Abstract

We show that recent claims of experimental verification of a negative index of refraction in metallic metamaterials, “left-handed” microwave frequencies, are questionable. At these frequencies the imaginary part of the dielectric permittivity is significant or even dominates its real part, and hence the effective medium behaves as a metal, i.e., with losses below the cutoff frequency of relevance. Then, the refractive index is complex, and there is not a distinction between right- and left-handed material because the electromagnetic wave is inhomogeneous. Just by using this idea we explain the transmittivities that were recently obtained in experiments by Shelby et al. [Science 292, 77 (2001) and Appl. Phys. Lett. 78, 489 (2001)].

© 2002 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968).
    [CrossRef]
  2. R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
    [CrossRef] [PubMed]
  3. L. D. Landau and E. M. Lifshitz, Electrodinámica de los Medios Continuos (Editorial Reverté, Barcelona, Spain, 1981).
  4. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, England, 1999).
    [CrossRef]
  5. J. D. Jackson, Electrodinámica Clasica (Editorial Alhambra, Madrid, Spain, 1980).
  6. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Ref. Lett. 84, 4184 (2000).
    [CrossRef]
  7. R. A. Shelby, D. R. Smith, S. C. Nemat-Nasser, and S. Schultz, Appl. Phys. Lett. 78, 489 (2001).
    [CrossRef]
  8. N. Garcia and E. V. Ponizowskaya are preparing a manuscript to be called “Determination of effective permittivity from finite-difference time-domain calculations.”
  9. N. Garcia and M. Nieto-Vesperinas “Left-handed materials do not make a perfect lens,” Phys. Rev. Lett. (to be published).

2001 (2)

R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
[CrossRef] [PubMed]

R. A. Shelby, D. R. Smith, S. C. Nemat-Nasser, and S. Schultz, Appl. Phys. Lett. 78, 489 (2001).
[CrossRef]

2000 (1)

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Ref. Lett. 84, 4184 (2000).
[CrossRef]

1968 (1)

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

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, England, 1999).
[CrossRef]

Garcia, N.

N. Garcia and E. V. Ponizowskaya are preparing a manuscript to be called “Determination of effective permittivity from finite-difference time-domain calculations.”

N. Garcia and M. Nieto-Vesperinas “Left-handed materials do not make a perfect lens,” Phys. Rev. Lett. (to be published).

Jackson, J. D.

J. D. Jackson, Electrodinámica Clasica (Editorial Alhambra, Madrid, Spain, 1980).

Landau, L. D.

L. D. Landau and E. M. Lifshitz, Electrodinámica de los Medios Continuos (Editorial Reverté, Barcelona, Spain, 1981).

Lifshitz, E. M.

L. D. Landau and E. M. Lifshitz, Electrodinámica de los Medios Continuos (Editorial Reverté, Barcelona, Spain, 1981).

Nemat-Nasser, S. C.

R. A. Shelby, D. R. Smith, S. C. Nemat-Nasser, and S. Schultz, Appl. Phys. Lett. 78, 489 (2001).
[CrossRef]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Ref. Lett. 84, 4184 (2000).
[CrossRef]

Nieto-Vesperinas, M.

N. Garcia and M. Nieto-Vesperinas “Left-handed materials do not make a perfect lens,” Phys. Rev. Lett. (to be published).

Padilla, W. J.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Ref. Lett. 84, 4184 (2000).
[CrossRef]

Ponizowskaya, E. V.

N. Garcia and E. V. Ponizowskaya are preparing a manuscript to be called “Determination of effective permittivity from finite-difference time-domain calculations.”

Schultz, S.

R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
[CrossRef] [PubMed]

R. A. Shelby, D. R. Smith, S. C. Nemat-Nasser, and S. Schultz, Appl. Phys. Lett. 78, 489 (2001).
[CrossRef]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Ref. Lett. 84, 4184 (2000).
[CrossRef]

Shelby, R. A.

R. A. Shelby, D. R. Smith, S. C. Nemat-Nasser, and S. Schultz, Appl. Phys. Lett. 78, 489 (2001).
[CrossRef]

R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
[CrossRef] [PubMed]

Smith, D. R.

R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
[CrossRef] [PubMed]

R. A. Shelby, D. R. Smith, S. C. Nemat-Nasser, and S. Schultz, Appl. Phys. Lett. 78, 489 (2001).
[CrossRef]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Ref. Lett. 84, 4184 (2000).
[CrossRef]

Veselago, V. G.

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

Vier, D. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Ref. Lett. 84, 4184 (2000).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, England, 1999).
[CrossRef]

Appl. Phys. Lett. (1)

R. A. Shelby, D. R. Smith, S. C. Nemat-Nasser, and S. Schultz, Appl. Phys. Lett. 78, 489 (2001).
[CrossRef]

Phys. Ref. Lett. (1)

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Ref. Lett. 84, 4184 (2000).
[CrossRef]

Science (1)

R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
[CrossRef] [PubMed]

Sov. Phys. Usp. (1)

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

Other (5)

N. Garcia and E. V. Ponizowskaya are preparing a manuscript to be called “Determination of effective permittivity from finite-difference time-domain calculations.”

N. Garcia and M. Nieto-Vesperinas “Left-handed materials do not make a perfect lens,” Phys. Rev. Lett. (to be published).

L. D. Landau and E. M. Lifshitz, Electrodinámica de los Medios Continuos (Editorial Reverté, Barcelona, Spain, 1981).

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, England, 1999).
[CrossRef]

J. D. Jackson, Electrodinámica Clasica (Editorial Alhambra, Madrid, Spain, 1980).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (2)

Fig. 1
Fig. 1

Plot of T for d=5,10,15 cm, using Eqs. (2), (3), (5), and (6). Notice that for left-handed region 1.03<f<1.095 the power T oscillates and is of the order of 1.

Fig. 2
Fig. 2

Top and middle panels, same as in Fig. 1 but with losses described in the text for fmp=1.05. Now we have only a peak near μt0. Bottom panel, transmitted intensity for the edged plate of Ref. 2 dx=5 cm+0.3x when the incident intensity is a sine function (solid curve) centered at 7.5 cm and a constant equal to 0.5 (dashed curve) for fmp=1.04. Notice that the intensity is pointing in the small values of x (negative angles in Ref. 2).

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

sin θt=ni sin θi/-nt,
εt=1-fep2-feo2/f2-feo2+iγf,
μt=1-fmp2-fmo2/f2-fmo2+iγf,
t=4qiqt/μtexp-iqidqi+qtμt2exp-iqtd-qi-qtμt2expiqtd,
T=4εt/μt4εt/μt+εt/μt-12 sin2qtd.
T=4εt/μt4εt/μt+εt/μt+12sinh2qtd.
T=4εtμt4εtμt+εtμt+12sin κd cosh κd2+cos κd sinh κd2,

Metrics