Abstract

In manufacturing left-handed media the interfaces will never be perfect; defects and other disturbances to interfaces and material parameters are unavoidable. We report an analytical calculation of electromagnetic wave propagation through a perfect lens with diffuse boundaries. Field localizations are generated in the boundary layers, and the lens’ ability to recover evanescent modes in the presence of these boundaries is analyzed and quantified. It is shown that such a diffuse layer produces an effect that is qualitatively similar to a lens with increased losses.

© 2009 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
    [CrossRef] [PubMed]
  2. A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, Phys. Rev. Lett. 99, 183901 (2007).
    [CrossRef] [PubMed]
  3. U. Leonhardt and T. Tyc, New J. Phys. 10, 115026 (2008).
    [CrossRef]
  4. K. L. Tsakmakidis, A. D. Boardman, and O. Hess, Nature 450, 397 (2007).
    [CrossRef] [PubMed]
  5. V. G. Veselago, Sov. Phys. Usp. 92, 517 (1968).
  6. J. B. Pendry, Phys. Rev. Lett. 85, 18 (2000).
    [CrossRef]
  7. J. B. Pendry, Phys. Rev. Lett. 87, 249702 (2001).
    [CrossRef]
  8. Z. Ruan, M. Yin, C. W. Neff, and M. Qin, Phys. Rev. Lett. 99, 113903 (2007).
    [CrossRef] [PubMed]
  9. O. E. French, K. I. Hopcraft, and E. Jakeman, New J. Phys. 8, 271 (2006).
    [CrossRef]
  10. O. E. French, K. I. Hopcraft, and E. Jakeman, New J. Phys. 9, 162 (2007).
    [CrossRef]
  11. P. C. Ingrey, K. I. Hopcraft, E. Jakeman, and O. French, Opt. Commun. 282, 5 (2009).
    [CrossRef]
  12. J. Lekner, Theory of Reflection (Martinus Nijhoff, 1987).
  13. N. M. Litchinitser, A. I. Maimistov, I. R. Gabitov, R. Z. Sagdeev, and V. M. Shalaev, Opt. Lett. 33, 2350 (2008).
    [CrossRef] [PubMed]
  14. M. Nieto-Vesperinas, J. Opt. Soc. Am. A 21, 491 (2003).
    [CrossRef]
  15. D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, Appl. Phys. Lett. 82, 1506 (2003).
    [CrossRef]

2009 (1)

P. C. Ingrey, K. I. Hopcraft, E. Jakeman, and O. French, Opt. Commun. 282, 5 (2009).
[CrossRef]

2008 (2)

2007 (4)

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, Nature 450, 397 (2007).
[CrossRef] [PubMed]

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, Phys. Rev. Lett. 99, 183901 (2007).
[CrossRef] [PubMed]

Z. Ruan, M. Yin, C. W. Neff, and M. Qin, Phys. Rev. Lett. 99, 113903 (2007).
[CrossRef] [PubMed]

O. E. French, K. I. Hopcraft, and E. Jakeman, New J. Phys. 9, 162 (2007).
[CrossRef]

2006 (2)

O. E. French, K. I. Hopcraft, and E. Jakeman, New J. Phys. 8, 271 (2006).
[CrossRef]

J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
[CrossRef] [PubMed]

2003 (2)

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, Appl. Phys. Lett. 82, 1506 (2003).
[CrossRef]

M. Nieto-Vesperinas, J. Opt. Soc. Am. A 21, 491 (2003).
[CrossRef]

2001 (1)

J. B. Pendry, Phys. Rev. Lett. 87, 249702 (2001).
[CrossRef]

2000 (1)

J. B. Pendry, Phys. Rev. Lett. 85, 18 (2000).
[CrossRef]

1968 (1)

V. G. Veselago, Sov. Phys. Usp. 92, 517 (1968).

Boardman, A. D.

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, Nature 450, 397 (2007).
[CrossRef] [PubMed]

French, O.

P. C. Ingrey, K. I. Hopcraft, E. Jakeman, and O. French, Opt. Commun. 282, 5 (2009).
[CrossRef]

French, O. E.

O. E. French, K. I. Hopcraft, and E. Jakeman, New J. Phys. 9, 162 (2007).
[CrossRef]

O. E. French, K. I. Hopcraft, and E. Jakeman, New J. Phys. 8, 271 (2006).
[CrossRef]

Gabitov, I. R.

Greenleaf, A.

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, Phys. Rev. Lett. 99, 183901 (2007).
[CrossRef] [PubMed]

Hess, O.

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, Nature 450, 397 (2007).
[CrossRef] [PubMed]

Hopcraft, K. I.

P. C. Ingrey, K. I. Hopcraft, E. Jakeman, and O. French, Opt. Commun. 282, 5 (2009).
[CrossRef]

O. E. French, K. I. Hopcraft, and E. Jakeman, New J. Phys. 9, 162 (2007).
[CrossRef]

O. E. French, K. I. Hopcraft, and E. Jakeman, New J. Phys. 8, 271 (2006).
[CrossRef]

Ingrey, P. C.

P. C. Ingrey, K. I. Hopcraft, E. Jakeman, and O. French, Opt. Commun. 282, 5 (2009).
[CrossRef]

Jakeman, E.

P. C. Ingrey, K. I. Hopcraft, E. Jakeman, and O. French, Opt. Commun. 282, 5 (2009).
[CrossRef]

O. E. French, K. I. Hopcraft, and E. Jakeman, New J. Phys. 9, 162 (2007).
[CrossRef]

O. E. French, K. I. Hopcraft, and E. Jakeman, New J. Phys. 8, 271 (2006).
[CrossRef]

Kurylev, Y.

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, Phys. Rev. Lett. 99, 183901 (2007).
[CrossRef] [PubMed]

Lassas, M.

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, Phys. Rev. Lett. 99, 183901 (2007).
[CrossRef] [PubMed]

Lekner, J.

J. Lekner, Theory of Reflection (Martinus Nijhoff, 1987).

Leonhardt, U.

U. Leonhardt and T. Tyc, New J. Phys. 10, 115026 (2008).
[CrossRef]

Litchinitser, N. M.

Maimistov, A. I.

Neff, C. W.

Z. Ruan, M. Yin, C. W. Neff, and M. Qin, Phys. Rev. Lett. 99, 113903 (2007).
[CrossRef] [PubMed]

Nieto-Vesperinas, M.

Pendry, J. B.

J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
[CrossRef] [PubMed]

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, Appl. Phys. Lett. 82, 1506 (2003).
[CrossRef]

J. B. Pendry, Phys. Rev. Lett. 87, 249702 (2001).
[CrossRef]

J. B. Pendry, Phys. Rev. Lett. 85, 18 (2000).
[CrossRef]

Qin, M.

Z. Ruan, M. Yin, C. W. Neff, and M. Qin, Phys. Rev. Lett. 99, 113903 (2007).
[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, 1506 (2003).
[CrossRef]

Rosenbluth, M.

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, Appl. Phys. Lett. 82, 1506 (2003).
[CrossRef]

Ruan, Z.

Z. Ruan, M. Yin, C. W. Neff, and M. Qin, Phys. Rev. Lett. 99, 113903 (2007).
[CrossRef] [PubMed]

Sagdeev, R. Z.

Schultz, S.

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, Appl. Phys. Lett. 82, 1506 (2003).
[CrossRef]

Schurig, D.

J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
[CrossRef] [PubMed]

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, Appl. Phys. Lett. 82, 1506 (2003).
[CrossRef]

Shalaev, V. M.

Smith, D. R.

J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
[CrossRef] [PubMed]

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, Appl. Phys. Lett. 82, 1506 (2003).
[CrossRef]

Tsakmakidis, K. L.

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, Nature 450, 397 (2007).
[CrossRef] [PubMed]

Tyc, T.

U. Leonhardt and T. Tyc, New J. Phys. 10, 115026 (2008).
[CrossRef]

Uhlmann, G.

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, Phys. Rev. Lett. 99, 183901 (2007).
[CrossRef] [PubMed]

Veselago, V. G.

V. G. Veselago, Sov. Phys. Usp. 92, 517 (1968).

Yin, M.

Z. Ruan, M. Yin, C. W. Neff, and M. Qin, Phys. Rev. Lett. 99, 113903 (2007).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, Appl. Phys. Lett. 82, 1506 (2003).
[CrossRef]

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

Nature (1)

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, Nature 450, 397 (2007).
[CrossRef] [PubMed]

New J. Phys. (3)

O. E. French, K. I. Hopcraft, and E. Jakeman, New J. Phys. 8, 271 (2006).
[CrossRef]

O. E. French, K. I. Hopcraft, and E. Jakeman, New J. Phys. 9, 162 (2007).
[CrossRef]

U. Leonhardt and T. Tyc, New J. Phys. 10, 115026 (2008).
[CrossRef]

Opt. Commun. (1)

P. C. Ingrey, K. I. Hopcraft, E. Jakeman, and O. French, Opt. Commun. 282, 5 (2009).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. Lett. (4)

J. B. Pendry, Phys. Rev. Lett. 85, 18 (2000).
[CrossRef]

J. B. Pendry, Phys. Rev. Lett. 87, 249702 (2001).
[CrossRef]

Z. Ruan, M. Yin, C. W. Neff, and M. Qin, Phys. Rev. Lett. 99, 113903 (2007).
[CrossRef] [PubMed]

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, Phys. Rev. Lett. 99, 183901 (2007).
[CrossRef] [PubMed]

Science (1)

J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
[CrossRef] [PubMed]

Sov. Phys. Usp. (1)

V. G. Veselago, Sov. Phys. Usp. 92, 517 (1968).

Other (1)

J. Lekner, Theory of Reflection (Martinus Nijhoff, 1987).

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 (4)

Fig. 1
Fig. 1

Illustration of (a) physical setup and (b) refractive index profile for a lens with diffuse boundaries.

Fig. 2
Fig. 2

Typical field profile across the lens normalized against E for the incoming wave at z = 2 h . Here κ = 10 5 , δ = 0.01 , a = 0.2 , k h = 10 , and k x h = 10.05 . The dotted vertical lines denote the GRIN layers at the surfaces of the lens.

Fig. 3
Fig. 3

(a) Real (triangle) and imaginary (square) parts of k z h and (b) transmission against k x h for a = 0 (circles), 0.01 (squares), and 0.05 (triangles), κ = 10 2 , h k = 1 , and δ = 0.01 . Also shown in (b) by the dashed curve is a = 0 and κ = 0.08 .

Fig. 4
Fig. 4

Transmission against a for FOM ( = 1 κ ) = 10 7 (triangles), 10 5 (circles), 10 4 (diamonds), and 10 3 (squares), k x h = 10.3 , k z h = 1.95 i , and δ = 0.01 .

Equations (1)

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

E ( z ) = { e ( i k z 1 z ) + r e ( i k z 1 z ) z < h a h E ̃ 1 ( z ) h a h < z < h E ̃ 2 ( z ) h < z < h + a h s e ( i k z 2 z ) + q e ( i k z 2 z ) h + a h < z < h a h , E ̃ 3 ( z ) h a h < z < h E ̃ 4 ( z ) h < z < h + a h t e ( i k z 1 z ) h + a h < z }

Metrics