Abstract

The diffraction of light by a single subwavelength hole in a highly conductive metallic sheet is analyzed with a recently developed differential theory that is able to plot the nearly electromagnetic field. Using rigorous electromagnetic and phenomenological analysis, we show that a single subwavelength hole can excite surface-plasmon resonance that contributes greatly to extraordinary transmission.

© 2005 Optical Society of America

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References

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  1. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, P. A. Wolff, “Extraordinary optical transmission through subwave-length hole arrays,” Nature 391, 667–669 (1998).
    [CrossRef]
  2. M. J. Levene, J. Korlach, S. W. Turner, M. Foquet, H. G. Craighead, W. W. Webb, “Zero-mode waveguides for single-molecule analysis at high concentrations,” Science 299, 682–686 (2003).
    [CrossRef] [PubMed]
  3. F. J. Garcia-Vidal, L. Martin-Moreno, H. J. Lezec, T. W. Ebbesen, “Focusing light with a single subwavelength aperture flanked by surface corrugations,” Appl. Phys. Lett. 83, 4500–4502 (2003).
    [CrossRef]
  4. L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, A. Degiron, T. W. Ebbesen, “Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,” Phys. Rev. Lett. 90, 167401 (2003).
    [CrossRef] [PubMed]
  5. A. Degiron, H. Lezec, N. Yamamoto, T. Ebbesen, “Optical transmission properties of a single subwavelength aperture in a real metal,” Opt. Commun. 239, 61–66 (2004).
    [CrossRef]
  6. A. Moreau, G. Granet, F. I. Baida, D. Van Labeke, “Light transmission by subwavelength square coaxial aperture arrays in metallic films,” Opt. Express 11, 1131–1136 (2003), http://www.opticsexpress.org .
    [CrossRef] [PubMed]
  7. R. Zakharian, M. Mansuripur, J. V. Moloney, “Transmission of ligth through small elliptical apertures,” Opt. Express 12, 2631–2648 (2004), http://www.opticsexpress.org .
    [CrossRef] [PubMed]
  8. L. Li, “Use of Fourier series in the analysis of discontinuous periodic structures,” J. Opt. Soc. Am. A 13, 1870–1876 (1996).
    [CrossRef]
  9. E. Popov, M. Nevière, “Maxwell equations in Fourier space: fast converging formulation for diffraction by arbitrary shaped, periodic, anisotropic media,” J. Opt. Soc. Am. A 18, 2886–2894 (2001).
    [CrossRef]
  10. M. Nevière, E. Popov, Light Propagation in Periodic Media: Differential Theory and Design (Marcel Dekker, New York, 2003).
  11. N. Bonod, E. Popov, M. Nevière, “Differential theory of diffraction by finite cylindrical objects,” J. Opt. Soc. Am. A (to be published).
  12. E. Popov, M. Nevière, N. Bonod, “Factorization of products of discontinuous functions applied to Fourier–Bessel basis,” J. Opt. Soc. Am. A 21, 46–52 (2004).
    [CrossRef]
  13. L. Yin, V. K. Vlasko-Vlasov, A. Rydh, J. Pearson, U. Welp, S. H. Chang, S. K. Gray, G. C. Schatz, D. B. Brown, C. W. Kimball, “Surface plasmons at single nanoholes in Au films,” Appl. Phys. Lett. 85, 467–469 (2004).
    [CrossRef]
  14. A. Snyder, J. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).
  15. R. Petit, ed., Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980), Chap. 5.
    [CrossRef]

2004 (4)

A. Degiron, H. Lezec, N. Yamamoto, T. Ebbesen, “Optical transmission properties of a single subwavelength aperture in a real metal,” Opt. Commun. 239, 61–66 (2004).
[CrossRef]

R. Zakharian, M. Mansuripur, J. V. Moloney, “Transmission of ligth through small elliptical apertures,” Opt. Express 12, 2631–2648 (2004), http://www.opticsexpress.org .
[CrossRef] [PubMed]

E. Popov, M. Nevière, N. Bonod, “Factorization of products of discontinuous functions applied to Fourier–Bessel basis,” J. Opt. Soc. Am. A 21, 46–52 (2004).
[CrossRef]

L. Yin, V. K. Vlasko-Vlasov, A. Rydh, J. Pearson, U. Welp, S. H. Chang, S. K. Gray, G. C. Schatz, D. B. Brown, C. W. Kimball, “Surface plasmons at single nanoholes in Au films,” Appl. Phys. Lett. 85, 467–469 (2004).
[CrossRef]

2003 (4)

A. Moreau, G. Granet, F. I. Baida, D. Van Labeke, “Light transmission by subwavelength square coaxial aperture arrays in metallic films,” Opt. Express 11, 1131–1136 (2003), http://www.opticsexpress.org .
[CrossRef] [PubMed]

M. J. Levene, J. Korlach, S. W. Turner, M. Foquet, H. G. Craighead, W. W. Webb, “Zero-mode waveguides for single-molecule analysis at high concentrations,” Science 299, 682–686 (2003).
[CrossRef] [PubMed]

F. J. Garcia-Vidal, L. Martin-Moreno, H. J. Lezec, T. W. Ebbesen, “Focusing light with a single subwavelength aperture flanked by surface corrugations,” Appl. Phys. Lett. 83, 4500–4502 (2003).
[CrossRef]

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, A. Degiron, T. W. Ebbesen, “Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,” Phys. Rev. Lett. 90, 167401 (2003).
[CrossRef] [PubMed]

2001 (1)

1998 (1)

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, P. A. Wolff, “Extraordinary optical transmission through subwave-length hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

1996 (1)

Baida, F. I.

Bonod, N.

E. Popov, M. Nevière, N. Bonod, “Factorization of products of discontinuous functions applied to Fourier–Bessel basis,” J. Opt. Soc. Am. A 21, 46–52 (2004).
[CrossRef]

N. Bonod, E. Popov, M. Nevière, “Differential theory of diffraction by finite cylindrical objects,” J. Opt. Soc. Am. A (to be published).

Brown, D. B.

L. Yin, V. K. Vlasko-Vlasov, A. Rydh, J. Pearson, U. Welp, S. H. Chang, S. K. Gray, G. C. Schatz, D. B. Brown, C. W. Kimball, “Surface plasmons at single nanoholes in Au films,” Appl. Phys. Lett. 85, 467–469 (2004).
[CrossRef]

Chang, S. H.

L. Yin, V. K. Vlasko-Vlasov, A. Rydh, J. Pearson, U. Welp, S. H. Chang, S. K. Gray, G. C. Schatz, D. B. Brown, C. W. Kimball, “Surface plasmons at single nanoholes in Au films,” Appl. Phys. Lett. 85, 467–469 (2004).
[CrossRef]

Craighead, H. G.

M. J. Levene, J. Korlach, S. W. Turner, M. Foquet, H. G. Craighead, W. W. Webb, “Zero-mode waveguides for single-molecule analysis at high concentrations,” Science 299, 682–686 (2003).
[CrossRef] [PubMed]

Degiron, A.

A. Degiron, H. Lezec, N. Yamamoto, T. Ebbesen, “Optical transmission properties of a single subwavelength aperture in a real metal,” Opt. Commun. 239, 61–66 (2004).
[CrossRef]

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, A. Degiron, T. W. Ebbesen, “Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,” Phys. Rev. Lett. 90, 167401 (2003).
[CrossRef] [PubMed]

Ebbesen, T.

A. Degiron, H. Lezec, N. Yamamoto, T. Ebbesen, “Optical transmission properties of a single subwavelength aperture in a real metal,” Opt. Commun. 239, 61–66 (2004).
[CrossRef]

Ebbesen, T. W.

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, A. Degiron, T. W. Ebbesen, “Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,” Phys. Rev. Lett. 90, 167401 (2003).
[CrossRef] [PubMed]

F. J. Garcia-Vidal, L. Martin-Moreno, H. J. Lezec, T. W. Ebbesen, “Focusing light with a single subwavelength aperture flanked by surface corrugations,” Appl. Phys. Lett. 83, 4500–4502 (2003).
[CrossRef]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, P. A. Wolff, “Extraordinary optical transmission through subwave-length hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

Foquet, M.

M. J. Levene, J. Korlach, S. W. Turner, M. Foquet, H. G. Craighead, W. W. Webb, “Zero-mode waveguides for single-molecule analysis at high concentrations,” Science 299, 682–686 (2003).
[CrossRef] [PubMed]

Garcia-Vidal, F. J.

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, A. Degiron, T. W. Ebbesen, “Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,” Phys. Rev. Lett. 90, 167401 (2003).
[CrossRef] [PubMed]

F. J. Garcia-Vidal, L. Martin-Moreno, H. J. Lezec, T. W. Ebbesen, “Focusing light with a single subwavelength aperture flanked by surface corrugations,” Appl. Phys. Lett. 83, 4500–4502 (2003).
[CrossRef]

Ghaemi, H. F.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, P. A. Wolff, “Extraordinary optical transmission through subwave-length hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

Granet, G.

Gray, S. K.

L. Yin, V. K. Vlasko-Vlasov, A. Rydh, J. Pearson, U. Welp, S. H. Chang, S. K. Gray, G. C. Schatz, D. B. Brown, C. W. Kimball, “Surface plasmons at single nanoholes in Au films,” Appl. Phys. Lett. 85, 467–469 (2004).
[CrossRef]

Kimball, C. W.

L. Yin, V. K. Vlasko-Vlasov, A. Rydh, J. Pearson, U. Welp, S. H. Chang, S. K. Gray, G. C. Schatz, D. B. Brown, C. W. Kimball, “Surface plasmons at single nanoholes in Au films,” Appl. Phys. Lett. 85, 467–469 (2004).
[CrossRef]

Korlach, J.

M. J. Levene, J. Korlach, S. W. Turner, M. Foquet, H. G. Craighead, W. W. Webb, “Zero-mode waveguides for single-molecule analysis at high concentrations,” Science 299, 682–686 (2003).
[CrossRef] [PubMed]

Levene, M. J.

M. J. Levene, J. Korlach, S. W. Turner, M. Foquet, H. G. Craighead, W. W. Webb, “Zero-mode waveguides for single-molecule analysis at high concentrations,” Science 299, 682–686 (2003).
[CrossRef] [PubMed]

Lezec, H.

A. Degiron, H. Lezec, N. Yamamoto, T. Ebbesen, “Optical transmission properties of a single subwavelength aperture in a real metal,” Opt. Commun. 239, 61–66 (2004).
[CrossRef]

Lezec, H. J.

F. J. Garcia-Vidal, L. Martin-Moreno, H. J. Lezec, T. W. Ebbesen, “Focusing light with a single subwavelength aperture flanked by surface corrugations,” Appl. Phys. Lett. 83, 4500–4502 (2003).
[CrossRef]

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, A. Degiron, T. W. Ebbesen, “Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,” Phys. Rev. Lett. 90, 167401 (2003).
[CrossRef] [PubMed]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, P. A. Wolff, “Extraordinary optical transmission through subwave-length hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

Li, L.

Love, J.

A. Snyder, J. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).

Mansuripur, M.

Martin-Moreno, L.

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, A. Degiron, T. W. Ebbesen, “Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,” Phys. Rev. Lett. 90, 167401 (2003).
[CrossRef] [PubMed]

F. J. Garcia-Vidal, L. Martin-Moreno, H. J. Lezec, T. W. Ebbesen, “Focusing light with a single subwavelength aperture flanked by surface corrugations,” Appl. Phys. Lett. 83, 4500–4502 (2003).
[CrossRef]

Moloney, J. V.

Moreau, A.

Nevière, M.

E. Popov, M. Nevière, N. Bonod, “Factorization of products of discontinuous functions applied to Fourier–Bessel basis,” J. Opt. Soc. Am. A 21, 46–52 (2004).
[CrossRef]

E. Popov, M. Nevière, “Maxwell equations in Fourier space: fast converging formulation for diffraction by arbitrary shaped, periodic, anisotropic media,” J. Opt. Soc. Am. A 18, 2886–2894 (2001).
[CrossRef]

M. Nevière, E. Popov, Light Propagation in Periodic Media: Differential Theory and Design (Marcel Dekker, New York, 2003).

N. Bonod, E. Popov, M. Nevière, “Differential theory of diffraction by finite cylindrical objects,” J. Opt. Soc. Am. A (to be published).

Pearson, J.

L. Yin, V. K. Vlasko-Vlasov, A. Rydh, J. Pearson, U. Welp, S. H. Chang, S. K. Gray, G. C. Schatz, D. B. Brown, C. W. Kimball, “Surface plasmons at single nanoholes in Au films,” Appl. Phys. Lett. 85, 467–469 (2004).
[CrossRef]

Popov, E.

E. Popov, M. Nevière, N. Bonod, “Factorization of products of discontinuous functions applied to Fourier–Bessel basis,” J. Opt. Soc. Am. A 21, 46–52 (2004).
[CrossRef]

E. Popov, M. Nevière, “Maxwell equations in Fourier space: fast converging formulation for diffraction by arbitrary shaped, periodic, anisotropic media,” J. Opt. Soc. Am. A 18, 2886–2894 (2001).
[CrossRef]

M. Nevière, E. Popov, Light Propagation in Periodic Media: Differential Theory and Design (Marcel Dekker, New York, 2003).

N. Bonod, E. Popov, M. Nevière, “Differential theory of diffraction by finite cylindrical objects,” J. Opt. Soc. Am. A (to be published).

Rydh, A.

L. Yin, V. K. Vlasko-Vlasov, A. Rydh, J. Pearson, U. Welp, S. H. Chang, S. K. Gray, G. C. Schatz, D. B. Brown, C. W. Kimball, “Surface plasmons at single nanoholes in Au films,” Appl. Phys. Lett. 85, 467–469 (2004).
[CrossRef]

Schatz, G. C.

L. Yin, V. K. Vlasko-Vlasov, A. Rydh, J. Pearson, U. Welp, S. H. Chang, S. K. Gray, G. C. Schatz, D. B. Brown, C. W. Kimball, “Surface plasmons at single nanoholes in Au films,” Appl. Phys. Lett. 85, 467–469 (2004).
[CrossRef]

Snyder, A.

A. Snyder, J. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).

Thio, T.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, P. A. Wolff, “Extraordinary optical transmission through subwave-length hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

Turner, S. W.

M. J. Levene, J. Korlach, S. W. Turner, M. Foquet, H. G. Craighead, W. W. Webb, “Zero-mode waveguides for single-molecule analysis at high concentrations,” Science 299, 682–686 (2003).
[CrossRef] [PubMed]

Van Labeke, D.

Vlasko-Vlasov, V. K.

L. Yin, V. K. Vlasko-Vlasov, A. Rydh, J. Pearson, U. Welp, S. H. Chang, S. K. Gray, G. C. Schatz, D. B. Brown, C. W. Kimball, “Surface plasmons at single nanoholes in Au films,” Appl. Phys. Lett. 85, 467–469 (2004).
[CrossRef]

Webb, W. W.

M. J. Levene, J. Korlach, S. W. Turner, M. Foquet, H. G. Craighead, W. W. Webb, “Zero-mode waveguides for single-molecule analysis at high concentrations,” Science 299, 682–686 (2003).
[CrossRef] [PubMed]

Welp, U.

L. Yin, V. K. Vlasko-Vlasov, A. Rydh, J. Pearson, U. Welp, S. H. Chang, S. K. Gray, G. C. Schatz, D. B. Brown, C. W. Kimball, “Surface plasmons at single nanoholes in Au films,” Appl. Phys. Lett. 85, 467–469 (2004).
[CrossRef]

Wolff, P. A.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, P. A. Wolff, “Extraordinary optical transmission through subwave-length hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

Yamamoto, N.

A. Degiron, H. Lezec, N. Yamamoto, T. Ebbesen, “Optical transmission properties of a single subwavelength aperture in a real metal,” Opt. Commun. 239, 61–66 (2004).
[CrossRef]

Yin, L.

L. Yin, V. K. Vlasko-Vlasov, A. Rydh, J. Pearson, U. Welp, S. H. Chang, S. K. Gray, G. C. Schatz, D. B. Brown, C. W. Kimball, “Surface plasmons at single nanoholes in Au films,” Appl. Phys. Lett. 85, 467–469 (2004).
[CrossRef]

Zakharian, R.

Appl. Phys. Lett. (2)

F. J. Garcia-Vidal, L. Martin-Moreno, H. J. Lezec, T. W. Ebbesen, “Focusing light with a single subwavelength aperture flanked by surface corrugations,” Appl. Phys. Lett. 83, 4500–4502 (2003).
[CrossRef]

L. Yin, V. K. Vlasko-Vlasov, A. Rydh, J. Pearson, U. Welp, S. H. Chang, S. K. Gray, G. C. Schatz, D. B. Brown, C. W. Kimball, “Surface plasmons at single nanoholes in Au films,” Appl. Phys. Lett. 85, 467–469 (2004).
[CrossRef]

J. Opt. Soc. Am. A (3)

Nature (1)

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, P. A. Wolff, “Extraordinary optical transmission through subwave-length hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

Opt. Commun. (1)

A. Degiron, H. Lezec, N. Yamamoto, T. Ebbesen, “Optical transmission properties of a single subwavelength aperture in a real metal,” Opt. Commun. 239, 61–66 (2004).
[CrossRef]

Opt. Express (2)

Phys. Rev. Lett. (1)

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, A. Degiron, T. W. Ebbesen, “Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,” Phys. Rev. Lett. 90, 167401 (2003).
[CrossRef] [PubMed]

Science (1)

M. J. Levene, J. Korlach, S. W. Turner, M. Foquet, H. G. Craighead, W. W. Webb, “Zero-mode waveguides for single-molecule analysis at high concentrations,” Science 299, 682–686 (2003).
[CrossRef] [PubMed]

Other (4)

M. Nevière, E. Popov, Light Propagation in Periodic Media: Differential Theory and Design (Marcel Dekker, New York, 2003).

N. Bonod, E. Popov, M. Nevière, “Differential theory of diffraction by finite cylindrical objects,” J. Opt. Soc. Am. A (to be published).

A. Snyder, J. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).

R. Petit, ed., Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980), Chap. 5.
[CrossRef]

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Figures (11)

Fig. 1
Fig. 1

Schematic representation of a hole in a metallic sheet.

Fig. 2
Fig. 2

Map of the square modulus of the electric field obtained at z = −15 nm (distances are in nanometers).

Fig.3
Fig.3

Map of |Ez| at z = −15 nm; the location of the hole’s cross section is represented by a thick circle.

Fig. 4
Fig. 4

Variation of |Ez| for y = 0 and z = − 1 nm as a function of x.

Fig. 5
Fig. 5

|Ez| field map of the xOz plane below the hole. For reasons of symmetry, only positive values of x are considered.

Fig. 6
Fig. 6

Variation of |Ez| in the xOz plane below the hole: triangles, |Ez| as a function of x at z = 0; squares, |Ez| as a function of z along the line x = R that crosses the hole ridge.

Fig. 7
Fig. 7

Same as in Fig. 4 but for |Er|.

Fig. 8
Fig. 8

Variation of |Eθ| for x = 0 and z = − 1 nm as a function of y.

Fig. 9
Fig. 9

Re ( b 1 E ) as a function of the normalized radial wave-vector component.

Fig. 10
Fig. 10

(a) Thin, solid curve, the same as in Fig. 4 but on a different scale; thick dotted curve, fitting by the sum of Eq. (2) and expression (3). (b) Thinner curve, dependence of |Ez, no plasmon| as a function of x for y = 0 and z = − 1; thicker curve, fit by Eq. (2).

Fig. 11
Fig. 11

Thin, wavy curve, the same as in Fig. 10 but for |Ez, plasmon|; thicker curve fit by expression (3).

Equations (3)

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

E r ( r , θ , z ) = i n = N N m = 0 Max Δ k m [ b n , m E ( z ) J n + 1 ( k m r ) c n , m E ( z ) J n 1 ( k m r ) ] exp ( i n θ ) , E θ ( r , θ , z ) = n = N N m = 0 Max Δ k m [ b n , m E ( z ) J n + 1 ( k m r ) + c n , m E ( z ) J n 1 ( k m r ) ] exp ( i n θ ) ,
| E z , no plasmon | = C no plasmon | x R | .
C plasmon x exp ( i α x ) ,

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