Abstract

We propose a new metamaterial with a gradient negative index of refraction, which can focus a collimated beam of light coming from a distant object. A slab of the negative refractive index metamaterial has a focal length that can be tuned by changing the gradient of the negative refractive index. A thin metal film pierced with holes of appropriate size or spacing between them can be used as a metamaterial with the gradient negative index of refraction. We use finite-difference time-domain calculations to show the focusing of a plane electromagnetic wave passing through a system of equidistantly spaced holes in a metal slab with decreasing diameters toward the edges of the slab.

© 2007 Optical Society of America

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  1. V. G. Veselago, "Electrodynamics of substances with simultaneously negative electrical and magnetic permeabilities," Sov. Phys. Usp. 10, 509-517 (1968).
    [CrossRef]
  2. V. G. Veselago, "Formulating Fermat's principle for light traveling in negative refraction materials," Phys. Usp. 45, 1097-1099 (2002).
    [CrossRef]
  3. J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
    [CrossRef] [PubMed]
  4. N. Fang, H. Lee, C. Sun, and X. Zhang, "Sub-diffraction-limited optical imaging with silver superlens," Science 308, 534-537 (2006).
    [CrossRef]
  5. R. J. Moerland, N. F. van Hulst, H. Gersen, and L. Kuipers, "Probing the negative permittivity perfect lens at optical frequencies using near-field optics and single molecule detection," Opt. Express 13, 1604-1614 (2005).
    [CrossRef] [PubMed]
  6. D. Schurig and D. R. Smith, "Negative index lens abberation," Phys. Rev. E 70, 65601-1-4 (2004).
    [CrossRef]
  7. J. Chen, C. Radu, and A. Puri, "Abberation-free negative-refractive-index lens," Appl. Phys. Lett. 88, 07119 (2006).
  8. D. T. Moore, "Gradient-index optics: a review," Appl. Opt. 19, 1035-1042 (1980).
    [CrossRef] [PubMed]
  9. D. R. Smith, J. J. Mock, A. F. Starr, and D. Schurig, "Gradient index metamaterials," Phys. Rev. E 71, 036609-1-4 (2005).
    [CrossRef]
  10. T. Driscoll, D. N. Basov, A. F. Starr, P. M. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, "Free-space microwave focusing by a negative-index gradient lens," Appl. Phys. Lett. 88, 081101 (2006).
    [CrossRef]
  11. R. B. Greegor, C. G. Parazzoli, J. A. Nielsen, M. A. Thompson, M. H. Tanielian, and D. R. Smith, "Simulation and testing of a gradient negative index of refraction lens," Appl. Phys. Lett. 87, 091114 (2005).
    [CrossRef]
  12. S. A. Ramakrishna, J. B. Pendry, D. Schurig, D. R. Smith, and S. Schultz, "The asymmetric lossy near-perfect lens," J. Mod. Opt. 49, 1747-1762 (2002).
    [CrossRef]
  13. P. Tassin, I. Veretennicoff, and G. Van der Sande, "Veselago's lens consisting of left-handed materials with arbitrary index of refraction," Opt. Commun. 264, 130-134 (2006).
    [CrossRef]
  14. C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, "Experimental verification and simulation of negative index of refraction using Snell's law," Phys. Rev. Lett. 90, 107401-14 (2003).
    [CrossRef] [PubMed]
  15. P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, "Photonic crystals--imaging by flat lens using negative refraction," Nature 426, 404-404 (2003).
    [CrossRef] [PubMed]
  16. X. Ao and S. He, "Negative refraction of left-handed behavior in porous alumina with infiltrated silver at an optical wavelength," Appl. Phys. Lett. 87, 101112 (2005).
    [CrossRef]
  17. J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, "Mimicking surface plasmons with structured surfaces," Science 305, 847-848 (2004).
    [CrossRef] [PubMed]
  18. M. W. McCall, A. Lakhtakia, and W. S. Weighlhofer, "The negative index of refraction demystified," Eur. J. Phys. 23, 353-359 (2002).
    [CrossRef]
  19. J. W. Lee, M. A. Seo, J. Y. Sohn, Y. H. Ahn, D. S. Kim, S. C. Jeoung, Ch. Lienau, and Q-Han Park, "Invisible plasmonic meta-materials through impedance matching to vacuum," Opt. Express 13, 10681-10687 (2005).
    [CrossRef] [PubMed]
  20. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941).
  21. T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, "Near-field microscopy through a SiC superlens," Science 313, 1595-1595 (2006).
    [CrossRef] [PubMed]

2006 (5)

T. Driscoll, D. N. Basov, A. F. Starr, P. M. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, "Free-space microwave focusing by a negative-index gradient lens," Appl. Phys. Lett. 88, 081101 (2006).
[CrossRef]

P. Tassin, I. Veretennicoff, and G. Van der Sande, "Veselago's lens consisting of left-handed materials with arbitrary index of refraction," Opt. Commun. 264, 130-134 (2006).
[CrossRef]

N. Fang, H. Lee, C. Sun, and X. Zhang, "Sub-diffraction-limited optical imaging with silver superlens," Science 308, 534-537 (2006).
[CrossRef]

J. Chen, C. Radu, and A. Puri, "Abberation-free negative-refractive-index lens," Appl. Phys. Lett. 88, 07119 (2006).

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, "Near-field microscopy through a SiC superlens," Science 313, 1595-1595 (2006).
[CrossRef] [PubMed]

2005 (5)

R. J. Moerland, N. F. van Hulst, H. Gersen, and L. Kuipers, "Probing the negative permittivity perfect lens at optical frequencies using near-field optics and single molecule detection," Opt. Express 13, 1604-1614 (2005).
[CrossRef] [PubMed]

J. W. Lee, M. A. Seo, J. Y. Sohn, Y. H. Ahn, D. S. Kim, S. C. Jeoung, Ch. Lienau, and Q-Han Park, "Invisible plasmonic meta-materials through impedance matching to vacuum," Opt. Express 13, 10681-10687 (2005).
[CrossRef] [PubMed]

R. B. Greegor, C. G. Parazzoli, J. A. Nielsen, M. A. Thompson, M. H. Tanielian, and D. R. Smith, "Simulation and testing of a gradient negative index of refraction lens," Appl. Phys. Lett. 87, 091114 (2005).
[CrossRef]

X. Ao and S. He, "Negative refraction of left-handed behavior in porous alumina with infiltrated silver at an optical wavelength," Appl. Phys. Lett. 87, 101112 (2005).
[CrossRef]

D. R. Smith, J. J. Mock, A. F. Starr, and D. Schurig, "Gradient index metamaterials," Phys. Rev. E 71, 036609-1-4 (2005).
[CrossRef]

2004 (2)

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, "Mimicking surface plasmons with structured surfaces," Science 305, 847-848 (2004).
[CrossRef] [PubMed]

D. Schurig and D. R. Smith, "Negative index lens abberation," Phys. Rev. E 70, 65601-1-4 (2004).
[CrossRef]

2003 (2)

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, "Experimental verification and simulation of negative index of refraction using Snell's law," Phys. Rev. Lett. 90, 107401-14 (2003).
[CrossRef] [PubMed]

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, "Photonic crystals--imaging by flat lens using negative refraction," Nature 426, 404-404 (2003).
[CrossRef] [PubMed]

2002 (3)

S. A. Ramakrishna, J. B. Pendry, D. Schurig, D. R. Smith, and S. Schultz, "The asymmetric lossy near-perfect lens," J. Mod. Opt. 49, 1747-1762 (2002).
[CrossRef]

M. W. McCall, A. Lakhtakia, and W. S. Weighlhofer, "The negative index of refraction demystified," Eur. J. Phys. 23, 353-359 (2002).
[CrossRef]

V. G. Veselago, "Formulating Fermat's principle for light traveling in negative refraction materials," Phys. Usp. 45, 1097-1099 (2002).
[CrossRef]

2000 (1)

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

1980 (1)

1968 (1)

V. G. Veselago, "Electrodynamics of substances with simultaneously negative electrical and magnetic permeabilities," Sov. Phys. Usp. 10, 509-517 (1968).
[CrossRef]

Ahn, Y. H.

Ao, X.

X. Ao and S. He, "Negative refraction of left-handed behavior in porous alumina with infiltrated silver at an optical wavelength," Appl. Phys. Lett. 87, 101112 (2005).
[CrossRef]

Basov, D. N.

T. Driscoll, D. N. Basov, A. F. Starr, P. M. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, "Free-space microwave focusing by a negative-index gradient lens," Appl. Phys. Lett. 88, 081101 (2006).
[CrossRef]

Chen, J.

J. Chen, C. Radu, and A. Puri, "Abberation-free negative-refractive-index lens," Appl. Phys. Lett. 88, 07119 (2006).

Driscoll, T.

T. Driscoll, D. N. Basov, A. F. Starr, P. M. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, "Free-space microwave focusing by a negative-index gradient lens," Appl. Phys. Lett. 88, 081101 (2006).
[CrossRef]

Fang, N.

N. Fang, H. Lee, C. Sun, and X. Zhang, "Sub-diffraction-limited optical imaging with silver superlens," Science 308, 534-537 (2006).
[CrossRef]

Garcia-Vidal, F. J.

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, "Mimicking surface plasmons with structured surfaces," Science 305, 847-848 (2004).
[CrossRef] [PubMed]

Gersen, H.

Greegor, R. B.

R. B. Greegor, C. G. Parazzoli, J. A. Nielsen, M. A. Thompson, M. H. Tanielian, and D. R. Smith, "Simulation and testing of a gradient negative index of refraction lens," Appl. Phys. Lett. 87, 091114 (2005).
[CrossRef]

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, "Experimental verification and simulation of negative index of refraction using Snell's law," Phys. Rev. Lett. 90, 107401-14 (2003).
[CrossRef] [PubMed]

He, S.

X. Ao and S. He, "Negative refraction of left-handed behavior in porous alumina with infiltrated silver at an optical wavelength," Appl. Phys. Lett. 87, 101112 (2005).
[CrossRef]

Hillenbrand, R.

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, "Near-field microscopy through a SiC superlens," Science 313, 1595-1595 (2006).
[CrossRef] [PubMed]

Jeoung, S. C.

Kim, D. S.

Koltenbah, B. E. C.

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, "Experimental verification and simulation of negative index of refraction using Snell's law," Phys. Rev. Lett. 90, 107401-14 (2003).
[CrossRef] [PubMed]

Korobkin, D.

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, "Near-field microscopy through a SiC superlens," Science 313, 1595-1595 (2006).
[CrossRef] [PubMed]

Kuipers, L.

Lakhtakia, A.

M. W. McCall, A. Lakhtakia, and W. S. Weighlhofer, "The negative index of refraction demystified," Eur. J. Phys. 23, 353-359 (2002).
[CrossRef]

Lee, H.

N. Fang, H. Lee, C. Sun, and X. Zhang, "Sub-diffraction-limited optical imaging with silver superlens," Science 308, 534-537 (2006).
[CrossRef]

Lee, J. W.

Li, K.

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, "Experimental verification and simulation of negative index of refraction using Snell's law," Phys. Rev. Lett. 90, 107401-14 (2003).
[CrossRef] [PubMed]

Lienau, Ch.

Lu, W. T.

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, "Photonic crystals--imaging by flat lens using negative refraction," Nature 426, 404-404 (2003).
[CrossRef] [PubMed]

Martin-Moreno, L.

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, "Mimicking surface plasmons with structured surfaces," Science 305, 847-848 (2004).
[CrossRef] [PubMed]

McCall, M. W.

M. W. McCall, A. Lakhtakia, and W. S. Weighlhofer, "The negative index of refraction demystified," Eur. J. Phys. 23, 353-359 (2002).
[CrossRef]

Mock, J. J.

D. R. Smith, J. J. Mock, A. F. Starr, and D. Schurig, "Gradient index metamaterials," Phys. Rev. E 71, 036609-1-4 (2005).
[CrossRef]

Moerland, R. J.

Moore, D. T.

Nemat-Nasser, S.

T. Driscoll, D. N. Basov, A. F. Starr, P. M. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, "Free-space microwave focusing by a negative-index gradient lens," Appl. Phys. Lett. 88, 081101 (2006).
[CrossRef]

Nielsen, J. A.

R. B. Greegor, C. G. Parazzoli, J. A. Nielsen, M. A. Thompson, M. H. Tanielian, and D. R. Smith, "Simulation and testing of a gradient negative index of refraction lens," Appl. Phys. Lett. 87, 091114 (2005).
[CrossRef]

Parazzoli, C. G.

R. B. Greegor, C. G. Parazzoli, J. A. Nielsen, M. A. Thompson, M. H. Tanielian, and D. R. Smith, "Simulation and testing of a gradient negative index of refraction lens," Appl. Phys. Lett. 87, 091114 (2005).
[CrossRef]

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, "Experimental verification and simulation of negative index of refraction using Snell's law," Phys. Rev. Lett. 90, 107401-14 (2003).
[CrossRef] [PubMed]

Parimi, P. V.

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, "Photonic crystals--imaging by flat lens using negative refraction," Nature 426, 404-404 (2003).
[CrossRef] [PubMed]

Park, Q-Han

Pendry, J. B.

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, "Mimicking surface plasmons with structured surfaces," Science 305, 847-848 (2004).
[CrossRef] [PubMed]

S. A. Ramakrishna, J. B. Pendry, D. Schurig, D. R. Smith, and S. Schultz, "The asymmetric lossy near-perfect lens," J. Mod. Opt. 49, 1747-1762 (2002).
[CrossRef]

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

Puri, A.

J. Chen, C. Radu, and A. Puri, "Abberation-free negative-refractive-index lens," Appl. Phys. Lett. 88, 07119 (2006).

Radu, C.

J. Chen, C. Radu, and A. Puri, "Abberation-free negative-refractive-index lens," Appl. Phys. Lett. 88, 07119 (2006).

Ramakrishna, S. A.

S. A. Ramakrishna, J. B. Pendry, D. Schurig, D. R. Smith, and S. Schultz, "The asymmetric lossy near-perfect lens," J. Mod. Opt. 49, 1747-1762 (2002).
[CrossRef]

Rye, P. M.

T. Driscoll, D. N. Basov, A. F. Starr, P. M. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, "Free-space microwave focusing by a negative-index gradient lens," Appl. Phys. Lett. 88, 081101 (2006).
[CrossRef]

Schultz, S.

S. A. Ramakrishna, J. B. Pendry, D. Schurig, D. R. Smith, and S. Schultz, "The asymmetric lossy near-perfect lens," J. Mod. Opt. 49, 1747-1762 (2002).
[CrossRef]

Schurig, D.

T. Driscoll, D. N. Basov, A. F. Starr, P. M. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, "Free-space microwave focusing by a negative-index gradient lens," Appl. Phys. Lett. 88, 081101 (2006).
[CrossRef]

D. R. Smith, J. J. Mock, A. F. Starr, and D. Schurig, "Gradient index metamaterials," Phys. Rev. E 71, 036609-1-4 (2005).
[CrossRef]

D. Schurig and D. R. Smith, "Negative index lens abberation," Phys. Rev. E 70, 65601-1-4 (2004).
[CrossRef]

S. A. Ramakrishna, J. B. Pendry, D. Schurig, D. R. Smith, and S. Schultz, "The asymmetric lossy near-perfect lens," J. Mod. Opt. 49, 1747-1762 (2002).
[CrossRef]

Seo, M. A.

Shvets, G.

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, "Near-field microscopy through a SiC superlens," Science 313, 1595-1595 (2006).
[CrossRef] [PubMed]

Smith, D. R.

T. Driscoll, D. N. Basov, A. F. Starr, P. M. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, "Free-space microwave focusing by a negative-index gradient lens," Appl. Phys. Lett. 88, 081101 (2006).
[CrossRef]

D. R. Smith, J. J. Mock, A. F. Starr, and D. Schurig, "Gradient index metamaterials," Phys. Rev. E 71, 036609-1-4 (2005).
[CrossRef]

R. B. Greegor, C. G. Parazzoli, J. A. Nielsen, M. A. Thompson, M. H. Tanielian, and D. R. Smith, "Simulation and testing of a gradient negative index of refraction lens," Appl. Phys. Lett. 87, 091114 (2005).
[CrossRef]

D. Schurig and D. R. Smith, "Negative index lens abberation," Phys. Rev. E 70, 65601-1-4 (2004).
[CrossRef]

S. A. Ramakrishna, J. B. Pendry, D. Schurig, D. R. Smith, and S. Schultz, "The asymmetric lossy near-perfect lens," J. Mod. Opt. 49, 1747-1762 (2002).
[CrossRef]

Sohn, J. Y.

Sridhar, S.

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, "Photonic crystals--imaging by flat lens using negative refraction," Nature 426, 404-404 (2003).
[CrossRef] [PubMed]

Starr, A. F.

T. Driscoll, D. N. Basov, A. F. Starr, P. M. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, "Free-space microwave focusing by a negative-index gradient lens," Appl. Phys. Lett. 88, 081101 (2006).
[CrossRef]

D. R. Smith, J. J. Mock, A. F. Starr, and D. Schurig, "Gradient index metamaterials," Phys. Rev. E 71, 036609-1-4 (2005).
[CrossRef]

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941).

Sun, C.

N. Fang, H. Lee, C. Sun, and X. Zhang, "Sub-diffraction-limited optical imaging with silver superlens," Science 308, 534-537 (2006).
[CrossRef]

Tanielian, M.

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, "Experimental verification and simulation of negative index of refraction using Snell's law," Phys. Rev. Lett. 90, 107401-14 (2003).
[CrossRef] [PubMed]

Tanielian, M. H.

R. B. Greegor, C. G. Parazzoli, J. A. Nielsen, M. A. Thompson, M. H. Tanielian, and D. R. Smith, "Simulation and testing of a gradient negative index of refraction lens," Appl. Phys. Lett. 87, 091114 (2005).
[CrossRef]

Tassin, P.

P. Tassin, I. Veretennicoff, and G. Van der Sande, "Veselago's lens consisting of left-handed materials with arbitrary index of refraction," Opt. Commun. 264, 130-134 (2006).
[CrossRef]

Taubner, T.

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, "Near-field microscopy through a SiC superlens," Science 313, 1595-1595 (2006).
[CrossRef] [PubMed]

Thompson, M. A.

R. B. Greegor, C. G. Parazzoli, J. A. Nielsen, M. A. Thompson, M. H. Tanielian, and D. R. Smith, "Simulation and testing of a gradient negative index of refraction lens," Appl. Phys. Lett. 87, 091114 (2005).
[CrossRef]

Urzhumov, Y.

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, "Near-field microscopy through a SiC superlens," Science 313, 1595-1595 (2006).
[CrossRef] [PubMed]

Van der Sande, G.

P. Tassin, I. Veretennicoff, and G. Van der Sande, "Veselago's lens consisting of left-handed materials with arbitrary index of refraction," Opt. Commun. 264, 130-134 (2006).
[CrossRef]

van Hulst, N. F.

Veretennicoff, I.

P. Tassin, I. Veretennicoff, and G. Van der Sande, "Veselago's lens consisting of left-handed materials with arbitrary index of refraction," Opt. Commun. 264, 130-134 (2006).
[CrossRef]

Veselago, V. G.

V. G. Veselago, "Formulating Fermat's principle for light traveling in negative refraction materials," Phys. Usp. 45, 1097-1099 (2002).
[CrossRef]

V. G. Veselago, "Electrodynamics of substances with simultaneously negative electrical and magnetic permeabilities," Sov. Phys. Usp. 10, 509-517 (1968).
[CrossRef]

Vodo, P.

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, "Photonic crystals--imaging by flat lens using negative refraction," Nature 426, 404-404 (2003).
[CrossRef] [PubMed]

Weighlhofer, W. S.

M. W. McCall, A. Lakhtakia, and W. S. Weighlhofer, "The negative index of refraction demystified," Eur. J. Phys. 23, 353-359 (2002).
[CrossRef]

Zhang, X.

N. Fang, H. Lee, C. Sun, and X. Zhang, "Sub-diffraction-limited optical imaging with silver superlens," Science 308, 534-537 (2006).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (4)

T. Driscoll, D. N. Basov, A. F. Starr, P. M. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, "Free-space microwave focusing by a negative-index gradient lens," Appl. Phys. Lett. 88, 081101 (2006).
[CrossRef]

R. B. Greegor, C. G. Parazzoli, J. A. Nielsen, M. A. Thompson, M. H. Tanielian, and D. R. Smith, "Simulation and testing of a gradient negative index of refraction lens," Appl. Phys. Lett. 87, 091114 (2005).
[CrossRef]

X. Ao and S. He, "Negative refraction of left-handed behavior in porous alumina with infiltrated silver at an optical wavelength," Appl. Phys. Lett. 87, 101112 (2005).
[CrossRef]

J. Chen, C. Radu, and A. Puri, "Abberation-free negative-refractive-index lens," Appl. Phys. Lett. 88, 07119 (2006).

Eur. J. Phys. (1)

M. W. McCall, A. Lakhtakia, and W. S. Weighlhofer, "The negative index of refraction demystified," Eur. J. Phys. 23, 353-359 (2002).
[CrossRef]

J. Mod. Opt. (1)

S. A. Ramakrishna, J. B. Pendry, D. Schurig, D. R. Smith, and S. Schultz, "The asymmetric lossy near-perfect lens," J. Mod. Opt. 49, 1747-1762 (2002).
[CrossRef]

Nature (1)

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, "Photonic crystals--imaging by flat lens using negative refraction," Nature 426, 404-404 (2003).
[CrossRef] [PubMed]

Opt. Commun. (1)

P. Tassin, I. Veretennicoff, and G. Van der Sande, "Veselago's lens consisting of left-handed materials with arbitrary index of refraction," Opt. Commun. 264, 130-134 (2006).
[CrossRef]

Opt. Express (2)

Phys. Rev. E (2)

D. R. Smith, J. J. Mock, A. F. Starr, and D. Schurig, "Gradient index metamaterials," Phys. Rev. E 71, 036609-1-4 (2005).
[CrossRef]

D. Schurig and D. R. Smith, "Negative index lens abberation," Phys. Rev. E 70, 65601-1-4 (2004).
[CrossRef]

Phys. Rev. Lett. (2)

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, "Experimental verification and simulation of negative index of refraction using Snell's law," Phys. Rev. Lett. 90, 107401-14 (2003).
[CrossRef] [PubMed]

Phys. Usp. (1)

V. G. Veselago, "Formulating Fermat's principle for light traveling in negative refraction materials," Phys. Usp. 45, 1097-1099 (2002).
[CrossRef]

Science (3)

N. Fang, H. Lee, C. Sun, and X. Zhang, "Sub-diffraction-limited optical imaging with silver superlens," Science 308, 534-537 (2006).
[CrossRef]

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, "Mimicking surface plasmons with structured surfaces," Science 305, 847-848 (2004).
[CrossRef] [PubMed]

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, "Near-field microscopy through a SiC superlens," Science 313, 1595-1595 (2006).
[CrossRef] [PubMed]

Sov. Phys. Usp. (1)

V. G. Veselago, "Electrodynamics of substances with simultaneously negative electrical and magnetic permeabilities," Sov. Phys. Usp. 10, 509-517 (1968).
[CrossRef]

Other (1)

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941).

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Figures (6)

Fig. 1
Fig. 1

(a) Macroscopically homogeneous left-handed metamaterial can focus a light source located near a plane slab (1) and cannot focus a light coming from distant objects (2). (b) Slab of a metamaterial with gradient negative index of refraction (NGRIN in figure) which can focus a parallel beam of light.

Fig. 2
Fig. 2

(a) Slab of a homogeneous positive refractive material, (b) slab of homogeneous negative refractive material, (c) slab with a gradient of a positive refractive material [given by Eq. (4)], (d) slab with an inverse gradient of positive refractive material, (e) slab with a gradient of negative refractive index material [given by Eq. (3)].

Fig. 3
Fig. 3

Solid curves, gradient negative index of refraction (NGRIN in figure) as a function of the distance from the optical axis of the lens r for three different focal lengths f. Dotted curve, gradient of the usual GRIN lens with the index of refraction given by Eq. (4); dashed curve, gradient of a positive index of refraction.

Fig. 4
Fig. 4

Profile of the diameters of the holes a as a function of the distance from the optical axis r for three given focal lengths f calculated with the complex effective dielectric permittivity of the film [Eqs. (8, 10)]. Refractive index at the optical axis is N = 1.12 , dielectric constant ϵ h = 1 , width of the slab is d = 0.4 .

Fig. 5
Fig. 5

Sketch of a thin metal film pierced by circular holes with decreasing radii. (a) Side view; (b) top view, where b is the distance between the centers of the holes and a is the diameter of the holes; (c) circular disc made of a thin metal film pierced with the holes having different diameters; this structure should focus a spatial 3D beam of light; (d) photonic crystal structure with varying distance between the rods.

Fig. 6
Fig. 6

Focusing of a plane electromagnetic wave by a structured metal film: 2D FDTD simulations of a paraxial light beam coming from a distant object (from the left side of the image) and passing through the structured metal film. The electric field is polarized in the y direction; the aperture of the lens is r m a x = 2 ; the refractive index of the film is n 0 = 50 + 300 i ; the thickness of the film is d = 0.1 ; the effective refractive index in the middle of the film, i.e., on the optical axis, is N = 1.12 . (a)–(c) The focal length is f = 0.2 , and the normalized wavelength is (a) λ = 0.2 , (b) λ = 0.25 , (c) λ = 0.3 . (d)–(f) The focal length is f = 0.5 , and the normalized wavelength is (d) λ = 0.2 , (e) λ = 0.25 , (f) λ = 0.3 .

Tables (1)

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Table 1 Diameters a of Equidistantly Spaced Holes Pierced in a Thin Metal Film for Three Focal Lengths f a

Equations (10)

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n ( r ) d + l = N d + f .
n ( r ) = N 1 d ( r 2 + f 2 f ) .
n ( r ) = N r 2 ( 2 d f ) .
n ( r ) = N r 2 ( 2 d f ) ;
ϵ e f f ( ω ) = 1 ω p 2 ω 2 ,
μ e f f ( ω ) = 1 η ω 2 ω 2 ω 0 2 + i ω Γ ,
ϵ e f f ( λ ) = π 2 b 2 ϵ h 8 a 2 ( 1 λ 2 4 a 2 ϵ h ) ,
n 2 = ϵ 2 + ϵ 2 + ϵ 2 ,
k 2 = ϵ 2 + ϵ 2 ϵ 2 .
ϵ e f f ( λ ) = π 2 b 2 ϵ h 8 a 2 ( 1 λ 2 4 a 2 ϵ h ( 1 + i λ λ d ) ) .

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