Abstract

We suggest, based on the principle of causality and for a material exhibiting adjacent absorptive and gain resonances, that there can be an intervening frequency where perfect imaging is in theory possible. At this frequency, both the dielectric constant and the permeability are negative, leading to a negative refractive index, and there is no loss. In such a material exhibiting a double resonance, the gain must be at the higher frequency. Through appropriate tuning of the refractive index, all propagating and evanescent fields from the object could then in principle be reconstructed at the image plane, subject to practical implementation limits.

© 2008 Optical Society of America

Full Article  |  PDF Article

Corrections

Kevin�J. Webb and Lars Thylén, "Perfect-lens-material condition from adjacent absorptive and gain resonances: erratum," Opt. Lett. 35, 1190-1190 (2010)
https://www.osapublishing.org/ol/abstract.cfm?uri=ol-35-8-1190

References

  • View by:
  • |
  • |
  • |

  1. V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968).
    [Crossref]
  2. J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
    [Crossref] [PubMed]
  3. D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, Appl. Phys. Lett. 82, 1056 (2003).
  4. K. J. Webb, M. Yang, D. W. Ward, and K. A. Nelson, Phys. Rev. E 70, 035602(R) (2004).
    [Crossref]
  5. M. Yang and K. J. Webb, Opt. Lett. 30, 2382 (2005).
    [Crossref] [PubMed]
  6. R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
    [Crossref] [PubMed]
  7. M. Stockman, Phys. Rev. Lett. 98, 177404 (2007).
    [Crossref]
  8. J. D. Jackson, Classical Electrodynamics (Wiley, 1999), 3rd ed.
  9. E. C. Titchmarsh, Introduction to the Theory of Fourier Integrals (Oxford U. Press, 1948).
  10. L. Brillouin, Wave Propagation and Group Velocity (Academic, 1960).
  11. A. Yariv, Quantum Electronics (Wiley, 1975), 2nd ed.

2007 (1)

M. Stockman, Phys. Rev. Lett. 98, 177404 (2007).
[Crossref]

2005 (1)

2004 (1)

K. J. Webb, M. Yang, D. W. Ward, and K. A. Nelson, Phys. Rev. E 70, 035602(R) (2004).
[Crossref]

2003 (1)

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, Appl. Phys. Lett. 82, 1056 (2003).

2001 (1)

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

2000 (1)

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

1999 (1)

J. D. Jackson, Classical Electrodynamics (Wiley, 1999), 3rd ed.

1975 (1)

A. Yariv, Quantum Electronics (Wiley, 1975), 2nd ed.

1968 (1)

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

1960 (1)

L. Brillouin, Wave Propagation and Group Velocity (Academic, 1960).

1948 (1)

E. C. Titchmarsh, Introduction to the Theory of Fourier Integrals (Oxford U. Press, 1948).

Brillouin, L.

L. Brillouin, Wave Propagation and Group Velocity (Academic, 1960).

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Wiley, 1999), 3rd ed.

Nelson, K. A.

K. J. Webb, M. Yang, D. W. Ward, and K. A. Nelson, Phys. Rev. E 70, 035602(R) (2004).
[Crossref]

Pendry, J. B.

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, Appl. Phys. Lett. 82, 1056 (2003).

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

Ramakrishna, S. A.

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, Appl. Phys. Lett. 82, 1056 (2003).

Rosenbluth, M.

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, Appl. Phys. Lett. 82, 1056 (2003).

Schultz, S.

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, Appl. Phys. Lett. 82, 1056 (2003).

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

Schurig, D.

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, Appl. Phys. Lett. 82, 1056 (2003).

Shelby, R. A.

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

Smith, D. R.

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, Appl. Phys. Lett. 82, 1056 (2003).

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

Stockman, M.

M. Stockman, Phys. Rev. Lett. 98, 177404 (2007).
[Crossref]

Titchmarsh, E. C.

E. C. Titchmarsh, Introduction to the Theory of Fourier Integrals (Oxford U. Press, 1948).

Veselago, V. G.

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

Ward, D. W.

K. J. Webb, M. Yang, D. W. Ward, and K. A. Nelson, Phys. Rev. E 70, 035602(R) (2004).
[Crossref]

Webb, K. J.

M. Yang and K. J. Webb, Opt. Lett. 30, 2382 (2005).
[Crossref] [PubMed]

K. J. Webb, M. Yang, D. W. Ward, and K. A. Nelson, Phys. Rev. E 70, 035602(R) (2004).
[Crossref]

Yang, M.

M. Yang and K. J. Webb, Opt. Lett. 30, 2382 (2005).
[Crossref] [PubMed]

K. J. Webb, M. Yang, D. W. Ward, and K. A. Nelson, Phys. Rev. E 70, 035602(R) (2004).
[Crossref]

Yariv, A.

A. Yariv, Quantum Electronics (Wiley, 1975), 2nd ed.

Appl. Phys. Lett. (1)

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, Appl. Phys. Lett. 82, 1056 (2003).

Opt. Lett. (1)

Phys. Rev. E (1)

K. J. Webb, M. Yang, D. W. Ward, and K. A. Nelson, Phys. Rev. E 70, 035602(R) (2004).
[Crossref]

Phys. Rev. Lett. (2)

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

M. Stockman, Phys. Rev. Lett. 98, 177404 (2007).
[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 (4)

J. D. Jackson, Classical Electrodynamics (Wiley, 1999), 3rd ed.

E. C. Titchmarsh, Introduction to the Theory of Fourier Integrals (Oxford U. Press, 1948).

L. Brillouin, Wave Propagation and Group Velocity (Academic, 1960).

A. Yariv, Quantum Electronics (Wiley, 1975), 2nd ed.

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

Susceptibilities χ = χ + i χ from Eqs. (7, 8), with ω 1 = 0.3 and ω 2 = 0.45 , for (a) a = ω 1 2 , giving a loss resonance at ω 1 and gain at ω 2 , and (b) a = ω 1 2 , producing gain at ω 1 and loss at ω 2 .

Fig. 2
Fig. 2

(a) Normalized frequency derivative of the wave number, or group index, using identical electric and magnetic susceptibilities given by χ in Fig. 1a. (b) Normalized group velocity corresponding to (a).

Equations (9)

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

ζ ( ω ) 1 = 2 π 0 ω ζ ( ω ) ω 2 ω 2 d ω ,
ζ ( ω ) = 2 ω π 0 ζ ( ω ) 1 ω 2 ω 2 d ω ,
χ ( ω ) = e 2 ϵ 0 m j Δ N j f j ω j 2 ω 2 i γ j ω ,
ω = ± 1 2 ( 4 ω j 2 γ j 2 ) i γ j 2 ,
χ = a 1 ω 1 2 ω 2 i ω γ 1 + a 2 ω 2 2 ω 2 i ω γ 2 .
ω = ω p = ± ω 1 2 + ω 2 2 2 .
χ ( ω p ) = 2 a ω 1 2 ω 2 2 .
χ ( ω ) a = ω 1 2 ω 2 ( ω 1 2 ω 2 ) 2 + ω 2 2 ( ω 2 ω 1 ) 2 ω 2 2 ω 2 ( ω 2 2 ω 2 ) 2 + ω 2 2 ( ω 2 ω 1 ) 2 ,
χ ( ω ) a = 1 2 [ ω ( ω 2 ω 1 ) ( ω 1 2 ω 2 ) 2 + ω 2 2 ( ω 2 ω 1 ) 2 ω ( ω 2 ω 1 ) ( ω 2 2 ω 2 ) 2 + ω 2 2 ( ω 2 ω 1 ) 2 ] .

Metrics