapshots are depicted. (b) (1.2 MB) The colored ball falls (i.e., moves away from the observer) with constant velocity v in a material with n =1 . (c) (1.3 MB) As (b), but n = - 1 . Note the reversed apparent velocity of the ball in (c) as well as the infinite size at a´ = a (compare Fig. 2).

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Fig. 4.
Fig. 4.

(a) Scheme of the movie scenery. The observer is at the cross and looks straight down. Four characteristic snapshots are depicted. (b) (1.6 MB) The tilted arrow falls with constant velocity v in a material with n =1 . (c) (2.3 MB) As (b), but n = -1 . Note the extreme distortions and rotation of the arrow in (c) when parts of it are in or near to the “focus” at a´ = a (compare Fig. 2). It even appears to be torn into pieces.

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Fig. 5.
Fig. 5.

Scenery as Fig. 1, but the observer position is much closer to the intersection of the rod with the “water” surface. (a) Normal water with n=1.2, (b) “water” with n=-1.2, (c) n=-1, and (d) n=-1.4.

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