Abstract

Resonant enhancement of electromagnetic waves propagating at oblique incidence in metamaterials, with dielectric permittivity and magnetic permeability linearly changing from positive to negative values, has been predicted and theoretically studied. This effect occurs for both TE and TM polarizations near the point where a refractive index changes its sign. Our model elucidates the unique features of the resonant enhancement in “positive-to-negative transition” metamaterials for a broad frequency range from microwaves to optics.

© 2008 Optical Society of America

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References

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  1. V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968).
    [CrossRef]
  2. J. B. Pendry, Phys. Rev. Lett. 85, 3966(4) (2000).
    [CrossRef] [PubMed]
  3. V. M. Shalaev, Nat. Photonics 1, 41 (2007).
    [CrossRef]
  4. N. M. Litchinitser, I. R. Gabitov, A. I. Maimistov, and V. M. Shalaev, in Progress in Optics, E.Wolf, ed. (Elsevier, 2008), Vol. 51, pp. 1-68.
    [CrossRef]
  5. M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, Photonics Nanostruct. Fundam. Appl. 6, 87 (2008).
    [CrossRef]
  6. A. V. Kildishev and V. M. Shalaev, Opt. Lett. 33, 43 (2008).
    [CrossRef]
  7. M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, Phys. Rev. Lett. 100, 063903(4) (2008).
    [CrossRef] [PubMed]
  8. J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
    [CrossRef] [PubMed]
  9. U. Leonhardt, Science 312, 1777 (2006).
    [CrossRef] [PubMed]
  10. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, D. R. Smith, Science 314, 977 (2006).
    [CrossRef] [PubMed]
  11. W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, Nat. Photonics 1, 224 (2007).
    [CrossRef]
  12. W. Cai, U. K. Chettiar, A. V. Kildishev, G. W. Milton, and V. M. Shalaev, Appl. Phys. Lett. 91, 111105(3) (2007).
    [CrossRef]
  13. V. L. Ginzburg, The Propagation of Electromagnetic Waves in Plasma (Pergamon, 1970).
  14. L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media, 2nd ed. (Butterworth-Heinemann, 1984), Vol. 8.
  15. A. O. Korotkevich, A. C. Newell, and V. E. Zakharov, J. Appl. Phys. 102, 083305(14) (2007).
    [CrossRef]

2008 (3)

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, Photonics Nanostruct. Fundam. Appl. 6, 87 (2008).
[CrossRef]

A. V. Kildishev and V. M. Shalaev, Opt. Lett. 33, 43 (2008).
[CrossRef]

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, Phys. Rev. Lett. 100, 063903(4) (2008).
[CrossRef] [PubMed]

2007 (4)

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, Nat. Photonics 1, 224 (2007).
[CrossRef]

W. Cai, U. K. Chettiar, A. V. Kildishev, G. W. Milton, and V. M. Shalaev, Appl. Phys. Lett. 91, 111105(3) (2007).
[CrossRef]

A. O. Korotkevich, A. C. Newell, and V. E. Zakharov, J. Appl. Phys. 102, 083305(14) (2007).
[CrossRef]

V. M. Shalaev, Nat. Photonics 1, 41 (2007).
[CrossRef]

2006 (3)

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

U. Leonhardt, Science 312, 1777 (2006).
[CrossRef] [PubMed]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, D. R. Smith, Science 314, 977 (2006).
[CrossRef] [PubMed]

2000 (1)

J. B. Pendry, Phys. Rev. Lett. 85, 3966(4) (2000).
[CrossRef] [PubMed]

1968 (1)

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

Cai, W.

W. Cai, U. K. Chettiar, A. V. Kildishev, G. W. Milton, and V. M. Shalaev, Appl. Phys. Lett. 91, 111105(3) (2007).
[CrossRef]

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, Nat. Photonics 1, 224 (2007).
[CrossRef]

Chettiar, U. K.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, Nat. Photonics 1, 224 (2007).
[CrossRef]

W. Cai, U. K. Chettiar, A. V. Kildishev, G. W. Milton, and V. M. Shalaev, Appl. Phys. Lett. 91, 111105(3) (2007).
[CrossRef]

Cummer, S. A.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, Photonics Nanostruct. Fundam. Appl. 6, 87 (2008).
[CrossRef]

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, Phys. Rev. Lett. 100, 063903(4) (2008).
[CrossRef] [PubMed]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, D. R. Smith, Science 314, 977 (2006).
[CrossRef] [PubMed]

Gabitov, I. R.

N. M. Litchinitser, I. R. Gabitov, A. I. Maimistov, and V. M. Shalaev, in Progress in Optics, E.Wolf, ed. (Elsevier, 2008), Vol. 51, pp. 1-68.
[CrossRef]

Ginzburg, V. L.

V. L. Ginzburg, The Propagation of Electromagnetic Waves in Plasma (Pergamon, 1970).

Justice, B. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, D. R. Smith, Science 314, 977 (2006).
[CrossRef] [PubMed]

Kildishev, A. V.

A. V. Kildishev and V. M. Shalaev, Opt. Lett. 33, 43 (2008).
[CrossRef]

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, Nat. Photonics 1, 224 (2007).
[CrossRef]

W. Cai, U. K. Chettiar, A. V. Kildishev, G. W. Milton, and V. M. Shalaev, Appl. Phys. Lett. 91, 111105(3) (2007).
[CrossRef]

Korotkevich, A. O.

A. O. Korotkevich, A. C. Newell, and V. E. Zakharov, J. Appl. Phys. 102, 083305(14) (2007).
[CrossRef]

Landau, L. D.

L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media, 2nd ed. (Butterworth-Heinemann, 1984), Vol. 8.

Leonhardt, U.

U. Leonhardt, Science 312, 1777 (2006).
[CrossRef] [PubMed]

Lifshitz, E. M.

L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media, 2nd ed. (Butterworth-Heinemann, 1984), Vol. 8.

Litchinitser, N. M.

N. M. Litchinitser, I. R. Gabitov, A. I. Maimistov, and V. M. Shalaev, in Progress in Optics, E.Wolf, ed. (Elsevier, 2008), Vol. 51, pp. 1-68.
[CrossRef]

Maimistov, A. I.

N. M. Litchinitser, I. R. Gabitov, A. I. Maimistov, and V. M. Shalaev, in Progress in Optics, E.Wolf, ed. (Elsevier, 2008), Vol. 51, pp. 1-68.
[CrossRef]

Milton, G. W.

W. Cai, U. K. Chettiar, A. V. Kildishev, G. W. Milton, and V. M. Shalaev, Appl. Phys. Lett. 91, 111105(3) (2007).
[CrossRef]

Mock, J. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, D. R. Smith, Science 314, 977 (2006).
[CrossRef] [PubMed]

Newell, A. C.

A. O. Korotkevich, A. C. Newell, and V. E. Zakharov, J. Appl. Phys. 102, 083305(14) (2007).
[CrossRef]

Pendry, J. B.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, Photonics Nanostruct. Fundam. Appl. 6, 87 (2008).
[CrossRef]

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, Phys. Rev. Lett. 100, 063903(4) (2008).
[CrossRef] [PubMed]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, D. R. Smith, Science 314, 977 (2006).
[CrossRef] [PubMed]

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

J. B. Pendry, Phys. Rev. Lett. 85, 3966(4) (2000).
[CrossRef] [PubMed]

Pitaevskii, L. P.

L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media, 2nd ed. (Butterworth-Heinemann, 1984), Vol. 8.

Rahm, M.

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, Phys. Rev. Lett. 100, 063903(4) (2008).
[CrossRef] [PubMed]

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, Photonics Nanostruct. Fundam. Appl. 6, 87 (2008).
[CrossRef]

Roberts, D. A.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, Photonics Nanostruct. Fundam. Appl. 6, 87 (2008).
[CrossRef]

Schurig, D.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, Photonics Nanostruct. Fundam. Appl. 6, 87 (2008).
[CrossRef]

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, Phys. Rev. Lett. 100, 063903(4) (2008).
[CrossRef] [PubMed]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, D. R. Smith, Science 314, 977 (2006).
[CrossRef] [PubMed]

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

Shalaev, V. M.

A. V. Kildishev and V. M. Shalaev, Opt. Lett. 33, 43 (2008).
[CrossRef]

V. M. Shalaev, Nat. Photonics 1, 41 (2007).
[CrossRef]

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, Nat. Photonics 1, 224 (2007).
[CrossRef]

W. Cai, U. K. Chettiar, A. V. Kildishev, G. W. Milton, and V. M. Shalaev, Appl. Phys. Lett. 91, 111105(3) (2007).
[CrossRef]

N. M. Litchinitser, I. R. Gabitov, A. I. Maimistov, and V. M. Shalaev, in Progress in Optics, E.Wolf, ed. (Elsevier, 2008), Vol. 51, pp. 1-68.
[CrossRef]

Smith, D. R.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, Photonics Nanostruct. Fundam. Appl. 6, 87 (2008).
[CrossRef]

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, Phys. Rev. Lett. 100, 063903(4) (2008).
[CrossRef] [PubMed]

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

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, D. R. Smith, Science 314, 977 (2006).
[CrossRef] [PubMed]

Starr, A. F.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, D. R. Smith, Science 314, 977 (2006).
[CrossRef] [PubMed]

Veselago, V. G.

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

Zakharov, V. E.

A. O. Korotkevich, A. C. Newell, and V. E. Zakharov, J. Appl. Phys. 102, 083305(14) (2007).
[CrossRef]

Appl. Phys. Lett. (1)

W. Cai, U. K. Chettiar, A. V. Kildishev, G. W. Milton, and V. M. Shalaev, Appl. Phys. Lett. 91, 111105(3) (2007).
[CrossRef]

J. Appl. Phys. (1)

A. O. Korotkevich, A. C. Newell, and V. E. Zakharov, J. Appl. Phys. 102, 083305(14) (2007).
[CrossRef]

Nat. Photonics (2)

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, Nat. Photonics 1, 224 (2007).
[CrossRef]

V. M. Shalaev, Nat. Photonics 1, 41 (2007).
[CrossRef]

Opt. Lett. (1)

Photonics Nanostruct. Fundam. Appl. (1)

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, Photonics Nanostruct. Fundam. Appl. 6, 87 (2008).
[CrossRef]

Phys. Rev. Lett. (2)

J. B. Pendry, Phys. Rev. Lett. 85, 3966(4) (2000).
[CrossRef] [PubMed]

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, Phys. Rev. Lett. 100, 063903(4) (2008).
[CrossRef] [PubMed]

Science (3)

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

U. Leonhardt, Science 312, 1777 (2006).
[CrossRef] [PubMed]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, D. R. Smith, Science 314, 977 (2006).
[CrossRef] [PubMed]

Sov. Phys. Usp. (1)

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

Other (3)

V. L. Ginzburg, The Propagation of Electromagnetic Waves in Plasma (Pergamon, 1970).

L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media, 2nd ed. (Butterworth-Heinemann, 1984), Vol. 8.

N. M. Litchinitser, I. R. Gabitov, A. I. Maimistov, and V. M. Shalaev, in Progress in Optics, E.Wolf, ed. (Elsevier, 2008), Vol. 51, pp. 1-68.
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Schematic of a transition layer between a homogeneous PIM layer and a homogeneous NIM layer. Dielectric permittivity and magnetic permeability in the transition region are real linear functions of the normalized coordinate ς.

Fig. 2
Fig. 2

Real part of the electric field component E y as a function of longitudinal coordinate ς for the case of oblique incidence at θ = π 17 (solid curve), the real part of the magnetic susceptibility μ as a function of longitudinal coordinate ς (long-dashed curve), and the boundary between the PIM and NIM (short-dashed line).

Fig. 3
Fig. 3

Absolute value of the normalized magnetic field component H x as a function of longitudinal coordinate ς for the case of oblique incidence at θ = π 17 .

Equations (7)

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2 E y x 2 + 2 E y z 2 1 μ μ x E y x + ω 2 c 2 ϵ μ E y = 0 ,
2 Φ ς 2 + 1 ( 1 ς ) Φ ς + ( a 2 ( 1 ς ) 2 b 2 ) Φ = 0 .
Φ ( ς ) = C 1 exp ( i a ( 1 ς ) 2 2 ) i a ( 1 ς ) 2 U ( 1 i b 2 4 a , 2 , i a ( 1 ς ) 2 ) + C 2 exp ( i a ( 1 ς ) 2 2 ) i a ( 1 ς ) 2 U ( 1 + i b 2 4 a , 2 , i a ( 1 ς ) 2 ) ,
Φ ( ς ) ( C 1 C 2 ) ( 1 + b 2 ( 1 ς ) 2 2 ln a ( 1 ς ) ) i 2 ( C 1 + C 2 ) ( 1 π b 2 4 a ) a ( 1 ς ) 2 .
E y = E 0 exp ( i β z i ω t ) + O ( ( 1 ς ) 2 ) ,
H x = E 0 ϵ 0 μ 0 ( 1 ς ) 1 sin θ 0 exp ( i β z i ω t ) + O ( ( 1 ς ) 2 ) ,
H z = 2 i π E 0 ϵ 0 ( h λ ) sin 2 θ 0 ln a ( 1 ς ) exp ( i β z i ω t ) + O ( ( 1 ς ) 2 ) ,

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