Abstract

Extraordinary transmission through subwavelength apertures is usually observed in a narrow bandwidth range, and the transmission outside this range is low, in agreement with classical results. The analysis presented here is based on the Babinet’s principle and hence scattering by the complementary structure, where the apertures are replaced by finite scatterers. It is shown that the transmission cross section of a set of apertures in an opaque screen satisfies a sum rule that relates the transmission cross section integrated over all wavelengths with the polarizability of the complementary structure as defined by Babinet’s principle. The theoretical results are illustrated with numerical examples.

© 2009 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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2009

Y. Cui and S. He, Opt. Lett. 34, 16 (2009).
[CrossRef]

M. Gustafsson, C. Sohl, and G. Kristensson, IEEE Trans. Antennas Propag. 57, 1319 (2009).
[CrossRef]

2007

C. Sohl, M. Gustafsson, and G. Kristensson, J. Phys. A 40, 11165 (2007).
[CrossRef]

C. Sohl, M. Gustafsson, and G. Kristensson, J. Phys. D 40, 7146 (2007).
[CrossRef]

M. Gustafsson, C. Sohl, and G. Kristensson, Proc. R. Soc. London, Ser. A 463, 2589 (2007).
[CrossRef]

2004

K. J. K. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, Phys. Rev. Lett. 92, 183901 (2004).
[CrossRef] [PubMed]

2003

2001

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef] [PubMed]

1985

D. S. Jones, Q. J. Mech. Appl. Math. 38, 135 (1985).
[CrossRef]

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
[CrossRef] [PubMed]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley & Sons, 1983).

Bonod, N.

Cui, Y.

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
[CrossRef] [PubMed]

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
[CrossRef] [PubMed]

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef] [PubMed]

Enoch, S.

K. J. K. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, Phys. Rev. Lett. 92, 183901 (2004).
[CrossRef] [PubMed]

N. Bonod, S. Enoch, L. Li, P. Evgeny, and M. Neviere, Opt. Express 11, 482 (2003).
[CrossRef] [PubMed]

Evgeny, P.

García-Vidal, F. J.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef] [PubMed]

Gustafsson, M.

M. Gustafsson, C. Sohl, and G. Kristensson, IEEE Trans. Antennas Propag. 57, 1319 (2009).
[CrossRef]

C. Sohl, M. Gustafsson, and G. Kristensson, J. Phys. D 40, 7146 (2007).
[CrossRef]

M. Gustafsson, C. Sohl, and G. Kristensson, Proc. R. Soc. London, Ser. A 463, 2589 (2007).
[CrossRef]

C. Sohl, M. Gustafsson, and G. Kristensson, J. Phys. A 40, 11165 (2007).
[CrossRef]

He, S.

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley & Sons, 1983).

Jones, D. S.

D. S. Jones, Q. J. Mech. Appl. Math. 38, 135 (1985).
[CrossRef]

Kleinman, R. E.

R. E. Kleinman and T. B. A. Senior, in Low and High Frequency Asymptotics, Vol. 2 of Handbook on Acoustic, Electromagnetic and Elastic Wave Scattering, V.V.Varadan and V.K.Varadan, eds. (Elsevier Science, 1986), Chap. 1, pp. 1-70.

Koerkamp, K. J. K.

K. J. K. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, Phys. Rev. Lett. 92, 183901 (2004).
[CrossRef] [PubMed]

Kraus, J. D.

J. D. Kraus and R. J. Marhefka, Antennas, 3rd ed. (McGraw-Hill, 2002).

Kristensson, G.

M. Gustafsson, C. Sohl, and G. Kristensson, IEEE Trans. Antennas Propag. 57, 1319 (2009).
[CrossRef]

C. Sohl, M. Gustafsson, and G. Kristensson, J. Phys. D 40, 7146 (2007).
[CrossRef]

M. Gustafsson, C. Sohl, and G. Kristensson, Proc. R. Soc. London, Ser. A 463, 2589 (2007).
[CrossRef]

C. Sohl, M. Gustafsson, and G. Kristensson, J. Phys. A 40, 11165 (2007).
[CrossRef]

Kuipers, L.

K. J. K. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, Phys. Rev. Lett. 92, 183901 (2004).
[CrossRef] [PubMed]

Landau, L. D.

L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskiĭ, Electrodynamics of Continuous Media, 2nd ed. (Pergamon, 1984).

Lezec, H. J.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef] [PubMed]

Li, L.

Lifshitz, E. M.

L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskiĭ, Electrodynamics of Continuous Media, 2nd ed. (Pergamon, 1984).

Maier, S. A.

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer-Verlag, 2007).

Marhefka, R. J.

J. D. Kraus and R. J. Marhefka, Antennas, 3rd ed. (McGraw-Hill, 2002).

Martín-Moreno, L.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef] [PubMed]

Neviere, M.

Nussenzveig, H. M.

H. M. Nussenzveig, Causality and Dispersion Relations (Academic, 1972).

Pellerin, K. M.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef] [PubMed]

Pendry, J. B.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef] [PubMed]

Pitaevskii, L. P.

L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskiĭ, Electrodynamics of Continuous Media, 2nd ed. (Pergamon, 1984).

Segerink, F. B.

K. J. K. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, Phys. Rev. Lett. 92, 183901 (2004).
[CrossRef] [PubMed]

Senior, T. B. A.

R. E. Kleinman and T. B. A. Senior, in Low and High Frequency Asymptotics, Vol. 2 of Handbook on Acoustic, Electromagnetic and Elastic Wave Scattering, V.V.Varadan and V.K.Varadan, eds. (Elsevier Science, 1986), Chap. 1, pp. 1-70.

Sohl, C.

M. Gustafsson, C. Sohl, and G. Kristensson, IEEE Trans. Antennas Propag. 57, 1319 (2009).
[CrossRef]

M. Gustafsson, C. Sohl, and G. Kristensson, Proc. R. Soc. London, Ser. A 463, 2589 (2007).
[CrossRef]

C. Sohl, M. Gustafsson, and G. Kristensson, J. Phys. A 40, 11165 (2007).
[CrossRef]

C. Sohl, M. Gustafsson, and G. Kristensson, J. Phys. D 40, 7146 (2007).
[CrossRef]

Thio, T.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef] [PubMed]

van Bladel, J.

J. van Bladel, Electromagnetic Fields, 2nd ed. (IEEE Press, 2007).
[CrossRef]

van Hulst, N. F.

K. J. K. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, Phys. Rev. Lett. 92, 183901 (2004).
[CrossRef] [PubMed]

Zemanian, A. H.

A. H. Zemanian, Realizability Theory for Continuous Linear Systems (Dover, 1996).

IEEE Trans. Antennas Propag.

M. Gustafsson, C. Sohl, and G. Kristensson, IEEE Trans. Antennas Propag. 57, 1319 (2009).
[CrossRef]

J. Phys. A

C. Sohl, M. Gustafsson, and G. Kristensson, J. Phys. A 40, 11165 (2007).
[CrossRef]

J. Phys. D

C. Sohl, M. Gustafsson, and G. Kristensson, J. Phys. D 40, 7146 (2007).
[CrossRef]

Nature

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef] [PubMed]

K. J. K. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, Phys. Rev. Lett. 92, 183901 (2004).
[CrossRef] [PubMed]

Proc. R. Soc. London, Ser. A

M. Gustafsson, C. Sohl, and G. Kristensson, Proc. R. Soc. London, Ser. A 463, 2589 (2007).
[CrossRef]

Q. J. Mech. Appl. Math.

D. S. Jones, Q. J. Mech. Appl. Math. 38, 135 (1985).
[CrossRef]

Other

J. D. Kraus and R. J. Marhefka, Antennas, 3rd ed. (McGraw-Hill, 2002).

L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskiĭ, Electrodynamics of Continuous Media, 2nd ed. (Pergamon, 1984).

J. van Bladel, Electromagnetic Fields, 2nd ed. (IEEE Press, 2007).
[CrossRef]

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer-Verlag, 2007).

H. M. Nussenzveig, Causality and Dispersion Relations (Academic, 1972).

A. H. Zemanian, Realizability Theory for Continuous Linear Systems (Dover, 1996).

R. E. Kleinman and T. B. A. Senior, in Low and High Frequency Asymptotics, Vol. 2 of Handbook on Acoustic, Electromagnetic and Elastic Wave Scattering, V.V.Varadan and V.K.Varadan, eds. (Elsevier Science, 1986), Chap. 1, pp. 1-70.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley & Sons, 1983).

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Figures (4)

Fig. 1
Fig. 1

Illustration of the Babinet’s principle where the field E t , transmitted though the aperture S m in (a), is determined by the scattered field E s of the complementary structure in (b), i.e., E t = E s .

Fig. 2
Fig. 2

High-contrast polarizability dyadics γ for the (a) solid disc and (b) the split-ring resonator.

Fig. 3
Fig. 3

Transmission cross sections for circular and split-ring apertures in an opaque screen for an incident plane wave propagating in the normal direction of the screen. The shaded boxes illustrate the bound [Eq. (5)], cf. Fig. 2.

Fig. 4
Fig. 4

Illustrations of the normalized power-flux density though the split-ring aperture at (a) λ = 5.6 a and (b) λ = 12.1 a , cf., Fig. 3.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

P t = Re 1 2 S m z ̂ E t × H t * dS = 1 2 η 0 σ t E i 2 ,
h ( λ ) = ( e ̂ γ e e ̂ + ( k ̂ × e ̂ ) γ m ( k ̂ × e ̂ ) ) 2 π λ + O ( λ 2 )
2 π 2 0 σ t ( λ ; k ̂ , e ̂ ) d λ = e ̂ γ e e ̂ + ( k ̂ × e ̂ ) γ m ( k ̂ × e ̂ ) .
2 π 2 0 σ t ( λ ; z ̂ , e ̂ ) d λ = ( z ̂ × e ̂ ) γ m ( z ̂ × e ̂ ) .
Λ min λ Λ σ t ( λ ; z ̂ , e ̂ ) π 2 2 ( z ̂ × e ̂ ) γ m ( z ̂ × e ̂ ) ,
γ e ̂ = S m r ρ ( r ) dS ,
r e ̂ + C = S m ρ ( r ) 4 π r r dS for r S m

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