Abstract

We investigate the effect of anomalous field enhancement in metamaterials (MMs) where the effective refractive index gradually changes from positive to negative values, i.e., transition MMs. We demonstrate that considerable field enhancement can be achieved in lossy optical transition MMs that have electromagnetic material properties obtained from experimental data. The field enhancement factor is found to be polarization dependent and largely determined by the material parameters and the width of the transition layer.

© 2010 Optical Society of America

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References

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    [CrossRef]
  4. A. V. Kildishev and V. M. Shalaev, Opt. Lett. 33, 43 (2008).
    [CrossRef]
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    [CrossRef]
  6. E. P. Furlani and A. Baev, Phys. Rev. E 79, 026607 (2009).
    [CrossRef]
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    [CrossRef] [PubMed]
  8. V. L. Ginzburg, The Propagation of Electromagnetic Waves in Plasma (Pergamon, 1970).
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    [CrossRef] [PubMed]
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2009 (4)

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

E. P. Furlani and A. Baev, Phys. Rev. E 79, 026607 (2009).
[CrossRef]

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

N. M. Litchinitser and V. M. Shalaev, J. Opt. Soc. Am. B 26, B161 (2009).
[CrossRef]

2008 (4)

2007 (1)

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

2006 (2)

Baev, A.

E. P. Furlani and A. Baev, Phys. Rev. E 79, 026607 (2009).
[CrossRef]

Cai, W.

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

Chettiar, U. K.

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

Dalarsson, M.

Dolling, G.

Enkrich, C.

Furlani, E. P.

E. P. Furlani and A. Baev, Phys. Rev. E 79, 026607 (2009).
[CrossRef]

Gabitov, I. R.

Ginzburg, V. L.

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

Kildishev, A. V.

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

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. Photon. 1, 224 (2007).
[CrossRef]

Kim, K.

Lee, D.-H.

Lim, H.

Linden, S.

Litchinitser, N. M.

Maimistov, A. I.

Narimanov, E. E.

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

Pendry, J. B.

Rahm, M.

Roberts, D. A.

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.

Soukoulis, C. M.

Tassin, P.

Wegener, M.

Appl. Phys. Lett. (1)

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

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

Nat. Photon. (1)

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

Opt. Express (3)

Opt. Lett. (3)

Phys. Rev. E (1)

E. P. Furlani and A. Baev, Phys. Rev. E 79, 026607 (2009).
[CrossRef]

Science (1)

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

Other (1)

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

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Figures (3)

Fig. 1
Fig. 1

(a) Schematic of the transition layer between PIM and NIM. (b) Real and imaginary parts of μ r (solid curve) and ε r (dashed curve) in the transition layer with L = 2 λ . (c) Surface plot of the y component of the electric field E y for a TE wave incident at an angle of α = π / 17 for the transition MM with the same parameters as in (b). (d) The same as in (c) but for transition MM with infinitesimal losses at the zero-index point.

Fig. 2
Fig. 2

Absolute value of the x component of the (a) magnetic field | H x | and (b) electric field | E x | in the transition layer with the experimentally obtained parameters as functions of x for different values of the width of the transition layer L.

Fig. 3
Fig. 3

Enhancement factor for TE and TM waves as functions of ε r 0 and μ r 0 . Dotted curve shows the FOM of the MM with ε r 0 = μ r 0 = 1 as a function of ε r 0 and μ r 0 .

Equations (5)

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2 E y x 2 + 2 E y z 2 1 μ r ( x ) μ r x E y x + ε r ( x ) μ r ( x ) k 0 2 E y = 0.
H x = ε r 0 μ r 0 sin α η 0 μ r ( x ) E y , E x = ε r 0 μ r 0 η 0 sin α ε r ( x ) H y ,
ε r ( x ) = ε r 0 tanh ( 2 x L ) + i ε r 0 f ( x ) , μ r ( x ) = μ r 0 tanh ( 2 x L ) + i μ r 0 f ( x ) ,
η TE 2 | E y ( 0 ) | | E y ( x ) | M , η TM 2 | H y ( 0 ) | | H y ( x ) | E ,
F = ( E + M ) / ( E M 1 + ( 1 + E 2 ) ( 1 + M 2 ) ) .

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