Abstract

We have studied theoretically and experimentally the influence of a dielectric substrate on the frequency-dependent terahertz electric near-field of a small hole in a metal layer. We find that the near-field transmission spectrum and the two-dimensional field distribution of an empty hole in a thin metal layer on a substrate are almost identical to that of a hole which is also filled with the same dielectric material as the substrate. For thicker metal layers, however, the near-field spectra of filled and unfilled holes become very different. In addition, for thick metal layers, the two-dimensional field distributions are more strongly affected by the substrate, especially if we allow for an air gap between the metal and the substrate. Our results validate the -somewhat unusual- two-dimensional field distribution measured beneath a hole in a thick metal foil and highlight the effect that a substrate can have on the measurement of the near-field of an object.

© 2009 Optical Society of America

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  1. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature (London) 391, 667-669 (1998).
    [CrossRef]
  2. C. Genet and T. W. Ebbesen, "Light in tiny holes," Nature (London) 445, 39-46 (2007).
    [CrossRef]
  3. R. Gordon, D. Sinton, K. L. Kavanagh and A. G. Brolo, "A New Generation of Sensors Based on Extraordinary Optical Transmission," Accounts of Chemical Research 41, 1049-1057 (2008).
    [CrossRef]
  4. M. Beruete, M. Sorolla, I. Campillo, J. S. Dolado, L. Martn-Moreno, J. Bravo-Abad, and F. J. Garca-Vidal, "Enhanced millimeter-wave transmission through subwavelength hole arrays," Opt. Lett. 29, 2500-2502 (2004).
    [CrossRef]
  5. T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, "Transmission resonances through aperiodic arrays of subwavelength apertures," Nature (London) 446, 517-521 (2007).
    [CrossRef]
  6. M. A. Seo, A. J. L. Adam, J. H. Kang, J. W. Lee, S. C. Jeoung, Q. H. Park, P. C. M. Planken, and D. S. Kim, "Fourier-transform terahertz near-eld imaging of one-dimensional slit arrays: mapping of electric field, magnetic field, and Poynting vectors," Opt. Express 15, 11781-11789 (2007).
    [CrossRef]
  7. O. Mitrofanov, L. N. Pfeiffer, and K. W. West, "Generation of low-frequency components due to phase-amplitude modulation of sub-cycle far-infrared pulses in the near-field diffraction," Appl. Phys. Lett. 81, 1579-1581 (2002).
    [CrossRef]
  8. M. van Exter and D. R. Grischkowsky, "Characterization of an Optoelectronic Terahertz Beam System," IEEE Trans. Microwave Theory Tech. 38, 1684-1691 (1990).
    [CrossRef]
  9. A. J. L. Adam, J. M. Brok, M. A. Seo, K. J. Ahn, D. S. Kim, J. H. Kang, Q. H. Park, M. Nagel, and P. C. M. Planken, "Advanced terahertz electric near-field measurements at sub-wavelength diameter metallic apertures," Opt. Express 16, 7407-7417 (2008).
    [CrossRef]
  10. C. J. Bouwkamp "On Bethe’s theory of diffraction by small holes," Philips Research Reports,  5, 321-332 (1950).
  11. F. Garcia de Abajo, "Light transmission through a single cylindrical hole in a metallic film," Opt. Express 10, 1475-1484 (2002).
  12. G. Zhao, R. N. Schouten, N. C. J. van der Valk, 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]
  13. A. J. L. Adam, J. M. Brok, P. C. M. Planken, M. A. Seo, and D. S. Kim, "THz near-field measurements of metal structures," C. R. Physique 9, 161-168 (2008).
    [CrossRef]
  14. A. Bitzer and M. Walther, "Terahertz near-field imaging of metallic subwavelength holes and hole arrays," Appl. Phys. Lett. 92, (7) 231101 (2008).
    [CrossRef]
  15. A. Bitzer, H. Merbold, A. Thoman, T. Feurer, H. Helm, and M. Walther, "Terahertz near-field imaging of electric and magnetic resonances of a planar metamaterial," Opt. Express 17, 3826-3834 (2009).
    [CrossRef]
  16. Field Theory of Guided Waves, R. E. Collin, 2nd Edition, Publisher (Oxford University Press, USA, 1996).
  17. J. R. Knab, A. J. L. Adam, M. Nagel, E. Shaner,M. A. Seo, D. S. Kim, and P. C. M. Planken, "Terahertz near-field vectorial imaging of subwavelength apertures and aperture arrays," Opt. Express 17, 15072-15086 (2009).
    [CrossRef]

2009 (2)

2008 (4)

A. J. L. Adam, J. M. Brok, M. A. Seo, K. J. Ahn, D. S. Kim, J. H. Kang, Q. H. Park, M. Nagel, and P. C. M. Planken, "Advanced terahertz electric near-field measurements at sub-wavelength diameter metallic apertures," Opt. Express 16, 7407-7417 (2008).
[CrossRef]

R. Gordon, D. Sinton, K. L. Kavanagh and A. G. Brolo, "A New Generation of Sensors Based on Extraordinary Optical Transmission," Accounts of Chemical Research 41, 1049-1057 (2008).
[CrossRef]

A. J. L. Adam, J. M. Brok, P. C. M. Planken, M. A. Seo, and D. S. Kim, "THz near-field measurements of metal structures," C. R. Physique 9, 161-168 (2008).
[CrossRef]

A. Bitzer and M. Walther, "Terahertz near-field imaging of metallic subwavelength holes and hole arrays," Appl. Phys. Lett. 92, (7) 231101 (2008).
[CrossRef]

2007 (3)

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

T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, "Transmission resonances through aperiodic arrays of subwavelength apertures," Nature (London) 446, 517-521 (2007).
[CrossRef]

M. A. Seo, A. J. L. Adam, J. H. Kang, J. W. Lee, S. C. Jeoung, Q. H. Park, P. C. M. Planken, and D. S. Kim, "Fourier-transform terahertz near-eld imaging of one-dimensional slit arrays: mapping of electric field, magnetic field, and Poynting vectors," Opt. Express 15, 11781-11789 (2007).
[CrossRef]

2004 (1)

2002 (3)

G. Zhao, R. N. Schouten, N. C. J. van der Valk, 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]

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

O. Mitrofanov, L. N. Pfeiffer, and K. W. West, "Generation of low-frequency components due to phase-amplitude modulation of sub-cycle far-infrared pulses in the near-field diffraction," Appl. Phys. Lett. 81, 1579-1581 (2002).
[CrossRef]

1998 (1)

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

1990 (1)

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

1950 (1)

C. J. Bouwkamp "On Bethe’s theory of diffraction by small holes," Philips Research Reports,  5, 321-332 (1950).

Adam, A. J. L.

Agrawal, A.

T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, "Transmission resonances through aperiodic arrays of subwavelength apertures," Nature (London) 446, 517-521 (2007).
[CrossRef]

Ahn, K. J.

Beruete, M.

Bitzer, A.

A. Bitzer, H. Merbold, A. Thoman, T. Feurer, H. Helm, and M. Walther, "Terahertz near-field imaging of electric and magnetic resonances of a planar metamaterial," Opt. Express 17, 3826-3834 (2009).
[CrossRef]

A. Bitzer and M. Walther, "Terahertz near-field imaging of metallic subwavelength holes and hole arrays," Appl. Phys. Lett. 92, (7) 231101 (2008).
[CrossRef]

Bouwkamp, C. J.

C. J. Bouwkamp "On Bethe’s theory of diffraction by small holes," Philips Research Reports,  5, 321-332 (1950).

Bravo-Abad, J.

Brok, J. M.

Brolo, A. G.

R. Gordon, D. Sinton, K. L. Kavanagh and A. G. Brolo, "A New Generation of Sensors Based on Extraordinary Optical Transmission," Accounts of Chemical Research 41, 1049-1057 (2008).
[CrossRef]

Campillo, I.

Dolado, J. S.

Ebbesen, T. W.

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

Feurer, T.

Garca-Vidal, F. J.

Garcia de Abajo, F.

Genet, C.

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

Ghaemi, H. F.

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

Gordon, R.

R. Gordon, D. Sinton, K. L. Kavanagh and A. G. Brolo, "A New Generation of Sensors Based on Extraordinary Optical Transmission," Accounts of Chemical Research 41, 1049-1057 (2008).
[CrossRef]

Grischkowsky, D. R.

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

Helm, H.

Jeoung, S. C.

Kang, J. H.

Kavanagh, K. L.

R. Gordon, D. Sinton, K. L. Kavanagh and A. G. Brolo, "A New Generation of Sensors Based on Extraordinary Optical Transmission," Accounts of Chemical Research 41, 1049-1057 (2008).
[CrossRef]

Kim, D. S.

Knab, J. R.

Lee, J. W.

Lezec, H. J.

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

Martn-Moreno, L.

Matsui, T.

T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, "Transmission resonances through aperiodic arrays of subwavelength apertures," Nature (London) 446, 517-521 (2007).
[CrossRef]

Merbold, H.

Mitrofanov, O.

O. Mitrofanov, L. N. Pfeiffer, and K. W. West, "Generation of low-frequency components due to phase-amplitude modulation of sub-cycle far-infrared pulses in the near-field diffraction," Appl. Phys. Lett. 81, 1579-1581 (2002).
[CrossRef]

Nagel, M.

Nahata, A.

T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, "Transmission resonances through aperiodic arrays of subwavelength apertures," Nature (London) 446, 517-521 (2007).
[CrossRef]

Park, Q. H.

Pfeiffer, L. N.

O. Mitrofanov, L. N. Pfeiffer, and K. W. West, "Generation of low-frequency components due to phase-amplitude modulation of sub-cycle far-infrared pulses in the near-field diffraction," Appl. Phys. Lett. 81, 1579-1581 (2002).
[CrossRef]

Planken, P. C. M.

Schouten, R. N.

G. Zhao, R. N. Schouten, N. C. J. van der Valk, 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.

Shaner, E.

Sinton, D.

R. Gordon, D. Sinton, K. L. Kavanagh and A. G. Brolo, "A New Generation of Sensors Based on Extraordinary Optical Transmission," Accounts of Chemical Research 41, 1049-1057 (2008).
[CrossRef]

Sorolla, M.

Thio, T.

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

Thoman, A.

van der Valk, N. C. J.

G. Zhao, R. N. Schouten, N. C. J. van der Valk, 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 Exter, M.

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

Vardeny, Z. V.

T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, "Transmission resonances through aperiodic arrays of subwavelength apertures," Nature (London) 446, 517-521 (2007).
[CrossRef]

Walther, M.

A. Bitzer, H. Merbold, A. Thoman, T. Feurer, H. Helm, and M. Walther, "Terahertz near-field imaging of electric and magnetic resonances of a planar metamaterial," Opt. Express 17, 3826-3834 (2009).
[CrossRef]

A. Bitzer and M. Walther, "Terahertz near-field imaging of metallic subwavelength holes and hole arrays," Appl. Phys. Lett. 92, (7) 231101 (2008).
[CrossRef]

West, K. W.

O. Mitrofanov, L. N. Pfeiffer, and K. W. West, "Generation of low-frequency components due to phase-amplitude modulation of sub-cycle far-infrared pulses in the near-field diffraction," Appl. Phys. Lett. 81, 1579-1581 (2002).
[CrossRef]

Wolff, P. A.

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

Zhao, G.

G. Zhao, R. N. Schouten, N. C. J. van der Valk, 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]

Accounts of Chemical Research (1)

R. Gordon, D. Sinton, K. L. Kavanagh and A. G. Brolo, "A New Generation of Sensors Based on Extraordinary Optical Transmission," Accounts of Chemical Research 41, 1049-1057 (2008).
[CrossRef]

Appl. Phys. Lett. (2)

O. Mitrofanov, L. N. Pfeiffer, and K. W. West, "Generation of low-frequency components due to phase-amplitude modulation of sub-cycle far-infrared pulses in the near-field diffraction," Appl. Phys. Lett. 81, 1579-1581 (2002).
[CrossRef]

A. Bitzer and M. Walther, "Terahertz near-field imaging of metallic subwavelength holes and hole arrays," Appl. Phys. Lett. 92, (7) 231101 (2008).
[CrossRef]

C. R. Physique (1)

A. J. L. Adam, J. M. Brok, P. C. M. Planken, M. A. Seo, and D. S. Kim, "THz near-field measurements of metal structures," C. R. Physique 9, 161-168 (2008).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

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

Nature (London) (3)

T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, "Transmission resonances through aperiodic arrays of subwavelength apertures," Nature (London) 446, 517-521 (2007).
[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]

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

Opt. Express (5)

Opt. Lett. (1)

Philips Research Reports (1)

C. J. Bouwkamp "On Bethe’s theory of diffraction by small holes," Philips Research Reports,  5, 321-332 (1950).

Rev. Sci. Instrum. (1)

G. Zhao, R. N. Schouten, N. C. J. van der Valk, 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]

Other (1)

Field Theory of Guided Waves, R. E. Collin, 2nd Edition, Publisher (Oxford University Press, USA, 1996).

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