Abstract

We demonstrate that the electromagnetic properties of a plasmonic metamaterial, composed of a perfectly conducting metal film perforated with an array of holes, can be effectively described by a structureless, three layer film. The enhanced transmission, first observed by Ebbessen, is identified with resonant tunneling in the equivalent three layer system and perfect transmission is shown to be possible below the critical thickness of a metamaterial. The nature of modes mediating perfect transmission is clarified.

© 2007 Optical Society of America

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References

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  1. See for example, N. Engheta and R. W. Ziolkowski, eds., Metamaterials, Physics and Engineering Applications, (IEEE Wiley Interscience, 2006).
  2. J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, "Mimicking surface plasmons with structured surfaces," Science 305, 847-848 (2004).
    [CrossRef] [PubMed]
  3. A. P. Hibbins, B. R. Evans, and J. R. Sambles, "Experimental verification of designer surface plasmons," Science 308, 670-672 (2005).
    [CrossRef] [PubMed]
  4. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998).
    [CrossRef]
  5. L. L. Chang, L. Esaki, and R. Tsu, "Resonant tunneling in semiconductor double barriers," Appl. Phys. Lett. 24, 593-595 (1974).
    [CrossRef]
  6. J. W. Lee, M. A. Seo, J. Y. So, Y. H. Ahn, D. S. Kim, S. C. Jeoung, C. Lienau, and Q. H. Park, "Invisible plasmonic meta-materials through impedance matching to vacuum," Opt. Express 13, 10681-10687 (2005);M. Tanaka, F. Miyamaru, M. Hangyo, T. Tanaka, M. Akazawa, and E. Sano, "Effect of a thin dielectric layer on terahertz transmission characteristics for metal hole arrays" Opt. Lett. 30, 1210-1212 (2005).
    [CrossRef] [PubMed]
  7. Similar double feature has been observed in A. P. Hibbins, M. J. Lockyear, I. R. Hooper, and J. R. Sambles, "Waveguide arrays as plasmonic metamaterials: transmission below cut-off" Phys. Rev. Lett. 96, 073904 (2006).
    [CrossRef] [PubMed]
  8. H. Lochbihler, "Surface polaritons on gold-wire gratings," Phys. Rev. B 50, 4795-4801 (1994).
    [CrossRef]
  9. K. G. Lee and Q-Han Park, "Coupling of surface plasmon polaritons and light in metallic nanoslits," Phys. Rev. Lett. 95, 103902, (2005).
    [CrossRef] [PubMed]
  10. M. Born and E. Wolf, Principles of Optics, (Cambridge U. P., 1999).
  11. R. Dragila, B. Luther-Davies, and S. Vukovic, "High transparency of classically opaque metallic films, " Phys. Rev. Lett. 55, 1117-1120 (1985).
    [CrossRef] [PubMed]
  12. L. Zhou, W. Wen, C. T. Chan, and P. Sheng, "Electromagnetic-wave tunneling through negative-permittivity media with high magnetic fields," Phys. Rev. Lett. 94, 243905 (2005).
    [CrossRef]
  13. I. R. Hooper, T. W. Preist, and J. R. Sambles, "Making tunnel barriers (including metals) transparent," Phys. Rev. Lett. 97, 053902 (2006).
    [CrossRef] [PubMed]

2006 (2)

Similar double feature has been observed in A. P. Hibbins, M. J. Lockyear, I. R. Hooper, and J. R. Sambles, "Waveguide arrays as plasmonic metamaterials: transmission below cut-off" Phys. Rev. Lett. 96, 073904 (2006).
[CrossRef] [PubMed]

I. R. Hooper, T. W. Preist, and J. R. Sambles, "Making tunnel barriers (including metals) transparent," Phys. Rev. Lett. 97, 053902 (2006).
[CrossRef] [PubMed]

2005 (3)

2004 (1)

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, "Mimicking surface plasmons with structured surfaces," Science 305, 847-848 (2004).
[CrossRef] [PubMed]

1998 (1)

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998).
[CrossRef]

1994 (1)

H. Lochbihler, "Surface polaritons on gold-wire gratings," Phys. Rev. B 50, 4795-4801 (1994).
[CrossRef]

1985 (1)

R. Dragila, B. Luther-Davies, and S. Vukovic, "High transparency of classically opaque metallic films, " Phys. Rev. Lett. 55, 1117-1120 (1985).
[CrossRef] [PubMed]

1974 (1)

L. L. Chang, L. Esaki, and R. Tsu, "Resonant tunneling in semiconductor double barriers," Appl. Phys. Lett. 24, 593-595 (1974).
[CrossRef]

Ahn, Y. H.

Akazawa, M.

Chan, C. T.

L. Zhou, W. Wen, C. T. Chan, and P. Sheng, "Electromagnetic-wave tunneling through negative-permittivity media with high magnetic fields," Phys. Rev. Lett. 94, 243905 (2005).
[CrossRef]

Chang, L. L.

L. L. Chang, L. Esaki, and R. Tsu, "Resonant tunneling in semiconductor double barriers," Appl. Phys. Lett. 24, 593-595 (1974).
[CrossRef]

Dragila, R.

R. Dragila, B. Luther-Davies, and S. Vukovic, "High transparency of classically opaque metallic films, " Phys. Rev. Lett. 55, 1117-1120 (1985).
[CrossRef] [PubMed]

Ebbesen, T. W.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998).
[CrossRef]

Esaki, L.

L. L. Chang, L. Esaki, and R. Tsu, "Resonant tunneling in semiconductor double barriers," Appl. Phys. Lett. 24, 593-595 (1974).
[CrossRef]

Evans, B. R.

A. P. Hibbins, B. R. Evans, and J. R. Sambles, "Experimental verification of designer surface plasmons," Science 308, 670-672 (2005).
[CrossRef] [PubMed]

Garcia-Vidal, F. J.

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, "Mimicking surface plasmons with structured surfaces," Science 305, 847-848 (2004).
[CrossRef] [PubMed]

Ghaemi, H. F.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998).
[CrossRef]

Hangyo, M.

Hibbins, A. P.

A. P. Hibbins, B. R. Evans, and J. R. Sambles, "Experimental verification of designer surface plasmons," Science 308, 670-672 (2005).
[CrossRef] [PubMed]

Hooper, I. R.

I. R. Hooper, T. W. Preist, and J. R. Sambles, "Making tunnel barriers (including metals) transparent," Phys. Rev. Lett. 97, 053902 (2006).
[CrossRef] [PubMed]

Jeoung, S. C.

Kim, D. S.

Lee, J. W.

Lezec, H. J.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998).
[CrossRef]

Lienau, C.

Lochbihler, H.

H. Lochbihler, "Surface polaritons on gold-wire gratings," Phys. Rev. B 50, 4795-4801 (1994).
[CrossRef]

Luther-Davies, B.

R. Dragila, B. Luther-Davies, and S. Vukovic, "High transparency of classically opaque metallic films, " Phys. Rev. Lett. 55, 1117-1120 (1985).
[CrossRef] [PubMed]

Martin-Moreno, L.

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, "Mimicking surface plasmons with structured surfaces," Science 305, 847-848 (2004).
[CrossRef] [PubMed]

Miyamaru, F.

Park, Q. H.

Pendry, J. B.

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, "Mimicking surface plasmons with structured surfaces," Science 305, 847-848 (2004).
[CrossRef] [PubMed]

Preist, T. W.

I. R. Hooper, T. W. Preist, and J. R. Sambles, "Making tunnel barriers (including metals) transparent," Phys. Rev. Lett. 97, 053902 (2006).
[CrossRef] [PubMed]

Sambles, J. R.

I. R. Hooper, T. W. Preist, and J. R. Sambles, "Making tunnel barriers (including metals) transparent," Phys. Rev. Lett. 97, 053902 (2006).
[CrossRef] [PubMed]

A. P. Hibbins, B. R. Evans, and J. R. Sambles, "Experimental verification of designer surface plasmons," Science 308, 670-672 (2005).
[CrossRef] [PubMed]

Sano, E.

Seo, M. A.

Sheng, P.

L. Zhou, W. Wen, C. T. Chan, and P. Sheng, "Electromagnetic-wave tunneling through negative-permittivity media with high magnetic fields," Phys. Rev. Lett. 94, 243905 (2005).
[CrossRef]

So, J. Y.

Tanaka, M.

Tanaka, T.

Thio, T.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998).
[CrossRef]

Tsu, R.

L. L. Chang, L. Esaki, and R. Tsu, "Resonant tunneling in semiconductor double barriers," Appl. Phys. Lett. 24, 593-595 (1974).
[CrossRef]

Vukovic, S.

R. Dragila, B. Luther-Davies, and S. Vukovic, "High transparency of classically opaque metallic films, " Phys. Rev. Lett. 55, 1117-1120 (1985).
[CrossRef] [PubMed]

Wen, W.

L. Zhou, W. Wen, C. T. Chan, and P. Sheng, "Electromagnetic-wave tunneling through negative-permittivity media with high magnetic fields," Phys. Rev. Lett. 94, 243905 (2005).
[CrossRef]

Wolff, P. A.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998).
[CrossRef]

Zhou, L.

L. Zhou, W. Wen, C. T. Chan, and P. Sheng, "Electromagnetic-wave tunneling through negative-permittivity media with high magnetic fields," Phys. Rev. Lett. 94, 243905 (2005).
[CrossRef]

Appl. Phys. Lett. (1)

L. L. Chang, L. Esaki, and R. Tsu, "Resonant tunneling in semiconductor double barriers," Appl. Phys. Lett. 24, 593-595 (1974).
[CrossRef]

Nature (1)

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998).
[CrossRef]

Opt. Express (1)

Phys. Rev. B (1)

H. Lochbihler, "Surface polaritons on gold-wire gratings," Phys. Rev. B 50, 4795-4801 (1994).
[CrossRef]

Phys. Rev. Lett. (4)

Similar double feature has been observed in A. P. Hibbins, M. J. Lockyear, I. R. Hooper, and J. R. Sambles, "Waveguide arrays as plasmonic metamaterials: transmission below cut-off" Phys. Rev. Lett. 96, 073904 (2006).
[CrossRef] [PubMed]

R. Dragila, B. Luther-Davies, and S. Vukovic, "High transparency of classically opaque metallic films, " Phys. Rev. Lett. 55, 1117-1120 (1985).
[CrossRef] [PubMed]

L. Zhou, W. Wen, C. T. Chan, and P. Sheng, "Electromagnetic-wave tunneling through negative-permittivity media with high magnetic fields," Phys. Rev. Lett. 94, 243905 (2005).
[CrossRef]

I. R. Hooper, T. W. Preist, and J. R. Sambles, "Making tunnel barriers (including metals) transparent," Phys. Rev. Lett. 97, 053902 (2006).
[CrossRef] [PubMed]

Science (2)

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, "Mimicking surface plasmons with structured surfaces," Science 305, 847-848 (2004).
[CrossRef] [PubMed]

A. P. Hibbins, B. R. Evans, and J. R. Sambles, "Experimental verification of designer surface plasmons," Science 308, 670-672 (2005).
[CrossRef] [PubMed]

Other (3)

See for example, N. Engheta and R. W. Ziolkowski, eds., Metamaterials, Physics and Engineering Applications, (IEEE Wiley Interscience, 2006).

K. G. Lee and Q-Han Park, "Coupling of surface plasmon polaritons and light in metallic nanoslits," Phys. Rev. Lett. 95, 103902, (2005).
[CrossRef] [PubMed]

M. Born and E. Wolf, Principles of Optics, (Cambridge U. P., 1999).

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Figures (5)

Fig. 1.
Fig. 1.

Transmission spectrum of PM(thick line) with a = 0.5L,h = 0.25L. Insets illustrate structures of (A) PM and (B) the three layer film. The cross symbols represent the transmission of three layer film with thickness d 1 = 4L,d 2 = 10L.

Fig. 2.
Fig. 2.

Dispersion of refractive indices n 1,n 2 and thickness d 1.

Fig. 3.
Fig. 3.

Transmission vs. thickness for PM. Two perfect transmission peaks merge into a single peak and then reduce as thickness h passes the critical value hc = 0.75 L.

Fig. 4.
Fig. 4.

Measured transmission spectrum in magnitude ∣T∣(filled circles) and in normalized argument Arg(T)/π (open circles). Sample parameters are d = 400μm,a = 200μm, thickness h = 17μm. Insets show a theoretical result from Eq. (1) with a close-up image.

Fig. 5.
Fig. 5.

FDTD calculation of transmission spectra for PM made of perfector, silver, gold with L = 800nm,a = 400nm,h = 200nm.

Equations (10)

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T = 32 k a 2 μ π 2 L 2 [ ( 1 + μ 1 kW ) 2 e iμh ( 1 μ 1 kW ) 2 e iμh ] 1
W = m , n = 1 ( 2 kL ) 2 1 ( m 2 + n 2 ) ( 2 π kL ) 2 a 2 2 L 2 [ sinc ( π 2 mπa L ) + ( π 2 + mπa L ) ] 2 [ sinc ( nπa L ) ] 2 ,
T ´ = 16 n 2 n 1 2 D + 2 e i n 2 k d 2 D 2 e i n 2 k d 2 , D ± ( n 1 1 ) ( n 1 ± 1 ) e ik n 1 d 1 ( n 1 + 1 ) ( n 1 n 2 ) e ik n 1 d 1 .
n 2 = μh k d 2 , n 1 2 = 8 h a 2 π 2 L 2 d 2 + h 2 π 2 L 2 β 2 8 h a 2 d 2 π 2 L 2 d 2 2 , cot ( k n 1 d 1 ) = h π 2 L 2 β n 1 ( π 1 L 2 d 2 8 h a 2 ) .
tanh ( μ ̅ h ) = 2 μ ̅ k 2 W 2 + μ ̅ 2 ,
β ± μ k coth ( μ ̅ h ) ± [ μ 2 k 2 sinh 2 ( μ ̅ h ) 64 a 4 π 2 d 4 ] 1 2 ,
tan ( α ± ) ± 8 a 2 π 2 d 2 [ μ ̅ 2 k 2 sinh 2 ( μ ̅ h ) 64 a 2 π 2 d 2 1 2 .
μ ̅ 2 k 2 sinh 2 ( μ ̅ h c ) 64 a 2 π 2 d 2 = 0 .
T = 4 a L [ e ikh ( 1 + kW ) 2 e ikh ( 1 kW ) 1 ] 1 , W = a kL + n = 1 L ( 1 cos ( 2 πna L ) ) π 2 n 2 a k 2 ( 2 πn L ) 2
n 2 = h d 2 , n 1 2 = [ a d 2 Lh + β 2 k 2 d 2 2 L a d 2 h L h 2 ] 1 , cot ( k n 1 d 1 ) = n 1 d 2 L a d 2 Lh ,

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