Abstract

We present an analytical model that shows that reflection from a rough surface causes a Gaussian frequency roll-off for the spectral magnitude of a terahertz wave and reduces the signal-to-noise ratio of terahertz time-domain spectroscopy. The parameter that determines the width of the frequency roll-off is the standard deviation of the surface height distribution. Measurements of terahertz waves reflected from copper powder samples provide experimental evidence for this effect.

© 2006 Optical Society of America

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References

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  1. M. Hangyo, T. Nagashima, and S. Nashima, Meas. Sci. Technol. 13, 1727 (2002).
    [CrossRef]
  2. M. Khazan, R. Meissner, and I. Wilke, Rev. Sci. Instrum. 72, 3427 (2001).
    [CrossRef]
  3. P. U. Jepsen and B. M. Fischer, Opt. Lett. 30, 29 (2005).
    [CrossRef] [PubMed]
  4. Y. C. Shen, T. Lo, P. F. Taday, B. E. Cole, W. R. Tribe, and M. C. Kemp, Appl. Phys. Lett. 86, 241116 (2005).
    [CrossRef]
  5. H. B. Liu, Y. Q. Chen, G. J. Bastiaans, and X. C. Zhang, Opt. Express 14, 415 (2006).
    [CrossRef] [PubMed]
  6. L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 1998).
  7. J. A. Ogilvy, Theory of Wave Scattering from Random Rough Surfaces (IOP, 1991).
  8. D. Grischkowsky, S. Keiding, M. van Exter, and C. Fattinger, J. Opt. Soc. Am. B 7, 2006 (1990).
    [CrossRef]
  9. Q. Wu, M. Litz, and X. C. Zhang, Appl. Phys. Lett. 68, 2924 (1996).
    [CrossRef]
  10. P. C. D. Hobbs, Building Electro-Optical Systems (Wiley, 2000).
    [CrossRef]

2006 (1)

2005 (2)

P. U. Jepsen and B. M. Fischer, Opt. Lett. 30, 29 (2005).
[CrossRef] [PubMed]

Y. C. Shen, T. Lo, P. F. Taday, B. E. Cole, W. R. Tribe, and M. C. Kemp, Appl. Phys. Lett. 86, 241116 (2005).
[CrossRef]

2002 (1)

M. Hangyo, T. Nagashima, and S. Nashima, Meas. Sci. Technol. 13, 1727 (2002).
[CrossRef]

2001 (1)

M. Khazan, R. Meissner, and I. Wilke, Rev. Sci. Instrum. 72, 3427 (2001).
[CrossRef]

1996 (1)

Q. Wu, M. Litz, and X. C. Zhang, Appl. Phys. Lett. 68, 2924 (1996).
[CrossRef]

1990 (1)

Andrews, L. C.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 1998).

Bastiaans, G. J.

Chen, Y. Q.

Cole, B. E.

Y. C. Shen, T. Lo, P. F. Taday, B. E. Cole, W. R. Tribe, and M. C. Kemp, Appl. Phys. Lett. 86, 241116 (2005).
[CrossRef]

Fattinger, C.

Fischer, B. M.

Grischkowsky, D.

Hangyo, M.

M. Hangyo, T. Nagashima, and S. Nashima, Meas. Sci. Technol. 13, 1727 (2002).
[CrossRef]

Hobbs, P. C. D.

P. C. D. Hobbs, Building Electro-Optical Systems (Wiley, 2000).
[CrossRef]

Jepsen, P. U.

Keiding, S.

Kemp, M. C.

Y. C. Shen, T. Lo, P. F. Taday, B. E. Cole, W. R. Tribe, and M. C. Kemp, Appl. Phys. Lett. 86, 241116 (2005).
[CrossRef]

Khazan, M.

M. Khazan, R. Meissner, and I. Wilke, Rev. Sci. Instrum. 72, 3427 (2001).
[CrossRef]

Litz, M.

Q. Wu, M. Litz, and X. C. Zhang, Appl. Phys. Lett. 68, 2924 (1996).
[CrossRef]

Liu, H. B.

Lo, T.

Y. C. Shen, T. Lo, P. F. Taday, B. E. Cole, W. R. Tribe, and M. C. Kemp, Appl. Phys. Lett. 86, 241116 (2005).
[CrossRef]

Meissner, R.

M. Khazan, R. Meissner, and I. Wilke, Rev. Sci. Instrum. 72, 3427 (2001).
[CrossRef]

Nagashima, T.

M. Hangyo, T. Nagashima, and S. Nashima, Meas. Sci. Technol. 13, 1727 (2002).
[CrossRef]

Nashima, S.

M. Hangyo, T. Nagashima, and S. Nashima, Meas. Sci. Technol. 13, 1727 (2002).
[CrossRef]

Ogilvy, J. A.

J. A. Ogilvy, Theory of Wave Scattering from Random Rough Surfaces (IOP, 1991).

Phillips, R. L.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 1998).

Shen, Y. C.

Y. C. Shen, T. Lo, P. F. Taday, B. E. Cole, W. R. Tribe, and M. C. Kemp, Appl. Phys. Lett. 86, 241116 (2005).
[CrossRef]

Taday, P. F.

Y. C. Shen, T. Lo, P. F. Taday, B. E. Cole, W. R. Tribe, and M. C. Kemp, Appl. Phys. Lett. 86, 241116 (2005).
[CrossRef]

Tribe, W. R.

Y. C. Shen, T. Lo, P. F. Taday, B. E. Cole, W. R. Tribe, and M. C. Kemp, Appl. Phys. Lett. 86, 241116 (2005).
[CrossRef]

van Exter, M.

Wilke, I.

M. Khazan, R. Meissner, and I. Wilke, Rev. Sci. Instrum. 72, 3427 (2001).
[CrossRef]

Wu, Q.

Q. Wu, M. Litz, and X. C. Zhang, Appl. Phys. Lett. 68, 2924 (1996).
[CrossRef]

Zhang, X. C.

Appl. Phys. Lett. (2)

Y. C. Shen, T. Lo, P. F. Taday, B. E. Cole, W. R. Tribe, and M. C. Kemp, Appl. Phys. Lett. 86, 241116 (2005).
[CrossRef]

Q. Wu, M. Litz, and X. C. Zhang, Appl. Phys. Lett. 68, 2924 (1996).
[CrossRef]

J. Opt. Soc. Am. B (1)

Meas. Sci. Technol. (1)

M. Hangyo, T. Nagashima, and S. Nashima, Meas. Sci. Technol. 13, 1727 (2002).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Rev. Sci. Instrum. (1)

M. Khazan, R. Meissner, and I. Wilke, Rev. Sci. Instrum. 72, 3427 (2001).
[CrossRef]

Other (3)

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 1998).

J. A. Ogilvy, Theory of Wave Scattering from Random Rough Surfaces (IOP, 1991).

P. C. D. Hobbs, Building Electro-Optical Systems (Wiley, 2000).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Schematic diagram of the experimental setup for terahertz reflection measurements.

Fig. 2
Fig. 2

(a) Time-domain waveforms for reflection from the reference surface and an untamped copper powder sample. (b) Discrete Fourier transforms of the reference and both tamped and untamped copper powder waveforms.

Fig. 3
Fig. 3

Magnitude ratios of the copper powder spectra to the reference spectrum: (a) before the samples were tamped, (b) after the samples were tamped.

Equations (4)

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a ( t ) = 1 N i = 1 N a 0 ( t τ i ) ,
A ( ω ) = 1 N i = 1 N A 0 ( ω ) exp ( j ω τ i ) = A 0 ( ω ) exp ( j ω τ ) ,
exp ( ψ ) = exp [ ψ + 1 2 ( ψ 2 ψ 2 ) ] .
A ( ω ) = A 0 ( ω ) exp ( j ω τ ) exp ( ω 2 σ τ 2 2 ) ,

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