Abstract

We present a simple theoretical model to study the effect of a substrate on the resonance of an aperture in a thin metal film. The transmitted energy through an aperture is shown to be governed by the coupling of aperture waveguide mode to the incoming and the outgoing electromagnetic waves into the substrate region. Aperture resonance in the energy transmission thus depends critically on the refractive index of a substrate. We explain the substrate effect on aperture resonance in terms of destructive interference among evanescent modes or impedance mismatch. Our model shows an excellent agreement with a rigorous FDTD calculation and is consistent with previous experimental observations.

© 2009 Optical Society of America

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  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]
  2. J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, "Transmission resonances on metallic gratings with very narrow slits," Phys. Rev. Lett. 83, 2845-2848 (1999).
    [CrossRef]
  3. M. M. J. Treacy, "Dynamical diffraction explanation of the anomalous transmission of light through metallic gratings," Phys. Rev. B 66, 195105 (2002).
    [CrossRef]
  4. Q. Cao and P. Lalanne, "Negative role of surface plasmons in the transmission of metallic gratings with very narrow slits," Phys. Rev. Lett. 88, 057403 (2002).
    [CrossRef]
  5. K. G. Lee, and Q. H. Park, "Coupling of surface plasmon polaritions and light in metallic nanoslits," Phys. Rev. Lett. 95, 103902 (2005).
    [CrossRef]
  6. Q. H. Park, "Optical antennas and plasmonics," Contemporary Phys. 50, 407-423 (2009).
    [CrossRef]
  7. F. J. Garcia-Vidal, E. Moreno, J. A. Porto, and L. Martin-Moreno, "Transmission of Light through a Single Rectangular Hole," Phys. Rev. Lett. 95, 193901 (2005).
    [CrossRef]
  8. M. A. Seo, A. J. L. Adam, J. H. Kang, J. W. Lee, K. J. Ahn, Q. H. Park, P. C. M. Planken, and D. S. Kim, "Near field imaging of terahertz focusing onto rectangular apertures," Opt. Express 16, 20484-20489 (2008).
    [CrossRef]
  9. Q. H. Park, J. H. Kang, J. W. Lee, and D. S. Kim, "Effective medium description of plasmonic metamaterials," Opt. Express 15, 6994-6999 (2007).
    [CrossRef]
  10. K. L. Shuford, S. K. Gray, M. A. Ratner, and G. C. Schatz, "Substrate effects on surface plasmons in single nanoholes," Chem. Phys. Lett. 435123-126 (2007).
    [CrossRef]
  11. M. A. Seo et al.,"Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit," Nature Photonics 3, 152-156 (2009).
    [CrossRef]
  12. J. H. Kang, D. S. Kim, and Q. H. Park, "Local capacitor model for plasmonic electric field enhancement," Phys. Rev. Lett. 102, 093906 (2009).
    [CrossRef]

2009 (3)

Q. H. Park, "Optical antennas and plasmonics," Contemporary Phys. 50, 407-423 (2009).
[CrossRef]

M. A. Seo et al.,"Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit," Nature Photonics 3, 152-156 (2009).
[CrossRef]

J. H. Kang, D. S. Kim, and Q. H. Park, "Local capacitor model for plasmonic electric field enhancement," Phys. Rev. Lett. 102, 093906 (2009).
[CrossRef]

2008 (1)

2007 (2)

Q. H. Park, J. H. Kang, J. W. Lee, and D. S. Kim, "Effective medium description of plasmonic metamaterials," Opt. Express 15, 6994-6999 (2007).
[CrossRef]

K. L. Shuford, S. K. Gray, M. A. Ratner, and G. C. Schatz, "Substrate effects on surface plasmons in single nanoholes," Chem. Phys. Lett. 435123-126 (2007).
[CrossRef]

2005 (2)

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

F. J. Garcia-Vidal, E. Moreno, J. A. Porto, and L. Martin-Moreno, "Transmission of Light through a Single Rectangular Hole," Phys. Rev. Lett. 95, 193901 (2005).
[CrossRef]

2002 (2)

M. M. J. Treacy, "Dynamical diffraction explanation of the anomalous transmission of light through metallic gratings," Phys. Rev. B 66, 195105 (2002).
[CrossRef]

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

1999 (1)

J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, "Transmission resonances on metallic gratings with very narrow slits," Phys. Rev. Lett. 83, 2845-2848 (1999).
[CrossRef]

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]

Adam, A. J. L.

Ahn, K. J.

Cao, Q.

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

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]

Garcia-Vidal, F. J.

F. J. Garcia-Vidal, E. Moreno, J. A. Porto, and L. Martin-Moreno, "Transmission of Light through a Single Rectangular Hole," Phys. Rev. Lett. 95, 193901 (2005).
[CrossRef]

J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, "Transmission resonances on metallic gratings with very narrow slits," Phys. Rev. Lett. 83, 2845-2848 (1999).
[CrossRef]

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]

Gray, S. K.

K. L. Shuford, S. K. Gray, M. A. Ratner, and G. C. Schatz, "Substrate effects on surface plasmons in single nanoholes," Chem. Phys. Lett. 435123-126 (2007).
[CrossRef]

Kang, J. H.

Kim, D. S.

Lalanne, P.

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

Lee, J. W.

Lee, K. G.

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

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]

Martin-Moreno, L.

F. J. Garcia-Vidal, E. Moreno, J. A. Porto, and L. Martin-Moreno, "Transmission of Light through a Single Rectangular Hole," Phys. Rev. Lett. 95, 193901 (2005).
[CrossRef]

Moreno, E.

F. J. Garcia-Vidal, E. Moreno, J. A. Porto, and L. Martin-Moreno, "Transmission of Light through a Single Rectangular Hole," Phys. Rev. Lett. 95, 193901 (2005).
[CrossRef]

Park, Q. H.

Q. H. Park, "Optical antennas and plasmonics," Contemporary Phys. 50, 407-423 (2009).
[CrossRef]

J. H. Kang, D. S. Kim, and Q. H. Park, "Local capacitor model for plasmonic electric field enhancement," Phys. Rev. Lett. 102, 093906 (2009).
[CrossRef]

M. A. Seo, A. J. L. Adam, J. H. Kang, J. W. Lee, K. J. Ahn, Q. H. Park, P. C. M. Planken, and D. S. Kim, "Near field imaging of terahertz focusing onto rectangular apertures," Opt. Express 16, 20484-20489 (2008).
[CrossRef]

Q. H. Park, J. H. Kang, J. W. Lee, and D. S. Kim, "Effective medium description of plasmonic metamaterials," Opt. Express 15, 6994-6999 (2007).
[CrossRef]

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

Pendry, J. B.

J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, "Transmission resonances on metallic gratings with very narrow slits," Phys. Rev. Lett. 83, 2845-2848 (1999).
[CrossRef]

Planken, P. C. M.

Porto, J. A.

F. J. Garcia-Vidal, E. Moreno, J. A. Porto, and L. Martin-Moreno, "Transmission of Light through a Single Rectangular Hole," Phys. Rev. Lett. 95, 193901 (2005).
[CrossRef]

J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, "Transmission resonances on metallic gratings with very narrow slits," Phys. Rev. Lett. 83, 2845-2848 (1999).
[CrossRef]

Ratner, M. A.

K. L. Shuford, S. K. Gray, M. A. Ratner, and G. C. Schatz, "Substrate effects on surface plasmons in single nanoholes," Chem. Phys. Lett. 435123-126 (2007).
[CrossRef]

Schatz, G. C.

K. L. Shuford, S. K. Gray, M. A. Ratner, and G. C. Schatz, "Substrate effects on surface plasmons in single nanoholes," Chem. Phys. Lett. 435123-126 (2007).
[CrossRef]

Seo, M. A.

Shuford, K. L.

K. L. Shuford, S. K. Gray, M. A. Ratner, and G. C. Schatz, "Substrate effects on surface plasmons in single nanoholes," Chem. Phys. Lett. 435123-126 (2007).
[CrossRef]

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]

Treacy, M. M. J.

M. M. J. Treacy, "Dynamical diffraction explanation of the anomalous transmission of light through metallic gratings," Phys. Rev. B 66, 195105 (2002).
[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]

Chem. Phys. Lett. (1)

K. L. Shuford, S. K. Gray, M. A. Ratner, and G. C. Schatz, "Substrate effects on surface plasmons in single nanoholes," Chem. Phys. Lett. 435123-126 (2007).
[CrossRef]

Contemporary Phys. (1)

Q. H. Park, "Optical antennas and plasmonics," Contemporary Phys. 50, 407-423 (2009).
[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]

Nature Photonics (1)

M. A. Seo et al.,"Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit," Nature Photonics 3, 152-156 (2009).
[CrossRef]

Opt. Express (2)

Phys. Rev. B (1)

M. M. J. Treacy, "Dynamical diffraction explanation of the anomalous transmission of light through metallic gratings," Phys. Rev. B 66, 195105 (2002).
[CrossRef]

Phys. Rev. Lett. (5)

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

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

J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, "Transmission resonances on metallic gratings with very narrow slits," Phys. Rev. Lett. 83, 2845-2848 (1999).
[CrossRef]

J. H. Kang, D. S. Kim, and Q. H. Park, "Local capacitor model for plasmonic electric field enhancement," Phys. Rev. Lett. 102, 093906 (2009).
[CrossRef]

F. J. Garcia-Vidal, E. Moreno, J. A. Porto, and L. Martin-Moreno, "Transmission of Light through a Single Rectangular Hole," Phys. Rev. Lett. 95, 193901 (2005).
[CrossRef]

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