Abstract

We report analytical and numerical studies of the effect of the separation distance between zeros of dielec tric permittivity and magnetic permeability on the phenomena of resonant absorption and anomalous field enhancement in transition metamaterials. Our studies indicate that these phenomena are robust and strongly polarization-dependent in the presence of the spatial shift between these points. These results are likely to be important for future fundamental and applied studies in the areas of transformation, polarization, and nonlinear optics in metamaterials.

© 2011 Optical Society of America

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References

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  1. J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
    [CrossRef] [PubMed]
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  3. W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, Nat. Photon. 1, 224 (2007).
    [CrossRef]
  4. E. E. Narimanov and A. V. Kildishev, Appl. Phys. Lett. 95, 041106 (2009).
    [CrossRef]
  5. A. V. Kildishev, L. J. Prokopeva, and E. E. Narimanov, Opt. Express 18, 16646 (2010).
    [CrossRef] [PubMed]
  6. Q. Cheng, T. J. Cui, W. X. Jiang, and B. G. Cai, New J. Phys. 12, 063006 (2010).
    [CrossRef]
  7. N. M. Litchinitser, A. I. Maimistov, I. R. Gabitov, R. Z. Sagdeev, and V. M. Shalaev, Opt. Lett. 33, 2350 (2008).
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    [CrossRef] [PubMed]
  9. M. Dalarsson and P. Tassin, Opt. Express 17, 6747 (2009).
    [CrossRef] [PubMed]
  10. I. Mozjerin, E. A. Gibson, E. P. Furlani, I. R. Gabitov, and N. M. Litchinitser, Opt. Lett. 35, 3240 (2010).
    [CrossRef] [PubMed]
  11. E. A. Gibson, M. Pennybacker, A. I. Maimistov, I. R. Gabitov, and N. M. Litchinitser, J. Opt. 13, 024013 (2011).
    [CrossRef]
  12. V. L. Ginzburg, Propagation of Electromagnetic Waves in Plasma (Gordon and Breach, 1962).
  13. L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media, 2nd ed. (Butterworth-Heinemann, 1984), Vol.  8.

2011 (1)

E. A. Gibson, M. Pennybacker, A. I. Maimistov, I. R. Gabitov, and N. M. Litchinitser, J. Opt. 13, 024013 (2011).
[CrossRef]

2010 (3)

2009 (2)

E. E. Narimanov and A. V. Kildishev, Appl. Phys. Lett. 95, 041106 (2009).
[CrossRef]

M. Dalarsson and P. Tassin, Opt. Express 17, 6747 (2009).
[CrossRef] [PubMed]

2008 (2)

2007 (1)

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

2006 (2)

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

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

Cai, B. G.

Q. Cheng, T. J. Cui, W. X. Jiang, and B. G. Cai, New J. Phys. 12, 063006 (2010).
[CrossRef]

Cai, W.

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

Cheng, Q.

Q. Cheng, T. J. Cui, W. X. Jiang, and B. G. Cai, New J. Phys. 12, 063006 (2010).
[CrossRef]

Chettiar, U. K.

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

Cui, T. J.

Q. Cheng, T. J. Cui, W. X. Jiang, and B. G. Cai, New J. Phys. 12, 063006 (2010).
[CrossRef]

Dalarsson, M.

Furlani, E. P.

Gabitov, I. R.

Gibson, E. A.

E. A. Gibson, M. Pennybacker, A. I. Maimistov, I. R. Gabitov, and N. M. Litchinitser, J. Opt. 13, 024013 (2011).
[CrossRef]

I. Mozjerin, E. A. Gibson, E. P. Furlani, I. R. Gabitov, and N. M. Litchinitser, Opt. Lett. 35, 3240 (2010).
[CrossRef] [PubMed]

Ginzburg, V. L.

V. L. Ginzburg, Propagation of Electromagnetic Waves in Plasma (Gordon and Breach, 1962).

Jiang, W. X.

Q. Cheng, T. J. Cui, W. X. Jiang, and B. G. Cai, New J. Phys. 12, 063006 (2010).
[CrossRef]

Kildishev, A. V.

A. V. Kildishev, L. J. Prokopeva, and E. E. Narimanov, Opt. Express 18, 16646 (2010).
[CrossRef] [PubMed]

E. E. Narimanov and A. V. Kildishev, Appl. Phys. Lett. 95, 041106 (2009).
[CrossRef]

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

Kim, K.

Landau, L. D.

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

Lee, D. H.

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.

Lim, H.

Litchinitser, N. M.

Maimistov, A. I.

E. A. Gibson, M. Pennybacker, A. I. Maimistov, I. R. Gabitov, and N. M. Litchinitser, J. Opt. 13, 024013 (2011).
[CrossRef]

N. M. Litchinitser, A. I. Maimistov, I. R. Gabitov, R. Z. Sagdeev, and V. M. Shalaev, Opt. Lett. 33, 2350 (2008).
[CrossRef] [PubMed]

Mozjerin, I.

Narimanov, E. E.

Pendry, J. B.

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

Pennybacker, M.

E. A. Gibson, M. Pennybacker, A. I. Maimistov, I. R. Gabitov, and N. M. Litchinitser, J. Opt. 13, 024013 (2011).
[CrossRef]

Pitaevskii, L. P.

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

Prokopeva, L. J.

Sagdeev, R. Z.

Schurig, D.

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

Shalaev, V. M.

Smith, D. R.

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

Tassin, P.

Appl. Phys. Lett. (1)

E. E. Narimanov and A. V. Kildishev, Appl. Phys. Lett. 95, 041106 (2009).
[CrossRef]

J. Opt. (1)

E. A. Gibson, M. Pennybacker, A. I. Maimistov, I. R. Gabitov, and N. M. Litchinitser, J. Opt. 13, 024013 (2011).
[CrossRef]

Nat. Photon. (1)

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

New J. Phys. (1)

Q. Cheng, T. J. Cui, W. X. Jiang, and B. G. Cai, New J. Phys. 12, 063006 (2010).
[CrossRef]

Opt. Express (3)

Opt. Lett. (2)

Science (2)

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

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

Other (2)

V. L. Ginzburg, Propagation of Electromagnetic Waves in Plasma (Gordon and Breach, 1962).

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

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Figures (3)

Fig. 1
Fig. 1

(a) Schematics of a transition metamaterial with ε and μ crossing zero at the same point. (b) Schematics of a transition metamaterial with ε and μ crossing zero at two different points in space.

Fig. 2
Fig. 2

(a) The absolute value of H x for TE wave as functions of x / h for l = 2 . (b) The absolute value of the magnetic field component H x for TE wave as functions of x / h for l = 4 for h = 10 , ε r , μ r = 4 , θ = π / 17 . The zero of μ is at x = 1 , the zero of ε is at x = l + 1 . (c) and (d) The absolute value of E x for TM wave as functions of x / h for the same parameters as in (a) and (b), respectively.

Fig. 3
Fig. 3

The value of (a) E 0 and (b) Δ S x / S 0 x as a function of l and θ for h = 10 , ε r , μ r = 4 .

Equations (8)

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Δ S x = c π E 0 2 ( h / λ ) ε r sin 2 θ ,
2 Φ ξ 2 μ ˜ ( ξ ) μ ˜ ( ξ ) Φ ξ + h 2 k 0 2 [ μ ˜ ( ξ ) ε ˜ ( ξ l / h ) sin 2 θ ] Φ = 0.
2 Φ ξ 2 1 ξ Φ ξ + h 2 k 0 2 [ ξ ( ξ l / h ) sin 2 θ ] Φ = 0.
ξ 1 , 2 = l / ( 2 h ) l 2 / ( 4 h 2 ) + sin 2 θ .
Φ 1 ( ξ ) = ξ 2 + sin 2 θ 8 ξ 4 + O ( ξ 5 ) .
Φ 2 ( ξ ) = 1 + l d 3 h ξ 3 8 d + 3 sin 4 θ 64 ξ 4 + O ( ξ 5 ) + ( sin 2 θ 2 ξ 2 + sin 4 θ 16 ξ 4 + O ( ξ 5 ) ) ln ξ ,
E ( x , z ) E 0 [ 1 + 1 2 sin 2 θ ( x h ) 2 ln ( x h ) ] exp ( i β z ) ,
ε ( x ) = ε r ( tanh ( ( x l 1 ) / h ) + i Δ ) μ ( x ) = μ r ( tanh ( ( x 1 ) / h ) + i Δ ) Δ = δ exp ( 0.5 ( x 1 ) 2 ) , δ = 10 3 .

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