Abstract

We examine the potential of ultra-thin metallic layers for broadband wave-impedance matching in the terahertz frequency range. The metallic layer is modeled using Fresnel formulae for stratified optical medium. Experimental data for chromium and indium-tin-oxide layers, measured using time-domain terahertz spectroscopy over the frequency range 0.4 – 4.5 THz, are compared with theoretical results.

© 2007 Optical Society of America

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References

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  1. D. M. Mittleman, Sensing with Terahertz radiation (Cambridge Press, Cambridge, 2003) and references therein.
  2. M. Born and E. Wolf, Principles of Optics, 7th edition (Cambridge Press, Cambridge, 1999), Section 1.6.4, pp. 64.
  3. M. Born and E. Wolf, Principles of Optics, 7th edition (Cambridge Press, Cambridge, 1999), Section 14.4 pp.752.
  4. B. Carli, "Reflectivity of metallic films in the infrared," J. Opt. Soc. Am. 67, 908-909 (1977).
    [CrossRef]
  5. B. P. Gorshunov, G. V. Kozlov, A. A. Volkov, S. P. Lebedev, I. V. Fedorov, A. R. Prokhorov, I. V. Makhov, J. Schuetzmann, and K. F. Renk, "Measurement of electrodynamic parameters of superconducting films in the far-infrared and submillimeter frequency ranges," Int. J. Infrared Millimeter Waves 14,683-702 (1993).
    [CrossRef]
  6. M. Dressel and G. Gruener, Electrodynamics of Solid (Cambridge Press, Cambridge, 2002), Chap. 5, pp. 92-135.
    [CrossRef]
  7. E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, New York, 1985).
  8. M. A. Ordal, J. J. Long, R. J. Bell, S. R. Bell, R. R. Bell, R. W. Alexander, and C. A. Ward, "Optical properties of the metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in the infrared and far infrared," Appl. Opt. 22,1099-1119 (1983).
    [CrossRef] [PubMed]
  9. M. A. Ordal, R. J. Bell, R. W. Alexander, Jr., L. L. Long, and M. R. Querry, "Optical properties of fourteen metals in the infrared and far infrared: Al, Co, Cu, Au, Pb, Mo, Ni, Pd, Pt, Ag, Ti, V, and W," Appl. Opt. 24,4493-4499 (1985).
    [CrossRef] [PubMed]
  10. T. Bauer, J. S. Kolb, T. Löffler, E. Mohler, H. G. Roskos, and U. C. Pernisz, "Indium-tin-oxide-coated glass as dichroic mirror for far-infrared electromagnetic radiation," J. Appl. Phys. 92,2210-2212 (2002).
    [CrossRef]
  11. Q. Wu, M. Litz, and X.-C. Zhang, "Broadband detection capability of ZnTe electro-optic field detectors," Appl. Phys. Lett. 68,2924-2926 (1996).
    [CrossRef]
  12. Q. Wu and X.-C. Zhang, "7 THz broadband GaP electro-optic sensor," Appl. Phys. Lett. 70,1784-1786 (1997).
    [CrossRef]
  13. J. Kröll, J. Darmo, and K. Unterrainer, "High-performance terahertz electro-optic detector," Electron. Lett. 40,763-764 (2004).
    [CrossRef]
  14. P. R. Griffiths and J. A. DeHaseth, Fourier transform infrared spectroscopy (Wiley, New York, 1986).

2004 (1)

J. Kröll, J. Darmo, and K. Unterrainer, "High-performance terahertz electro-optic detector," Electron. Lett. 40,763-764 (2004).
[CrossRef]

2002 (1)

T. Bauer, J. S. Kolb, T. Löffler, E. Mohler, H. G. Roskos, and U. C. Pernisz, "Indium-tin-oxide-coated glass as dichroic mirror for far-infrared electromagnetic radiation," J. Appl. Phys. 92,2210-2212 (2002).
[CrossRef]

1997 (1)

Q. Wu and X.-C. Zhang, "7 THz broadband GaP electro-optic sensor," Appl. Phys. Lett. 70,1784-1786 (1997).
[CrossRef]

1996 (1)

Q. Wu, M. Litz, and X.-C. Zhang, "Broadband detection capability of ZnTe electro-optic field detectors," Appl. Phys. Lett. 68,2924-2926 (1996).
[CrossRef]

1993 (1)

B. P. Gorshunov, G. V. Kozlov, A. A. Volkov, S. P. Lebedev, I. V. Fedorov, A. R. Prokhorov, I. V. Makhov, J. Schuetzmann, and K. F. Renk, "Measurement of electrodynamic parameters of superconducting films in the far-infrared and submillimeter frequency ranges," Int. J. Infrared Millimeter Waves 14,683-702 (1993).
[CrossRef]

1985 (1)

1983 (1)

1977 (1)

Alexander, R. W.

Bauer, T.

T. Bauer, J. S. Kolb, T. Löffler, E. Mohler, H. G. Roskos, and U. C. Pernisz, "Indium-tin-oxide-coated glass as dichroic mirror for far-infrared electromagnetic radiation," J. Appl. Phys. 92,2210-2212 (2002).
[CrossRef]

Bell, R. J.

Bell, R. R.

Bell, S. R.

Carli, B.

Darmo, J.

J. Kröll, J. Darmo, and K. Unterrainer, "High-performance terahertz electro-optic detector," Electron. Lett. 40,763-764 (2004).
[CrossRef]

Fedorov, I. V.

B. P. Gorshunov, G. V. Kozlov, A. A. Volkov, S. P. Lebedev, I. V. Fedorov, A. R. Prokhorov, I. V. Makhov, J. Schuetzmann, and K. F. Renk, "Measurement of electrodynamic parameters of superconducting films in the far-infrared and submillimeter frequency ranges," Int. J. Infrared Millimeter Waves 14,683-702 (1993).
[CrossRef]

Gorshunov, B. P.

B. P. Gorshunov, G. V. Kozlov, A. A. Volkov, S. P. Lebedev, I. V. Fedorov, A. R. Prokhorov, I. V. Makhov, J. Schuetzmann, and K. F. Renk, "Measurement of electrodynamic parameters of superconducting films in the far-infrared and submillimeter frequency ranges," Int. J. Infrared Millimeter Waves 14,683-702 (1993).
[CrossRef]

Kolb, J. S.

T. Bauer, J. S. Kolb, T. Löffler, E. Mohler, H. G. Roskos, and U. C. Pernisz, "Indium-tin-oxide-coated glass as dichroic mirror for far-infrared electromagnetic radiation," J. Appl. Phys. 92,2210-2212 (2002).
[CrossRef]

Kozlov, G. V.

B. P. Gorshunov, G. V. Kozlov, A. A. Volkov, S. P. Lebedev, I. V. Fedorov, A. R. Prokhorov, I. V. Makhov, J. Schuetzmann, and K. F. Renk, "Measurement of electrodynamic parameters of superconducting films in the far-infrared and submillimeter frequency ranges," Int. J. Infrared Millimeter Waves 14,683-702 (1993).
[CrossRef]

Kröll, J.

J. Kröll, J. Darmo, and K. Unterrainer, "High-performance terahertz electro-optic detector," Electron. Lett. 40,763-764 (2004).
[CrossRef]

Lebedev, S. P.

B. P. Gorshunov, G. V. Kozlov, A. A. Volkov, S. P. Lebedev, I. V. Fedorov, A. R. Prokhorov, I. V. Makhov, J. Schuetzmann, and K. F. Renk, "Measurement of electrodynamic parameters of superconducting films in the far-infrared and submillimeter frequency ranges," Int. J. Infrared Millimeter Waves 14,683-702 (1993).
[CrossRef]

Litz, M.

Q. Wu, M. Litz, and X.-C. Zhang, "Broadband detection capability of ZnTe electro-optic field detectors," Appl. Phys. Lett. 68,2924-2926 (1996).
[CrossRef]

Löffler, T.

T. Bauer, J. S. Kolb, T. Löffler, E. Mohler, H. G. Roskos, and U. C. Pernisz, "Indium-tin-oxide-coated glass as dichroic mirror for far-infrared electromagnetic radiation," J. Appl. Phys. 92,2210-2212 (2002).
[CrossRef]

Long, J. J.

Long, L. L.

Makhov, I. V.

B. P. Gorshunov, G. V. Kozlov, A. A. Volkov, S. P. Lebedev, I. V. Fedorov, A. R. Prokhorov, I. V. Makhov, J. Schuetzmann, and K. F. Renk, "Measurement of electrodynamic parameters of superconducting films in the far-infrared and submillimeter frequency ranges," Int. J. Infrared Millimeter Waves 14,683-702 (1993).
[CrossRef]

Mohler, E.

T. Bauer, J. S. Kolb, T. Löffler, E. Mohler, H. G. Roskos, and U. C. Pernisz, "Indium-tin-oxide-coated glass as dichroic mirror for far-infrared electromagnetic radiation," J. Appl. Phys. 92,2210-2212 (2002).
[CrossRef]

Ordal, M. A.

Pernisz, U. C.

T. Bauer, J. S. Kolb, T. Löffler, E. Mohler, H. G. Roskos, and U. C. Pernisz, "Indium-tin-oxide-coated glass as dichroic mirror for far-infrared electromagnetic radiation," J. Appl. Phys. 92,2210-2212 (2002).
[CrossRef]

Prokhorov, A. R.

B. P. Gorshunov, G. V. Kozlov, A. A. Volkov, S. P. Lebedev, I. V. Fedorov, A. R. Prokhorov, I. V. Makhov, J. Schuetzmann, and K. F. Renk, "Measurement of electrodynamic parameters of superconducting films in the far-infrared and submillimeter frequency ranges," Int. J. Infrared Millimeter Waves 14,683-702 (1993).
[CrossRef]

Querry, M. R.

Renk, K. F.

B. P. Gorshunov, G. V. Kozlov, A. A. Volkov, S. P. Lebedev, I. V. Fedorov, A. R. Prokhorov, I. V. Makhov, J. Schuetzmann, and K. F. Renk, "Measurement of electrodynamic parameters of superconducting films in the far-infrared and submillimeter frequency ranges," Int. J. Infrared Millimeter Waves 14,683-702 (1993).
[CrossRef]

Roskos, H. G.

T. Bauer, J. S. Kolb, T. Löffler, E. Mohler, H. G. Roskos, and U. C. Pernisz, "Indium-tin-oxide-coated glass as dichroic mirror for far-infrared electromagnetic radiation," J. Appl. Phys. 92,2210-2212 (2002).
[CrossRef]

Schuetzmann, J.

B. P. Gorshunov, G. V. Kozlov, A. A. Volkov, S. P. Lebedev, I. V. Fedorov, A. R. Prokhorov, I. V. Makhov, J. Schuetzmann, and K. F. Renk, "Measurement of electrodynamic parameters of superconducting films in the far-infrared and submillimeter frequency ranges," Int. J. Infrared Millimeter Waves 14,683-702 (1993).
[CrossRef]

Unterrainer, K.

J. Kröll, J. Darmo, and K. Unterrainer, "High-performance terahertz electro-optic detector," Electron. Lett. 40,763-764 (2004).
[CrossRef]

Volkov, A. A.

B. P. Gorshunov, G. V. Kozlov, A. A. Volkov, S. P. Lebedev, I. V. Fedorov, A. R. Prokhorov, I. V. Makhov, J. Schuetzmann, and K. F. Renk, "Measurement of electrodynamic parameters of superconducting films in the far-infrared and submillimeter frequency ranges," Int. J. Infrared Millimeter Waves 14,683-702 (1993).
[CrossRef]

Ward, C. A.

Wu, Q.

Q. Wu and X.-C. Zhang, "7 THz broadband GaP electro-optic sensor," Appl. Phys. Lett. 70,1784-1786 (1997).
[CrossRef]

Q. Wu, M. Litz, and X.-C. Zhang, "Broadband detection capability of ZnTe electro-optic field detectors," Appl. Phys. Lett. 68,2924-2926 (1996).
[CrossRef]

Zhang, X.-C.

Q. Wu and X.-C. Zhang, "7 THz broadband GaP electro-optic sensor," Appl. Phys. Lett. 70,1784-1786 (1997).
[CrossRef]

Q. Wu, M. Litz, and X.-C. Zhang, "Broadband detection capability of ZnTe electro-optic field detectors," Appl. Phys. Lett. 68,2924-2926 (1996).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (2)

Q. Wu, M. Litz, and X.-C. Zhang, "Broadband detection capability of ZnTe electro-optic field detectors," Appl. Phys. Lett. 68,2924-2926 (1996).
[CrossRef]

Q. Wu and X.-C. Zhang, "7 THz broadband GaP electro-optic sensor," Appl. Phys. Lett. 70,1784-1786 (1997).
[CrossRef]

Electron. Lett. (1)

J. Kröll, J. Darmo, and K. Unterrainer, "High-performance terahertz electro-optic detector," Electron. Lett. 40,763-764 (2004).
[CrossRef]

Int. J. Infrared Millimeter Waves (1)

B. P. Gorshunov, G. V. Kozlov, A. A. Volkov, S. P. Lebedev, I. V. Fedorov, A. R. Prokhorov, I. V. Makhov, J. Schuetzmann, and K. F. Renk, "Measurement of electrodynamic parameters of superconducting films in the far-infrared and submillimeter frequency ranges," Int. J. Infrared Millimeter Waves 14,683-702 (1993).
[CrossRef]

J. Appl. Phys. (1)

T. Bauer, J. S. Kolb, T. Löffler, E. Mohler, H. G. Roskos, and U. C. Pernisz, "Indium-tin-oxide-coated glass as dichroic mirror for far-infrared electromagnetic radiation," J. Appl. Phys. 92,2210-2212 (2002).
[CrossRef]

J. Opt. Soc. Am. (1)

Other (6)

M. Dressel and G. Gruener, Electrodynamics of Solid (Cambridge Press, Cambridge, 2002), Chap. 5, pp. 92-135.
[CrossRef]

E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, New York, 1985).

D. M. Mittleman, Sensing with Terahertz radiation (Cambridge Press, Cambridge, 2003) and references therein.

M. Born and E. Wolf, Principles of Optics, 7th edition (Cambridge Press, Cambridge, 1999), Section 1.6.4, pp. 64.

M. Born and E. Wolf, Principles of Optics, 7th edition (Cambridge Press, Cambridge, 1999), Section 14.4 pp.752.

P. R. Griffiths and J. A. DeHaseth, Fourier transform infrared spectroscopy (Wiley, New York, 1986).

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Figures (7)

Fig. 1.
Fig. 1.

Schematic of an optical system consisting of an optically thick material 1/thin metal layer (M)/optical material 2.

Fig. 2.
Fig. 2.

Dependence of (a) the reflection and (b) absorption losses of 1.5 THz radiation on the metallic layer sheet conductance for the optical system depicted in Fig. 1 for different refractive index ratios n1 /n2 . (c) Absorption losses at 1.5 THz in the metallic wave-impedance matching layer as a function of the refractive index mismatch (given in ratio n1 /n2 ). The losses are independent from the metal conductivity (σ0 - reference metal conductivity).

Fig. 3.
Fig. 3.

Amplitude of the reflection coefficient at the interface GaAs (n1=3.415) and air as a function of frequency with (a) dielectric λ0/4 antireflection layer and (b) metallic antireflection layer (metal conductivity σ0 of 7.87×106 S/cm, thickness 16.3 nm). Antireflection layers were optimized for the frequency of 1.5 THz. In that case the total reflection coefficient is less than 0.1% in the frequency range 0.1 – 4.5 THz, while the reflection coefficient stays below 1% in the frequency range as narrow as 30 GHz for the dielectric antireflection layer. This bandwidth can be increased for the hypothetical dielectric material for which n scales as λ 0 1/2 (blue line).

Fig. 4.
Fig. 4.

Amplitude of the main and the first reflected THz pulses transmitted through (a) 400 μm thick silicon plate with a chromium film; (b) 510 μm thick gallium-arsenide with an indium-tin-oxide film. (lines – simulation using the theory [6]).

Fig. 5.
Fig. 5.

Transmitted THz-TDS signal for (a) a 400μm thick silicon plate both uncoated (red line) and Cr-coated (black line) and (c) a highly resistive uncoated (red) GaAs wafer and its ITO-coated (black) counterpart. Spectral ratio of transmitted THz pulses through the silicon (b) and GaAs (d) with optimized antireflection coatings.

Fig. 6.
Fig. 6.

Electric field of THz transient sensed with a 300μm thick uncoated gallium phosphide electro-optic crystal and gallium phosphide crystal with ITO based MARC. In the uncoated crystal THz pulse several times bounces leading to ~7 ps delayed gradually attenuated pulses.

Fig. 7.
Fig. 7.

(a). Spectra obtained by a Fourier transform infrared spectroscopic system with GaAs beam splitter without and with metallic antireflection layer; (b) Details of the spectra from the left panel. The CO2 absorption line at 667.6 cm-1 (14.978 μm) is well resolved for when the antireflection layer is applied to the beam splitter.

Equations (6)

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

E R = E I ( r 1 M + r M 2 t M 2 1 + r 1 M r M 2 t M 2 ) ,
r 1 M + r M 2 exp [ i d 4 π λ 0 ( n + i k ) cos θ M ] = 0 .
r 1 M = r M 2 exp ( 4 π λ 0 d k )
exp ( i ϕ 1 M ) = exp ( i ( ϕ M 2 + 4 π λ 0 d n ) ) ,
r 1 M = r M 2 ( 1 4 π λ 0 d k ) ,
ϕ 1 M ϕ M 2 4 π λ 0 d n = ( 2 m + 1 ) π for m = 0,1,2 ,

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