Abstract

In this paper we analytically study the resonance response of cylindrical subwavelength apertures embedded in metal films at near-UV, optical, and near-IR frequencies. This analysis is concise, and allows accurate and intuitive prediction of both propagating and evanescent modes, which are key contributors to enhanced optical transmission through thin metal films. In this approach we do not analyze the detailed behavior of the fields inside the metal walls, but still obtain the effects of the implicit buildup of charges within those walls. We calculate the modal dispersion relation, cutoff dependence on cylinder radius, and waveguide attenuation for a cylindrical aperture embedded in metal. We support our findings with finite element simulations and find strong agreement with our theory.

© 2012 Optical Society of America

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  1. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemil, T. Thiol, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
    [CrossRef]
  2. D. Zhou and R. Biswas, “Photonic crystal enhanced light-trapping in thin film solar cells,” J. Appl. Phys. 103, 093102 (2008).
    [CrossRef]
  3. M. Bayindir, B. Temelkuran, and E. Ozbay, “Photonic-crystal-based beam splitters,” Appl. Phys. Lett. 77, 3902–3904 (2000).
    [CrossRef]
  4. M. Z. Tidrow and W. R. Dyer, “Infrared sensors for ballistic missile defense,” Infrared Phys. Technol. 42, 333–336 (2001).
    [CrossRef]
  5. D. Kim, C. Warde, K. Vaccaro, and C. Woods, “Imaging multispectral polarimetric sensor: single-pixel design, fabrication, and characterization,” Appl. Opt. 42, 3756–3764 (2003).
    [CrossRef]
  6. C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445, 39–46 (2007).
    [CrossRef]
  7. H. Cao, A. Agrawal, and A. Nahata, “Controlling the transmission resonance lineshape of a single subwavelength aperture,” Opt. Express 13, 763–769 (2005).
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    [CrossRef]
  11. 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]
  12. F. J. García-Vidal and L. Martín-Moreno, “Transmission and focusing of light in one-dimensional periodically nanostructured metals,” Phys. Rev. B 66, 155412 (2002).
    [CrossRef]
  13. A. Barbara, P. Quémerais, E. Bustarret, and T. Lopez-Rios, “Optical transmission through subwavelength metallic gratings,” Phys. Rev. B 66, 161403 (2002).
    [CrossRef]
  14. D. Crouse, “Numerical modeling and electromagnetic resonant modes in complex grating structures and optoelectronic device applications,” IEEE Trans. Electron Devices 52, 2365–2373 (2005).
    [CrossRef]
  15. D. Crouse, A. P. Hibbins, and M. J. Lockyear, “Tuning the polarization state of enhanced transmission in gratings,” Appl. Phys. Lett. 92, 191105 (2008).
    [CrossRef]
  16. D. Crouse and P. Keshavareddy, “Polarization independent enhanced optical transmission in one-dimensional gratings and device applications,” Opt. Express 15, 1415–1427(2007).
    [CrossRef]
  17. H. A. Bethe, “Theory of diffraction by small holes,” Phys. Rev. 66, 163–182 (1944).
    [CrossRef]
  18. R. Gordon, “Bethe’s aperture theory for arrays,” Phys. Rev. A 76, 053806 (2007).
    [CrossRef]
  19. A. Y. Nikitin, D. Zueco, F. J. García-Vidal, and L. Martín-Moreno, “Electromagnetic wave transmission through a small hole in a perfect electric conductor of finite thickness,” Phys. Rev. B 78, 165429 (2008).
    [CrossRef]
  20. F. J. García-Vidal, L. Martín-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82, 729–787 (2010).
    [CrossRef]
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    [CrossRef]
  22. H. Shin, P. B. Catrysse, and S. Fan, “Effect of the plasmonic dispersion relation on the transmission properties of subwavelength cylindrical holes,” Phys. Rev. B 72, 085436 (2005).
    [CrossRef]
  23. P. B. Catrysse and S. Fan, “Propagating plasmonic mode in nanoscale apertures and its implications for extraordinary transmission,” J. Nanophoton. 2, 021790 (2008).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2010 (1)

F. J. García-Vidal, L. Martín-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82, 729–787 (2010).
[CrossRef]

2008 (5)

A. Y. Nikitin, D. Zueco, F. J. García-Vidal, and L. Martín-Moreno, “Electromagnetic wave transmission through a small hole in a perfect electric conductor of finite thickness,” Phys. Rev. B 78, 165429 (2008).
[CrossRef]

P. B. Catrysse and S. Fan, “Propagating plasmonic mode in nanoscale apertures and its implications for extraordinary transmission,” J. Nanophoton. 2, 021790 (2008).
[CrossRef]

P. Lalanne, C. Sauvan, and J. Hugonin, “Photon confinement in photonic crystal nanocavities,” Laser Photon. Rev. 2, 514–526 (2008).
[CrossRef]

D. Zhou and R. Biswas, “Photonic crystal enhanced light-trapping in thin film solar cells,” J. Appl. Phys. 103, 093102 (2008).
[CrossRef]

D. Crouse, A. P. Hibbins, and M. J. Lockyear, “Tuning the polarization state of enhanced transmission in gratings,” Appl. Phys. Lett. 92, 191105 (2008).
[CrossRef]

2007 (3)

D. Crouse and P. Keshavareddy, “Polarization independent enhanced optical transmission in one-dimensional gratings and device applications,” Opt. Express 15, 1415–1427(2007).
[CrossRef]

R. Gordon, “Bethe’s aperture theory for arrays,” Phys. Rev. A 76, 053806 (2007).
[CrossRef]

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445, 39–46 (2007).
[CrossRef]

2005 (3)

H. Cao, A. Agrawal, and A. Nahata, “Controlling the transmission resonance lineshape of a single subwavelength aperture,” Opt. Express 13, 763–769 (2005).
[CrossRef]

D. Crouse, “Numerical modeling and electromagnetic resonant modes in complex grating structures and optoelectronic device applications,” IEEE Trans. Electron Devices 52, 2365–2373 (2005).
[CrossRef]

H. Shin, P. B. Catrysse, and S. Fan, “Effect of the plasmonic dispersion relation on the transmission properties of subwavelength cylindrical holes,” Phys. Rev. B 72, 085436 (2005).
[CrossRef]

2004 (2)

2003 (1)

2002 (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]

F. J. García-Vidal and L. Martín-Moreno, “Transmission and focusing of light in one-dimensional periodically nanostructured metals,” Phys. Rev. B 66, 155412 (2002).
[CrossRef]

A. Barbara, P. Quémerais, E. Bustarret, and T. Lopez-Rios, “Optical transmission through subwavelength metallic gratings,” Phys. Rev. B 66, 161403 (2002).
[CrossRef]

G. R. Hadley, “High-accuracy finite-difference equations for dielectric waveguide analysis II: dielectric corners,” J. Lightwave Technol. 20, 1219 (2002).
[CrossRef]

2001 (1)

M. Z. Tidrow and W. R. Dyer, “Infrared sensors for ballistic missile defense,” Infrared Phys. Technol. 42, 333–336 (2001).
[CrossRef]

2000 (1)

M. Bayindir, B. Temelkuran, and E. Ozbay, “Photonic-crystal-based beam splitters,” Appl. Phys. Lett. 77, 3902–3904 (2000).
[CrossRef]

1999 (1)

J. A. Porto, F. J. García-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. Ghaemil, T. Thiol, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

1994 (1)

L. Novotny and C. Hafner, “Light propagation in a cylindrical waveguide with a complex, metallic, dielectric function,” Phys. Rev. E 50, 4094–4106 (1994).
[CrossRef]

1993 (1)

1992 (1)

A. Sudbo, “Why are accurate computations of mode fields in rectangular dielectric waveguides difficult?,” J. Lightwave Technol. 10, 418–419 (1992).
[CrossRef]

1985 (1)

1944 (1)

H. A. Bethe, “Theory of diffraction by small holes,” Phys. Rev. 66, 163–182 (1944).
[CrossRef]

Agrawal, A.

Alexander, J. R. W.

Barbara, A.

A. Barbara, P. Quémerais, E. Bustarret, and T. Lopez-Rios, “Optical transmission through subwavelength metallic gratings,” Phys. Rev. B 66, 161403 (2002).
[CrossRef]

Bayindir, M.

M. Bayindir, B. Temelkuran, and E. Ozbay, “Photonic-crystal-based beam splitters,” Appl. Phys. Lett. 77, 3902–3904 (2000).
[CrossRef]

Bell, R. J.

Bethe, H. A.

H. A. Bethe, “Theory of diffraction by small holes,” Phys. Rev. 66, 163–182 (1944).
[CrossRef]

Biswas, R.

D. Zhou and R. Biswas, “Photonic crystal enhanced light-trapping in thin film solar cells,” J. Appl. Phys. 103, 093102 (2008).
[CrossRef]

Bustarret, E.

A. Barbara, P. Quémerais, E. Bustarret, and T. Lopez-Rios, “Optical transmission through subwavelength metallic gratings,” Phys. Rev. B 66, 161403 (2002).
[CrossRef]

Cao, H.

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]

Catrysse, P. B.

P. B. Catrysse and S. Fan, “Propagating plasmonic mode in nanoscale apertures and its implications for extraordinary transmission,” J. Nanophoton. 2, 021790 (2008).
[CrossRef]

H. Shin, P. B. Catrysse, and S. Fan, “Effect of the plasmonic dispersion relation on the transmission properties of subwavelength cylindrical holes,” Phys. Rev. B 72, 085436 (2005).
[CrossRef]

Crouse, D.

D. Crouse, A. P. Hibbins, and M. J. Lockyear, “Tuning the polarization state of enhanced transmission in gratings,” Appl. Phys. Lett. 92, 191105 (2008).
[CrossRef]

D. Crouse and P. Keshavareddy, “Polarization independent enhanced optical transmission in one-dimensional gratings and device applications,” Opt. Express 15, 1415–1427(2007).
[CrossRef]

D. Crouse, “Numerical modeling and electromagnetic resonant modes in complex grating structures and optoelectronic device applications,” IEEE Trans. Electron Devices 52, 2365–2373 (2005).
[CrossRef]

Degiron, A.

Depine, R.

Dyer, W. R.

M. Z. Tidrow and W. R. Dyer, “Infrared sensors for ballistic missile defense,” Infrared Phys. Technol. 42, 333–336 (2001).
[CrossRef]

Ebbesen, T.

Ebbesen, T. W.

F. J. García-Vidal, L. Martín-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82, 729–787 (2010).
[CrossRef]

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445, 39–46 (2007).
[CrossRef]

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

Fan, S.

P. B. Catrysse and S. Fan, “Propagating plasmonic mode in nanoscale apertures and its implications for extraordinary transmission,” J. Nanophoton. 2, 021790 (2008).
[CrossRef]

H. Shin, P. B. Catrysse, and S. Fan, “Effect of the plasmonic dispersion relation on the transmission properties of subwavelength cylindrical holes,” Phys. Rev. B 72, 085436 (2005).
[CrossRef]

García-Vidal, F. J.

F. J. García-Vidal, L. Martín-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82, 729–787 (2010).
[CrossRef]

A. Y. Nikitin, D. Zueco, F. J. García-Vidal, and L. Martín-Moreno, “Electromagnetic wave transmission through a small hole in a perfect electric conductor of finite thickness,” Phys. Rev. B 78, 165429 (2008).
[CrossRef]

F. J. García-Vidal and L. Martín-Moreno, “Transmission and focusing of light in one-dimensional periodically nanostructured metals,” Phys. Rev. B 66, 155412 (2002).
[CrossRef]

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

Genet, C.

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445, 39–46 (2007).
[CrossRef]

Ghaemil, H. F.

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

Gordon, R.

R. Gordon, “Bethe’s aperture theory for arrays,” Phys. Rev. A 76, 053806 (2007).
[CrossRef]

Hadley, G. R.

Hafner, C.

L. Novotny and C. Hafner, “Light propagation in a cylindrical waveguide with a complex, metallic, dielectric function,” Phys. Rev. E 50, 4094–4106 (1994).
[CrossRef]

Hibbins, A. P.

D. Crouse, A. P. Hibbins, and M. J. Lockyear, “Tuning the polarization state of enhanced transmission in gratings,” Appl. Phys. Lett. 92, 191105 (2008).
[CrossRef]

Hugonin, J.

P. Lalanne, C. Sauvan, and J. Hugonin, “Photon confinement in photonic crystal nanocavities,” Laser Photon. Rev. 2, 514–526 (2008).
[CrossRef]

Jackson, J.

J. Jackson, Classical Electrodynamics2nd ed. (Wiley, 1975).

Kawata, S.

S. Kawata and V. M. Shalaev, eds., Tip Enhancement (Elsevier Science, 2007).

Keshavareddy, P.

Kim, D.

Kuipers, L.

F. J. García-Vidal, L. Martín-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82, 729–787 (2010).
[CrossRef]

Lalanne, P.

P. Lalanne, C. Sauvan, and J. Hugonin, “Photon confinement in photonic crystal nanocavities,” Laser Photon. Rev. 2, 514–526 (2008).
[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]

Lezec, H.

Lezec, H. J.

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

Lochbihler, H.

Lockyear, M. J.

D. Crouse, A. P. Hibbins, and M. J. Lockyear, “Tuning the polarization state of enhanced transmission in gratings,” Appl. Phys. Lett. 92, 191105 (2008).
[CrossRef]

Long, L. L.

Lopez-Rios, T.

A. Barbara, P. Quémerais, E. Bustarret, and T. Lopez-Rios, “Optical transmission through subwavelength metallic gratings,” Phys. Rev. B 66, 161403 (2002).
[CrossRef]

Martín-Moreno, L.

F. J. García-Vidal, L. Martín-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82, 729–787 (2010).
[CrossRef]

A. Y. Nikitin, D. Zueco, F. J. García-Vidal, and L. Martín-Moreno, “Electromagnetic wave transmission through a small hole in a perfect electric conductor of finite thickness,” Phys. Rev. B 78, 165429 (2008).
[CrossRef]

F. J. García-Vidal and L. Martín-Moreno, “Transmission and focusing of light in one-dimensional periodically nanostructured metals,” Phys. Rev. B 66, 155412 (2002).
[CrossRef]

Nahata, A.

Nikitin, A. Y.

A. Y. Nikitin, D. Zueco, F. J. García-Vidal, and L. Martín-Moreno, “Electromagnetic wave transmission through a small hole in a perfect electric conductor of finite thickness,” Phys. Rev. B 78, 165429 (2008).
[CrossRef]

Novotny, L.

L. Novotny and C. Hafner, “Light propagation in a cylindrical waveguide with a complex, metallic, dielectric function,” Phys. Rev. E 50, 4094–4106 (1994).
[CrossRef]

Ordal, M. A.

Ozbay, E.

M. Bayindir, B. Temelkuran, and E. Ozbay, “Photonic-crystal-based beam splitters,” Appl. Phys. Lett. 77, 3902–3904 (2000).
[CrossRef]

Pendry, J. B.

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

Porto, J. A.

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

Quémerais, P.

A. Barbara, P. Quémerais, E. Bustarret, and T. Lopez-Rios, “Optical transmission through subwavelength metallic gratings,” Phys. Rev. B 66, 161403 (2002).
[CrossRef]

Querry, M. R.

Sauvan, C.

P. Lalanne, C. Sauvan, and J. Hugonin, “Photon confinement in photonic crystal nanocavities,” Laser Photon. Rev. 2, 514–526 (2008).
[CrossRef]

Shalaev, V. M.

S. Kawata and V. M. Shalaev, eds., Tip Enhancement (Elsevier Science, 2007).

Shin, H.

H. Shin, P. B. Catrysse, and S. Fan, “Effect of the plasmonic dispersion relation on the transmission properties of subwavelength cylindrical holes,” Phys. Rev. B 72, 085436 (2005).
[CrossRef]

Sudbo, A.

A. Sudbo, “Why are accurate computations of mode fields in rectangular dielectric waveguides difficult?,” J. Lightwave Technol. 10, 418–419 (1992).
[CrossRef]

Temelkuran, B.

M. Bayindir, B. Temelkuran, and E. Ozbay, “Photonic-crystal-based beam splitters,” Appl. Phys. Lett. 77, 3902–3904 (2000).
[CrossRef]

Thio, T.

Thiol, T.

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

Tidrow, M. Z.

M. Z. Tidrow and W. R. Dyer, “Infrared sensors for ballistic missile defense,” Infrared Phys. Technol. 42, 333–336 (2001).
[CrossRef]

Vaccaro, K.

Warde, C.

Wolff, P. A.

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

Woods, C.

Zhou, D.

D. Zhou and R. Biswas, “Photonic crystal enhanced light-trapping in thin film solar cells,” J. Appl. Phys. 103, 093102 (2008).
[CrossRef]

Zueco, D.

A. Y. Nikitin, D. Zueco, F. J. García-Vidal, and L. Martín-Moreno, “Electromagnetic wave transmission through a small hole in a perfect electric conductor of finite thickness,” Phys. Rev. B 78, 165429 (2008).
[CrossRef]

Appl. Opt. (3)

Appl. Phys. Lett. (2)

D. Crouse, A. P. Hibbins, and M. J. Lockyear, “Tuning the polarization state of enhanced transmission in gratings,” Appl. Phys. Lett. 92, 191105 (2008).
[CrossRef]

M. Bayindir, B. Temelkuran, and E. Ozbay, “Photonic-crystal-based beam splitters,” Appl. Phys. Lett. 77, 3902–3904 (2000).
[CrossRef]

IEEE Trans. Electron Devices (1)

D. Crouse, “Numerical modeling and electromagnetic resonant modes in complex grating structures and optoelectronic device applications,” IEEE Trans. Electron Devices 52, 2365–2373 (2005).
[CrossRef]

Infrared Phys. Technol. (1)

M. Z. Tidrow and W. R. Dyer, “Infrared sensors for ballistic missile defense,” Infrared Phys. Technol. 42, 333–336 (2001).
[CrossRef]

J. Appl. Phys. (1)

D. Zhou and R. Biswas, “Photonic crystal enhanced light-trapping in thin film solar cells,” J. Appl. Phys. 103, 093102 (2008).
[CrossRef]

J. Lightwave Technol. (2)

A. Sudbo, “Why are accurate computations of mode fields in rectangular dielectric waveguides difficult?,” J. Lightwave Technol. 10, 418–419 (1992).
[CrossRef]

G. R. Hadley, “High-accuracy finite-difference equations for dielectric waveguide analysis II: dielectric corners,” J. Lightwave Technol. 20, 1219 (2002).
[CrossRef]

J. Nanophoton. (1)

P. B. Catrysse and S. Fan, “Propagating plasmonic mode in nanoscale apertures and its implications for extraordinary transmission,” J. Nanophoton. 2, 021790 (2008).
[CrossRef]

Laser Photon. Rev. (1)

P. Lalanne, C. Sauvan, and J. Hugonin, “Photon confinement in photonic crystal nanocavities,” Laser Photon. Rev. 2, 514–526 (2008).
[CrossRef]

Nature (2)

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

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445, 39–46 (2007).
[CrossRef]

Opt. Express (4)

Phys. Rev. (1)

H. A. Bethe, “Theory of diffraction by small holes,” Phys. Rev. 66, 163–182 (1944).
[CrossRef]

Phys. Rev. A (1)

R. Gordon, “Bethe’s aperture theory for arrays,” Phys. Rev. A 76, 053806 (2007).
[CrossRef]

Phys. Rev. B (4)

A. Y. Nikitin, D. Zueco, F. J. García-Vidal, and L. Martín-Moreno, “Electromagnetic wave transmission through a small hole in a perfect electric conductor of finite thickness,” Phys. Rev. B 78, 165429 (2008).
[CrossRef]

F. J. García-Vidal and L. Martín-Moreno, “Transmission and focusing of light in one-dimensional periodically nanostructured metals,” Phys. Rev. B 66, 155412 (2002).
[CrossRef]

A. Barbara, P. Quémerais, E. Bustarret, and T. Lopez-Rios, “Optical transmission through subwavelength metallic gratings,” Phys. Rev. B 66, 161403 (2002).
[CrossRef]

H. Shin, P. B. Catrysse, and S. Fan, “Effect of the plasmonic dispersion relation on the transmission properties of subwavelength cylindrical holes,” Phys. Rev. B 72, 085436 (2005).
[CrossRef]

Phys. Rev. E (1)

L. Novotny and C. Hafner, “Light propagation in a cylindrical waveguide with a complex, metallic, dielectric function,” Phys. Rev. E 50, 4094–4106 (1994).
[CrossRef]

Phys. Rev. Lett. (2)

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

Rev. Mod. Phys. (1)

F. J. García-Vidal, L. Martín-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82, 729–787 (2010).
[CrossRef]

Other (2)

J. Jackson, Classical Electrodynamics2nd ed. (Wiley, 1975).

S. Kawata and V. M. Shalaev, eds., Tip Enhancement (Elsevier Science, 2007).

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Figures (8)

Fig. 1.
Fig. 1.

Schematic of cylinder waveguide geometry and solution strategy. The gray region represents the metal and the white region is the dielectric-filled aperture. The dotted line is the depth at which we apply the PEC boundary condition (BC).

Fig. 2.
Fig. 2.

Ratio of δ / λ for a few metals over a range of frequencies.

Fig. 3.
Fig. 3.

Real (solid) and imaginary (dashed) dispersion curves calculated and simulated (points) for cylindrical apertures of radius a = 190 nm filled with a dielectric ϵ = 3 embedded in Drude silver. Here k p ω p / c . Inset shows results using this method (solid) compared to PEC modal dispersion (dashed).

Fig. 4.
Fig. 4.

TM cutoff frequency f cutoff as a function of the radius a for a few modes m = 0 , 1 , 2 and n = 1 in silver. The solid curves are calculated using the method described in this paper; the dashed curves are those from using a perfect conductor.

Fig. 5.
Fig. 5.

Calculated TM ψ fields in silver with ξ = 0.15 .

Fig. 6.
Fig. 6.

Radial field dependence of ψ for a TM mode using Eq. (11) for m = 0 , n = 2 , and ξ = 0.1 . The thin curve is the perfect conductor waveguide mode, the dashed curve is the contribution due to additional charges in the metal, and the thick curve is the superposition of the two. The vertical dashed line indicates the position of the cavity walls. The rapid decay of the field inside the cavity walls is also plotted.

Fig. 7.
Fig. 7.

Fractional power loss α per unit length of a cylindrical aperture of radius a = 190 nm filled with a dielectric ϵ = 3 embedded in Drude silver. The loss is plotted for a few resonant modes.

Fig. 8.
Fig. 8.

Schematic of an arbitrarily shaped cavity and solution strategy. The gray region represents the metal, and the white region is the dielectric-filled cavity. The dotted line is the depth at which we apply the PEC BC.

Equations (26)

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[ 2 + ( ϵ κ 0 2 k z 2 ) ] ψ m n = 0 ,
ψ m n ( r , ϕ ) = e i m ϕ J m ( β m n r ) ,
E z ( r , ϕ , z ) = ψ e i k z z .
n ^ × E = 0 ,
n ^ · H = 0 ,
ϵ ω 2 c 2 = k z 2 + β 2 ,
β = ( 1 1 + ξ ) β 0 ,
δ ( ω ) = c ω κ ( ω ) ,
κ ( ω ) = 1 2 [ ϵ m ( ω ) ] 2 + [ ϵ m ( ω ) ] 2 1 2 [ ϵ m ( ω ) ]
ϵ m ( ω ) = 1 ω p 2 ω ( ω i ω τ ) ,
a = c ω cutoff χ m n ϵ δ ( ω cutoff ) ,
ψ ( r , ϕ ) = { J m ( β 0 r ) 1 2 ξ ( ξ 2 ) β 0 r J m + 1 ( β 0 r ) + 1 2 ξ [ m ( m ξ + ξ 2 ) ξ β 0 2 r 2 ] J m ( β 0 r ) } e i m ϕ .
E z = 1 2 ξ ( ξ 2 ) χ m n J m + 1 [ χ m n ] e i m ϕ .
σ = σ pec + σ sp .
n ^ · ( D 2 D 1 ) = 4 π σ ,
σ pec = i ϵ k z 4 π β 0 β 2 J m + 1 [ χ m n ] e i m ϕ ,
σ sp = 1 2 ξ 2 ( χ m n 2 m 2 ) σ pec ,
J = J pec + J sp ,
n ^ × ( B 2 B 1 ) = 4 π c J ,
J pec = z ^ i c ϵ κ 0 4 π β 0 β 2 J m + 1 [ χ m n ] e i m ϕ ,
J sp = 1 2 ξ 2 ( χ m n 2 m 2 ) J pec ,
P abs = a ω δ 4 | H ϕ | 2 ,
α P abs P trans = 2 ξ ( 1 + 4 ξ ) ϵ κ 0 2 k z
P ( z ) = P 0 e α z ,
ϵ κ 0 2 β 0 2 = 2 ξ ( 1 + 5 ξ ) + ( 1 + 2 ξ + 4 ξ 2 ) ω ξ ξ ( 1 + 7 ξ ) + ( 1 + 3 ξ + 3 ξ 2 ) ω ξ
ϵ ω 2 c 2 = k z 2 + γ 2 ,

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