Abstract

A new lens that is a modification of the Veselago lens is proposed. It consists of a slab of the left-handed material embedded into a regular material. The materials for the new lens should have the same refractive index, unlike that of the Veselago lens in which the materials should in addition have the same impedance. Therefore the new lens should be easier to manufacture. As the Veselago lens, the new lens might be useful for the three dimensional imaging. In contrast to the Veselago lens the new lens has multiple foci, and it may image an object that is located at any large distance from the slab.

© 2003 Optical Society of America

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  1. V. G. Veselago, “Properties of materials having simultaneously negative values of the dielectric (∊) and magnetic (μ) susceptibilities,” Sov. Phys. Solid State 8, 2854–2856 (1967).
  2. N. Garcia, M. Nieto-Vesperinas, “Left-handed materials do not make a perfect lens,” Phys. Rev. Lett. 88, 207403(1–4) (2002).
    [CrossRef]
  3. P. M. Valanju, R. M. Walser, A. P. Valanju, “Wave refraction in negative-index media: always positive and very inhomogeneous.” Phys. Rev. Lett. 88, 187401(1–4) (2002).
    [CrossRef]
  4. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
    [CrossRef] [PubMed]
  5. R. A. Shelby, D. R. Smith, S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
    [CrossRef] [PubMed]
  6. A. L. Pokrovsky, A. L. Efros, “Sign of refractive index and group velocity in left-handed media,” Solid State Commun. 124, 283–287 (2002).
    [CrossRef]
  7. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
    [CrossRef] [PubMed]
  8. P. Markos, C. M. Soukoulis, “Transmission studies of left-handed materials,” Phys. Rev. B 65, 033401(1–4) (2001).
    [CrossRef]
  9. A. L. Pokrovsky, A. L. Efros, “Electrodynamics of metallic photonic crystals and the problem of left-handed materials,” Phys. Rev. Lett. 89, 093901(1–4) (2002).
    [CrossRef]
  10. R. W. Ziolkowski, E. Heyman, “Wave propagation in media having negative permittivity and permeability,” Phys. Rev. E 64, 056625(1–15) (2001).
    [CrossRef]
  11. D. R. Smith, D. Schurig, J. B. Pendry, “Negative refraction of modulated electromagnetic waves,” Appl. Phys. Lett. 81, 2713–2715 (2002).
    [CrossRef]
  12. G. W. ’t Hooft, “Comment on “Negative refraction makes a perfect lens”,” Phys. Rev. Lett. 87, 249701(1) (2001).
    [CrossRef]
  13. J. M. Williams, “Some problems with negative refraction,” Phys. Rev. Lett. 87, 249703(1) (2001).
    [CrossRef]
  14. F. D. M. Haldane, “Electromagnetic surface modes at interfaces with negative refractive index make a “not-quite-perfect” lens,” (arXiv, Cornell University, Ithaca, NY, 29June2002), retrieved 29 June 2002, http://arxiv.org , cond-mat/0206420 , 2002.
  15. A. L. Pokrovsky, A. L. Efros, “Diffraction in left-handed materials and theory of Veselago lens,” (arXiv, Cornell University, Ithaca, NY, 29June2002), retrieved 29 June 2002, http://arxiv.org , cond-mat/0202078 , 2002.
  16. M. Born, E. Wolf, Principles of Optics (Cambridge University Press, Cambridge, UK, 1999), Chap. 4, p. 153.
  17. We emphasize that this result is valid for a single interface only.
  18. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1998), Chap. 7, p. 305.
  19. L. D. Landau, E. M. Lifshitz, The Classical Theory of Fields (Butterworth Heinemann, Oxford, UK, 2000), Chap. 7, p. 140.

2002

N. Garcia, M. Nieto-Vesperinas, “Left-handed materials do not make a perfect lens,” Phys. Rev. Lett. 88, 207403(1–4) (2002).
[CrossRef]

P. M. Valanju, R. M. Walser, A. P. Valanju, “Wave refraction in negative-index media: always positive and very inhomogeneous.” Phys. Rev. Lett. 88, 187401(1–4) (2002).
[CrossRef]

A. L. Pokrovsky, A. L. Efros, “Sign of refractive index and group velocity in left-handed media,” Solid State Commun. 124, 283–287 (2002).
[CrossRef]

A. L. Pokrovsky, A. L. Efros, “Electrodynamics of metallic photonic crystals and the problem of left-handed materials,” Phys. Rev. Lett. 89, 093901(1–4) (2002).
[CrossRef]

D. R. Smith, D. Schurig, J. B. Pendry, “Negative refraction of modulated electromagnetic waves,” Appl. Phys. Lett. 81, 2713–2715 (2002).
[CrossRef]

2001

G. W. ’t Hooft, “Comment on “Negative refraction makes a perfect lens”,” Phys. Rev. Lett. 87, 249701(1) (2001).
[CrossRef]

J. M. Williams, “Some problems with negative refraction,” Phys. Rev. Lett. 87, 249703(1) (2001).
[CrossRef]

P. Markos, C. M. Soukoulis, “Transmission studies of left-handed materials,” Phys. Rev. B 65, 033401(1–4) (2001).
[CrossRef]

R. W. Ziolkowski, E. Heyman, “Wave propagation in media having negative permittivity and permeability,” Phys. Rev. E 64, 056625(1–15) (2001).
[CrossRef]

R. A. Shelby, D. R. Smith, S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
[CrossRef] [PubMed]

2000

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[CrossRef] [PubMed]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[CrossRef] [PubMed]

1967

V. G. Veselago, “Properties of materials having simultaneously negative values of the dielectric (∊) and magnetic (μ) susceptibilities,” Sov. Phys. Solid State 8, 2854–2856 (1967).

’t Hooft, G. W.

G. W. ’t Hooft, “Comment on “Negative refraction makes a perfect lens”,” Phys. Rev. Lett. 87, 249701(1) (2001).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Cambridge University Press, Cambridge, UK, 1999), Chap. 4, p. 153.

Efros, A. L.

A. L. Pokrovsky, A. L. Efros, “Electrodynamics of metallic photonic crystals and the problem of left-handed materials,” Phys. Rev. Lett. 89, 093901(1–4) (2002).
[CrossRef]

A. L. Pokrovsky, A. L. Efros, “Sign of refractive index and group velocity in left-handed media,” Solid State Commun. 124, 283–287 (2002).
[CrossRef]

A. L. Pokrovsky, A. L. Efros, “Diffraction in left-handed materials and theory of Veselago lens,” (arXiv, Cornell University, Ithaca, NY, 29June2002), retrieved 29 June 2002, http://arxiv.org , cond-mat/0202078 , 2002.

Garcia, N.

N. Garcia, M. Nieto-Vesperinas, “Left-handed materials do not make a perfect lens,” Phys. Rev. Lett. 88, 207403(1–4) (2002).
[CrossRef]

Haldane, F. D. M.

F. D. M. Haldane, “Electromagnetic surface modes at interfaces with negative refractive index make a “not-quite-perfect” lens,” (arXiv, Cornell University, Ithaca, NY, 29June2002), retrieved 29 June 2002, http://arxiv.org , cond-mat/0206420 , 2002.

Heyman, E.

R. W. Ziolkowski, E. Heyman, “Wave propagation in media having negative permittivity and permeability,” Phys. Rev. E 64, 056625(1–15) (2001).
[CrossRef]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1998), Chap. 7, p. 305.

Landau, L. D.

L. D. Landau, E. M. Lifshitz, The Classical Theory of Fields (Butterworth Heinemann, Oxford, UK, 2000), Chap. 7, p. 140.

Lifshitz, E. M.

L. D. Landau, E. M. Lifshitz, The Classical Theory of Fields (Butterworth Heinemann, Oxford, UK, 2000), Chap. 7, p. 140.

Markos, P.

P. Markos, C. M. Soukoulis, “Transmission studies of left-handed materials,” Phys. Rev. B 65, 033401(1–4) (2001).
[CrossRef]

Nemat-Nasser, S. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[CrossRef] [PubMed]

Nieto-Vesperinas, M.

N. Garcia, M. Nieto-Vesperinas, “Left-handed materials do not make a perfect lens,” Phys. Rev. Lett. 88, 207403(1–4) (2002).
[CrossRef]

Padilla, W. J.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[CrossRef] [PubMed]

Pendry, J. B.

D. R. Smith, D. Schurig, J. B. Pendry, “Negative refraction of modulated electromagnetic waves,” Appl. Phys. Lett. 81, 2713–2715 (2002).
[CrossRef]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[CrossRef] [PubMed]

Pokrovsky, A. L.

A. L. Pokrovsky, A. L. Efros, “Sign of refractive index and group velocity in left-handed media,” Solid State Commun. 124, 283–287 (2002).
[CrossRef]

A. L. Pokrovsky, A. L. Efros, “Electrodynamics of metallic photonic crystals and the problem of left-handed materials,” Phys. Rev. Lett. 89, 093901(1–4) (2002).
[CrossRef]

A. L. Pokrovsky, A. L. Efros, “Diffraction in left-handed materials and theory of Veselago lens,” (arXiv, Cornell University, Ithaca, NY, 29June2002), retrieved 29 June 2002, http://arxiv.org , cond-mat/0202078 , 2002.

Schultz, S.

R. A. Shelby, D. R. Smith, S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
[CrossRef] [PubMed]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[CrossRef] [PubMed]

Schurig, D.

D. R. Smith, D. Schurig, J. B. Pendry, “Negative refraction of modulated electromagnetic waves,” Appl. Phys. Lett. 81, 2713–2715 (2002).
[CrossRef]

Shelby, R. A.

R. A. Shelby, D. R. Smith, S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
[CrossRef] [PubMed]

Smith, D. R.

D. R. Smith, D. Schurig, J. B. Pendry, “Negative refraction of modulated electromagnetic waves,” Appl. Phys. Lett. 81, 2713–2715 (2002).
[CrossRef]

R. A. Shelby, D. R. Smith, S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
[CrossRef] [PubMed]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[CrossRef] [PubMed]

Soukoulis, C. M.

P. Markos, C. M. Soukoulis, “Transmission studies of left-handed materials,” Phys. Rev. B 65, 033401(1–4) (2001).
[CrossRef]

Valanju, A. P.

P. M. Valanju, R. M. Walser, A. P. Valanju, “Wave refraction in negative-index media: always positive and very inhomogeneous.” Phys. Rev. Lett. 88, 187401(1–4) (2002).
[CrossRef]

Valanju, P. M.

P. M. Valanju, R. M. Walser, A. P. Valanju, “Wave refraction in negative-index media: always positive and very inhomogeneous.” Phys. Rev. Lett. 88, 187401(1–4) (2002).
[CrossRef]

Veselago, V. G.

V. G. Veselago, “Properties of materials having simultaneously negative values of the dielectric (∊) and magnetic (μ) susceptibilities,” Sov. Phys. Solid State 8, 2854–2856 (1967).

Vier, D. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[CrossRef] [PubMed]

Walser, R. M.

P. M. Valanju, R. M. Walser, A. P. Valanju, “Wave refraction in negative-index media: always positive and very inhomogeneous.” Phys. Rev. Lett. 88, 187401(1–4) (2002).
[CrossRef]

Williams, J. M.

J. M. Williams, “Some problems with negative refraction,” Phys. Rev. Lett. 87, 249703(1) (2001).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Cambridge University Press, Cambridge, UK, 1999), Chap. 4, p. 153.

Ziolkowski, R. W.

R. W. Ziolkowski, E. Heyman, “Wave propagation in media having negative permittivity and permeability,” Phys. Rev. E 64, 056625(1–15) (2001).
[CrossRef]

Appl. Phys. Lett.

D. R. Smith, D. Schurig, J. B. Pendry, “Negative refraction of modulated electromagnetic waves,” Appl. Phys. Lett. 81, 2713–2715 (2002).
[CrossRef]

Phys. Rev. B

P. Markos, C. M. Soukoulis, “Transmission studies of left-handed materials,” Phys. Rev. B 65, 033401(1–4) (2001).
[CrossRef]

Phys. Rev. E

R. W. Ziolkowski, E. Heyman, “Wave propagation in media having negative permittivity and permeability,” Phys. Rev. E 64, 056625(1–15) (2001).
[CrossRef]

Phys. Rev. Lett.

A. L. Pokrovsky, A. L. Efros, “Electrodynamics of metallic photonic crystals and the problem of left-handed materials,” Phys. Rev. Lett. 89, 093901(1–4) (2002).
[CrossRef]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[CrossRef] [PubMed]

N. Garcia, M. Nieto-Vesperinas, “Left-handed materials do not make a perfect lens,” Phys. Rev. Lett. 88, 207403(1–4) (2002).
[CrossRef]

P. M. Valanju, R. M. Walser, A. P. Valanju, “Wave refraction in negative-index media: always positive and very inhomogeneous.” Phys. Rev. Lett. 88, 187401(1–4) (2002).
[CrossRef]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[CrossRef] [PubMed]

G. W. ’t Hooft, “Comment on “Negative refraction makes a perfect lens”,” Phys. Rev. Lett. 87, 249701(1) (2001).
[CrossRef]

J. M. Williams, “Some problems with negative refraction,” Phys. Rev. Lett. 87, 249703(1) (2001).
[CrossRef]

Science

R. A. Shelby, D. R. Smith, S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
[CrossRef] [PubMed]

Solid State Commun.

A. L. Pokrovsky, A. L. Efros, “Sign of refractive index and group velocity in left-handed media,” Solid State Commun. 124, 283–287 (2002).
[CrossRef]

Sov. Phys. Solid State

V. G. Veselago, “Properties of materials having simultaneously negative values of the dielectric (∊) and magnetic (μ) susceptibilities,” Sov. Phys. Solid State 8, 2854–2856 (1967).

Other

F. D. M. Haldane, “Electromagnetic surface modes at interfaces with negative refractive index make a “not-quite-perfect” lens,” (arXiv, Cornell University, Ithaca, NY, 29June2002), retrieved 29 June 2002, http://arxiv.org , cond-mat/0206420 , 2002.

A. L. Pokrovsky, A. L. Efros, “Diffraction in left-handed materials and theory of Veselago lens,” (arXiv, Cornell University, Ithaca, NY, 29June2002), retrieved 29 June 2002, http://arxiv.org , cond-mat/0202078 , 2002.

M. Born, E. Wolf, Principles of Optics (Cambridge University Press, Cambridge, UK, 1999), Chap. 4, p. 153.

We emphasize that this result is valid for a single interface only.

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1998), Chap. 7, p. 305.

L. D. Landau, E. M. Lifshitz, The Classical Theory of Fields (Butterworth Heinemann, Oxford, UK, 2000), Chap. 7, p. 140.

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Figures (2)

Fig. 1
Fig. 1

Reflection and refraction of light outgoing from a point source at z = -a in the presence of the LHM slab located at 0 < z < d. Refraction of light is described by the anomalous Snell’s law. The arrows represent the directions of the wave vectors. The reflected waves are shown by dashed lines near each interface only. The slab is surrounded by the usual RHM. (a) n′ > n. (b) The VL (∊′ = -∊, μ′ = -μ). In this case the reflected waves are absent, and the rays form two foci.

Fig. 2
Fig. 2

Propagation of rays in the new lens. The object (“fish”) is marked by the bulb. Multiple 3D images of this object are shown. The lens is a slab made of the LHM with ∊′ < 0, μ′ < 0 embedded into a RHM with ∊ > 0, μ > 0. The matching condition is that refractive indices of both materials are the same ∊′μ′ = ∊μ, but ∊′ ≠ -∊ and μ′ ≠ -μ. The arrows show the directions of the wave vectors, which are opposite to the Poynting vector inside the slab. (a) a < d; (b) d < a < 2d.

Equations (23)

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

sin θi/sin θr=-n/n,
=-, μ = -μ,
z=a-m0d,z=±2dm-a,m=m0+1, m0+2, m0-evenor zero,z=±2dm-a,m=m0, m0+1, m0-odd,
Ei=E0i expikxx+ikzz,
Er=E0r expikxx-ikzz,
Et=E0t expikxx-ikzz,
c2kx2+kz2=ω2μ,c2kx2+kz2=ω2μ.
Ezi+Ezr=-||Ezt,
Hyi+Hyr=Hyt.
t=|E0t||E0i|=2n cos θin2-n2 sin2 θi1/2+||n cos θi,
r=|E0r||E0i|=-n2-n2 sin2 θi1/2+n||cos θin2-n2 sin2 θi1/2+n||cos θi.
t=2+||, r=||-||+,
t=2||+||, r=-||+||.
t=2|μ|μ+|μ|, r=μ-|μ|μ+μ.
tt+r2=1, r=-r, t=t||/,
Ia=1-r2I0,
I2d-a=tt2I0=1-r22I0.
Ia=1-r2I0,
I2dm-a=1-r22r4m-4I0, m=1, 2,
I-2dm-a=1-r22r4m-2I0, m=1, 2.
I2d-a=1-r2r2I0,
I2dm-a=1-r22r4m-4I0, m=2, 3,
I-2dm-a=1-r22r4m-2I0, m=1, 2.

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