Abstract

Metamaterials composed of metal-dielectric nanostructures are engineered to have an effective refractive index less than unity at optical wavelengths. The effect of total external reflection is demonstrated when light from vacuum is incident onto these materials at an angle exceeding the critical angle defined by Snell’s law. Novel approaches are discussed to derive the effective index of refraction from the reflection and refraction properties of finite slabs. The effect of losses and dispersion are analyzed in the visible range of frequencies by consideration of the measured properties of silver. The differences among ultralow refractive-index metamaterials, photonic bandgap materials, and metals are discussed. Remarkably, a bandgap is not required to obtain total external reflection.

© 2003 Optical Society of America

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References

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  1. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton U. Press, Princeton, N.J., 1995).
  2. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
    [CrossRef] [PubMed]
  3. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
    [CrossRef] [PubMed]
  4. P. M. Valanju, R. M. Walser, and A. P. Valanju, “Wave refraction in negative-index media: always positive and very inhomogeneous,” Phys. Rev. Lett. 88, 187401 (2002).
    [CrossRef] [PubMed]
  5. N. Garcia and M. Nieto-Vesperinas, “Is there an experimental verification of a negative index of refraction yet?” Opt. Lett. 27, 885–887 (2002).
    [CrossRef]
  6. N. Garcia and M. Nieto-Vesperinas, “Left-handed materials do not make a perfect lens,” Phys. Rev. Lett. 88, 207403 (2002).
    [CrossRef] [PubMed]
  7. B. T. Schwartz and R. Piestun, “Total external reflection at optical wavelengths,” in Diffractive Optics and Micro-Optics, R. Magnusson, ed., Vol. 75 of OSA Trends in Optics and Photonics (Optical Society of America, Washington D.C., 2002), pp. 175–177.
  8. J. Brown, “Artificial dielectrics,” Prog. Dielectr. 2, 193–225 (1960).
  9. D. E. Aspnes, “Local-field effects and effective medium theory: a microscopic perspective,” Am. J. Phys. 50, 704–709 (1982).
    [CrossRef]
  10. D. Felbacq and G. Bouchitté, “Homogenization of a set of parallel fibres,” Waves Random Media 7, 245–256 (1997).
    [CrossRef]
  11. J. Brown, “Artificial dielectrics having refractive indices less than unity,” Proc. IEE 100C, 51–62 (1953).
  12. K. C. Gupta, “Narrow-beam antennas using an artificial dielectric medium with permittivity less than unity,” Electron. Lett. 7, 16–17 (1971).
    [CrossRef]
  13. S. Enoch, G. Tayeb, P. Sabouroux, N. Guerin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89, 213902 (2002).
    [CrossRef] [PubMed]
  14. N. Garcia, E. V. Ponizovskaya, and J. Q. Xiao, “Zero permittivity materials: band gaps at the visible,” Appl. Phys. Lett. 80, 1120–1122 (2002).
    [CrossRef]
  15. D. Sievenpiper, “High-impedance electromagnetic surfaces,” Ph.D. thesis (University of California at Los Angeles, Los Angeles, Calif., 1999).
  16. D. Attwood, Soft X-Rays and Extreme Ultraviolet Radiation: Principles and Applications (Cambridge U. Press, Cambridge, U.K., 1999).
  17. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Low frequency plasmons in thin-wire structures,” J. Phys.: Condens. Matter 10, 4785–4809 (1998).
  18. J. R. Reitz, F. J. Milford, and R. W. Christy, Foundations of Electromagnetic Theory, 4th ed. (Addison-Wesley, Reading, Mass., 1993).
  19. D. W. Lynch and W. R. Hunter, “Comments on the optical constants of metals and an introduction to the data for several metals,” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, San Diego, Calif., 1991), pp. 275–368.
  20. A. L. Pokrovsky and A. L. Efros, “Electrodynamics of metallic photonic crystals and the problem of left-handed materials,” Phys. Rev. Lett. 89, 093901 (2002).
    [CrossRef] [PubMed]
  21. R. M. Walser, A. P. Valanju, and P. M. Valanju, “Comment on ‘Extremely low frequency plasmons in metallic mesostructures’,” Phys. Rev. Lett. 87, 119701 (2001).
    [CrossRef]
  22. W. Rotman, “Plasma simulation by artificial dielectrics and parallel-plate media,” IRE Trans. Antennas Propag. AP10, 82–95 (1962).
    [CrossRef]
  23. Ansoft HFSS Version 8.0.25 (Ansoft Corporation, Pittsburgh, Pa., 2001).
  24. M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: refraction-like behavior in the vicinity of the photonic bandgap,” Phys. Rev. B 62, 10696 (2000).
    [CrossRef]
  25. D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65, 195104 (2002).
    [CrossRef]
  26. O. Acher, A. L. Adenot, and F. Duverger, “Fresnel coefficients at an interface with a lamellar composite material,” Phys. Rev. B 62, 13748–13756 (2000).
    [CrossRef]
  27. Femlab Version 2.30.145 (Comsol Corporation, Burlington, Mass., 2002).
  28. G. Guida, D. Maystre, G. Tayeb, and P. Vincent, “Mean-field theory of two-dimensional metallic photonic crystals,” J. Opt. Soc. Am. B 15, 2308–2315 (1998).
    [CrossRef]
  29. P. M. Bell, J. B. Pendry, L. M. Moreno, and A. J. Ward, “A program for calculating photonic band structures and transmission coefficients of complex structures,” Comput. Phys. Commun. 85, 306–322 (1995).
    [CrossRef]
  30. A. L. Reynolds, Translight Software (Optoelectronics Research Group, Dept. of Electronics and Electrical Engineering, Univ. of Glasgow, Glasgow, Scotland, 2000).

2002 (7)

N. Garcia and M. Nieto-Vesperinas, “Left-handed materials do not make a perfect lens,” Phys. Rev. Lett. 88, 207403 (2002).
[CrossRef] [PubMed]

S. Enoch, G. Tayeb, P. Sabouroux, N. Guerin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89, 213902 (2002).
[CrossRef] [PubMed]

N. Garcia, E. V. Ponizovskaya, and J. Q. Xiao, “Zero permittivity materials: band gaps at the visible,” Appl. Phys. Lett. 80, 1120–1122 (2002).
[CrossRef]

A. L. Pokrovsky and A. L. Efros, “Electrodynamics of metallic photonic crystals and the problem of left-handed materials,” Phys. Rev. Lett. 89, 093901 (2002).
[CrossRef] [PubMed]

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65, 195104 (2002).
[CrossRef]

P. M. Valanju, R. M. Walser, and A. P. Valanju, “Wave refraction in negative-index media: always positive and very inhomogeneous,” Phys. Rev. Lett. 88, 187401 (2002).
[CrossRef] [PubMed]

N. Garcia and M. Nieto-Vesperinas, “Is there an experimental verification of a negative index of refraction yet?” Opt. Lett. 27, 885–887 (2002).
[CrossRef]

2001 (2)

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
[CrossRef] [PubMed]

R. M. Walser, A. P. Valanju, and P. M. Valanju, “Comment on ‘Extremely low frequency plasmons in metallic mesostructures’,” Phys. Rev. Lett. 87, 119701 (2001).
[CrossRef]

2000 (3)

O. Acher, A. L. Adenot, and F. Duverger, “Fresnel coefficients at an interface with a lamellar composite material,” Phys. Rev. B 62, 13748–13756 (2000).
[CrossRef]

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

M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: refraction-like behavior in the vicinity of the photonic bandgap,” Phys. Rev. B 62, 10696 (2000).
[CrossRef]

1998 (2)

G. Guida, D. Maystre, G. Tayeb, and P. Vincent, “Mean-field theory of two-dimensional metallic photonic crystals,” J. Opt. Soc. Am. B 15, 2308–2315 (1998).
[CrossRef]

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Low frequency plasmons in thin-wire structures,” J. Phys.: Condens. Matter 10, 4785–4809 (1998).

1997 (1)

D. Felbacq and G. Bouchitté, “Homogenization of a set of parallel fibres,” Waves Random Media 7, 245–256 (1997).
[CrossRef]

1995 (1)

P. M. Bell, J. B. Pendry, L. M. Moreno, and A. J. Ward, “A program for calculating photonic band structures and transmission coefficients of complex structures,” Comput. Phys. Commun. 85, 306–322 (1995).
[CrossRef]

1982 (1)

D. E. Aspnes, “Local-field effects and effective medium theory: a microscopic perspective,” Am. J. Phys. 50, 704–709 (1982).
[CrossRef]

1971 (1)

K. C. Gupta, “Narrow-beam antennas using an artificial dielectric medium with permittivity less than unity,” Electron. Lett. 7, 16–17 (1971).
[CrossRef]

1962 (1)

W. Rotman, “Plasma simulation by artificial dielectrics and parallel-plate media,” IRE Trans. Antennas Propag. AP10, 82–95 (1962).
[CrossRef]

1960 (1)

J. Brown, “Artificial dielectrics,” Prog. Dielectr. 2, 193–225 (1960).

1953 (1)

J. Brown, “Artificial dielectrics having refractive indices less than unity,” Proc. IEE 100C, 51–62 (1953).

Acher, O.

O. Acher, A. L. Adenot, and F. Duverger, “Fresnel coefficients at an interface with a lamellar composite material,” Phys. Rev. B 62, 13748–13756 (2000).
[CrossRef]

Adenot, A. L.

O. Acher, A. L. Adenot, and F. Duverger, “Fresnel coefficients at an interface with a lamellar composite material,” Phys. Rev. B 62, 13748–13756 (2000).
[CrossRef]

Aspnes, D. E.

D. E. Aspnes, “Local-field effects and effective medium theory: a microscopic perspective,” Am. J. Phys. 50, 704–709 (1982).
[CrossRef]

Bell, P. M.

P. M. Bell, J. B. Pendry, L. M. Moreno, and A. J. Ward, “A program for calculating photonic band structures and transmission coefficients of complex structures,” Comput. Phys. Commun. 85, 306–322 (1995).
[CrossRef]

Bouchitté, G.

D. Felbacq and G. Bouchitté, “Homogenization of a set of parallel fibres,” Waves Random Media 7, 245–256 (1997).
[CrossRef]

Brown, J.

J. Brown, “Artificial dielectrics,” Prog. Dielectr. 2, 193–225 (1960).

J. Brown, “Artificial dielectrics having refractive indices less than unity,” Proc. IEE 100C, 51–62 (1953).

Duverger, F.

O. Acher, A. L. Adenot, and F. Duverger, “Fresnel coefficients at an interface with a lamellar composite material,” Phys. Rev. B 62, 13748–13756 (2000).
[CrossRef]

Efros, A. L.

A. L. Pokrovsky and A. L. Efros, “Electrodynamics of metallic photonic crystals and the problem of left-handed materials,” Phys. Rev. Lett. 89, 093901 (2002).
[CrossRef] [PubMed]

Enoch, S.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guerin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89, 213902 (2002).
[CrossRef] [PubMed]

Felbacq, D.

D. Felbacq and G. Bouchitté, “Homogenization of a set of parallel fibres,” Waves Random Media 7, 245–256 (1997).
[CrossRef]

Garcia, N.

N. Garcia, E. V. Ponizovskaya, and J. Q. Xiao, “Zero permittivity materials: band gaps at the visible,” Appl. Phys. Lett. 80, 1120–1122 (2002).
[CrossRef]

N. Garcia and M. Nieto-Vesperinas, “Left-handed materials do not make a perfect lens,” Phys. Rev. Lett. 88, 207403 (2002).
[CrossRef] [PubMed]

N. Garcia and M. Nieto-Vesperinas, “Is there an experimental verification of a negative index of refraction yet?” Opt. Lett. 27, 885–887 (2002).
[CrossRef]

Guerin, N.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guerin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89, 213902 (2002).
[CrossRef] [PubMed]

Guida, G.

Gupta, K. C.

K. C. Gupta, “Narrow-beam antennas using an artificial dielectric medium with permittivity less than unity,” Electron. Lett. 7, 16–17 (1971).
[CrossRef]

Holden, A. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Low frequency plasmons in thin-wire structures,” J. Phys.: Condens. Matter 10, 4785–4809 (1998).

Markos, P.

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65, 195104 (2002).
[CrossRef]

Maystre, D.

Moreno, L. M.

P. M. Bell, J. B. Pendry, L. M. Moreno, and A. J. Ward, “A program for calculating photonic band structures and transmission coefficients of complex structures,” Comput. Phys. Commun. 85, 306–322 (1995).
[CrossRef]

Nieto-Vesperinas, M.

N. Garcia and M. Nieto-Vesperinas, “Is there an experimental verification of a negative index of refraction yet?” Opt. Lett. 27, 885–887 (2002).
[CrossRef]

N. Garcia and M. Nieto-Vesperinas, “Left-handed materials do not make a perfect lens,” Phys. Rev. Lett. 88, 207403 (2002).
[CrossRef] [PubMed]

Notomi, M.

M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: refraction-like behavior in the vicinity of the photonic bandgap,” Phys. Rev. B 62, 10696 (2000).
[CrossRef]

Pendry, J. B.

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

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Low frequency plasmons in thin-wire structures,” J. Phys.: Condens. Matter 10, 4785–4809 (1998).

P. M. Bell, J. B. Pendry, L. M. Moreno, and A. J. Ward, “A program for calculating photonic band structures and transmission coefficients of complex structures,” Comput. Phys. Commun. 85, 306–322 (1995).
[CrossRef]

Pokrovsky, A. L.

A. L. Pokrovsky and A. L. Efros, “Electrodynamics of metallic photonic crystals and the problem of left-handed materials,” Phys. Rev. Lett. 89, 093901 (2002).
[CrossRef] [PubMed]

Ponizovskaya, E. V.

N. Garcia, E. V. Ponizovskaya, and J. Q. Xiao, “Zero permittivity materials: band gaps at the visible,” Appl. Phys. Lett. 80, 1120–1122 (2002).
[CrossRef]

Robbins, D. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Low frequency plasmons in thin-wire structures,” J. Phys.: Condens. Matter 10, 4785–4809 (1998).

Rotman, W.

W. Rotman, “Plasma simulation by artificial dielectrics and parallel-plate media,” IRE Trans. Antennas Propag. AP10, 82–95 (1962).
[CrossRef]

Sabouroux, P.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guerin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89, 213902 (2002).
[CrossRef] [PubMed]

Schultz, S.

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65, 195104 (2002).
[CrossRef]

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
[CrossRef] [PubMed]

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, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65, 195104 (2002).
[CrossRef]

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.

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65, 195104 (2002).
[CrossRef]

Stewart, W. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Low frequency plasmons in thin-wire structures,” J. Phys.: Condens. Matter 10, 4785–4809 (1998).

Tayeb, G.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guerin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89, 213902 (2002).
[CrossRef] [PubMed]

G. Guida, D. Maystre, G. Tayeb, and P. Vincent, “Mean-field theory of two-dimensional metallic photonic crystals,” J. Opt. Soc. Am. B 15, 2308–2315 (1998).
[CrossRef]

Valanju, A. P.

P. M. Valanju, R. M. Walser, and A. P. Valanju, “Wave refraction in negative-index media: always positive and very inhomogeneous,” Phys. Rev. Lett. 88, 187401 (2002).
[CrossRef] [PubMed]

R. M. Walser, A. P. Valanju, and P. M. Valanju, “Comment on ‘Extremely low frequency plasmons in metallic mesostructures’,” Phys. Rev. Lett. 87, 119701 (2001).
[CrossRef]

Valanju, P. M.

P. M. Valanju, R. M. Walser, and A. P. Valanju, “Wave refraction in negative-index media: always positive and very inhomogeneous,” Phys. Rev. Lett. 88, 187401 (2002).
[CrossRef] [PubMed]

R. M. Walser, A. P. Valanju, and P. M. Valanju, “Comment on ‘Extremely low frequency plasmons in metallic mesostructures’,” Phys. Rev. Lett. 87, 119701 (2001).
[CrossRef]

Vincent, P.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guerin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89, 213902 (2002).
[CrossRef] [PubMed]

G. Guida, D. Maystre, G. Tayeb, and P. Vincent, “Mean-field theory of two-dimensional metallic photonic crystals,” J. Opt. Soc. Am. B 15, 2308–2315 (1998).
[CrossRef]

Walser, R. M.

P. M. Valanju, R. M. Walser, and A. P. Valanju, “Wave refraction in negative-index media: always positive and very inhomogeneous,” Phys. Rev. Lett. 88, 187401 (2002).
[CrossRef] [PubMed]

R. M. Walser, A. P. Valanju, and P. M. Valanju, “Comment on ‘Extremely low frequency plasmons in metallic mesostructures’,” Phys. Rev. Lett. 87, 119701 (2001).
[CrossRef]

Ward, A. J.

P. M. Bell, J. B. Pendry, L. M. Moreno, and A. J. Ward, “A program for calculating photonic band structures and transmission coefficients of complex structures,” Comput. Phys. Commun. 85, 306–322 (1995).
[CrossRef]

Xiao, J. Q.

N. Garcia, E. V. Ponizovskaya, and J. Q. Xiao, “Zero permittivity materials: band gaps at the visible,” Appl. Phys. Lett. 80, 1120–1122 (2002).
[CrossRef]

Am. J. Phys. (1)

D. E. Aspnes, “Local-field effects and effective medium theory: a microscopic perspective,” Am. J. Phys. 50, 704–709 (1982).
[CrossRef]

Appl. Phys. Lett. (1)

N. Garcia, E. V. Ponizovskaya, and J. Q. Xiao, “Zero permittivity materials: band gaps at the visible,” Appl. Phys. Lett. 80, 1120–1122 (2002).
[CrossRef]

Comput. Phys. Commun. (1)

P. M. Bell, J. B. Pendry, L. M. Moreno, and A. J. Ward, “A program for calculating photonic band structures and transmission coefficients of complex structures,” Comput. Phys. Commun. 85, 306–322 (1995).
[CrossRef]

Electron. Lett. (1)

K. C. Gupta, “Narrow-beam antennas using an artificial dielectric medium with permittivity less than unity,” Electron. Lett. 7, 16–17 (1971).
[CrossRef]

IRE Trans. Antennas Propag. (1)

W. Rotman, “Plasma simulation by artificial dielectrics and parallel-plate media,” IRE Trans. Antennas Propag. AP10, 82–95 (1962).
[CrossRef]

J. Opt. Soc. Am. B (1)

J. Phys.: Condens. Matter (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Low frequency plasmons in thin-wire structures,” J. Phys.: Condens. Matter 10, 4785–4809 (1998).

Opt. Lett. (1)

Phys. Rev. B (3)

M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: refraction-like behavior in the vicinity of the photonic bandgap,” Phys. Rev. B 62, 10696 (2000).
[CrossRef]

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65, 195104 (2002).
[CrossRef]

O. Acher, A. L. Adenot, and F. Duverger, “Fresnel coefficients at an interface with a lamellar composite material,” Phys. Rev. B 62, 13748–13756 (2000).
[CrossRef]

Phys. Rev. Lett. (6)

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

P. M. Valanju, R. M. Walser, and A. P. Valanju, “Wave refraction in negative-index media: always positive and very inhomogeneous,” Phys. Rev. Lett. 88, 187401 (2002).
[CrossRef] [PubMed]

A. L. Pokrovsky and A. L. Efros, “Electrodynamics of metallic photonic crystals and the problem of left-handed materials,” Phys. Rev. Lett. 89, 093901 (2002).
[CrossRef] [PubMed]

R. M. Walser, A. P. Valanju, and P. M. Valanju, “Comment on ‘Extremely low frequency plasmons in metallic mesostructures’,” Phys. Rev. Lett. 87, 119701 (2001).
[CrossRef]

S. Enoch, G. Tayeb, P. Sabouroux, N. Guerin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89, 213902 (2002).
[CrossRef] [PubMed]

N. Garcia and M. Nieto-Vesperinas, “Left-handed materials do not make a perfect lens,” Phys. Rev. Lett. 88, 207403 (2002).
[CrossRef] [PubMed]

Proc. IEE (1)

J. Brown, “Artificial dielectrics having refractive indices less than unity,” Proc. IEE 100C, 51–62 (1953).

Prog. Dielectr. (1)

J. Brown, “Artificial dielectrics,” Prog. Dielectr. 2, 193–225 (1960).

Science (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]

Waves Random Media (1)

D. Felbacq and G. Bouchitté, “Homogenization of a set of parallel fibres,” Waves Random Media 7, 245–256 (1997).
[CrossRef]

Other (9)

B. T. Schwartz and R. Piestun, “Total external reflection at optical wavelengths,” in Diffractive Optics and Micro-Optics, R. Magnusson, ed., Vol. 75 of OSA Trends in Optics and Photonics (Optical Society of America, Washington D.C., 2002), pp. 175–177.

Ansoft HFSS Version 8.0.25 (Ansoft Corporation, Pittsburgh, Pa., 2001).

J. R. Reitz, F. J. Milford, and R. W. Christy, Foundations of Electromagnetic Theory, 4th ed. (Addison-Wesley, Reading, Mass., 1993).

D. W. Lynch and W. R. Hunter, “Comments on the optical constants of metals and an introduction to the data for several metals,” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, San Diego, Calif., 1991), pp. 275–368.

D. Sievenpiper, “High-impedance electromagnetic surfaces,” Ph.D. thesis (University of California at Los Angeles, Los Angeles, Calif., 1999).

D. Attwood, Soft X-Rays and Extreme Ultraviolet Radiation: Principles and Applications (Cambridge U. Press, Cambridge, U.K., 1999).

A. L. Reynolds, Translight Software (Optoelectronics Research Group, Dept. of Electronics and Electrical Engineering, Univ. of Glasgow, Glasgow, Scotland, 2000).

Femlab Version 2.30.145 (Comsol Corporation, Burlington, Mass., 2002).

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton U. Press, Princeton, N.J., 1995).

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Figures (8)

Fig. 1
Fig. 1

Refraction and reflection at the interface of air and a two-dimensional metamaterial with ultralow effective refractive index. Light is refracted off the normal to the surface, and the refracted waves are inhomogeneous. In the specific design the metamaterial is composed of a square array of cylindrical wires, and the incident light is polarized parallel to the wires.

Fig. 2
Fig. 2

Experimental values and best-fit Drude model predictions (νPAg=1174.8 THz,γAg=205.2 THz) for the refractive index of silver for wavelengths between 0.45 and 1.6 μm.

Fig. 3
Fig. 3

Square root of the effective relative dielectric constant [Eq. (1)] of a silver–air metamaterial as a function of free-space wavelength. Wire radius, r=15 nm; unit-cell size, a=200 nm.

Fig. 4
Fig. 4

Dispersion diagram of a two-dimensional square array of silver wires. The wires have radius r=15 nm and are spaced 200 nm apart. The two straight lines are the dispersion curves of light in free space.

Fig. 5
Fig. 5

Electric field magnitude (parallel to the wires) of λ0=1.0 μm light normally incident on a silver–air metamaterial.

Fig. 6
Fig. 6

Refractive index (real and imaginary parts) of the metamaterial as a function of a free-space wavelength as predicted by its normal incidence refraction (finite-elements method) and angle-dependent reflectivity (TMM). Wire radius, r=15 nm; unit-cell size, a=200 nm.

Fig. 7
Fig. 7

TER: reflectivity at λ0=0.5 μm as a function of incident angle. Thick curve, TMM predictions for silver wire metamaterials. Thin curve, analytical calculations based on Fresnel formulas for homogeneous n=0.935+0.0038i slabs of the same thickness as the metamaterial. Wire radius, r=15 nm; unit-cell size, a=200 nm; homogeneous slab thickness d.

Fig. 8
Fig. 8

Transmission at λ0=0.5 μm as a function of incident angle. Thick curve, T-MM predictions for silver wire metamaterials. Thin curve, analytical calculations based on Fresnel formulas for homogeneous n=0.935+0.0038i slabs of the same thickness as the metamaterial. Wire radius, r=15 nm; unit-cell size, a=200 nm; homogeneous slab thickness d.

Equations (1)

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r=1-ωp2ω(ω+iγ),

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