Abstract

Using terahertz-light excitation, we have measured with sub-wavelength spatial, and sub-cycle temporal resolution the time- and frequency-dependent electric-field and surface-charge density in the vicinity of small metallic holes. In addition to a singularity like concentration of the electric field near the hole edges, we observe, that holes can act as differential operators whose near-field output is the time-derivative of the incident electric field. Our results confirm the well-known predictions made by Bouwkamp, Philips Res. Rep. 5, 321–332 (1950), and reveal, with unprecedented detail, what physically happens when light passes through a small hole.

© 2008 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 (London) 391, 667-669 (1998)
    [CrossRef]
  2. T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, "Transmission resonances through aperiodic arrays of subwavelength apertures," Nature (London) 447, 517-521 (2007)
    [CrossRef]
  3. L. Novotny, D. W. Pohl, B. Hecht, "Scanning near-field optical probe with ultrasmall spot size," Opt. Lett. 20, 970-972 (1995)
    [CrossRef] [PubMed]
  4. E. Betzig and J. K. Trautman, "Single Molecules Observed by Near-Field Scanning Optical Microscopy," Science 257, 189-195 (1992)
    [CrossRef] [PubMed]
  5. B. Hecht, B. Sick, U. P. Wild, V. Deckert, R. Zenobi, O. J. F. Martin, D. W. Pohl, "Scanning near-field optical microscopy with aperture probes: Fundamentals and applications," J. Chem. Phys. 112, 7761-7774 (2000)
    [CrossRef]
  6. J. T. Bahns, F. Yan, D. Qiu, R. Wang, L. Chen, "Hole-enhanced Raman scattering," Appl. Spectrosc. 60, 989-993 (2006)
    [CrossRef] [PubMed]
  7. A. G. Brolo, E. Arctander, R. Gordon, B. Leathem, K. L. Kavanagh, "Nanohole-enhanced Raman scattering," Nano Lett. 4, 2015-2018 (2004)
    [CrossRef]
  8. A. Degiron, H. J. Lezec, N. Yamamoto, T. W. Ebbesen, "Optical transmission properties of a single subwavelength aperture in a real metal," Opt. Commun. 239, 61-66 (2004)
    [CrossRef]
  9. R. S. Decca, H. D. Drew, K. L. Empson, "Investigation of the electric-field distribution at the subwavelength aperture of a near-field scanning optical microscope," Appl. Phys. Lett. 70, 1932-1934 (1997)
    [CrossRef]
  10. C. Genet, T. W. Ebbesen, "Light in tiny holes," Nature (London) 445, 39-46 (2007)
    [CrossRef] [PubMed]
  11. E. Betzig, R. J. Chichester, "Single molecules observed by near-field scanning optical microscopy," Science 262, 1422-1425 (1993)
    [CrossRef] [PubMed]
  12. J. A. Veerman, M. F. Garcia-Parajo, L. Kuipers, N. F. Van Hulst, "Single molecule mapping of the optical field distribution of probes for near-field microscopy," J. Microsc. 194, 477-482 (1999)
    [CrossRef]
  13. A. Drezet, S. Huant, J. C. Woehl, "In situ characterization of optical tips using single fluorescent nanobeads," J. Lumin. 107, 176-181 (2004)
    [CrossRef]
  14. H. A. Bethe, "Theory of diffraction by small holes," Phys. Rev. 66, 163-182 (1944)
    [CrossRef]
  15. C. J. Bouwkamp, "On the diffraction of electromagnetic waves by circular disks and apertures," Philips Res. Rep. 5, 401-422 (1950)
  16. C. J. Bouwkamp, "On Bethe�??s theory of diffraction by small holes," Philips Res. Rep. 5, 321-332 (1950)
  17. A. Agrawal, H. Cao, and A. Nahata,"Time-domain analysis of enhanced transmission through a single subwavelength aperture," Opt. Express 13, 3535-3542 (2005)
    [CrossRef] [PubMed]
  18. A. Agrawal and A. Nahata, "Time-domain radiative properties of a single subwavelength aperture surrounded by an exit side surface corrugation," Opt. Express 14, 1973-1981 (2006)
    [CrossRef] [PubMed]
  19. M. van Exter, D. R. Grischkowsky, "Characterization of an Optoelectronic Terahertz Beam System," IEEE Trans. Microwave Theory Tech. 38, 1684-1691 (1990)
    [CrossRef]
  20. G. Zhao, R. N. Schouten, N. van der Valk, W. Th. Wenckebach, and P. C. M. Planken, "Design and performance of a THz emission and detection setup based on a semi-insulating GaAs emitter," Rev. Sci. Instrum. 73, 1715-1719 (2002)
    [CrossRef]
  21. N. C. J. van der Valk, P. C. M. Planken, "Electro-optic detection of sub-wavelength terahertz spot sizes in the near-field of a metal tip," Appl. Phys. Lett. 81, 1558-1560 (2002)
    [CrossRef]
  22. M. A. Seo, et al., "Fourier-transform terahertz near-field imaging of one-dimensional slit arrays: mapping of electric-field-, magnetic-field-, and Poynting vectors," Opt. Express 15, 11781-11789 (2007)
    [CrossRef] [PubMed]
  23. F. J. Garcıa de Abajo, J. J. Saenz, I. Campillo, and J. S. Dolado, "Site and lattice resonances in metallic hole arrays," Opt. Express 14, 7-18 (2006)
    [CrossRef]
  24. R. Gordon and A. G. Brolo, "Increased cut-off wavelength for a subwavelength hole in a real metal," Opt. Express 13, 1933-1938 (2005)
    [CrossRef] [PubMed]
  25. F. J. Garcıa de Abajo, "Light transmission through a single cylindrical hole in a metallic film," Opt. Express 10, 1475-1484 (2002)
  26. T. Thio, et al., "Giant optical transmission of sub-wavelength apertures: physics and applications," Nanotechnology 13, 429-432 (2002)
    [CrossRef]
  27. O. Mitrofanov, et al., "Terahertz pulse propagation through small apertures," Appl. Phys. Lett. 79, 907-909 (2001)
    [CrossRef]
  28. G. A. Massey, J. A. Davis, S. M. Katnik, and E. Ornon, "Subwavelength resolution far-infrared microscopy," Appl. Opt. 24, 1498-1501 (1985)
    [CrossRef] [PubMed]
  29. E. F. Barnett and J. K. Hunton, "A precision directional coupler using multi-hole coupling," Hewlett Packard Journal,  3 (No. 7-8) (1952).
  30. J. F. Nye, W. Liang, and G. Hygate, "Mapping a diffraction field close to an obstacle," IEEE Trans. Electromagn. Compat. 37, 288-292 (1995).
    [CrossRef]
  31. J. F. Nye and W. Liang, "Superposition of the diffraction fields of apertures: an experimental test," Proc. R. Soc. Lond. A 453, 1963-1974 (1997).
    [CrossRef]

2007

C. Genet, T. W. Ebbesen, "Light in tiny holes," Nature (London) 445, 39-46 (2007)
[CrossRef] [PubMed]

T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, "Transmission resonances through aperiodic arrays of subwavelength apertures," Nature (London) 447, 517-521 (2007)
[CrossRef]

M. A. Seo, et al., "Fourier-transform terahertz near-field imaging of one-dimensional slit arrays: mapping of electric-field-, magnetic-field-, and Poynting vectors," Opt. Express 15, 11781-11789 (2007)
[CrossRef] [PubMed]

2006

2005

2004

A. G. Brolo, E. Arctander, R. Gordon, B. Leathem, K. L. Kavanagh, "Nanohole-enhanced Raman scattering," Nano Lett. 4, 2015-2018 (2004)
[CrossRef]

A. Degiron, H. J. Lezec, N. Yamamoto, T. W. Ebbesen, "Optical transmission properties of a single subwavelength aperture in a real metal," Opt. Commun. 239, 61-66 (2004)
[CrossRef]

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

2002

G. Zhao, R. N. Schouten, N. van der Valk, W. Th. Wenckebach, and P. C. M. Planken, "Design and performance of a THz emission and detection setup based on a semi-insulating GaAs emitter," Rev. Sci. Instrum. 73, 1715-1719 (2002)
[CrossRef]

N. C. J. van der Valk, P. C. M. Planken, "Electro-optic detection of sub-wavelength terahertz spot sizes in the near-field of a metal tip," Appl. Phys. Lett. 81, 1558-1560 (2002)
[CrossRef]

T. Thio, et al., "Giant optical transmission of sub-wavelength apertures: physics and applications," Nanotechnology 13, 429-432 (2002)
[CrossRef]

F. J. Garcıa de Abajo, "Light transmission through a single cylindrical hole in a metallic film," Opt. Express 10, 1475-1484 (2002)

2001

O. Mitrofanov, et al., "Terahertz pulse propagation through small apertures," Appl. Phys. Lett. 79, 907-909 (2001)
[CrossRef]

2000

B. Hecht, B. Sick, U. P. Wild, V. Deckert, R. Zenobi, O. J. F. Martin, D. W. Pohl, "Scanning near-field optical microscopy with aperture probes: Fundamentals and applications," J. Chem. Phys. 112, 7761-7774 (2000)
[CrossRef]

1999

J. A. Veerman, M. F. Garcia-Parajo, L. Kuipers, N. F. Van Hulst, "Single molecule mapping of the optical field distribution of probes for near-field microscopy," J. Microsc. 194, 477-482 (1999)
[CrossRef]

1998

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]

1997

R. S. Decca, H. D. Drew, K. L. Empson, "Investigation of the electric-field distribution at the subwavelength aperture of a near-field scanning optical microscope," Appl. Phys. Lett. 70, 1932-1934 (1997)
[CrossRef]

J. F. Nye and W. Liang, "Superposition of the diffraction fields of apertures: an experimental test," Proc. R. Soc. Lond. A 453, 1963-1974 (1997).
[CrossRef]

1995

J. F. Nye, W. Liang, and G. Hygate, "Mapping a diffraction field close to an obstacle," IEEE Trans. Electromagn. Compat. 37, 288-292 (1995).
[CrossRef]

L. Novotny, D. W. Pohl, B. Hecht, "Scanning near-field optical probe with ultrasmall spot size," Opt. Lett. 20, 970-972 (1995)
[CrossRef] [PubMed]

1993

E. Betzig, R. J. Chichester, "Single molecules observed by near-field scanning optical microscopy," Science 262, 1422-1425 (1993)
[CrossRef] [PubMed]

1992

E. Betzig and J. K. Trautman, "Single Molecules Observed by Near-Field Scanning Optical Microscopy," Science 257, 189-195 (1992)
[CrossRef] [PubMed]

1990

M. van Exter, D. R. Grischkowsky, "Characterization of an Optoelectronic Terahertz Beam System," IEEE Trans. Microwave Theory Tech. 38, 1684-1691 (1990)
[CrossRef]

1985

1952

E. F. Barnett and J. K. Hunton, "A precision directional coupler using multi-hole coupling," Hewlett Packard Journal,  3 (No. 7-8) (1952).

1950

C. J. Bouwkamp, "On the diffraction of electromagnetic waves by circular disks and apertures," Philips Res. Rep. 5, 401-422 (1950)

C. J. Bouwkamp, "On Bethe�??s theory of diffraction by small holes," Philips Res. Rep. 5, 321-332 (1950)

1944

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

Agrawal, A.

Arctander, E.

A. G. Brolo, E. Arctander, R. Gordon, B. Leathem, K. L. Kavanagh, "Nanohole-enhanced Raman scattering," Nano Lett. 4, 2015-2018 (2004)
[CrossRef]

Bahns, J. T.

Barnett, E. F.

E. F. Barnett and J. K. Hunton, "A precision directional coupler using multi-hole coupling," Hewlett Packard Journal,  3 (No. 7-8) (1952).

Bethe, H. A.

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

Betzig, E.

E. Betzig, R. J. Chichester, "Single molecules observed by near-field scanning optical microscopy," Science 262, 1422-1425 (1993)
[CrossRef] [PubMed]

E. Betzig and J. K. Trautman, "Single Molecules Observed by Near-Field Scanning Optical Microscopy," Science 257, 189-195 (1992)
[CrossRef] [PubMed]

Bouwkamp, C. J.

C. J. Bouwkamp, "On the diffraction of electromagnetic waves by circular disks and apertures," Philips Res. Rep. 5, 401-422 (1950)

C. J. Bouwkamp, "On Bethe�??s theory of diffraction by small holes," Philips Res. Rep. 5, 321-332 (1950)

Brolo, A. G.

R. Gordon and A. G. Brolo, "Increased cut-off wavelength for a subwavelength hole in a real metal," Opt. Express 13, 1933-1938 (2005)
[CrossRef] [PubMed]

A. G. Brolo, E. Arctander, R. Gordon, B. Leathem, K. L. Kavanagh, "Nanohole-enhanced Raman scattering," Nano Lett. 4, 2015-2018 (2004)
[CrossRef]

Cao, H.

Chen, L.

Chichester, R. J.

E. Betzig, R. J. Chichester, "Single molecules observed by near-field scanning optical microscopy," Science 262, 1422-1425 (1993)
[CrossRef] [PubMed]

Davis, J. A.

Decca, R. S.

R. S. Decca, H. D. Drew, K. L. Empson, "Investigation of the electric-field distribution at the subwavelength aperture of a near-field scanning optical microscope," Appl. Phys. Lett. 70, 1932-1934 (1997)
[CrossRef]

Deckert, V.

B. Hecht, B. Sick, U. P. Wild, V. Deckert, R. Zenobi, O. J. F. Martin, D. W. Pohl, "Scanning near-field optical microscopy with aperture probes: Fundamentals and applications," J. Chem. Phys. 112, 7761-7774 (2000)
[CrossRef]

Degiron, A.

A. Degiron, H. J. Lezec, N. Yamamoto, T. W. Ebbesen, "Optical transmission properties of a single subwavelength aperture in a real metal," Opt. Commun. 239, 61-66 (2004)
[CrossRef]

Drew, H. D.

R. S. Decca, H. D. Drew, K. L. Empson, "Investigation of the electric-field distribution at the subwavelength aperture of a near-field scanning optical microscope," Appl. Phys. Lett. 70, 1932-1934 (1997)
[CrossRef]

Drezet, A.

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

Ebbesen, T. W.

C. Genet, T. W. Ebbesen, "Light in tiny holes," Nature (London) 445, 39-46 (2007)
[CrossRef] [PubMed]

A. Degiron, H. J. Lezec, N. Yamamoto, T. W. Ebbesen, "Optical transmission properties of a single subwavelength aperture in a real metal," Opt. Commun. 239, 61-66 (2004)
[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]

Empson, K. L.

R. S. Decca, H. D. Drew, K. L. Empson, "Investigation of the electric-field distribution at the subwavelength aperture of a near-field scanning optical microscope," Appl. Phys. Lett. 70, 1932-1934 (1997)
[CrossRef]

Garc???ia de Abajo, F. J.

Garcia de Abajo, F. J.

Garcia-Parajo, M. F.

J. A. Veerman, M. F. Garcia-Parajo, L. Kuipers, N. F. Van Hulst, "Single molecule mapping of the optical field distribution of probes for near-field microscopy," J. Microsc. 194, 477-482 (1999)
[CrossRef]

Genet, C.

C. Genet, T. W. Ebbesen, "Light in tiny holes," Nature (London) 445, 39-46 (2007)
[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]

Gordon, R.

R. Gordon and A. G. Brolo, "Increased cut-off wavelength for a subwavelength hole in a real metal," Opt. Express 13, 1933-1938 (2005)
[CrossRef] [PubMed]

A. G. Brolo, E. Arctander, R. Gordon, B. Leathem, K. L. Kavanagh, "Nanohole-enhanced Raman scattering," Nano Lett. 4, 2015-2018 (2004)
[CrossRef]

Grischkowsky, D. R.

M. van Exter, D. R. Grischkowsky, "Characterization of an Optoelectronic Terahertz Beam System," IEEE Trans. Microwave Theory Tech. 38, 1684-1691 (1990)
[CrossRef]

Hecht, B.

B. Hecht, B. Sick, U. P. Wild, V. Deckert, R. Zenobi, O. J. F. Martin, D. W. Pohl, "Scanning near-field optical microscopy with aperture probes: Fundamentals and applications," J. Chem. Phys. 112, 7761-7774 (2000)
[CrossRef]

L. Novotny, D. W. Pohl, B. Hecht, "Scanning near-field optical probe with ultrasmall spot size," Opt. Lett. 20, 970-972 (1995)
[CrossRef] [PubMed]

Huant, S.

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

Hunton, J. K.

E. F. Barnett and J. K. Hunton, "A precision directional coupler using multi-hole coupling," Hewlett Packard Journal,  3 (No. 7-8) (1952).

Hygate, G.

J. F. Nye, W. Liang, and G. Hygate, "Mapping a diffraction field close to an obstacle," IEEE Trans. Electromagn. Compat. 37, 288-292 (1995).
[CrossRef]

Katnik, S. M.

Kavanagh, K. L.

A. G. Brolo, E. Arctander, R. Gordon, B. Leathem, K. L. Kavanagh, "Nanohole-enhanced Raman scattering," Nano Lett. 4, 2015-2018 (2004)
[CrossRef]

Kuipers, L.

J. A. Veerman, M. F. Garcia-Parajo, L. Kuipers, N. F. Van Hulst, "Single molecule mapping of the optical field distribution of probes for near-field microscopy," J. Microsc. 194, 477-482 (1999)
[CrossRef]

Leathem, B.

A. G. Brolo, E. Arctander, R. Gordon, B. Leathem, K. L. Kavanagh, "Nanohole-enhanced Raman scattering," Nano Lett. 4, 2015-2018 (2004)
[CrossRef]

Lezec, H. J.

A. Degiron, H. J. Lezec, N. Yamamoto, T. W. Ebbesen, "Optical transmission properties of a single subwavelength aperture in a real metal," Opt. Commun. 239, 61-66 (2004)
[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]

Liang, W.

J. F. Nye and W. Liang, "Superposition of the diffraction fields of apertures: an experimental test," Proc. R. Soc. Lond. A 453, 1963-1974 (1997).
[CrossRef]

J. F. Nye, W. Liang, and G. Hygate, "Mapping a diffraction field close to an obstacle," IEEE Trans. Electromagn. Compat. 37, 288-292 (1995).
[CrossRef]

Martin, O. J. F.

B. Hecht, B. Sick, U. P. Wild, V. Deckert, R. Zenobi, O. J. F. Martin, D. W. Pohl, "Scanning near-field optical microscopy with aperture probes: Fundamentals and applications," J. Chem. Phys. 112, 7761-7774 (2000)
[CrossRef]

Massey, G. A.

Matsui, T.

T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, "Transmission resonances through aperiodic arrays of subwavelength apertures," Nature (London) 447, 517-521 (2007)
[CrossRef]

Mitrofanov, O.

O. Mitrofanov, et al., "Terahertz pulse propagation through small apertures," Appl. Phys. Lett. 79, 907-909 (2001)
[CrossRef]

Nahata, A.

Novotny, L.

Nye, J. F.

J. F. Nye and W. Liang, "Superposition of the diffraction fields of apertures: an experimental test," Proc. R. Soc. Lond. A 453, 1963-1974 (1997).
[CrossRef]

J. F. Nye, W. Liang, and G. Hygate, "Mapping a diffraction field close to an obstacle," IEEE Trans. Electromagn. Compat. 37, 288-292 (1995).
[CrossRef]

Ornon, E.

Planken, P. C. M.

N. C. J. van der Valk, P. C. M. Planken, "Electro-optic detection of sub-wavelength terahertz spot sizes in the near-field of a metal tip," Appl. Phys. Lett. 81, 1558-1560 (2002)
[CrossRef]

G. Zhao, R. N. Schouten, N. van der Valk, W. Th. Wenckebach, and P. C. M. Planken, "Design and performance of a THz emission and detection setup based on a semi-insulating GaAs emitter," Rev. Sci. Instrum. 73, 1715-1719 (2002)
[CrossRef]

Pohl, D. W.

B. Hecht, B. Sick, U. P. Wild, V. Deckert, R. Zenobi, O. J. F. Martin, D. W. Pohl, "Scanning near-field optical microscopy with aperture probes: Fundamentals and applications," J. Chem. Phys. 112, 7761-7774 (2000)
[CrossRef]

L. Novotny, D. W. Pohl, B. Hecht, "Scanning near-field optical probe with ultrasmall spot size," Opt. Lett. 20, 970-972 (1995)
[CrossRef] [PubMed]

Qiu, D.

Schouten, R. N.

G. Zhao, R. N. Schouten, N. van der Valk, W. Th. Wenckebach, and P. C. M. Planken, "Design and performance of a THz emission and detection setup based on a semi-insulating GaAs emitter," Rev. Sci. Instrum. 73, 1715-1719 (2002)
[CrossRef]

Seo, M. A.

Sick, B.

B. Hecht, B. Sick, U. P. Wild, V. Deckert, R. Zenobi, O. J. F. Martin, D. W. Pohl, "Scanning near-field optical microscopy with aperture probes: Fundamentals and applications," J. Chem. Phys. 112, 7761-7774 (2000)
[CrossRef]

Thio, T.

T. Thio, et al., "Giant optical transmission of sub-wavelength apertures: physics and applications," Nanotechnology 13, 429-432 (2002)
[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]

Trautman, J. K.

E. Betzig and J. K. Trautman, "Single Molecules Observed by Near-Field Scanning Optical Microscopy," Science 257, 189-195 (1992)
[CrossRef] [PubMed]

van der Valk, N.

G. Zhao, R. N. Schouten, N. van der Valk, W. Th. Wenckebach, and P. C. M. Planken, "Design and performance of a THz emission and detection setup based on a semi-insulating GaAs emitter," Rev. Sci. Instrum. 73, 1715-1719 (2002)
[CrossRef]

van der Valk, N. C. J.

N. C. J. van der Valk, P. C. M. Planken, "Electro-optic detection of sub-wavelength terahertz spot sizes in the near-field of a metal tip," Appl. Phys. Lett. 81, 1558-1560 (2002)
[CrossRef]

van Exter, M.

M. van Exter, D. R. Grischkowsky, "Characterization of an Optoelectronic Terahertz Beam System," IEEE Trans. Microwave Theory Tech. 38, 1684-1691 (1990)
[CrossRef]

Van Hulst, N. F.

J. A. Veerman, M. F. Garcia-Parajo, L. Kuipers, N. F. Van Hulst, "Single molecule mapping of the optical field distribution of probes for near-field microscopy," J. Microsc. 194, 477-482 (1999)
[CrossRef]

Vardeny, Z. V.

T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, "Transmission resonances through aperiodic arrays of subwavelength apertures," Nature (London) 447, 517-521 (2007)
[CrossRef]

Veerman, J. A.

J. A. Veerman, M. F. Garcia-Parajo, L. Kuipers, N. F. Van Hulst, "Single molecule mapping of the optical field distribution of probes for near-field microscopy," J. Microsc. 194, 477-482 (1999)
[CrossRef]

Wang, R.

Wenckebach, W. Th.

G. Zhao, R. N. Schouten, N. van der Valk, W. Th. Wenckebach, and P. C. M. Planken, "Design and performance of a THz emission and detection setup based on a semi-insulating GaAs emitter," Rev. Sci. Instrum. 73, 1715-1719 (2002)
[CrossRef]

Wild, U. P.

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Supplementary Material (1)

» Media 1: MOV (3998 KB)     

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Figures (8)

Fig. 1.
Fig. 1.

Detail of the experimental setup to measure the z-component of the near-field of a hole. The electric field of a THz pulse is incident on the hole. The local electric field Ez is measured using the synchronized probe laser pulse (red). A highly reflective combination of a Germanium (Ge) and a SiO2 layer, prevents the probe from reflecting off the gold layer.

Fig. 2.
Fig. 2.

(a)–(d) Two-dimensional maps of the THz near-electric field component Ez , measured near a 150 µm diameter hole in a 200 nm thick gold film, for four different times indicated in the figures. Scale bars show the relative strength of the measured fields. Blue indicates negative electric fields, red indicates positive electric fields. The dashed circles indicate the circumference of the hole. A movie showing the field at intermediate times is shown online (3.9 Mbyte)(e) Time dependent electric field transients measured at the edges of the hole at the locations indicated in the photograph of the hole shown in (f). [Media 1]

Fig. 3.
Fig. 3.

Comparison between the measured electric field of the incident pulse (b), the calculated time-derivative of the field of the incident pulse and the measured near electric fields (a). The figure shows that as hole size decreases, the measured near-field at the edge increasingly resembles the time-differentiated incident electric field.

Fig. 4.
Fig. 4.

(a)–(f) Two-dimensional maps of the THz near-electric field component Ez , measured near a 200×200 µm2 square hole in a 200 nm thick gold film on GaP, for six different times indicated in the figures. Scale bars show the relative strength of the measured fields. Blue indicates negative electric fields, red indicates positive electric fields. The dashed squares outline the edges of the square hole. The fairly large size of the scanned area, makes it possible to see the formation of a spherical wave propagating outwards from the hole.

Fig. 5.
Fig. 5.

(a) Measured spatial distribution of the z-component |Ez | of the electric field behind a 150 µm hole in a 200 nm thick gold film deposited on a GaP electro-optic crystal, at 0.2 THz. The dashed circle indicate the circumference of the hole. (b) Spatial distribution of |Ez |, calculated using the Bouwkamp model. White indicates electric field values higher than the range of values indicated by the scale bar. (c) Spatial distribution of |Ez | at a height of 10 µm above the metal, obtained using FDTD calculations. (d) Electric field |Ez , measured along the line y=152 µm, across a 100 µm diameter hole, for different frequencies. (e) FDTD calculations of the field along a line through the center of the 100 µm hole, at z=10 µm.

Fig. 6.
Fig. 6.

Measured electric field at the edge of the hole as a function of frequency, for hole diameters of 100, 150, and 200 µm. The spectra are divided by the spectrum of the incident THz pulse. The straight lines originating from the origin are guides to the eye.

Fig. 7.
Fig. 7.

Normalized and scaled version of Fig. 4 to allow a comparison with the paper by Garcia de Abajo. [25] To within measurement signal-to-noise, the curves are identical, which is a manifestation of the scale-invariance of Maxwell’s equations at THz frequencies, where the perfect conductor approximation is a valid assumption.

Fig. 8.
Fig. 8.

Electric near-field Ez around a hole, at 5 times during a single period of a sinusoidal incident electric field (black curve) with a frequency of 0.2 THz, showing maximum near-field amplitudes during a zero-crossing of the incident electric field, and zero near-field strength during a maximum of the incident electric field. Blue and red indicate positive and negative Ez respectively. The 2D near-field distributions were obtained from a Fourier analysis of the measured electric near-field pulse. Note that the phase-shift between the incident field and the near-field is implied by our measurements even though our setup can currently not measure the absolute phase difference between the incident electric field and the electric near-field.

Equations (1)

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E z = E 0 4 i 3 ka a ρ ρ 2 a 2 1 cos ( ϕ ) , ( ρ > a )

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