Abstract

We show that the application of ultrafast techniques, especially terahertz time-domain spectroscopy, allows simultaneous measurements of material thickness and optical constants from transmission measurements, by analyzing not only the phase difference between the main terahertz pulse through the medium but also the subsequent multireflection pulse (an echo) from the medium. Such a method provides a fast and precise characterization of the optical properties and can extract thickness information and hence other optical constants in a broad bandwidth. It may have applications in science and engineering such as in situ film thickness and quality monitoring, optical constants measurement, medical imaging, noninvasive detection, and remote sensing.

© 2004 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  3. J. Orenstein and A. J. Millis, Science 288, 468 (2000).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]

2004 (3)

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, Science 303, 1494 (2004).
[CrossRef] [PubMed]

P. Emma, K. Bane, M. Cornacchia, Z. Huang, H. Schlarb, G. Stupakov, and D. Walz, Phys. Rev. Lett. 92, 074801 (2004).
[CrossRef]

L.-S. Ma, Z. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, Science 303, 1843 (2004).
[CrossRef] [PubMed]

2001 (3)

2000 (1)

J. Orenstein and A. J. Millis, Science 288, 468 (2000).
[CrossRef] [PubMed]

1999 (1)

1998 (1)

1997 (1)

G. J. Tearney, E. Brezinski, B. E. Bouma, S. A. Boppart, C. Pitris, J. F. Southern, and J. G. Fujimoto, Science 276, 2037 (1997).
[CrossRef] [PubMed]

1993 (1)

1991 (1)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

1990 (1)

1989 (2)

M. van Exter, Ch. Fattinger, and D. Grischkowsky, Opt. Lett. 14, 1128 (1989).
[CrossRef]

M. van Exter, Ch. Fattinger, and D. Grischkowsky, Appl. Phys. Lett. 55, 337 (1989).
[CrossRef]

1987 (1)

M. C. Nuss, D. H. Auston, and F. Cappasso, Phys. Rev. Lett. 58, 2355 (1987).
[CrossRef] [PubMed]

1984 (1)

D. H. Auston, K. P. Cheung, and P. R. Smith, Appl. Phys. Lett. 45, 284 (1984).
[CrossRef]

1973 (1)

1967 (2)

1963 (1)

J. E. Chamberlin, J. E. Gibbs, and H. A. Gebbie, Nature 198, 874 (1963).
[CrossRef]

Auston, D. H.

M. C. Nuss, D. H. Auston, and F. Cappasso, Phys. Rev. Lett. 58, 2355 (1987).
[CrossRef] [PubMed]

D. H. Auston, K. P. Cheung, and P. R. Smith, Appl. Phys. Lett. 45, 284 (1984).
[CrossRef]

Bane, K.

P. Emma, K. Bane, M. Cornacchia, Z. Huang, H. Schlarb, G. Stupakov, and D. Walz, Phys. Rev. Lett. 92, 074801 (2004).
[CrossRef]

Baraniuk, R. G.

Bartels, A.

L.-S. Ma, Z. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, Science 303, 1843 (2004).
[CrossRef] [PubMed]

Basov, D. N.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, Science 303, 1494 (2004).
[CrossRef] [PubMed]

Bell, E. E.

E. E. Russell and E. E. Bell, J. Opt. Soc. Am. 57, 341 (1967).
[CrossRef]

E. E. Bell, presented at the Symposium on Molecular Structure and Spectroscopy, Columbus, Ohio, June 14–16, 1962.

Bi, Z.

L.-S. Ma, Z. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, Science 303, 1843 (2004).
[CrossRef] [PubMed]

Boppart, S. A.

G. J. Tearney, E. Brezinski, B. E. Bouma, S. A. Boppart, C. Pitris, J. F. Southern, and J. G. Fujimoto, Science 276, 2037 (1997).
[CrossRef] [PubMed]

Bouma, B. E.

G. J. Tearney, E. Brezinski, B. E. Bouma, S. A. Boppart, C. Pitris, J. F. Southern, and J. G. Fujimoto, Science 276, 2037 (1997).
[CrossRef] [PubMed]

Brezinski, E.

G. J. Tearney, E. Brezinski, B. E. Bouma, S. A. Boppart, C. Pitris, J. F. Southern, and J. G. Fujimoto, Science 276, 2037 (1997).
[CrossRef] [PubMed]

Cappasso, F.

M. C. Nuss, D. H. Auston, and F. Cappasso, Phys. Rev. Lett. 58, 2355 (1987).
[CrossRef] [PubMed]

Chamberlin, J. E.

J. E. Chamberlin, J. E. Gibbs, and H. A. Gebbie, Nature 198, 874 (1963).
[CrossRef]

Chang, W.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Cheung, K. P.

D. H. Auston, K. P. Cheung, and P. R. Smith, Appl. Phys. Lett. 45, 284 (1984).
[CrossRef]

Christov, I. P.

H. C. Kapteyn, M. M. Murnane, and I. P. Christov, X-Ray Lasers 1998: Proceedings of the 6th International Conference on X-Ray Lasers (Institute of Physics, London, 1999), pp. 17–23.

Cornacchia, M.

P. Emma, K. Bane, M. Cornacchia, Z. Huang, H. Schlarb, G. Stupakov, and D. Walz, Phys. Rev. Lett. 92, 074801 (2004).
[CrossRef]

Coutaz, J.-L.

Diddams, S. A.

L.-S. Ma, Z. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, Science 303, 1843 (2004).
[CrossRef] [PubMed]

Dorney, T. D.

J. L. Johnson, T. D. Dorney, and D. M. Mittleman, Appl. Phys. Lett. 78, 835 (2001).
[CrossRef]

T. D. Dorney, R. G. Baraniuk, and D. M. Mittleman, J. Opt. Soc. Am. A 18, 1562 (2001).
[CrossRef]

Duvillaret, L.

Emma, P.

P. Emma, K. Bane, M. Cornacchia, Z. Huang, H. Schlarb, G. Stupakov, and D. Walz, Phys. Rev. Lett. 92, 074801 (2004).
[CrossRef]

Fang, N.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, Science 303, 1494 (2004).
[CrossRef] [PubMed]

Fattinger, Ch.

Flotte, T.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Fortin, J.

K. S. Lee, J. Y. Kim, J. Fortin, Z. P. Jiang, M. Li, T. M. Lu, and X.-C. Zhang, Ultrafast Phenomena XII (Springer, New York, 2000).

Fujimoto, J. G.

G. J. Tearney, E. Brezinski, B. E. Bouma, S. A. Boppart, C. Pitris, J. F. Southern, and J. G. Fujimoto, Science 276, 2037 (1997).
[CrossRef] [PubMed]

E. A. Swanson, J. A. Izatt, M. R. Hee, D. Huang, C. A. Puliafito, J. S. Schuman, and J. G. Fujimoto, Opt. Lett. 18, 1864 (1993).
[CrossRef] [PubMed]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Garet, F.

Gebbie, H. A.

J. E. Chamberlin, J. E. Gibbs, and H. A. Gebbie, Nature 198, 874 (1963).
[CrossRef]

Gibbs, J. E.

J. E. Chamberlin, J. E. Gibbs, and H. A. Gebbie, Nature 198, 874 (1963).
[CrossRef]

Gregory, K.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Grischkowsky, D.

M. van Exter, Ch. Fattinger, and D. Grischkowsky, Appl. Phys. Lett. 55, 337 (1989).
[CrossRef]

M. van Exter, Ch. Fattinger, and D. Grischkowsky, Opt. Lett. 14, 1128 (1989).
[CrossRef]

Grischokowsky, D.

Hee, M. R.

E. A. Swanson, J. A. Izatt, M. R. Hee, D. Huang, C. A. Puliafito, J. S. Schuman, and J. G. Fujimoto, Opt. Lett. 18, 1864 (1993).
[CrossRef] [PubMed]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Hollberg, L.

L.-S. Ma, Z. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, Science 303, 1843 (2004).
[CrossRef] [PubMed]

Huang, D.

E. A. Swanson, J. A. Izatt, M. R. Hee, D. Huang, C. A. Puliafito, J. S. Schuman, and J. G. Fujimoto, Opt. Lett. 18, 1864 (1993).
[CrossRef] [PubMed]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Huang, F.

Huang, Z.

P. Emma, K. Bane, M. Cornacchia, Z. Huang, H. Schlarb, G. Stupakov, and D. Walz, Phys. Rev. Lett. 92, 074801 (2004).
[CrossRef]

Iaconis, C.

Izatt, J. A.

Jiang, Z. P.

K. S. Lee, J. Y. Kim, J. Fortin, Z. P. Jiang, M. Li, T. M. Lu, and X.-C. Zhang, Ultrafast Phenomena XII (Springer, New York, 2000).

Johnson, J. L.

J. L. Johnson, T. D. Dorney, and D. M. Mittleman, Appl. Phys. Lett. 78, 835 (2001).
[CrossRef]

Kapteyn, H. C.

H. C. Kapteyn, M. M. Murnane, and I. P. Christov, X-Ray Lasers 1998: Proceedings of the 6th International Conference on X-Ray Lasers (Institute of Physics, London, 1999), pp. 17–23.

Keiding, S.

Kim, J. Y.

K. S. Lee, J. Y. Kim, J. Fortin, Z. P. Jiang, M. Li, T. M. Lu, and X.-C. Zhang, Ultrafast Phenomena XII (Springer, New York, 2000).

Lee, K. S.

K. S. Lee, J. Y. Kim, J. Fortin, Z. P. Jiang, M. Li, T. M. Lu, and X.-C. Zhang, Ultrafast Phenomena XII (Springer, New York, 2000).

Li, M.

K. S. Lee, J. Y. Kim, J. Fortin, Z. P. Jiang, M. Li, T. M. Lu, and X.-C. Zhang, Ultrafast Phenomena XII (Springer, New York, 2000).

Lin, C. P.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Loewenstein, E. V.

Lu, T. M.

K. S. Lee, J. Y. Kim, J. Fortin, Z. P. Jiang, M. Li, T. M. Lu, and X.-C. Zhang, Ultrafast Phenomena XII (Springer, New York, 2000).

Ma, L.-S.

L.-S. Ma, Z. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, Science 303, 1843 (2004).
[CrossRef] [PubMed]

Millis, A. J.

J. Orenstein and A. J. Millis, Science 288, 468 (2000).
[CrossRef] [PubMed]

Mittleman, D. M.

T. D. Dorney, R. G. Baraniuk, and D. M. Mittleman, J. Opt. Soc. Am. A 18, 1562 (2001).
[CrossRef]

J. L. Johnson, T. D. Dorney, and D. M. Mittleman, Appl. Phys. Lett. 78, 835 (2001).
[CrossRef]

Morgan, R. L.

Murnane, M. M.

H. C. Kapteyn, M. M. Murnane, and I. P. Christov, X-Ray Lasers 1998: Proceedings of the 6th International Conference on X-Ray Lasers (Institute of Physics, London, 1999), pp. 17–23.

Nuss, M. C.

M. C. Nuss, D. H. Auston, and F. Cappasso, Phys. Rev. Lett. 58, 2355 (1987).
[CrossRef] [PubMed]

Oates, C.

L.-S. Ma, Z. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, Science 303, 1843 (2004).
[CrossRef] [PubMed]

Orenstein, J.

J. Orenstein and A. J. Millis, Science 288, 468 (2000).
[CrossRef] [PubMed]

Padilla, W. J.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, Science 303, 1494 (2004).
[CrossRef] [PubMed]

Pendry, J. B.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, Science 303, 1494 (2004).
[CrossRef] [PubMed]

Pitris, C.

G. J. Tearney, E. Brezinski, B. E. Bouma, S. A. Boppart, C. Pitris, J. F. Southern, and J. G. Fujimoto, Science 276, 2037 (1997).
[CrossRef] [PubMed]

Puliafito, C. A.

E. A. Swanson, J. A. Izatt, M. R. Hee, D. Huang, C. A. Puliafito, J. S. Schuman, and J. G. Fujimoto, Opt. Lett. 18, 1864 (1993).
[CrossRef] [PubMed]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Randall, C. M.

Rawcliffe, R. D.

Robertsson, L.

L.-S. Ma, Z. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, Science 303, 1843 (2004).
[CrossRef] [PubMed]

Russell, E. E.

Schlarb, H.

P. Emma, K. Bane, M. Cornacchia, Z. Huang, H. Schlarb, G. Stupakov, and D. Walz, Phys. Rev. Lett. 92, 074801 (2004).
[CrossRef]

Schuman, J. S.

E. A. Swanson, J. A. Izatt, M. R. Hee, D. Huang, C. A. Puliafito, J. S. Schuman, and J. G. Fujimoto, Opt. Lett. 18, 1864 (1993).
[CrossRef] [PubMed]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Smith, D. R.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, Science 303, 1494 (2004).
[CrossRef] [PubMed]

E. V. Loewenstein, D. R. Smith, and R. L. Morgan, Appl. Opt. 12, 398 (1973).
[CrossRef] [PubMed]

Smith, P. R.

D. H. Auston, K. P. Cheung, and P. R. Smith, Appl. Phys. Lett. 45, 284 (1984).
[CrossRef]

Southern, J. F.

G. J. Tearney, E. Brezinski, B. E. Bouma, S. A. Boppart, C. Pitris, J. F. Southern, and J. G. Fujimoto, Science 276, 2037 (1997).
[CrossRef] [PubMed]

Stinson, W. G.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Stupakov, G.

P. Emma, K. Bane, M. Cornacchia, Z. Huang, H. Schlarb, G. Stupakov, and D. Walz, Phys. Rev. Lett. 92, 074801 (2004).
[CrossRef]

Swanson, E. A.

E. A. Swanson, J. A. Izatt, M. R. Hee, D. Huang, C. A. Puliafito, J. S. Schuman, and J. G. Fujimoto, Opt. Lett. 18, 1864 (1993).
[CrossRef] [PubMed]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Tearney, G. J.

G. J. Tearney, E. Brezinski, B. E. Bouma, S. A. Boppart, C. Pitris, J. F. Southern, and J. G. Fujimoto, Science 276, 2037 (1997).
[CrossRef] [PubMed]

van Exter, M.

Vier, D. C.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, Science 303, 1494 (2004).
[CrossRef] [PubMed]

Walmsley, I. A.

Walz, D.

P. Emma, K. Bane, M. Cornacchia, Z. Huang, H. Schlarb, G. Stupakov, and D. Walz, Phys. Rev. Lett. 92, 074801 (2004).
[CrossRef]

Warren, W. S.

Wilpers, G.

L.-S. Ma, Z. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, Science 303, 1843 (2004).
[CrossRef] [PubMed]

Windeler, R. S.

L.-S. Ma, Z. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, Science 303, 1843 (2004).
[CrossRef] [PubMed]

Yang, W.

Yen, T. J.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, Science 303, 1494 (2004).
[CrossRef] [PubMed]

Zhang, X.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, Science 303, 1494 (2004).
[CrossRef] [PubMed]

Zhang, X.-C.

K. S. Lee, J. Y. Kim, J. Fortin, Z. P. Jiang, M. Li, T. M. Lu, and X.-C. Zhang, Ultrafast Phenomena XII (Springer, New York, 2000).

Zucco, M.

L.-S. Ma, Z. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, Science 303, 1843 (2004).
[CrossRef] [PubMed]

Appl. Opt. (3)

Appl. Phys. Lett. (3)

D. H. Auston, K. P. Cheung, and P. R. Smith, Appl. Phys. Lett. 45, 284 (1984).
[CrossRef]

M. van Exter, Ch. Fattinger, and D. Grischkowsky, Appl. Phys. Lett. 55, 337 (1989).
[CrossRef]

J. L. Johnson, T. D. Dorney, and D. M. Mittleman, Appl. Phys. Lett. 78, 835 (2001).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

THz-TDS system and echo analysis method. The echo analysis is shown in the upper left with the THz-TDS signal shown on the right. The lower figure shows the THz-TDS system: OPM1–OPM4, optical parabolic mirrors; BS, beam splitter.

Fig. 2
Fig. 2

Sample thickness can be deducted through a difference of two phase measurements. The fluctuation of the thickness around 1.2 THz was a result of a poor signal-to-noise ratio in this frequency range. One can also estimate n and L of the silicon wafer from the peak-to-peak positions of the primary and echo pulses. The measured n and L are 3.4 and 0.71 mm, respectively, which are in agreement with the values determined in Ref. 17.

Fig. 3
Fig. 3

Echo analysis of ammonium nitrate. The echo does not appear in the 1-mm sample, but it appears in a 0.37-mm sample, a one-third reduction in thickness.

Fig. 4
Fig. 4

Larger oscillation corresponds to a delay of 2.9±0.2 ps, the delay between the air peak and the glass peak. The small oscillation in the top figure is estimated to be 15.5±0.2 ps, corresponding to a delay between the air peak and the echo. The resulting n is 1.82 with a thickness of 1.04±0.06 mm, and it agrees well with the measured n and L values of the flint glass. The precision in this determination is limited by the simple algorithm used.

Equations (6)

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Erefω=Einωexp-jnairωL/c,
Eprimaryω=t12t23Einωexp-jnsampleωL/c,
Eecho1ω=r12r23Eprimaryωexp-jnsampleω2L/c,
T1=EprimaryEref=t12t23 exp-jnsample-nairωL/c,
T2=EechoEprimary=r12r23 exp[-j(nsampleω2L/c].
L=T2-2T1/2nairc/ω.

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