Abstract

The diffraction of light that emerges from a metallic circular aperture is studied. Near- and far-field results are presented. Spectral angular transmitted intensities are performed versus the incident wavelength for four kinds of aperture. It is shown that, for a definite configuration, a large enhancement of transmission—compared with the basic case of a single hole—occurs combined with a spectacular angular confinement of light. Such effects are, for example, of great interest in optical near-field microscopy for which the probe is a nanosource.

© 2003 Optical Society of America

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  1. H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
    [CrossRef] [PubMed]
  2. L. Martín-Moreno, F. J. García-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]
  3. U. C. Fischer, M. Zapletal, “The concept of a coaxial tip as a probe for scanning near field optical microscopy and steps towards a realisation,” Ultramicroscopy 42–44, 393–398 (1992).
    [CrossRef]
  4. T. Leinhos, O. Rudow, M. Stopka, A. Vollkopf, E. Oesterschulze, “Coaxial probes for scanning near-field microscopy,” J. Microsc. (Oxford) 194, 349–352 (1999).
    [CrossRef]
  5. F. I. Baida, D. Van Labeke, “Light transmission by subwavelength annular aperture arrays in metallic films,” Opt. Commun. 209, 17–22 (2002).
    [CrossRef]
  6. F. I. Baida, D. Van Labeke, “Three-dimensional structures for enhanced transmission through a metallic film: annular aperture arrays,” Phys. Rev. B 67, 155314 (2003).
    [CrossRef]
  7. A. Taflove, S. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method, 2nd ed. (Artech House, Boston, Mass., 2000).
  8. M. N. O. Sadiku, Numerical Techniques in Electrodynamics, 2nd ed. (CRC Press, Boca Raton, Fla., 2000).
  9. G. Parent, D. Van Labeke, F. I. Baida, “Theoretical study of transient phenomena in near-field optics,” J. Microsc. (Oxford) 202, 296–306 (2001).
    [CrossRef]
  10. P. B. Johnson, R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 12, 4370–4379 (1972).
    [CrossRef]
  11. J. J. Stamnes, Waves in Focal Regions: Propagation, Diffraction, and Focusing of Light, Sound and Water Waves, Adam Hilger Series on Optics and Optoelectronics (Adam Hilger, Bristol, UK, 1986).
  12. G. C. Sherman, J. J. Stamnes, E. Lalor, “Asymptotic approximations to angular-spectrum representations,” J. Math. Phys. 17, 760–776 (1976).
    [CrossRef]
  13. F. I. Baida, D. Van Labeke, G. Granet, A. Moreau, A. Belkhir, “Origin of the super-enhanced light transmission through a 3D metallic annular aperture array,” submitted to Appl. Phys. A.

2003 (2)

L. Martín-Moreno, F. J. García-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. I. Baida, D. Van Labeke, “Three-dimensional structures for enhanced transmission through a metallic film: annular aperture arrays,” Phys. Rev. B 67, 155314 (2003).
[CrossRef]

2002 (2)

F. I. Baida, D. Van Labeke, “Light transmission by subwavelength annular aperture arrays in metallic films,” Opt. Commun. 209, 17–22 (2002).
[CrossRef]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
[CrossRef] [PubMed]

2001 (1)

G. Parent, D. Van Labeke, F. I. Baida, “Theoretical study of transient phenomena in near-field optics,” J. Microsc. (Oxford) 202, 296–306 (2001).
[CrossRef]

1999 (1)

T. Leinhos, O. Rudow, M. Stopka, A. Vollkopf, E. Oesterschulze, “Coaxial probes for scanning near-field microscopy,” J. Microsc. (Oxford) 194, 349–352 (1999).
[CrossRef]

1992 (1)

U. C. Fischer, M. Zapletal, “The concept of a coaxial tip as a probe for scanning near field optical microscopy and steps towards a realisation,” Ultramicroscopy 42–44, 393–398 (1992).
[CrossRef]

1976 (1)

G. C. Sherman, J. J. Stamnes, E. Lalor, “Asymptotic approximations to angular-spectrum representations,” J. Math. Phys. 17, 760–776 (1976).
[CrossRef]

1972 (1)

P. B. Johnson, R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 12, 4370–4379 (1972).
[CrossRef]

Baida, F. I.

F. I. Baida, D. Van Labeke, “Three-dimensional structures for enhanced transmission through a metallic film: annular aperture arrays,” Phys. Rev. B 67, 155314 (2003).
[CrossRef]

F. I. Baida, D. Van Labeke, “Light transmission by subwavelength annular aperture arrays in metallic films,” Opt. Commun. 209, 17–22 (2002).
[CrossRef]

G. Parent, D. Van Labeke, F. I. Baida, “Theoretical study of transient phenomena in near-field optics,” J. Microsc. (Oxford) 202, 296–306 (2001).
[CrossRef]

F. I. Baida, D. Van Labeke, G. Granet, A. Moreau, A. Belkhir, “Origin of the super-enhanced light transmission through a 3D metallic annular aperture array,” submitted to Appl. Phys. A.

Belkhir, A.

F. I. Baida, D. Van Labeke, G. Granet, A. Moreau, A. Belkhir, “Origin of the super-enhanced light transmission through a 3D metallic annular aperture array,” submitted to Appl. Phys. A.

Christy, R. W.

P. B. Johnson, R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 12, 4370–4379 (1972).
[CrossRef]

Degiron, A.

L. Martín-Moreno, F. J. García-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]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
[CrossRef] [PubMed]

Devaux, E.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
[CrossRef] [PubMed]

Ebbesen, T. W.

L. Martín-Moreno, F. J. García-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]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
[CrossRef] [PubMed]

Fischer, U. C.

U. C. Fischer, M. Zapletal, “The concept of a coaxial tip as a probe for scanning near field optical microscopy and steps towards a realisation,” Ultramicroscopy 42–44, 393–398 (1992).
[CrossRef]

Garcia-Vidal, F. J.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
[CrossRef] [PubMed]

García-Vidal, F. J.

L. Martín-Moreno, F. J. García-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]

Granet, G.

F. I. Baida, D. Van Labeke, G. Granet, A. Moreau, A. Belkhir, “Origin of the super-enhanced light transmission through a 3D metallic annular aperture array,” submitted to Appl. Phys. A.

Hagness, S.

A. Taflove, S. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method, 2nd ed. (Artech House, Boston, Mass., 2000).

Johnson, P. B.

P. B. Johnson, R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 12, 4370–4379 (1972).
[CrossRef]

Lalor, E.

G. C. Sherman, J. J. Stamnes, E. Lalor, “Asymptotic approximations to angular-spectrum representations,” J. Math. Phys. 17, 760–776 (1976).
[CrossRef]

Leinhos, T.

T. Leinhos, O. Rudow, M. Stopka, A. Vollkopf, E. Oesterschulze, “Coaxial probes for scanning near-field microscopy,” J. Microsc. (Oxford) 194, 349–352 (1999).
[CrossRef]

Lezec, H. J.

L. Martín-Moreno, F. J. García-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]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
[CrossRef] [PubMed]

Linke, R. A.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
[CrossRef] [PubMed]

Martin-Moreno, L.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
[CrossRef] [PubMed]

Martín-Moreno, L.

L. Martín-Moreno, F. J. García-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]

Moreau, A.

F. I. Baida, D. Van Labeke, G. Granet, A. Moreau, A. Belkhir, “Origin of the super-enhanced light transmission through a 3D metallic annular aperture array,” submitted to Appl. Phys. A.

Oesterschulze, E.

T. Leinhos, O. Rudow, M. Stopka, A. Vollkopf, E. Oesterschulze, “Coaxial probes for scanning near-field microscopy,” J. Microsc. (Oxford) 194, 349–352 (1999).
[CrossRef]

Parent, G.

G. Parent, D. Van Labeke, F. I. Baida, “Theoretical study of transient phenomena in near-field optics,” J. Microsc. (Oxford) 202, 296–306 (2001).
[CrossRef]

Rudow, O.

T. Leinhos, O. Rudow, M. Stopka, A. Vollkopf, E. Oesterschulze, “Coaxial probes for scanning near-field microscopy,” J. Microsc. (Oxford) 194, 349–352 (1999).
[CrossRef]

Sadiku, M. N. O.

M. N. O. Sadiku, Numerical Techniques in Electrodynamics, 2nd ed. (CRC Press, Boca Raton, Fla., 2000).

Sherman, G. C.

G. C. Sherman, J. J. Stamnes, E. Lalor, “Asymptotic approximations to angular-spectrum representations,” J. Math. Phys. 17, 760–776 (1976).
[CrossRef]

Stamnes, J. J.

G. C. Sherman, J. J. Stamnes, E. Lalor, “Asymptotic approximations to angular-spectrum representations,” J. Math. Phys. 17, 760–776 (1976).
[CrossRef]

J. J. Stamnes, Waves in Focal Regions: Propagation, Diffraction, and Focusing of Light, Sound and Water Waves, Adam Hilger Series on Optics and Optoelectronics (Adam Hilger, Bristol, UK, 1986).

Stopka, M.

T. Leinhos, O. Rudow, M. Stopka, A. Vollkopf, E. Oesterschulze, “Coaxial probes for scanning near-field microscopy,” J. Microsc. (Oxford) 194, 349–352 (1999).
[CrossRef]

Taflove, A.

A. Taflove, S. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method, 2nd ed. (Artech House, Boston, Mass., 2000).

Van Labeke, D.

F. I. Baida, D. Van Labeke, “Three-dimensional structures for enhanced transmission through a metallic film: annular aperture arrays,” Phys. Rev. B 67, 155314 (2003).
[CrossRef]

F. I. Baida, D. Van Labeke, “Light transmission by subwavelength annular aperture arrays in metallic films,” Opt. Commun. 209, 17–22 (2002).
[CrossRef]

G. Parent, D. Van Labeke, F. I. Baida, “Theoretical study of transient phenomena in near-field optics,” J. Microsc. (Oxford) 202, 296–306 (2001).
[CrossRef]

F. I. Baida, D. Van Labeke, G. Granet, A. Moreau, A. Belkhir, “Origin of the super-enhanced light transmission through a 3D metallic annular aperture array,” submitted to Appl. Phys. A.

Vollkopf, A.

T. Leinhos, O. Rudow, M. Stopka, A. Vollkopf, E. Oesterschulze, “Coaxial probes for scanning near-field microscopy,” J. Microsc. (Oxford) 194, 349–352 (1999).
[CrossRef]

Zapletal, M.

U. C. Fischer, M. Zapletal, “The concept of a coaxial tip as a probe for scanning near field optical microscopy and steps towards a realisation,” Ultramicroscopy 42–44, 393–398 (1992).
[CrossRef]

J. Math. Phys. (1)

G. C. Sherman, J. J. Stamnes, E. Lalor, “Asymptotic approximations to angular-spectrum representations,” J. Math. Phys. 17, 760–776 (1976).
[CrossRef]

J. Microsc. (Oxford) (2)

T. Leinhos, O. Rudow, M. Stopka, A. Vollkopf, E. Oesterschulze, “Coaxial probes for scanning near-field microscopy,” J. Microsc. (Oxford) 194, 349–352 (1999).
[CrossRef]

G. Parent, D. Van Labeke, F. I. Baida, “Theoretical study of transient phenomena in near-field optics,” J. Microsc. (Oxford) 202, 296–306 (2001).
[CrossRef]

Opt. Commun. (1)

F. I. Baida, D. Van Labeke, “Light transmission by subwavelength annular aperture arrays in metallic films,” Opt. Commun. 209, 17–22 (2002).
[CrossRef]

Phys. Rev. B (2)

F. I. Baida, D. Van Labeke, “Three-dimensional structures for enhanced transmission through a metallic film: annular aperture arrays,” Phys. Rev. B 67, 155314 (2003).
[CrossRef]

P. B. Johnson, R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 12, 4370–4379 (1972).
[CrossRef]

Phys. Rev. Lett. (1)

L. Martín-Moreno, F. J. García-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)

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
[CrossRef] [PubMed]

Ultramicroscopy (1)

U. C. Fischer, M. Zapletal, “The concept of a coaxial tip as a probe for scanning near field optical microscopy and steps towards a realisation,” Ultramicroscopy 42–44, 393–398 (1992).
[CrossRef]

Other (4)

J. J. Stamnes, Waves in Focal Regions: Propagation, Diffraction, and Focusing of Light, Sound and Water Waves, Adam Hilger Series on Optics and Optoelectronics (Adam Hilger, Bristol, UK, 1986).

A. Taflove, S. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method, 2nd ed. (Artech House, Boston, Mass., 2000).

M. N. O. Sadiku, Numerical Techniques in Electrodynamics, 2nd ed. (CRC Press, Boca Raton, Fla., 2000).

F. I. Baida, D. Van Labeke, G. Granet, A. Moreau, A. Belkhir, “Origin of the super-enhanced light transmission through a 3D metallic annular aperture array,” submitted to Appl. Phys. A.

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Figures (4)

Fig. 1
Fig. 1

Schematics of the four studied structures.

Fig. 2
Fig. 2

Zero-order efficiencies for the four kinds of aperture: (a) CA, (b) CAG, (c) CCA, (d) CCAG.

Fig. 3
Fig. 3

Normalized angular spectra for the four apertures in the xz plane (ψ = 0°) calculated for the λ marked by dots in Fig. 2.

Fig. 4
Fig. 4

Near-field intensity distributions (on a logarithmic gray-level scale) at 20 nm from the output of the structure: (a) CA configuration at λ = 709 nm, CAG configuration at (b) λ = 709 nm and (c) λ = 404 nm, (d) CCAG configuration at λ = 681 nm. The beaming effect occurs only in (b) and (d).

Equations (3)

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

Exx, y, z=Exr, θ, z=Errcos2 θ-Eθrsin2 θ, Eyx, y, z=Eyr, θ, z=cos θ sin θErr+Eθr, Ezx, y, z=Ezr, θ, z=cos θ Ezr,
Exϕ, ψ=-2iπ cos ϕλ0+ r J0mcos2 ψErr-sin2 ψEθr-cos 2ψ J1mm×Err+Eθrdr Eyϕ, ψ=-iπ cos ϕλsin 2ψ 0+rErr+Eθr]×[J0m-2J1mmdr,Ezϕ, ψ=2πλcos ϕ cos ψ 0+ rEzrJ1mdr,
Ex0, 0=-iπλ0+ rErr-Eθrdr.

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