Abstract

The transmission of light through a subwavelength hole drilled in a metallic thin film is calculated by numerically solving Maxwell’s equations both for a simple hole and for a hole with additional structure. A maximum in the transmission cross section is observed for hole diameters of the order of but smaller than the wavelength. Transmission cross sections well above the hole area are shown to be attainable by filling the hole with a high-index material. The effect of adding a small particle inside the hole is also analyzed.

© 2002 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, and P. A. Wolff, �??Extraordinary optical transmission through subwavelength hole arrays,�?? Nature 391, 667 (1998).
    [CrossRef]
  2. T. Thio, K. M. Pellerin, R. A. Linke, H. J. Lezec, and T. W. Ebbesen, �??Enhanced light transmission through a single subwavelength aperture,�?? Opt. Lett. 26, 1972 (2001).
    [CrossRef]
  3. H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martyn-Moreno, F. J. Garcya-Vidal, and T.W. Ebbesen, �??Beaming light from a subwavelength aperture,�?? Science 297, 820 (2002).
    [CrossRef] [PubMed]
  4. U. Schroter and D. Heitmann, �??Surface-plamon-enhanced transmission through metallic gratings,�?? Phys. Rev. B 58, 15419 (1998).
    [CrossRef]
  5. Y. Takakura, �??Optical resonance in a narrow slit in a thick metallic screen,�?? Phys. Rev. Lett. 86, 5601 (2001).
    [CrossRef] [PubMed]
  6. F. Yang and J. R. Sambles, �??Resonant transmission of microwaves through a narrow metallic slit,�?? Phys. Rev. Lett. 89, 63901 (2002).
    [CrossRef]
  7. H. A. Bethe, �??Theory of diffraction by small holes,�?? Phys. Rev. 66, 163 (1944).
    [CrossRef]
  8. C. J. Bouwkamp, �??Diffraction theory,�?? Reports on Progress in Physics XVIII, 35 (1954).
    [CrossRef]
  9. R. Wannemacher, "Plasmon-supported transmission of light through nanometric holes in metallic thin films,�?? Opt. Commun. 195, 107 (2001).
    [CrossRef]
  10. F. J. Garcya de Abajo and A. Howie, �??Relativistic electron energy loss and electron induced photon emission in inhomogeneous dielectrics,�?? Phys. Rev. Lett. 80, 5180 (1998); �??Retarded field calculation of electron energy loss in inhomogeneous dielectrics�??, Phys. Rev. B 65, 115418 (2002).
    [CrossRef]
  11. J. Aizpurua, P. Hanarp, D. S. Sutherland, M. Kall, G. W. Bryant, and F. J. Garcya de Abajo, "Optical properties of gold nanorings," submitted to Phys. Rev. Lett.
  12. When Maxwell's equations are satisfied at both sides of a given interface, the continuity of the parallel components of the electric field and the magnetic field implies the continuity of the normal electric displacement and the normal magnetic induction.
  13. J. A. Porto, F. J. Garcya-Vidal, and J. B. Pendry, "Transmission resonances on metallic gratings with very narrow slits," Phys. Rev. Lett. 83, 2845 (1999).
    [CrossRef]
  14. S. Astilean, Ph. Lalanne, and M. Palamaru, "Light transmission through metallic channels much smaller than the wavelength," Opt. Commun. 175, 265 (2000).
    [CrossRef]
  15. Q. Cao and Ph. Lalanne, "Negative role of surface plasmons in the transmission of metallic gratings with very narrow slits," Phys. Rev. Lett. 88, 057403 (2002).
    [CrossRef] [PubMed]

Nature

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, �??Extraordinary optical transmission through subwavelength hole arrays,�?? Nature 391, 667 (1998).
[CrossRef]

Opt. Commun.

S. Astilean, Ph. Lalanne, and M. Palamaru, "Light transmission through metallic channels much smaller than the wavelength," Opt. Commun. 175, 265 (2000).
[CrossRef]

R. Wannemacher, "Plasmon-supported transmission of light through nanometric holes in metallic thin films,�?? Opt. Commun. 195, 107 (2001).
[CrossRef]

Opt. Lett.

Phys. Rev.

H. A. Bethe, �??Theory of diffraction by small holes,�?? Phys. Rev. 66, 163 (1944).
[CrossRef]

Phys. Rev. B

U. Schroter and D. Heitmann, �??Surface-plamon-enhanced transmission through metallic gratings,�?? Phys. Rev. B 58, 15419 (1998).
[CrossRef]

Phys. Rev. Lett.

Y. Takakura, �??Optical resonance in a narrow slit in a thick metallic screen,�?? Phys. Rev. Lett. 86, 5601 (2001).
[CrossRef] [PubMed]

F. Yang and J. R. Sambles, �??Resonant transmission of microwaves through a narrow metallic slit,�?? Phys. Rev. Lett. 89, 63901 (2002).
[CrossRef]

F. J. Garcya de Abajo and A. Howie, �??Relativistic electron energy loss and electron induced photon emission in inhomogeneous dielectrics,�?? Phys. Rev. Lett. 80, 5180 (1998); �??Retarded field calculation of electron energy loss in inhomogeneous dielectrics�??, Phys. Rev. B 65, 115418 (2002).
[CrossRef]

Q. Cao and Ph. Lalanne, "Negative role of surface plasmons in the transmission of metallic gratings with very narrow slits," Phys. Rev. Lett. 88, 057403 (2002).
[CrossRef] [PubMed]

J. A. Porto, F. J. Garcya-Vidal, and J. B. Pendry, "Transmission resonances on metallic gratings with very narrow slits," Phys. Rev. Lett. 83, 2845 (1999).
[CrossRef]

Science

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martyn-Moreno, F. J. Garcya-Vidal, and T.W. Ebbesen, �??Beaming light from a subwavelength aperture,�?? Science 297, 820 (2002).
[CrossRef] [PubMed]

Other

J. Aizpurua, P. Hanarp, D. S. Sutherland, M. Kall, G. W. Bryant, and F. J. Garcya de Abajo, "Optical properties of gold nanorings," submitted to Phys. Rev. Lett.

When Maxwell's equations are satisfied at both sides of a given interface, the continuity of the parallel components of the electric field and the magnetic field implies the continuity of the normal electric displacement and the normal magnetic induction.

C. J. Bouwkamp, �??Diffraction theory,�?? Reports on Progress in Physics XVIII, 35 (1954).
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

Boundary element method approach to the transmission through a small hole. The problem is solved in terms of magnetic boundary charges and currents distributed around the hole boundary. See text for more details.

Fig. 2.
Fig. 2.

Transmission cross section of a cylindrical hole in a perfect-metal slab as a function of the hole radius. The slab thickness is 0.1 times the radius. The cross section is normalized to the area of the hole, and the radius is normalized to the wavelength. The incidence of the light is perpendicular to the slab. The contour-plot inset shows the polar angle distribution of transmitted light as a function of hole radius (brighter regions stand for higher transmission intensity).

Fig. 3.
Fig. 3.

(a) Transmission cross section of a cylindrical hole drilled in a perfect-metal film as a function of the hole radius for different ratios of the slab thickness to the radius (see labels). The light is coming perpendicular to the film. (b) Same as (a) in log - log scale and compared with the asymptotic formulas of Bethe (Ref. [7]) and Bouwkamp (Ref. [8]), which are valid for vanishing thickness [see Eq. (2)].

Fig. 4.
Fig. 4.

Transmission cross section of a cylindrical hole drilled in a perfect-metal thin film and filled with Si (solid curve) as a function of hole radius. The broken curve represents the transmittance of a homogeneous Si film of the same thickness. The dependence of the transmitted intensity on the polar angle upon exit is shown in the inset (brighter regions stand for higher transmission intensity).

Fig. 5.
Fig. 5.

Transmission cross section of a cylindrical hole drilled in a perfect-metal thin film and containing a perfect-metal sphere in its center (solid curve). The light is coming perpendicular to the film. The broken curve corresponds to the transmission of the same geometry but with the hole filled with Si (see insets).

Equations (5)

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E ( r ) = E j ext + i k S j d s [ 1 + 1 k 2 j μ j ] G j ( r s ) h j ( s )
H ( r ) = H j ext + 1 μ j S j d s G j ( r s ) × h j ( s ) ,
E ( r ) = E j ext 1 j S j d s G j ( r s ) × m j ( s )
H ( r ) = H j ext + ik S j d s [ 1 + 1 k 2 j μ j ] G j ( r s ) m j ( s ) ,
σ π a 2 = 64 27 π 2 ( ka ) 4 [ 1 + 22 25 ( ka ) 2 + 7312 18375 ( ka ) 4 + ] ,

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