Abstract

A slab of left-handed material (LHM) with refractive index 1 forms a perfect lens that retains subwavelength information about a source or object. Such lenses are highly susceptible to perturbations affecting their performance. It is shown that illuminating a roughened interface between air and an LHM produces a regime for enhanced focusing of light close to the boundary. This generates caustics that are brighter, fluctuate more, and cause Gaussian speckle at distances closer to the interface than in right-handed matter. These effects present fresh challenges for perfecting the perfect lens.

© 2010 Optical Society of America

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    [CrossRef] [PubMed]
  2. J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, Science 321, 930 (2008).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  8. R. A. Depine, A. Lakhtakia, and D. R. Smith, Phys. Lett. A 337, 155 (2005).
    [CrossRef]
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    [CrossRef]
  11. C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, Appl. Phys. Lett. 84, 3232 (2004).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  16. Small perturbation theory predicts that the statistics of the field evolves from a real Gaussian process at the interface to a complex Gaussian process far from it and that this saturation occurs at a shorter distance in an LHM than for an equivalent RHM.
  17. E. Jakeman, E. R. Pike, and P. Pusey, Nature 263, 215 (1976).
    [CrossRef]
  18. J. C. Dainty, Laser Speckle and Related Phenomena, 2nd ed. (Springer-Verlag, 1984).

2010 (1)

P. C. Ingrey, K. I. Hopcraft, and E. Jakeman, Opt. Commun. 283, 1188 (2010).
[CrossRef]

2009 (2)

P. C. Ingrey, K. I. Hopcraft, E. Jakeman, and O. E. French, Opt. Commun. 282, 1020 (2009).
[CrossRef]

P. C. Ingrey, K. I. Hopcraft, O. French, and E. Jakeman, Opt. Lett. 34, 1015 (2009).
[CrossRef] [PubMed]

2008 (1)

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, Science 321, 930 (2008).
[CrossRef] [PubMed]

2005 (2)

R. A. Depine, A. Lakhtakia, and D. R. Smith, Phys. Lett. A 337, 155 (2005).
[CrossRef]

R. A. Depine and A. Lakhtakia, Optik (Jena) 116, 31 (2005).

2004 (1)

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, Appl. Phys. Lett. 84, 3232 (2004).
[CrossRef]

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]

1994 (1)

1976 (1)

E. Jakeman, E. R. Pike, and P. Pusey, Nature 263, 215 (1976).
[CrossRef]

1968 (1)

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

Abramowitz, M.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, 1965).

Acklin, B.

Bartal, G.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, Science 321, 930 (2008).
[CrossRef] [PubMed]

Born, M.

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

Dainty, J. C.

J. C. Dainty, Laser Speckle and Related Phenomena, 2nd ed. (Springer-Verlag, 1984).

Depine, R. A.

R. A. Depine, A. Lakhtakia, and D. R. Smith, Phys. Lett. A 337, 155 (2005).
[CrossRef]

R. A. Depine and A. Lakhtakia, Optik (Jena) 116, 31 (2005).

Dupertuis, M. A.

French, O.

French, O. E.

P. C. Ingrey, K. I. Hopcraft, E. Jakeman, and O. E. French, Opt. Commun. 282, 1020 (2009).
[CrossRef]

Greegor, R. B.

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, Appl. Phys. Lett. 84, 3232 (2004).
[CrossRef]

Hopcraft, K. I.

P. C. Ingrey, K. I. Hopcraft, and E. Jakeman, Opt. Commun. 283, 1188 (2010).
[CrossRef]

P. C. Ingrey, K. I. Hopcraft, O. French, and E. Jakeman, Opt. Lett. 34, 1015 (2009).
[CrossRef] [PubMed]

P. C. Ingrey, K. I. Hopcraft, E. Jakeman, and O. E. French, Opt. Commun. 282, 1020 (2009).
[CrossRef]

Ingrey, P. C.

P. C. Ingrey, K. I. Hopcraft, and E. Jakeman, Opt. Commun. 283, 1188 (2010).
[CrossRef]

P. C. Ingrey, K. I. Hopcraft, O. French, and E. Jakeman, Opt. Lett. 34, 1015 (2009).
[CrossRef] [PubMed]

P. C. Ingrey, K. I. Hopcraft, E. Jakeman, and O. E. French, Opt. Commun. 282, 1020 (2009).
[CrossRef]

Jackson, J. D.

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

Jakeman, E.

P. C. Ingrey, K. I. Hopcraft, and E. Jakeman, Opt. Commun. 283, 1188 (2010).
[CrossRef]

P. C. Ingrey, K. I. Hopcraft, O. French, and E. Jakeman, Opt. Lett. 34, 1015 (2009).
[CrossRef] [PubMed]

P. C. Ingrey, K. I. Hopcraft, E. Jakeman, and O. E. French, Opt. Commun. 282, 1020 (2009).
[CrossRef]

E. Jakeman, E. R. Pike, and P. Pusey, Nature 263, 215 (1976).
[CrossRef]

E. Jakeman and K. D. Ridley, Modelling Fluctuations in Scattered Waves (Taylor & Francis, 2006).
[CrossRef]

Lakhtakia, A.

R. A. Depine and A. Lakhtakia, Optik (Jena) 116, 31 (2005).

R. A. Depine, A. Lakhtakia, and D. R. Smith, Phys. Lett. A 337, 155 (2005).
[CrossRef]

Li, K.

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, Appl. Phys. Lett. 84, 3232 (2004).
[CrossRef]

Liu, Y.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, Science 321, 930 (2008).
[CrossRef] [PubMed]

Liu, Z.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, Science 321, 930 (2008).
[CrossRef] [PubMed]

Nielsen, J. A.

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, Appl. Phys. Lett. 84, 3232 (2004).
[CrossRef]

Parazzoli, C. G.

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, Appl. Phys. Lett. 84, 3232 (2004).
[CrossRef]

Pendry, J. B.

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

Pike, E. R.

E. Jakeman, E. R. Pike, and P. Pusey, Nature 263, 215 (1976).
[CrossRef]

Proctor, M.

Pusey, P.

E. Jakeman, E. R. Pike, and P. Pusey, Nature 263, 215 (1976).
[CrossRef]

Ridley, K. D.

E. Jakeman and K. D. Ridley, Modelling Fluctuations in Scattered Waves (Taylor & Francis, 2006).
[CrossRef]

Schultz, S.

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

Shelby, R. A.

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

Smith, D. R.

R. A. Depine, A. Lakhtakia, and D. R. Smith, Phys. Lett. A 337, 155 (2005).
[CrossRef]

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

Stacy, A. M.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, Science 321, 930 (2008).
[CrossRef] [PubMed]

Stegun, I. A.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, 1965).

Sun, C.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, Science 321, 930 (2008).
[CrossRef] [PubMed]

Tanielian, M. H.

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, Appl. Phys. Lett. 84, 3232 (2004).
[CrossRef]

Thompson, M. A.

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, Appl. Phys. Lett. 84, 3232 (2004).
[CrossRef]

Veselago, V. G.

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

Vetter, A. M.

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, Appl. Phys. Lett. 84, 3232 (2004).
[CrossRef]

Vier, D. C.

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, Appl. Phys. Lett. 84, 3232 (2004).
[CrossRef]

Wang, Y.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, Science 321, 930 (2008).
[CrossRef] [PubMed]

Wolf, E.

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

Yao, J.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, Science 321, 930 (2008).
[CrossRef] [PubMed]

Zhang, X.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, Science 321, 930 (2008).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, Appl. Phys. Lett. 84, 3232 (2004).
[CrossRef]

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

Nature (1)

E. Jakeman, E. R. Pike, and P. Pusey, Nature 263, 215 (1976).
[CrossRef]

Opt. Commun. (2)

P. C. Ingrey, K. I. Hopcraft, E. Jakeman, and O. E. French, Opt. Commun. 282, 1020 (2009).
[CrossRef]

P. C. Ingrey, K. I. Hopcraft, and E. Jakeman, Opt. Commun. 283, 1188 (2010).
[CrossRef]

Opt. Lett. (1)

Optik (Jena) (1)

R. A. Depine and A. Lakhtakia, Optik (Jena) 116, 31 (2005).

Phys. Lett. A (1)

R. A. Depine, A. Lakhtakia, and D. R. Smith, Phys. Lett. A 337, 155 (2005).
[CrossRef]

Phys. Rev. Lett. (1)

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

Science (2)

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

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, Science 321, 930 (2008).
[CrossRef] [PubMed]

Sov. Phys. Usp. (1)

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

Other (6)

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

J. C. Dainty, Laser Speckle and Related Phenomena, 2nd ed. (Springer-Verlag, 1984).

E. Jakeman and K. D. Ridley, Modelling Fluctuations in Scattered Waves (Taylor & Francis, 2006).
[CrossRef]

Small perturbation theory predicts that the statistics of the field evolves from a real Gaussian process at the interface to a complex Gaussian process far from it and that this saturation occurs at a shorter distance in an LHM than for an equivalent RHM.

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

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, 1965).

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Figures (4)

Fig. 1
Fig. 1

Intensity from (a), (c) physical optics and (b), (d) ray optics of a planar wave traversing at normal incidence to a sinusoidal interface, from air ( n = 1 ) into (a), (b) n = 3 or (c), (d) n = 1 . For clarity, only those rays resulting from one protuberance are drawn in (b) and (d). Lengths are calibrated in units of wavelength.

Fig. 2
Fig. 2

Distance to the focus, when the interface is a sinusoid of amplitude λ / 4 (yellow circles), λ / 2 (blue triangles), and λ (purple squares). Solid curves are ray optics results [10], with parameters chosen by utilizing the (known) surface profile and determining an appropriate ray separation distance, d, determined from the data to be λ / 4 , d = 2.0 ; λ / 2 , d = 1.6 ; λ, d = 1.4 .

Fig. 3
Fig. 3

Peak mean intensity for a Gaussian rough surface as a function of n 2 . In all curves, / λ = 10 , with σ / λ = 5.0 (yellow circles), 2.5 (purple squares), and 1.0 (blue triangles).

Fig. 4
Fig. 4

I [ 2 ] as a function of distance for a Gaussian rough surface, with / λ = 10 . The parameters are σ / λ = 1 4 , n 2 = 1 + 10 5 i (black diamonds), n 2 = 3 + 10 5 i (purple stars); σ / λ = 1 2 , n 2 = 1 + 10 5 i (green squares), n 2 = 3 + 10 5 i (yellow circles); σ / λ = 1 , n 2 = 1 + 10 5 i (blue triangles).

Equations (1)

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E 2 ( x ) = ( E 1 ( x ) G ( x , x ) ν μ 2 μ 1 G ( x , x ) E 1 ( x ) ν ) d S ( x ) ,

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