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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References

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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] [PubMed]
  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] [PubMed]
  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] [PubMed]
  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]
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    [CrossRef] [PubMed]
  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).
    [PubMed]
  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] [PubMed]
  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] [PubMed]

2009

2008

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]

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] [PubMed]

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] [PubMed]

2007

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] [PubMed]

2004

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]

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

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]

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]

1990

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

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.

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] [PubMed]

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] [PubMed]

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] [PubMed]

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] [PubMed]

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.

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

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] [PubMed]

Appl. Phys. Lett.

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

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.

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)

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]

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]

Opt. Express

Opt. Lett.

Philips Research Reports

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

Rev. Sci. Instrum.

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

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

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Figures (8)

Fig. 1.
Fig. 1.

Drawing of the three different configurations used in the calculations of the electric near-field under a thin metal layer containing a hole. The terahertz pulse is incident from above and polarised along the x-axis. In the three cases, the circular hole has a diameter of 100 µm. The thickness of the gold layer is 0.5 µm. All fields were calculated in a plane 10 µm below the metal layer. Left: the metal is free standing. Middle: a layer of GaP, index n=3.4, is placed in contact with the metal layer. Right: the GaP crystal is in contact with the metal layer and also fills the hole.

Fig. 2.
Fig. 2.

Calculated electric field component a) |Ex | and b) |Ez | as a function of frequency, 10 µm below a 100 µm diameter hole made in a 0.5 µm thick metal layer. The red dotted line corresponds to the ”Free standing” case. The broken lines correspond to the configuration in which the GaP is in contact with the metal and fills the hole (see Fig. 1). The solid line is the data from a measurement performed on a 100 µm diameter hole made in a 200 nm thick gold layer which is directly deposited onto a GaP crystal. All near-field spectra are normalized with respect to the spectrum of the incident pulse.

Fig. 3.
Fig. 3.

a) Optical image of the 100 µm hole made in a 200 nm thick layer of gold deposited on the 300 µm thick GaP crystal. b) 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 from above. 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 reaching the gold layer.

Fig. 4.
Fig. 4.

Spatial distribution of the electric near-field components, |Ex |, |Ey | and |Ez |, below a 100 µm circular hole at 300 GHz in the x-y plane; top row: measurements taken beneath a 200 nm thick gold layer; lower rows: calculations using a 0.5 µm thick gold layer. The size of the figures is 200 µm by 200 µm. The distance to the metal at which these distributions are calculated is indicated on the left. The incident THz field is polarized along the x-axis. The dotted white line represents the position of the hole. For the calculations, the color scales are the same for each component separately. Different color scales were used for the measured field components.

Fig. 5.
Fig. 5.

Drawing of the different configurations used to calculate the electric field beneath a hole in a thick metal layer. The terahertz pulse is incident from above the metal and polarised along the x-axis. In the four cases, the circular hole has a diameter of 150 µm, the thickness of the gold layer, which in the calculations is assumed to be a perfect conductor, is 200 µm. All the calculated results have been taken 10 µm below the metal layer except for the ”30 µm air gap” for which the total distance to the metal was 40 µm.

Fig. 6.
Fig. 6.

a) Electric near-fields |Ex | and b) |Ez | as a function of frequency, measured beneath a 150 µm hole in a 200 µm thick aluminum foil lying on top of a GaP crystal. The curves in a) and b) are guides to the eye. Electric near-fields c) |Ex | and d) |Ez | as a function of frequency, calculated below a 150 µm diameter hole defined in a 200 µm thick metallic foil, for four different configurations shown in Fig. 5. All near-field spectra are normalized with respect to the spectrum of the incident pulse. Vertical scales of the measurements and the calculations should not be compared directly.

Fig. 7.
Fig. 7.

Electric near-field components |Ex | (left) under the center of a 100 µm diameter hole and |Ez | (right) underneath the edge of the hole, calculated as a function of frequency in a plane that is 10 µm below the metal layer. a) and b): the ”Free standing” case, for four different metal layer thicknesses: 0.5, 2, 50 and 200 µm ; c) and d): the GaP ”In contact”; e) and f): the GaP ”In contact and filled” cases. The latter two cases are plotted for four different metal layer thicknesses of 0.5, 2, 10 and 25 µm.

Fig. 8.
Fig. 8.

Spatial distribution of the electric near-field components, |Ex |, |Ey | and |Ez |, underneath a 150 µm circular hole in a 200 µm thick plate at 1 THz in the x-y plane. Top row: measurements; lower rows: calculations. The size of the figure is 400 µm by 400 µm. The distance between this plane and the metal layer is indicated on the left in each case (10 or 40 µm). The incident THz field is polarized along the x-axis. The dotted white line represents the position of the hole. For the calculations, the color scales are the same for each component separately. Different color scales were used for the measured field components.

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