Abstract

We present an analytical calculation of near– and far–field radiation emitted from a metal–coated tapered fiber probe. From FDTD simulations made in Cartesian coordinates we find that charge distribution on a tip is rim localized and its density is a bipolar periodic and continuous function. Similar angular charge density distributions may result from random irregularities of tip surfaces created in the fabrication process. Thus forward emission from a tip can be described as emission of quasi–dipoles and multi–quasi–dipoles. Analytically calculated characteristics are in agreement with our FDTD simulations and previous measurements of Obermüller and Karrai.

© 2007 Optical Society of America

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  1. H. A. Bethe, “Theory of diffraction by small holes,” Phys. Rev. 66, 163–182 (1944).
    [CrossRef]
  2. C. J. Bouwkamp, “On Bethe’s theory of diffraction by small holes,” Philips Res. Rep. 5, 321–332 (1950).
  3. Y. Leviatan, “Study of near-zone fields of a small aperture,” J. Appl. Phys. 60, 1577–1583 (1986).
    [CrossRef]
  4. D. W. Pohl, W. Denk, and M. Lanz, “Optical stethoscopy: Image recording with resolution λ/20,” Appl. Phys. Lett. 44, 651–653 (1984).
    [CrossRef]
  5. E. Betzig and J. K. Trautman, “Near-field optics: microscopy, spectroscopy, and surface modification beyond the diffraction limit,“ Science 257, 189–95 (1992).
    [CrossRef] [PubMed]
  6. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature (London) 391, 667–669 (1998).
    [CrossRef]
  7. D. E. Grupp, H. J. Lezec, T. W. Ebbesen, K. M. Pellerin, and T. Thio,“ Crucial role of metal surface in enhanced transmission through subwavelength apertures,” Appl. Phys. Lett. 77, 1569–1571 (2000).
    [CrossRef]
  8. H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820 (2002).
    [CrossRef] [PubMed]
  9. L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and 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]
  10. F. I. Baida, D. Van Labeke, and B. Guizal,“ Enhanced confined light transmission by single subwavelength apertures in metallic films,” Appl. Opt. 42, 6811ℓ6815 (2003).
    [CrossRef] [PubMed]
  11. S. Astilean, P. Lalanne, and M. Palamaru, “Light transmission through metallic channels much smaller than the wavelength,” Opt. Commun. 175, 265–273 (2000).
    [CrossRef]
  12. de Abajo F. Garcia, “Light transmission through a single cylindrical hole in a metallic film,” Opt. Express 10, 1475–1484 (2002).
  13. K. Y. Kim, Y. K. Cho, H. S. Tae, and J. H. Lee, “Optical guided dispersions and subwavelength transmissions in dispersive plasmonic circular holes,” Opto-Electron. Rev. 14, 233–241 (2006).
    [CrossRef]
  14. M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett. 93, 137404-1-4 (2004).
    [CrossRef] [PubMed]
  15. N. A. Janunts, K. S. Baghdasaryan, K. V. Nerkararyan, and B. Hecht, “Excitation and superfocusing of surface plasmon polaritons on a silver-coated optical fiber tip,” Opt. Commun. 253, 118–124 (2005).
    [CrossRef]
  16. E. X. Jin and X. Xu, “Obtaining super resolution light spot using surface plasmon assisted sharp ridge nanoaperture,” Appl. Phys. Lett. 86, 111106 (2005).
    [CrossRef]
  17. K. Tanaka, M. Tanaka, and T. Sugiyama, “Creation of strongly localized and strongly enhanced optical near-field on metallic probe-tip with surface plasmon polaritons,” Opt. Express 14, 832–846 (2006).
    [CrossRef] [PubMed]
  18. H. F. Arnoldus and J. T. Foley, –Spatial separation of the traveling and evanescent parts of dipole radiation,– Opt. Lett. 28, 1299–1301 (2003).
    [CrossRef] [PubMed]
  19. H. F. Arnoldus and J. T. Foley, “Highly directed transmission of multipole radiation by an interface,” Opt. Commun. 246, 45–56 (2005).
    [CrossRef]
  20. D. J. Shin, A. Chavez-Pirson, and Y. H. Lee, “Multipole analysis of the radiation from near-field optical probes,” Opt. Lett. 25, 171–173 (2000).
    [CrossRef]
  21. A. Drezet, J. C. Woehl, and S. Huant, “Far-field emission of a tapered optical fibre tip: a theoretical; analysis,” J. Microsc. 202, 359–361 (2001).
    [CrossRef] [PubMed]
  22. A. Drezet, J. C. Woehl, and S. Huant, “Diffraction by a small aperture in conical geometry: Application to metal-coated tips used in near-field optical microscopy,” Phys. Rev. E 65, 046611 (2002).
    [CrossRef]
  23. A. Drezet, S. Huant, and J. C. Woehl, “In situ characterization of optical tips using single fluorescent nanobeads,” J. Lumin. 107, 176–181 (2004).
    [CrossRef]
  24. C. Durkan and I. V. Shvets, “Polarization effects in reflection-mode scanning near-field optical microscopy,” J. Appl. Phys. 83, 1837–1843 (1998).
    [CrossRef]
  25. A. Gademann, I. V. Shvets, and C. Durkan, “Study of polarization-dependant energy coupling between near-field optical probe and mesoscopic metal structure,” J. Appl. Phys. 95, 3988–3993 (2004).
    [CrossRef]
  26. C. Obermüller and K. Karrai, “Far field characterization of diffracting circular aperture,” Appl. Phys. Lett. 67, 3408–3410 (1995).
    [CrossRef]
  27. J. H. Kim and K. B. Song, “Recent progress of nano-technology with NSOM,” Micron 38, 409–426 (2007).
    [CrossRef]
  28. T. Szoplik, W. M. Saj, J. Pniewski, and T. J. Antosiewicz, “Transmission of radially polarized light beams through nanoholes,” Abstracts of the EOS Topical Meeting on Nanophotonics, Metamaterials and Optical Microcavities, 16–19 October 2006, Paris, France.
  29. J. D. Jackson, Classical Electrodynamisc 3rd Ed., (John Wiley & Sons, Inc., New York1998).
  30. O. D. Jefimenko, Electricity and Magnetism, (Appleton-Century-Crofts, New York1966).
  31. K. T. McDonald, “The relation between expressions for time-dependent electromagnetic fields given by Jefimenko and by Panofsky and Phillips,” Am. J. Phys. 65, 1074 (1997).
    [CrossRef]

2007 (1)

J. H. Kim and K. B. Song, “Recent progress of nano-technology with NSOM,” Micron 38, 409–426 (2007).
[CrossRef]

2006 (3)

T. Szoplik, W. M. Saj, J. Pniewski, and T. J. Antosiewicz, “Transmission of radially polarized light beams through nanoholes,” Abstracts of the EOS Topical Meeting on Nanophotonics, Metamaterials and Optical Microcavities, 16–19 October 2006, Paris, France.

K. Y. Kim, Y. K. Cho, H. S. Tae, and J. H. Lee, “Optical guided dispersions and subwavelength transmissions in dispersive plasmonic circular holes,” Opto-Electron. Rev. 14, 233–241 (2006).
[CrossRef]

K. Tanaka, M. Tanaka, and T. Sugiyama, “Creation of strongly localized and strongly enhanced optical near-field on metallic probe-tip with surface plasmon polaritons,” Opt. Express 14, 832–846 (2006).
[CrossRef] [PubMed]

2005 (3)

N. A. Janunts, K. S. Baghdasaryan, K. V. Nerkararyan, and B. Hecht, “Excitation and superfocusing of surface plasmon polaritons on a silver-coated optical fiber tip,” Opt. Commun. 253, 118–124 (2005).
[CrossRef]

E. X. Jin and X. Xu, “Obtaining super resolution light spot using surface plasmon assisted sharp ridge nanoaperture,” Appl. Phys. Lett. 86, 111106 (2005).
[CrossRef]

H. F. Arnoldus and J. T. Foley, “Highly directed transmission of multipole radiation by an interface,” Opt. Commun. 246, 45–56 (2005).
[CrossRef]

2004 (3)

A. Drezet, S. Huant, and J. C. Woehl, “In situ characterization of optical tips using single fluorescent nanobeads,” J. Lumin. 107, 176–181 (2004).
[CrossRef]

A. Gademann, I. V. Shvets, and C. Durkan, “Study of polarization-dependant energy coupling between near-field optical probe and mesoscopic metal structure,” J. Appl. Phys. 95, 3988–3993 (2004).
[CrossRef]

M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett. 93, 137404-1-4 (2004).
[CrossRef] [PubMed]

2003 (3)

2002 (3)

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

de Abajo F. Garcia, “Light transmission through a single cylindrical hole in a metallic film,” Opt. Express 10, 1475–1484 (2002).

A. Drezet, J. C. Woehl, and S. Huant, “Diffraction by a small aperture in conical geometry: Application to metal-coated tips used in near-field optical microscopy,” Phys. Rev. E 65, 046611 (2002).
[CrossRef]

2001 (1)

A. Drezet, J. C. Woehl, and S. Huant, “Far-field emission of a tapered optical fibre tip: a theoretical; analysis,” J. Microsc. 202, 359–361 (2001).
[CrossRef] [PubMed]

2000 (3)

D. J. Shin, A. Chavez-Pirson, and Y. H. Lee, “Multipole analysis of the radiation from near-field optical probes,” Opt. Lett. 25, 171–173 (2000).
[CrossRef]

D. E. Grupp, H. J. Lezec, T. W. Ebbesen, K. M. Pellerin, and T. Thio,“ Crucial role of metal surface in enhanced transmission through subwavelength apertures,” Appl. Phys. Lett. 77, 1569–1571 (2000).
[CrossRef]

S. Astilean, P. Lalanne, and M. Palamaru, “Light transmission through metallic channels much smaller than the wavelength,” Opt. Commun. 175, 265–273 (2000).
[CrossRef]

1998 (3)

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

C. Durkan and I. V. Shvets, “Polarization effects in reflection-mode scanning near-field optical microscopy,” J. Appl. Phys. 83, 1837–1843 (1998).
[CrossRef]

J. D. Jackson, Classical Electrodynamisc 3rd Ed., (John Wiley & Sons, Inc., New York1998).

1997 (1)

K. T. McDonald, “The relation between expressions for time-dependent electromagnetic fields given by Jefimenko and by Panofsky and Phillips,” Am. J. Phys. 65, 1074 (1997).
[CrossRef]

1995 (1)

C. Obermüller and K. Karrai, “Far field characterization of diffracting circular aperture,” Appl. Phys. Lett. 67, 3408–3410 (1995).
[CrossRef]

1992 (1)

E. Betzig and J. K. Trautman, “Near-field optics: microscopy, spectroscopy, and surface modification beyond the diffraction limit,“ Science 257, 189–95 (1992).
[CrossRef] [PubMed]

1986 (1)

Y. Leviatan, “Study of near-zone fields of a small aperture,” J. Appl. Phys. 60, 1577–1583 (1986).
[CrossRef]

1984 (1)

D. W. Pohl, W. Denk, and M. Lanz, “Optical stethoscopy: Image recording with resolution λ/20,” Appl. Phys. Lett. 44, 651–653 (1984).
[CrossRef]

1966 (1)

O. D. Jefimenko, Electricity and Magnetism, (Appleton-Century-Crofts, New York1966).

1950 (1)

C. J. Bouwkamp, “On Bethe’s theory of diffraction by small holes,” Philips Res. Rep. 5, 321–332 (1950).

1944 (1)

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

Antosiewicz, T. J.

T. Szoplik, W. M. Saj, J. Pniewski, and T. J. Antosiewicz, “Transmission of radially polarized light beams through nanoholes,” Abstracts of the EOS Topical Meeting on Nanophotonics, Metamaterials and Optical Microcavities, 16–19 October 2006, Paris, France.

Arnoldus, H. F.

H. F. Arnoldus and J. T. Foley, “Highly directed transmission of multipole radiation by an interface,” Opt. Commun. 246, 45–56 (2005).
[CrossRef]

H. F. Arnoldus and J. T. Foley, –Spatial separation of the traveling and evanescent parts of dipole radiation,– Opt. Lett. 28, 1299–1301 (2003).
[CrossRef] [PubMed]

Astilean, S.

S. Astilean, P. Lalanne, and M. Palamaru, “Light transmission through metallic channels much smaller than the wavelength,” Opt. Commun. 175, 265–273 (2000).
[CrossRef]

Baghdasaryan, K. S.

N. A. Janunts, K. S. Baghdasaryan, K. V. Nerkararyan, and B. Hecht, “Excitation and superfocusing of surface plasmon polaritons on a silver-coated optical fiber tip,” Opt. Commun. 253, 118–124 (2005).
[CrossRef]

Baida, F. I.

Bethe, H. A.

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

Betzig, E.

E. Betzig and J. K. Trautman, “Near-field optics: microscopy, spectroscopy, and surface modification beyond the diffraction limit,“ Science 257, 189–95 (1992).
[CrossRef] [PubMed]

Bouwkamp, C. J.

C. J. Bouwkamp, “On Bethe’s theory of diffraction by small holes,” Philips Res. Rep. 5, 321–332 (1950).

Chavez-Pirson, A.

Cho, Y. K.

K. Y. Kim, Y. K. Cho, H. S. Tae, and J. H. Lee, “Optical guided dispersions and subwavelength transmissions in dispersive plasmonic circular holes,” Opto-Electron. Rev. 14, 233–241 (2006).
[CrossRef]

Degiron, A.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and 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]

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

Denk, W.

D. W. Pohl, W. Denk, and M. Lanz, “Optical stethoscopy: Image recording with resolution λ/20,” Appl. Phys. Lett. 44, 651–653 (1984).
[CrossRef]

Devaux, E.

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

Drezet, A.

A. Drezet, S. Huant, and J. C. Woehl, “In situ characterization of optical tips using single fluorescent nanobeads,” J. Lumin. 107, 176–181 (2004).
[CrossRef]

A. Drezet, J. C. Woehl, and S. Huant, “Diffraction by a small aperture in conical geometry: Application to metal-coated tips used in near-field optical microscopy,” Phys. Rev. E 65, 046611 (2002).
[CrossRef]

A. Drezet, J. C. Woehl, and S. Huant, “Far-field emission of a tapered optical fibre tip: a theoretical; analysis,” J. Microsc. 202, 359–361 (2001).
[CrossRef] [PubMed]

Durkan, C.

A. Gademann, I. V. Shvets, and C. Durkan, “Study of polarization-dependant energy coupling between near-field optical probe and mesoscopic metal structure,” J. Appl. Phys. 95, 3988–3993 (2004).
[CrossRef]

C. Durkan and I. V. Shvets, “Polarization effects in reflection-mode scanning near-field optical microscopy,” J. Appl. Phys. 83, 1837–1843 (1998).
[CrossRef]

Ebbesen, T. W.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and 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]

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

D. E. Grupp, H. J. Lezec, T. W. Ebbesen, K. M. Pellerin, and T. Thio,“ Crucial role of metal surface in enhanced transmission through subwavelength apertures,” Appl. Phys. Lett. 77, 1569–1571 (2000).
[CrossRef]

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

F. Garcia, de Abajo

Foley, J. T.

H. F. Arnoldus and J. T. Foley, “Highly directed transmission of multipole radiation by an interface,” Opt. Commun. 246, 45–56 (2005).
[CrossRef]

H. F. Arnoldus and J. T. Foley, –Spatial separation of the traveling and evanescent parts of dipole radiation,– Opt. Lett. 28, 1299–1301 (2003).
[CrossRef] [PubMed]

Gademann, A.

A. Gademann, I. V. Shvets, and C. Durkan, “Study of polarization-dependant energy coupling between near-field optical probe and mesoscopic metal structure,” J. Appl. Phys. 95, 3988–3993 (2004).
[CrossRef]

Garcia-Vidal, F. J.

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

García-Vidal, F. J.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and 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]

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 (London) 391, 667–669 (1998).
[CrossRef]

Grupp, D. E.

D. E. Grupp, H. J. Lezec, T. W. Ebbesen, K. M. Pellerin, and T. Thio,“ Crucial role of metal surface in enhanced transmission through subwavelength apertures,” Appl. Phys. Lett. 77, 1569–1571 (2000).
[CrossRef]

Guizal, B.

Hecht, B.

N. A. Janunts, K. S. Baghdasaryan, K. V. Nerkararyan, and B. Hecht, “Excitation and superfocusing of surface plasmon polaritons on a silver-coated optical fiber tip,” Opt. Commun. 253, 118–124 (2005).
[CrossRef]

Huant, S.

A. Drezet, S. Huant, and J. C. Woehl, “In situ characterization of optical tips using single fluorescent nanobeads,” J. Lumin. 107, 176–181 (2004).
[CrossRef]

A. Drezet, J. C. Woehl, and S. Huant, “Diffraction by a small aperture in conical geometry: Application to metal-coated tips used in near-field optical microscopy,” Phys. Rev. E 65, 046611 (2002).
[CrossRef]

A. Drezet, J. C. Woehl, and S. Huant, “Far-field emission of a tapered optical fibre tip: a theoretical; analysis,” J. Microsc. 202, 359–361 (2001).
[CrossRef] [PubMed]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamisc 3rd Ed., (John Wiley & Sons, Inc., New York1998).

Janunts, N. A.

N. A. Janunts, K. S. Baghdasaryan, K. V. Nerkararyan, and B. Hecht, “Excitation and superfocusing of surface plasmon polaritons on a silver-coated optical fiber tip,” Opt. Commun. 253, 118–124 (2005).
[CrossRef]

Jefimenko, O. D.

O. D. Jefimenko, Electricity and Magnetism, (Appleton-Century-Crofts, New York1966).

Jin, E. X.

E. X. Jin and X. Xu, “Obtaining super resolution light spot using surface plasmon assisted sharp ridge nanoaperture,” Appl. Phys. Lett. 86, 111106 (2005).
[CrossRef]

Karrai, K.

C. Obermüller and K. Karrai, “Far field characterization of diffracting circular aperture,” Appl. Phys. Lett. 67, 3408–3410 (1995).
[CrossRef]

Kim, J. H.

J. H. Kim and K. B. Song, “Recent progress of nano-technology with NSOM,” Micron 38, 409–426 (2007).
[CrossRef]

Kim, K. Y.

K. Y. Kim, Y. K. Cho, H. S. Tae, and J. H. Lee, “Optical guided dispersions and subwavelength transmissions in dispersive plasmonic circular holes,” Opto-Electron. Rev. 14, 233–241 (2006).
[CrossRef]

Lalanne, P.

S. Astilean, P. Lalanne, and M. Palamaru, “Light transmission through metallic channels much smaller than the wavelength,” Opt. Commun. 175, 265–273 (2000).
[CrossRef]

Lanz, M.

D. W. Pohl, W. Denk, and M. Lanz, “Optical stethoscopy: Image recording with resolution λ/20,” Appl. Phys. Lett. 44, 651–653 (1984).
[CrossRef]

Lee, J. H.

K. Y. Kim, Y. K. Cho, H. S. Tae, and J. H. Lee, “Optical guided dispersions and subwavelength transmissions in dispersive plasmonic circular holes,” Opto-Electron. Rev. 14, 233–241 (2006).
[CrossRef]

Lee, Y. H.

Leviatan, Y.

Y. Leviatan, “Study of near-zone fields of a small aperture,” J. Appl. Phys. 60, 1577–1583 (1986).
[CrossRef]

Lezec, H. J.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and 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]

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

D. E. Grupp, H. J. Lezec, T. W. Ebbesen, K. M. Pellerin, and T. Thio,“ Crucial role of metal surface in enhanced transmission through subwavelength apertures,” Appl. Phys. Lett. 77, 1569–1571 (2000).
[CrossRef]

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

Linke, R. A.

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

Martin-Moreno, L.

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

Martín-Moreno, L.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and 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]

McDonald, K. T.

K. T. McDonald, “The relation between expressions for time-dependent electromagnetic fields given by Jefimenko and by Panofsky and Phillips,” Am. J. Phys. 65, 1074 (1997).
[CrossRef]

Nerkararyan, K. V.

N. A. Janunts, K. S. Baghdasaryan, K. V. Nerkararyan, and B. Hecht, “Excitation and superfocusing of surface plasmon polaritons on a silver-coated optical fiber tip,” Opt. Commun. 253, 118–124 (2005).
[CrossRef]

Obermüller, C.

C. Obermüller and K. Karrai, “Far field characterization of diffracting circular aperture,” Appl. Phys. Lett. 67, 3408–3410 (1995).
[CrossRef]

Palamaru, M.

S. Astilean, P. Lalanne, and M. Palamaru, “Light transmission through metallic channels much smaller than the wavelength,” Opt. Commun. 175, 265–273 (2000).
[CrossRef]

Pellerin, K. M.

D. E. Grupp, H. J. Lezec, T. W. Ebbesen, K. M. Pellerin, and T. Thio,“ Crucial role of metal surface in enhanced transmission through subwavelength apertures,” Appl. Phys. Lett. 77, 1569–1571 (2000).
[CrossRef]

Pniewski, J.

T. Szoplik, W. M. Saj, J. Pniewski, and T. J. Antosiewicz, “Transmission of radially polarized light beams through nanoholes,” Abstracts of the EOS Topical Meeting on Nanophotonics, Metamaterials and Optical Microcavities, 16–19 October 2006, Paris, France.

Pohl, D. W.

D. W. Pohl, W. Denk, and M. Lanz, “Optical stethoscopy: Image recording with resolution λ/20,” Appl. Phys. Lett. 44, 651–653 (1984).
[CrossRef]

Saj, W. M.

T. Szoplik, W. M. Saj, J. Pniewski, and T. J. Antosiewicz, “Transmission of radially polarized light beams through nanoholes,” Abstracts of the EOS Topical Meeting on Nanophotonics, Metamaterials and Optical Microcavities, 16–19 October 2006, Paris, France.

Shin, D. J.

Shvets, I. V.

A. Gademann, I. V. Shvets, and C. Durkan, “Study of polarization-dependant energy coupling between near-field optical probe and mesoscopic metal structure,” J. Appl. Phys. 95, 3988–3993 (2004).
[CrossRef]

C. Durkan and I. V. Shvets, “Polarization effects in reflection-mode scanning near-field optical microscopy,” J. Appl. Phys. 83, 1837–1843 (1998).
[CrossRef]

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T. Szoplik, W. M. Saj, J. Pniewski, and T. J. Antosiewicz, “Transmission of radially polarized light beams through nanoholes,” Abstracts of the EOS Topical Meeting on Nanophotonics, Metamaterials and Optical Microcavities, 16–19 October 2006, Paris, France.

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K. Y. Kim, Y. K. Cho, H. S. Tae, and J. H. Lee, “Optical guided dispersions and subwavelength transmissions in dispersive plasmonic circular holes,” Opto-Electron. Rev. 14, 233–241 (2006).
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Woehl, J. C.

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T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature (London) 391, 667–669 (1998).
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A. Drezet, J. C. Woehl, and S. Huant, “Far-field emission of a tapered optical fibre tip: a theoretical; analysis,” J. Microsc. 202, 359–361 (2001).
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Micron (1)

J. H. Kim and K. B. Song, “Recent progress of nano-technology with NSOM,” Micron 38, 409–426 (2007).
[CrossRef]

Nature (London) (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 (London) 391, 667–669 (1998).
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[CrossRef]

Phys. Rev. Lett. (2)

M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett. 93, 137404-1-4 (2004).
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T. Szoplik, W. M. Saj, J. Pniewski, and T. J. Antosiewicz, “Transmission of radially polarized light beams through nanoholes,” Abstracts of the EOS Topical Meeting on Nanophotonics, Metamaterials and Optical Microcavities, 16–19 October 2006, Paris, France.

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Figures (9)

Fig. 1.
Fig. 1.

Rim charge density distributions in arbitrary units for: a) N=1; b) N=2; c) N=3; d) N=4. Red indicates a value greater than zero, blue negative.

Fig. 2.
Fig. 2.

Far-field angular intensities radiated by diluted dipoles of various apertures.

Fig. 3.
Fig. 3.

Amplitude of components of the electric field (a) Ez and (b) Ex in the plane of the probe aperture. The colors indicate charges of opposite signs on the adverse sides of the aperture. The input Gaussian beam is linearly polarized along the x-axis.

Fig. 4.
Fig. 4.

Beam intensity profiles calculated at increasing distances z = 1, 11, 21, 31 nm from the aperture; (a) quasi-dipole model, (b) 2D FDTD simulation. Intensity curves are normalized to their respective maximum values.

Fig. 5.
Fig. 5.

(a). Field intensity in the aperture plane calculated by FDTD (red) and the multi-quasi-dipole method (blue); (b). FWHM calculated 10 nm behind the aperture using both methods, FDTD (red) and the multi-quasi-dipole method (blue).

Fig. 6.
Fig. 6.

Beam intensity normalized to the number of quasi–dipoles N for various multi–quasi–dipoles at a distance of 5nm from the tips of aperture diameters a) 40 nm and b) 80 nm.

Fig. 7.
Fig. 7.

Beam widths calculated within 1 nm accuracy for 40 nm (a), (b) and 80 nm (c), (d) apertures at a distance of 5 nm (a), (c) and 25 nm (b), (d) from the aperture.

Fig. 8.
Fig. 8.

Polarization of the electric field for wavelength λ = 500 nm at a distance of 25 nm from the radiating plane for an arbitrary time frame for (a) 1 quasi–dipole, (b) 2 quasi–dipoles, (c) 3 quasi–dipoles.

Fig. 9.
Fig. 9.

Beam profiles calculated for wavelength λ = 500 nm at a distance of 25 nm from the radiating plane for (a) 1 dipole, (b) 2 quasi–dipoles, (c) 3 quasi–dipoles, (d) 4 quasi–dipole, (e) 5 quasi–dipoles, (f) 6 quasi–dipoles (not in intensity scale).

Equations (5)

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ρ ( r , ϕ ) cos ( N ϕ ) cos ( ω t ) δ ( r R ) ,
ρ ( r , ϕ ) cos ( N ϕ ) cos ( ω t ) r n
t ρ + J = 0 .
E ( r , t ) = 1 4 π ε 0 × [ ρ ( r ' , t r ) 2 ̂ + ρ ( r ' , t r ) c ̂ J ( r ' , t r ) c 2 ] d τ ' ,
B ( r , t ) = μ 0 4 π [ J ( r ' , t r ) 2 + J ( r ' , t r ) c ] × ̂ '

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