Abstract

We present experimental and theoretical work showing that a flat metallic slab can collimate and focus light impinging on the slab from a point source. The effect is optimized when the radiation is around the bulk, not at the surface, plasma frequency. Also, the smaller the imaginary part of the permittivity is, the better the collimation. Experiments for Ag in the visible as well as calculations are presented. We also discuss the interesting case of Al, whose imaginary part of permittivity is very small at the plasma frequency in UV radiation. Generalization to other materials and radiations are also discussed.

© 2005 Optical Society of America

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References

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  1. V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968).
    [CrossRef]
  2. J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
    [CrossRef] [PubMed]
  3. N. Garcia and M. Nieto-Vesperinas, Phys. Rev. Lett. 88, 207403 (2002).
    [CrossRef]
  4. E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
    [CrossRef] [PubMed]
  5. S. John, Phys. Rev. Lett. 58, 2486 (1987).
    [CrossRef] [PubMed]
  6. M. Notomi. Phys. Rev. B 62, 10696 (2000).
    [CrossRef]
  7. N. Garcia, E. V. Ponizovskaya, and J. Q. Xiao, Appl. Phys. Lett. 80, 1120 (2002).
    [CrossRef]
  8. N. Garcia, E. V. Ponizovskaya, H. Zhu, J. Q. Xiao, and A. Pons, Appl. Phys. Lett. 82, 3147 (2003).
    [CrossRef]
  9. D. Garcia-Pablos, M. Sigalas, F. R.M. Espinosa, M. Torres, M. Kafesaki, and N. Garcia, Phys. Rev. Lett. 84, 4349 (2000).
    [CrossRef] [PubMed]
  10. M. Kafesaki, R. S. Penciu, and E. N. Economou, Phys. Rev. Lett. 84, 6050 (2000)
    [CrossRef] [PubMed]
  11. N. Garcia, M. Nieto-Vesperinas, E. V. Ponizovskaya, and M. Torres, Phys. Rev. E 67, 046606 (2003).
    [CrossRef]
  12. L. D. Landau and E. M. Lifschitz, Quantum Mechanics (Non-Relativistic Theory), 3rd ed. (Pergamon, 1977).
  13. P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972)
    [CrossRef]
  14. J. H. Weaver, C. Krafka, D. W. Lynch, and E. E. Koch, Physics Data (Fachinformationszentrum Energie, 1981).

2003 (2)

N. Garcia, E. V. Ponizovskaya, H. Zhu, J. Q. Xiao, and A. Pons, Appl. Phys. Lett. 82, 3147 (2003).
[CrossRef]

N. Garcia, M. Nieto-Vesperinas, E. V. Ponizovskaya, and M. Torres, Phys. Rev. E 67, 046606 (2003).
[CrossRef]

2002 (2)

N. Garcia, E. V. Ponizovskaya, and J. Q. Xiao, Appl. Phys. Lett. 80, 1120 (2002).
[CrossRef]

N. Garcia and M. Nieto-Vesperinas, Phys. Rev. Lett. 88, 207403 (2002).
[CrossRef]

2000 (4)

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef] [PubMed]

M. Notomi. Phys. Rev. B 62, 10696 (2000).
[CrossRef]

D. Garcia-Pablos, M. Sigalas, F. R.M. Espinosa, M. Torres, M. Kafesaki, and N. Garcia, Phys. Rev. Lett. 84, 4349 (2000).
[CrossRef] [PubMed]

M. Kafesaki, R. S. Penciu, and E. N. Economou, Phys. Rev. Lett. 84, 6050 (2000)
[CrossRef] [PubMed]

1987 (2)

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef] [PubMed]

S. John, Phys. Rev. Lett. 58, 2486 (1987).
[CrossRef] [PubMed]

1972 (1)

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972)
[CrossRef]

1968 (1)

V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

Christy, R. W.

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972)
[CrossRef]

Economou, E. N.

M. Kafesaki, R. S. Penciu, and E. N. Economou, Phys. Rev. Lett. 84, 6050 (2000)
[CrossRef] [PubMed]

Espinosa, F. R.M.

D. Garcia-Pablos, M. Sigalas, F. R.M. Espinosa, M. Torres, M. Kafesaki, and N. Garcia, Phys. Rev. Lett. 84, 4349 (2000).
[CrossRef] [PubMed]

Garcia, N.

N. Garcia, E. V. Ponizovskaya, H. Zhu, J. Q. Xiao, and A. Pons, Appl. Phys. Lett. 82, 3147 (2003).
[CrossRef]

N. Garcia, M. Nieto-Vesperinas, E. V. Ponizovskaya, and M. Torres, Phys. Rev. E 67, 046606 (2003).
[CrossRef]

N. Garcia and M. Nieto-Vesperinas, Phys. Rev. Lett. 88, 207403 (2002).
[CrossRef]

N. Garcia, E. V. Ponizovskaya, and J. Q. Xiao, Appl. Phys. Lett. 80, 1120 (2002).
[CrossRef]

D. Garcia-Pablos, M. Sigalas, F. R.M. Espinosa, M. Torres, M. Kafesaki, and N. Garcia, Phys. Rev. Lett. 84, 4349 (2000).
[CrossRef] [PubMed]

Garcia-Pablos, D.

D. Garcia-Pablos, M. Sigalas, F. R.M. Espinosa, M. Torres, M. Kafesaki, and N. Garcia, Phys. Rev. Lett. 84, 4349 (2000).
[CrossRef] [PubMed]

John, S.

S. John, Phys. Rev. Lett. 58, 2486 (1987).
[CrossRef] [PubMed]

Johnson, P. B.

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972)
[CrossRef]

Kafesaki, M.

D. Garcia-Pablos, M. Sigalas, F. R.M. Espinosa, M. Torres, M. Kafesaki, and N. Garcia, Phys. Rev. Lett. 84, 4349 (2000).
[CrossRef] [PubMed]

M. Kafesaki, R. S. Penciu, and E. N. Economou, Phys. Rev. Lett. 84, 6050 (2000)
[CrossRef] [PubMed]

Koch, E. E.

J. H. Weaver, C. Krafka, D. W. Lynch, and E. E. Koch, Physics Data (Fachinformationszentrum Energie, 1981).

Krafka, C.

J. H. Weaver, C. Krafka, D. W. Lynch, and E. E. Koch, Physics Data (Fachinformationszentrum Energie, 1981).

Landau, L. D.

L. D. Landau and E. M. Lifschitz, Quantum Mechanics (Non-Relativistic Theory), 3rd ed. (Pergamon, 1977).

Lifschitz, E. M.

L. D. Landau and E. M. Lifschitz, Quantum Mechanics (Non-Relativistic Theory), 3rd ed. (Pergamon, 1977).

Lynch, D. W.

J. H. Weaver, C. Krafka, D. W. Lynch, and E. E. Koch, Physics Data (Fachinformationszentrum Energie, 1981).

Nieto-Vesperinas, M.

N. Garcia, M. Nieto-Vesperinas, E. V. Ponizovskaya, and M. Torres, Phys. Rev. E 67, 046606 (2003).
[CrossRef]

N. Garcia and M. Nieto-Vesperinas, Phys. Rev. Lett. 88, 207403 (2002).
[CrossRef]

Notomi, M.

M. Notomi. Phys. Rev. B 62, 10696 (2000).
[CrossRef]

Penciu, R. S.

M. Kafesaki, R. S. Penciu, and E. N. Economou, Phys. Rev. Lett. 84, 6050 (2000)
[CrossRef] [PubMed]

Pendry, J. B.

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef] [PubMed]

Ponizovskaya, E. V.

N. Garcia, E. V. Ponizovskaya, H. Zhu, J. Q. Xiao, and A. Pons, Appl. Phys. Lett. 82, 3147 (2003).
[CrossRef]

N. Garcia, M. Nieto-Vesperinas, E. V. Ponizovskaya, and M. Torres, Phys. Rev. E 67, 046606 (2003).
[CrossRef]

N. Garcia, E. V. Ponizovskaya, and J. Q. Xiao, Appl. Phys. Lett. 80, 1120 (2002).
[CrossRef]

Pons, A.

N. Garcia, E. V. Ponizovskaya, H. Zhu, J. Q. Xiao, and A. Pons, Appl. Phys. Lett. 82, 3147 (2003).
[CrossRef]

Sigalas, M.

D. Garcia-Pablos, M. Sigalas, F. R.M. Espinosa, M. Torres, M. Kafesaki, and N. Garcia, Phys. Rev. Lett. 84, 4349 (2000).
[CrossRef] [PubMed]

Torres, M.

N. Garcia, M. Nieto-Vesperinas, E. V. Ponizovskaya, and M. Torres, Phys. Rev. E 67, 046606 (2003).
[CrossRef]

D. Garcia-Pablos, M. Sigalas, F. R.M. Espinosa, M. Torres, M. Kafesaki, and N. Garcia, Phys. Rev. Lett. 84, 4349 (2000).
[CrossRef] [PubMed]

Veselago, V. G.

V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

Weaver, J. H.

J. H. Weaver, C. Krafka, D. W. Lynch, and E. E. Koch, Physics Data (Fachinformationszentrum Energie, 1981).

Xiao, J. Q.

N. Garcia, E. V. Ponizovskaya, H. Zhu, J. Q. Xiao, and A. Pons, Appl. Phys. Lett. 82, 3147 (2003).
[CrossRef]

N. Garcia, E. V. Ponizovskaya, and J. Q. Xiao, Appl. Phys. Lett. 80, 1120 (2002).
[CrossRef]

Yablonovitch, E.

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef] [PubMed]

Zhu, H.

N. Garcia, E. V. Ponizovskaya, H. Zhu, J. Q. Xiao, and A. Pons, Appl. Phys. Lett. 82, 3147 (2003).
[CrossRef]

Appl. Phys. Lett. (2)

N. Garcia, E. V. Ponizovskaya, and J. Q. Xiao, Appl. Phys. Lett. 80, 1120 (2002).
[CrossRef]

N. Garcia, E. V. Ponizovskaya, H. Zhu, J. Q. Xiao, and A. Pons, Appl. Phys. Lett. 82, 3147 (2003).
[CrossRef]

Phys. Rev. B (2)

M. Notomi. Phys. Rev. B 62, 10696 (2000).
[CrossRef]

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972)
[CrossRef]

Phys. Rev. E (1)

N. Garcia, M. Nieto-Vesperinas, E. V. Ponizovskaya, and M. Torres, Phys. Rev. E 67, 046606 (2003).
[CrossRef]

Phys. Rev. Lett. (6)

D. Garcia-Pablos, M. Sigalas, F. R.M. Espinosa, M. Torres, M. Kafesaki, and N. Garcia, Phys. Rev. Lett. 84, 4349 (2000).
[CrossRef] [PubMed]

M. Kafesaki, R. S. Penciu, and E. N. Economou, Phys. Rev. Lett. 84, 6050 (2000)
[CrossRef] [PubMed]

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef] [PubMed]

N. Garcia and M. Nieto-Vesperinas, Phys. Rev. Lett. 88, 207403 (2002).
[CrossRef]

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef] [PubMed]

S. John, Phys. Rev. Lett. 58, 2486 (1987).
[CrossRef] [PubMed]

Sov. Phys. Usp. (1)

V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

Other (2)

L. D. Landau and E. M. Lifschitz, Quantum Mechanics (Non-Relativistic Theory), 3rd ed. (Pergamon, 1977).

J. H. Weaver, C. Krafka, D. W. Lynch, and E. E. Koch, Physics Data (Fachinformationszentrum Energie, 1981).

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Figures (3)

Fig. 1
Fig. 1

(a) Scattering geometry with the energy-dependent optical potential of Eq. (1). with incident frequency ω = c k 0 2 . (b) Experimental scheme for measuring the angular distribution of the transmitted intensity from a metal film with a PMT detector. Ag film was deposited on a glass subtrate. An s-polarized laser beam was focused onto one side of the sample slab by a cylinder lens to produce a point source.

Fig. 2
Fig. 2

Angular transmission distribution versus outgoing angle through a 150 nm Ag film deposited on a 0.15 mm thick glass substrate. (a) Experimental transmission with incident lasers at 633, 488, and 325 nm. The dashed horizontal line shows the angular distribution for the incident intensity of the point source. (b) Calculated transmission with incident lasers from 633 to 280 nm in wavelength. For comparison, the result of a 250 nm thick Ag film for a 325 nm (plasma frequency) laser is also presented (open circles). Inset, corresponding transmission intensity and Ag optical constant versus wavelength for the Ag film. (c) Simulation of the collimation effect of a 150 nm Ag film at its plasma frequency (3.8 eV, 325 nm). The intensity distribution was log scaled. Notice the higher intensity near the surface in front of the source.

Fig. 3
Fig. 3

Calculated angular transmission distribution versus the outgoing angle through a 150 nm Al thin film, with incident laser wavelengths ranging from 633 to 75 nm. For 75 nm, above the plasma frequency (83 nm), the angular spread is wider than 83 nm, because the wave does not tunnel but propagates in the film. Inset, corresponding transmission intensity and Al optical constant versus wavelength.

Equations (2)

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V = k 0 2 ( ϵ 1 ) ,
sin θ m = ( sin θ ) ϵ ,

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