Abstract

The electromagnetic properties of finite checkerboards consisting of alternating rectangular cells of positive refractive index (ε=+1, μ=+1) and negative refractive index (ε=-1, μ=-1) have been investigated numerically. We show that the numerical calculations have to be carried out with very fine discretization to accurately model the highly singular behaviour of these checkerboards. Our solutions show that, within the accuracy of the numerical calculations, the focussing properties of these checkerboards are reasonably robust in the presence of moderate levels of dissipation. We also show that even small systems of checkerboards can display focussing effects to some extent.

© 2006 Optical Society of America

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References

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  1. S.A. Ramakrishna, "Physics of negative refractive index materials," Rep. Prog. Phys. 68, 449-521 (2005)
    [CrossRef]
  2. J.B. Pendry, "Negative refraction," Contemp. Phys. 45, 191-202 (2004)
    [CrossRef]
  3. T. Itoh and C. Caloz, Electromagnetic Metamaterials, (Wiley-Interscience, New Jersey, 2006)
  4. J.B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85,3966-3969 (2000) "Negative refraction makes a perfect lens", Phys. Rev. Lett. 85, 3966-3969 (2000)
    [CrossRef] [PubMed]
  5. V.G. Veselago, "The electrodynamics of substances with simultaneously negative values of ε and μ," Sov. Phys. Uspekhi 10, 509-514 (1968)
  6. S.A. Ramakrishna, J.B. Pendry, D. Schurig, D.R. Smith and S. Schultz, "The asymmetric lossy near-perfect lens," J. Mod. Opt. 491747-1762 (2002)
    [CrossRef]
  7. D.R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S.A. Ramakrishna and J.B. Pendry, "Limitations on Sub-Diffraction Imaging with a Negative Refractive Index Slab," Appl. Phys. Lett. 82, 1506-1508 (2003)
    [CrossRef]
  8. J.B. Pendry, S.A. Ramakrishna, "Focussing light using negative refraction," J. Phys. Cond.Matter 15, 6345-6364 (2003)
    [CrossRef]
  9. S. Guenneau, B. Gralak and J.B. Pendry, "Perfect corner reflector" Opt. Lett. 30, 1204-1206 (2005)
    [CrossRef] [PubMed]
  10. S. Guenneau, A.C. Vutha and S.A. Ramakrishna, "Negative refraction in 2D checkerboards related by mirror anti-symmetry and 3D corner lenses," New J. Phys. 7, 164 (2005)
    [CrossRef]
  11. A.A. Sukhorukov, I.V. Shadrivov, Y.S. Kivshar, "Waves scattering by metamaterial wedges and interfaces," Int. J. Numer. Model. 19, 105-117 (2006)
    [CrossRef]
  12. X. S. Rao and C.K. Ong,"Subwavelength imaging by a left-handed material superlens," Phys. Rev. E 68, 067601 (2003)
    [CrossRef]
  13. R. Ziolkowski, "Pulsed and CW Gaussian beam interactions with double negative metamaterial slabs," Opt. Express 11, 662-681 (2003)
    [CrossRef] [PubMed]
  14. J. J. Chen, T. M. Grzegorczyk, B. -I. Wu, and J. A. Kong, "Limitation of FDTD in simulation of a perfect lens imaging system," Opt. Express 13, 10840-10845 (2005)
    [CrossRef] [PubMed]
  15. J.B. Pendry and A. Mackinnon, "Calculation of photon dispersion-relations," Phys. Rev. Lett. 69, 2772-2775 (1992)
    [CrossRef] [PubMed]
  16. P.M. Bell, J.B. Pendry, L.M. Moreno, A.J. Ward, "A program for calculating photonic band structures and transmission coefficients of complex structures," Comput. Phys. Commun. 85, 206-233 (1995)
    [CrossRef]
  17. J.B. Pendry,"Photonic band structures," Jour. Mod. Opt. 41, No. 2, 209-229 (1994)
    [CrossRef]
  18. S. Cummer, "Simulated causal subwavelength focussing by an negative refractive index slab" Appl. Phys. Lett. 82, 1503-1505 (2003)
    [CrossRef]
  19. N. Fang, H. Lee, C. Sun, X. Zhang, "Sub-diffraction-limited optical imaging with a sliver superlens," Science 308, 534-537 (2005)
    [CrossRef] [PubMed]
  20. A. Bossavit, "Solving Maxwell equations in a closed cavity, and the question of spurious modes," IEEE Trans. Mag. 26, 702-705 (1990)
    [CrossRef]
  21. J. P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comp. Phy. 114, 185-200 (1994)
    [CrossRef]
  22. D. Maystre and S. Enoch, "Perfect lenses made with left-handed materials: Alice’s mirror," J. Opt. Soc. Am. A 21, 122-131 (2004)
    [CrossRef]
  23. G.W. Milton and N.A. Nicorovici "On the cloaking effects associated with anomalous localised resonance," Proc. Roy. Lond. A 462, 3027-3059 (2006)
    [CrossRef]
  24. T.J. Cui, Q. Cheng, W.B. Lu, Q. Jiang and J.A. Kong, "Localization fo electromagnetic energy using a lefthanded-medium slab," Phys. Rev. B 71, 045114 (2005)
    [CrossRef]
  25. A.D. Boardman and K. Marinov, "Non-radiating and radiating configurations driven by left-handed materials," J. Opt. Soc. Am. B 23, 543 (2006)
    [CrossRef]

2006 (3)

A.A. Sukhorukov, I.V. Shadrivov, Y.S. Kivshar, "Waves scattering by metamaterial wedges and interfaces," Int. J. Numer. Model. 19, 105-117 (2006)
[CrossRef]

G.W. Milton and N.A. Nicorovici "On the cloaking effects associated with anomalous localised resonance," Proc. Roy. Lond. A 462, 3027-3059 (2006)
[CrossRef]

A.D. Boardman and K. Marinov, "Non-radiating and radiating configurations driven by left-handed materials," J. Opt. Soc. Am. B 23, 543 (2006)
[CrossRef]

2005 (6)

T.J. Cui, Q. Cheng, W.B. Lu, Q. Jiang and J.A. Kong, "Localization fo electromagnetic energy using a lefthanded-medium slab," Phys. Rev. B 71, 045114 (2005)
[CrossRef]

N. Fang, H. Lee, C. Sun, X. Zhang, "Sub-diffraction-limited optical imaging with a sliver superlens," Science 308, 534-537 (2005)
[CrossRef] [PubMed]

J. J. Chen, T. M. Grzegorczyk, B. -I. Wu, and J. A. Kong, "Limitation of FDTD in simulation of a perfect lens imaging system," Opt. Express 13, 10840-10845 (2005)
[CrossRef] [PubMed]

S.A. Ramakrishna, "Physics of negative refractive index materials," Rep. Prog. Phys. 68, 449-521 (2005)
[CrossRef]

S. Guenneau, B. Gralak and J.B. Pendry, "Perfect corner reflector" Opt. Lett. 30, 1204-1206 (2005)
[CrossRef] [PubMed]

S. Guenneau, A.C. Vutha and S.A. Ramakrishna, "Negative refraction in 2D checkerboards related by mirror anti-symmetry and 3D corner lenses," New J. Phys. 7, 164 (2005)
[CrossRef]

2004 (2)

2003 (5)

D.R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S.A. Ramakrishna and J.B. Pendry, "Limitations on Sub-Diffraction Imaging with a Negative Refractive Index Slab," Appl. Phys. Lett. 82, 1506-1508 (2003)
[CrossRef]

J.B. Pendry, S.A. Ramakrishna, "Focussing light using negative refraction," J. Phys. Cond.Matter 15, 6345-6364 (2003)
[CrossRef]

X. S. Rao and C.K. Ong,"Subwavelength imaging by a left-handed material superlens," Phys. Rev. E 68, 067601 (2003)
[CrossRef]

R. Ziolkowski, "Pulsed and CW Gaussian beam interactions with double negative metamaterial slabs," Opt. Express 11, 662-681 (2003)
[CrossRef] [PubMed]

S. Cummer, "Simulated causal subwavelength focussing by an negative refractive index slab" Appl. Phys. Lett. 82, 1503-1505 (2003)
[CrossRef]

2002 (1)

S.A. Ramakrishna, J.B. Pendry, D. Schurig, D.R. Smith and S. Schultz, "The asymmetric lossy near-perfect lens," J. Mod. Opt. 491747-1762 (2002)
[CrossRef]

2000 (1)

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

1995 (1)

P.M. Bell, J.B. Pendry, L.M. Moreno, A.J. Ward, "A program for calculating photonic band structures and transmission coefficients of complex structures," Comput. Phys. Commun. 85, 206-233 (1995)
[CrossRef]

1994 (2)

J.B. Pendry,"Photonic band structures," Jour. Mod. Opt. 41, No. 2, 209-229 (1994)
[CrossRef]

J. P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comp. Phy. 114, 185-200 (1994)
[CrossRef]

1992 (1)

J.B. Pendry and A. Mackinnon, "Calculation of photon dispersion-relations," Phys. Rev. Lett. 69, 2772-2775 (1992)
[CrossRef] [PubMed]

1990 (1)

A. Bossavit, "Solving Maxwell equations in a closed cavity, and the question of spurious modes," IEEE Trans. Mag. 26, 702-705 (1990)
[CrossRef]

1968 (1)

V.G. Veselago, "The electrodynamics of substances with simultaneously negative values of ε and μ," Sov. Phys. Uspekhi 10, 509-514 (1968)

Bell, P.M.

P.M. Bell, J.B. Pendry, L.M. Moreno, A.J. Ward, "A program for calculating photonic band structures and transmission coefficients of complex structures," Comput. Phys. Commun. 85, 206-233 (1995)
[CrossRef]

Berenger, J. P.

J. P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comp. Phy. 114, 185-200 (1994)
[CrossRef]

Boardman, A.D.

Bossavit, A.

A. Bossavit, "Solving Maxwell equations in a closed cavity, and the question of spurious modes," IEEE Trans. Mag. 26, 702-705 (1990)
[CrossRef]

Chen, J. J.

Cheng, Q.

T.J. Cui, Q. Cheng, W.B. Lu, Q. Jiang and J.A. Kong, "Localization fo electromagnetic energy using a lefthanded-medium slab," Phys. Rev. B 71, 045114 (2005)
[CrossRef]

Cui, T.J.

T.J. Cui, Q. Cheng, W.B. Lu, Q. Jiang and J.A. Kong, "Localization fo electromagnetic energy using a lefthanded-medium slab," Phys. Rev. B 71, 045114 (2005)
[CrossRef]

Cummer, S.

S. Cummer, "Simulated causal subwavelength focussing by an negative refractive index slab" Appl. Phys. Lett. 82, 1503-1505 (2003)
[CrossRef]

Enoch, S.

Fang, N.

N. Fang, H. Lee, C. Sun, X. Zhang, "Sub-diffraction-limited optical imaging with a sliver superlens," Science 308, 534-537 (2005)
[CrossRef] [PubMed]

Gralak, B.

Grzegorczyk, T. M.

Guenneau, S.

S. Guenneau, B. Gralak and J.B. Pendry, "Perfect corner reflector" Opt. Lett. 30, 1204-1206 (2005)
[CrossRef] [PubMed]

S. Guenneau, A.C. Vutha and S.A. Ramakrishna, "Negative refraction in 2D checkerboards related by mirror anti-symmetry and 3D corner lenses," New J. Phys. 7, 164 (2005)
[CrossRef]

Jiang, Q.

T.J. Cui, Q. Cheng, W.B. Lu, Q. Jiang and J.A. Kong, "Localization fo electromagnetic energy using a lefthanded-medium slab," Phys. Rev. B 71, 045114 (2005)
[CrossRef]

Kivshar, Y.S.

A.A. Sukhorukov, I.V. Shadrivov, Y.S. Kivshar, "Waves scattering by metamaterial wedges and interfaces," Int. J. Numer. Model. 19, 105-117 (2006)
[CrossRef]

Kong, J. A.

Kong, J.A.

T.J. Cui, Q. Cheng, W.B. Lu, Q. Jiang and J.A. Kong, "Localization fo electromagnetic energy using a lefthanded-medium slab," Phys. Rev. B 71, 045114 (2005)
[CrossRef]

Lee, H.

N. Fang, H. Lee, C. Sun, X. Zhang, "Sub-diffraction-limited optical imaging with a sliver superlens," Science 308, 534-537 (2005)
[CrossRef] [PubMed]

Lu, W.B.

T.J. Cui, Q. Cheng, W.B. Lu, Q. Jiang and J.A. Kong, "Localization fo electromagnetic energy using a lefthanded-medium slab," Phys. Rev. B 71, 045114 (2005)
[CrossRef]

Mackinnon, A.

J.B. Pendry and A. Mackinnon, "Calculation of photon dispersion-relations," Phys. Rev. Lett. 69, 2772-2775 (1992)
[CrossRef] [PubMed]

Marinov, K.

Maystre, D.

Milton, G.W.

G.W. Milton and N.A. Nicorovici "On the cloaking effects associated with anomalous localised resonance," Proc. Roy. Lond. A 462, 3027-3059 (2006)
[CrossRef]

Moreno, L.M.

P.M. Bell, J.B. Pendry, L.M. Moreno, A.J. Ward, "A program for calculating photonic band structures and transmission coefficients of complex structures," Comput. Phys. Commun. 85, 206-233 (1995)
[CrossRef]

Nicorovici, N.A.

G.W. Milton and N.A. Nicorovici "On the cloaking effects associated with anomalous localised resonance," Proc. Roy. Lond. A 462, 3027-3059 (2006)
[CrossRef]

Ong, C.K.

X. S. Rao and C.K. Ong,"Subwavelength imaging by a left-handed material superlens," Phys. Rev. E 68, 067601 (2003)
[CrossRef]

Pendry, J.B.

S. Guenneau, B. Gralak and J.B. Pendry, "Perfect corner reflector" Opt. Lett. 30, 1204-1206 (2005)
[CrossRef] [PubMed]

J.B. Pendry, "Negative refraction," Contemp. Phys. 45, 191-202 (2004)
[CrossRef]

D.R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S.A. Ramakrishna and J.B. Pendry, "Limitations on Sub-Diffraction Imaging with a Negative Refractive Index Slab," Appl. Phys. Lett. 82, 1506-1508 (2003)
[CrossRef]

J.B. Pendry, S.A. Ramakrishna, "Focussing light using negative refraction," J. Phys. Cond.Matter 15, 6345-6364 (2003)
[CrossRef]

S.A. Ramakrishna, J.B. Pendry, D. Schurig, D.R. Smith and S. Schultz, "The asymmetric lossy near-perfect lens," J. Mod. Opt. 491747-1762 (2002)
[CrossRef]

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

P.M. Bell, J.B. Pendry, L.M. Moreno, A.J. Ward, "A program for calculating photonic band structures and transmission coefficients of complex structures," Comput. Phys. Commun. 85, 206-233 (1995)
[CrossRef]

J.B. Pendry,"Photonic band structures," Jour. Mod. Opt. 41, No. 2, 209-229 (1994)
[CrossRef]

J.B. Pendry and A. Mackinnon, "Calculation of photon dispersion-relations," Phys. Rev. Lett. 69, 2772-2775 (1992)
[CrossRef] [PubMed]

Ramakrishna, S.A.

S.A. Ramakrishna, "Physics of negative refractive index materials," Rep. Prog. Phys. 68, 449-521 (2005)
[CrossRef]

S. Guenneau, A.C. Vutha and S.A. Ramakrishna, "Negative refraction in 2D checkerboards related by mirror anti-symmetry and 3D corner lenses," New J. Phys. 7, 164 (2005)
[CrossRef]

J.B. Pendry, S.A. Ramakrishna, "Focussing light using negative refraction," J. Phys. Cond.Matter 15, 6345-6364 (2003)
[CrossRef]

D.R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S.A. Ramakrishna and J.B. Pendry, "Limitations on Sub-Diffraction Imaging with a Negative Refractive Index Slab," Appl. Phys. Lett. 82, 1506-1508 (2003)
[CrossRef]

S.A. Ramakrishna, J.B. Pendry, D. Schurig, D.R. Smith and S. Schultz, "The asymmetric lossy near-perfect lens," J. Mod. Opt. 491747-1762 (2002)
[CrossRef]

Rao, X. S.

X. S. Rao and C.K. Ong,"Subwavelength imaging by a left-handed material superlens," Phys. Rev. E 68, 067601 (2003)
[CrossRef]

Rosenbluth, M.

D.R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S.A. Ramakrishna and J.B. Pendry, "Limitations on Sub-Diffraction Imaging with a Negative Refractive Index Slab," Appl. Phys. Lett. 82, 1506-1508 (2003)
[CrossRef]

Schultz, S.

D.R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S.A. Ramakrishna and J.B. Pendry, "Limitations on Sub-Diffraction Imaging with a Negative Refractive Index Slab," Appl. Phys. Lett. 82, 1506-1508 (2003)
[CrossRef]

S.A. Ramakrishna, J.B. Pendry, D. Schurig, D.R. Smith and S. Schultz, "The asymmetric lossy near-perfect lens," J. Mod. Opt. 491747-1762 (2002)
[CrossRef]

Schurig, D.

D.R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S.A. Ramakrishna and J.B. Pendry, "Limitations on Sub-Diffraction Imaging with a Negative Refractive Index Slab," Appl. Phys. Lett. 82, 1506-1508 (2003)
[CrossRef]

S.A. Ramakrishna, J.B. Pendry, D. Schurig, D.R. Smith and S. Schultz, "The asymmetric lossy near-perfect lens," J. Mod. Opt. 491747-1762 (2002)
[CrossRef]

Shadrivov, I.V.

A.A. Sukhorukov, I.V. Shadrivov, Y.S. Kivshar, "Waves scattering by metamaterial wedges and interfaces," Int. J. Numer. Model. 19, 105-117 (2006)
[CrossRef]

Smith, D.R.

D.R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S.A. Ramakrishna and J.B. Pendry, "Limitations on Sub-Diffraction Imaging with a Negative Refractive Index Slab," Appl. Phys. Lett. 82, 1506-1508 (2003)
[CrossRef]

S.A. Ramakrishna, J.B. Pendry, D. Schurig, D.R. Smith and S. Schultz, "The asymmetric lossy near-perfect lens," J. Mod. Opt. 491747-1762 (2002)
[CrossRef]

Sukhorukov, A.A.

A.A. Sukhorukov, I.V. Shadrivov, Y.S. Kivshar, "Waves scattering by metamaterial wedges and interfaces," Int. J. Numer. Model. 19, 105-117 (2006)
[CrossRef]

Sun, C.

N. Fang, H. Lee, C. Sun, X. Zhang, "Sub-diffraction-limited optical imaging with a sliver superlens," Science 308, 534-537 (2005)
[CrossRef] [PubMed]

Veselago, V.G.

V.G. Veselago, "The electrodynamics of substances with simultaneously negative values of ε and μ," Sov. Phys. Uspekhi 10, 509-514 (1968)

Vutha, A.C.

S. Guenneau, A.C. Vutha and S.A. Ramakrishna, "Negative refraction in 2D checkerboards related by mirror anti-symmetry and 3D corner lenses," New J. Phys. 7, 164 (2005)
[CrossRef]

Ward, A.J.

P.M. Bell, J.B. Pendry, L.M. Moreno, A.J. Ward, "A program for calculating photonic band structures and transmission coefficients of complex structures," Comput. Phys. Commun. 85, 206-233 (1995)
[CrossRef]

Wu, B. -I.

Zhang, X.

N. Fang, H. Lee, C. Sun, X. Zhang, "Sub-diffraction-limited optical imaging with a sliver superlens," Science 308, 534-537 (2005)
[CrossRef] [PubMed]

Ziolkowski, R.

Appl. Phys. Lett. (2)

D.R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S.A. Ramakrishna and J.B. Pendry, "Limitations on Sub-Diffraction Imaging with a Negative Refractive Index Slab," Appl. Phys. Lett. 82, 1506-1508 (2003)
[CrossRef]

S. Cummer, "Simulated causal subwavelength focussing by an negative refractive index slab" Appl. Phys. Lett. 82, 1503-1505 (2003)
[CrossRef]

Comput. Phys. Commun. (1)

P.M. Bell, J.B. Pendry, L.M. Moreno, A.J. Ward, "A program for calculating photonic band structures and transmission coefficients of complex structures," Comput. Phys. Commun. 85, 206-233 (1995)
[CrossRef]

Contemp. Phys. (1)

J.B. Pendry, "Negative refraction," Contemp. Phys. 45, 191-202 (2004)
[CrossRef]

IEEE Trans. Mag. (1)

A. Bossavit, "Solving Maxwell equations in a closed cavity, and the question of spurious modes," IEEE Trans. Mag. 26, 702-705 (1990)
[CrossRef]

Int. J. Numer. Model. (1)

A.A. Sukhorukov, I.V. Shadrivov, Y.S. Kivshar, "Waves scattering by metamaterial wedges and interfaces," Int. J. Numer. Model. 19, 105-117 (2006)
[CrossRef]

J. Comp. Phy. (1)

J. P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comp. Phy. 114, 185-200 (1994)
[CrossRef]

J. Mod. Opt. (1)

S.A. Ramakrishna, J.B. Pendry, D. Schurig, D.R. Smith and S. Schultz, "The asymmetric lossy near-perfect lens," J. Mod. Opt. 491747-1762 (2002)
[CrossRef]

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

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

J. Phys. Cond.Matter (1)

J.B. Pendry, S.A. Ramakrishna, "Focussing light using negative refraction," J. Phys. Cond.Matter 15, 6345-6364 (2003)
[CrossRef]

Jour. Mod. Opt. (1)

J.B. Pendry,"Photonic band structures," Jour. Mod. Opt. 41, No. 2, 209-229 (1994)
[CrossRef]

New J. Phys. (1)

S. Guenneau, A.C. Vutha and S.A. Ramakrishna, "Negative refraction in 2D checkerboards related by mirror anti-symmetry and 3D corner lenses," New J. Phys. 7, 164 (2005)
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. B (1)

T.J. Cui, Q. Cheng, W.B. Lu, Q. Jiang and J.A. Kong, "Localization fo electromagnetic energy using a lefthanded-medium slab," Phys. Rev. B 71, 045114 (2005)
[CrossRef]

Phys. Rev. E (1)

X. S. Rao and C.K. Ong,"Subwavelength imaging by a left-handed material superlens," Phys. Rev. E 68, 067601 (2003)
[CrossRef]

Phys. Rev. Lett. (2)

J.B. Pendry and A. Mackinnon, "Calculation of photon dispersion-relations," Phys. Rev. Lett. 69, 2772-2775 (1992)
[CrossRef] [PubMed]

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

Proc. Roy. Lond. A (1)

G.W. Milton and N.A. Nicorovici "On the cloaking effects associated with anomalous localised resonance," Proc. Roy. Lond. A 462, 3027-3059 (2006)
[CrossRef]

Rep. Prog. Phys. (1)

S.A. Ramakrishna, "Physics of negative refractive index materials," Rep. Prog. Phys. 68, 449-521 (2005)
[CrossRef]

Science (1)

N. Fang, H. Lee, C. Sun, X. Zhang, "Sub-diffraction-limited optical imaging with a sliver superlens," Science 308, 534-537 (2005)
[CrossRef] [PubMed]

Sov. Phys. Uspekhi (1)

V.G. Veselago, "The electrodynamics of substances with simultaneously negative values of ε and μ," Sov. Phys. Uspekhi 10, 509-514 (1968)

Other (1)

T. Itoh and C. Caloz, Electromagnetic Metamaterials, (Wiley-Interscience, New Jersey, 2006)

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Figures (4)

Fig. 1.
Fig. 1.

A pair of complementary checkerboard layers with ε=±1 and μ=±1. Positive and negative refractive index are schematically depicted by white and coloured regions. A ray can be transmitted with no change in direction or retro- reflected.

Fig. 2.
Fig. 2.

The transmission and reflection coefficients for a pair of complementary checker-board layers with ε=±1 and μ=±1. (a) and (b) are the results for inadequate differencing with 202 points across d, while (c) and (d) are the results for better differencing with 262 points across d.

Fig. 3.
Fig. 3.

The transmittivity and reflectivity for dissipative checkerboard systems with ε=μ=-1+i0.1 (top panel) and a silver checkerboard with ε=-1+i0.4 and μ=+1 everywhere (bottom panel). Resonant excitation of surface plasmon modes at subwavelength kx can be seen for the silver checkerboard.

Fig. 4.
Fig. 4.

Left panel: P-polarized eigenfield associated with a line source of wavelength 0.5d (d is about 9µm in section 3) placed at a distance 0.2d from a silver checkerboard slab consisting of 30 cells of side length 0.1d, alternating air and weakly dissipative silver cells (ε=-1+i0.01 and μ=+1). The scale on the right is in arbitrary units. (a) 2D plot of the field; (c) Profile of the field computed along a vertical segment with endpoints (0, 1)d and (0,-1)d. Right panel: Same with two pairs of complementary checkerboard layers (60 cells); (b) 2D plot of the field; (d) 3D plot of the field.

Equations (6)

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𝒯 ( k x ) = 1 , 𝓡 ( k x ) = 0 ,
ω 2 ( k ) = c 2 ε μ a 2 4 sin 2 ( 1 2 k a ) c 2 ε μ k 2 [ 1 1 12 ( k a ) 2 ] ,
k 2 = ε μ ω 2 c 2 [ 1 + 1 12 ( k a ) 2 ] ,
δ μ = μ k 2 a 2 12 ,
k x t = ln ( δ μ 2 ) = ln ( k x 2 a 2 24 )
w e = λ i λ j λ j λ i

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