Abstract

In terahertz transmission spectroscopy, there is a typical problem of thickness uncertainty, which hampers to determine precise optical parameters of samples. In order to resolve this experimental problem, a method optimizing sample thickness using singly subtractive Kramers–Kronig relations is proposed. For tens of micrometers thick water samples, we improved the accuracy of sample thickness by an order of magnitude (up to sub-micrometer) using the algorithm leading to obtain precise optical parameters of water. The broad applicability of the method is demonstrated for measuring various materials in addition to highly absorbing liquid water in the spectral range from 0.3 to 1.6 THz.

© 2017 Optical Society of America

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References

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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]
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    [Crossref]

2016 (2)

M. Bernier, F. Garet, J. L. Coutaz, H. Minamide, and A. Sato, “Accurate characterization of resonant samples in the terahertz regime through a technique combining time-domain spectroscopy and Kramers–Kronig analysis,” IEEE Trans. Terahertz Sci. Technol. 6(3), 442–450 (2016).
[Crossref]

F. Yang, L. Liu, M. Song, F. Han, L. Shen, P. Hu, and F. Zhang, “Uncertainty in terahertz time-domain spectroscopy measurement of liquids,” J. Infrared Millim. Terahertz Waves 38, 1–19 (2016).

2011 (1)

M. Krüger, S. Funkner, E. Bründermann, and M. Havenith, “Uncertainty and ambiguity in terahertz parameter extraction and data analysis,” J. Infrared Millim. Terahertz Waves 32(5), 699–715 (2011).
[Crossref]

2009 (2)

M. Scheller, C. Jansen, and M. Koch, “Analyzing sub-100-μm samples with transmission terahertz time domain spectroscopy,” Opt. Commun. 282(7), 1304–1306 (2009).
[Crossref]

B. Born, H. Weingärtner, E. Bründermann, and M. Havenith, “Solvation dynamics of model peptides probed by terahertz spectroscopy. Observation of the onset of collective network motions,” J. Am. Chem. Soc. 131(10), 3752–3755 (2009).
[Crossref] [PubMed]

2008 (2)

2007 (3)

I. Pupeza, R. Wilk, and M. Koch, “Highly accurate optical material parameter determination with THz time-domain spectroscopy,” Opt. Express 15(7), 4335–4350 (2007).
[Crossref] [PubMed]

W. J. Ellison, “Permittivity of pure water, at standard atmospheric pressure, over the frequency range 0–25 THz and the temperature range 0–100 C,” J. Phys. Chem. Ref. Data 36(1), 1–18 (2007).
[Crossref]

R. Piesiewicz, C. Jansen, S. Wietzke, D. Mittleman, M. Koch, and T. Kürner, “Properties of building and plastic materials in the THz range,” Int. J. Infrared Millieter Waves 28(5), 363–371 (2007).
[Crossref]

2006 (2)

S. Woutersen and H. J. Bakker, “Ultrafast vibrational and structural dynamics of the proton in liquid water,” Phys. Rev. Lett. 96(13), 138305 (2006).
[Crossref] [PubMed]

J. Xu, K. W. Plaxco, and S. J. Allen, “Absorption spectra of liquid water and aqueous buffers between 0.3 and 3.72 THz,” J. Chem. Phys. 124(3), 036101 (2006).
[Crossref] [PubMed]

2005 (1)

V. Lucarini, Y. Ino, K.-E. Peiponen, and M. Kuwata-Gonokami, “Detection and correction of the misplacement error in terahertz spectroscopy by application of singly subtractive Kramers–Kronig relations,” Phys. Rev. B 72(12), 125107 (2005).
[Crossref]

2004 (1)

S. P. Mickan, R. Shvartsman, J. Munch, X. C. Zhang, and D. Abbott, “Low noise laser-based T-ray spectroscopy of liquids using double-modulated differential time-domain spectroscopy,” J. Opt. B Quantum Semiclassical Opt. 6(8), S786–S795 (2004).
[Crossref]

2003 (1)

V. Lucarini, J. J. Saarinen, and K.-E. Peiponen, “Multiply subtractive Kramers–Krönig relations for arbitrary-order harmonic generation susceptibilities,” Opt. Commun. 218(4), 409–414 (2003).
[Crossref]

2001 (1)

2000 (1)

M. Walther, B. Fischer, M. Schall, H. Helm, and P. U. Jepsen, “Far-infrared vibrational spectra of all-trans, 9-cis and 13-cis retinal measured by THz time-domain spectroscopy,” Chem. Phys. Lett. 332(3), 389–395 (2000).
[Crossref]

1999 (1)

1998 (1)

D. M. Mittleman, R. H. Jacobsen, R. Neelamani, R. G. Baraniuk, and M. C. Nuss, “Gas sensing using terahertz time-domain spectroscopy,” Appl. Phys. B 67(3), 379–390 (1998).
[Crossref]

1996 (1)

J. T. Kindt and C. A. Schmuttenmaer, “Far-infrared dielectric properties of polar liquids probed by femtosecond terahertz pulse spectroscopy,” J. Phys. Chem. 100(24), 10373–10379 (1996).
[Crossref]

1990 (1)

1988 (1)

Ch. Fattinger and D. Grischkowsky, “Point source terahertz optics,” Appl. Phys. Lett. 53(16), 1480–1482 (1988).
[Crossref]

1975 (1)

D. H. Auston, “Picosecond optoelectronic switching and gating in silicon,” Appl. Phys. Lett. 26(3), 101–103 (1975).
[Crossref]

1926 (1)

Abbott, D.

Allen, S. J.

J. Xu, K. W. Plaxco, and S. J. Allen, “Absorption spectra of liquid water and aqueous buffers between 0.3 and 3.72 THz,” J. Chem. Phys. 124(3), 036101 (2006).
[Crossref] [PubMed]

Auston, D. H.

D. H. Auston, “Picosecond optoelectronic switching and gating in silicon,” Appl. Phys. Lett. 26(3), 101–103 (1975).
[Crossref]

Bakker, H. J.

S. Woutersen and H. J. Bakker, “Ultrafast vibrational and structural dynamics of the proton in liquid water,” Phys. Rev. Lett. 96(13), 138305 (2006).
[Crossref] [PubMed]

Baraniuk, R. G.

T. D. Dorney, R. G. Baraniuk, and D. M. Mittleman, “Material parameter estimation with terahertz time-domain spectroscopy,” J. Opt. Soc. Am. A 18(7), 1562–1571 (2001).
[Crossref] [PubMed]

D. M. Mittleman, R. H. Jacobsen, R. Neelamani, R. G. Baraniuk, and M. C. Nuss, “Gas sensing using terahertz time-domain spectroscopy,” Appl. Phys. B 67(3), 379–390 (1998).
[Crossref]

Bernier, M.

M. Bernier, F. Garet, J. L. Coutaz, H. Minamide, and A. Sato, “Accurate characterization of resonant samples in the terahertz regime through a technique combining time-domain spectroscopy and Kramers–Kronig analysis,” IEEE Trans. Terahertz Sci. Technol. 6(3), 442–450 (2016).
[Crossref]

Born, B.

B. Born, H. Weingärtner, E. Bründermann, and M. Havenith, “Solvation dynamics of model peptides probed by terahertz spectroscopy. Observation of the onset of collective network motions,” J. Am. Chem. Soc. 131(10), 3752–3755 (2009).
[Crossref] [PubMed]

Bründermann, E.

M. Krüger, S. Funkner, E. Bründermann, and M. Havenith, “Uncertainty and ambiguity in terahertz parameter extraction and data analysis,” J. Infrared Millim. Terahertz Waves 32(5), 699–715 (2011).
[Crossref]

B. Born, H. Weingärtner, E. Bründermann, and M. Havenith, “Solvation dynamics of model peptides probed by terahertz spectroscopy. Observation of the onset of collective network motions,” J. Am. Chem. Soc. 131(10), 3752–3755 (2009).
[Crossref] [PubMed]

Coutaz, J. L.

M. Bernier, F. Garet, J. L. Coutaz, H. Minamide, and A. Sato, “Accurate characterization of resonant samples in the terahertz regime through a technique combining time-domain spectroscopy and Kramers–Kronig analysis,” IEEE Trans. Terahertz Sci. Technol. 6(3), 442–450 (2016).
[Crossref]

Coutaz, J.-L.

Dorney, T. D.

Duvillaret, L.

Ellison, W. J.

W. J. Ellison, “Permittivity of pure water, at standard atmospheric pressure, over the frequency range 0–25 THz and the temperature range 0–100 C,” J. Phys. Chem. Ref. Data 36(1), 1–18 (2007).
[Crossref]

Fattinger, C.

Fattinger, Ch.

Ch. Fattinger and D. Grischkowsky, “Point source terahertz optics,” Appl. Phys. Lett. 53(16), 1480–1482 (1988).
[Crossref]

Fischer, B.

M. Walther, B. Fischer, M. Schall, H. Helm, and P. U. Jepsen, “Far-infrared vibrational spectra of all-trans, 9-cis and 13-cis retinal measured by THz time-domain spectroscopy,” Chem. Phys. Lett. 332(3), 389–395 (2000).
[Crossref]

Fischer, B. M.

Funkner, S.

M. Krüger, S. Funkner, E. Bründermann, and M. Havenith, “Uncertainty and ambiguity in terahertz parameter extraction and data analysis,” J. Infrared Millim. Terahertz Waves 32(5), 699–715 (2011).
[Crossref]

Garet, F.

M. Bernier, F. Garet, J. L. Coutaz, H. Minamide, and A. Sato, “Accurate characterization of resonant samples in the terahertz regime through a technique combining time-domain spectroscopy and Kramers–Kronig analysis,” IEEE Trans. Terahertz Sci. Technol. 6(3), 442–450 (2016).
[Crossref]

L. Duvillaret, F. Garet, and J.-L. Coutaz, “Highly precise determination of optical constants and sample thickness in terahertz time-domain spectroscopy,” Appl. Opt. 38(2), 409–415 (1999).
[Crossref] [PubMed]

Grischkowsky, D.

Han, F.

F. Yang, L. Liu, M. Song, F. Han, L. Shen, P. Hu, and F. Zhang, “Uncertainty in terahertz time-domain spectroscopy measurement of liquids,” J. Infrared Millim. Terahertz Waves 38, 1–19 (2016).

Havenith, M.

M. Krüger, S. Funkner, E. Bründermann, and M. Havenith, “Uncertainty and ambiguity in terahertz parameter extraction and data analysis,” J. Infrared Millim. Terahertz Waves 32(5), 699–715 (2011).
[Crossref]

B. Born, H. Weingärtner, E. Bründermann, and M. Havenith, “Solvation dynamics of model peptides probed by terahertz spectroscopy. Observation of the onset of collective network motions,” J. Am. Chem. Soc. 131(10), 3752–3755 (2009).
[Crossref] [PubMed]

Helm, H.

M. Walther, B. Fischer, M. Schall, H. Helm, and P. U. Jepsen, “Far-infrared vibrational spectra of all-trans, 9-cis and 13-cis retinal measured by THz time-domain spectroscopy,” Chem. Phys. Lett. 332(3), 389–395 (2000).
[Crossref]

Hu, P.

F. Yang, L. Liu, M. Song, F. Han, L. Shen, P. Hu, and F. Zhang, “Uncertainty in terahertz time-domain spectroscopy measurement of liquids,” J. Infrared Millim. Terahertz Waves 38, 1–19 (2016).

Ino, Y.

V. Lucarini, Y. Ino, K.-E. Peiponen, and M. Kuwata-Gonokami, “Detection and correction of the misplacement error in terahertz spectroscopy by application of singly subtractive Kramers–Kronig relations,” Phys. Rev. B 72(12), 125107 (2005).
[Crossref]

Jacobsen, R. H.

D. M. Mittleman, R. H. Jacobsen, R. Neelamani, R. G. Baraniuk, and M. C. Nuss, “Gas sensing using terahertz time-domain spectroscopy,” Appl. Phys. B 67(3), 379–390 (1998).
[Crossref]

Jansen, C.

M. Scheller, C. Jansen, and M. Koch, “Analyzing sub-100-μm samples with transmission terahertz time domain spectroscopy,” Opt. Commun. 282(7), 1304–1306 (2009).
[Crossref]

R. Piesiewicz, C. Jansen, S. Wietzke, D. Mittleman, M. Koch, and T. Kürner, “Properties of building and plastic materials in the THz range,” Int. J. Infrared Millieter Waves 28(5), 363–371 (2007).
[Crossref]

Jepsen, P. U.

M. Walther, B. Fischer, M. Schall, H. Helm, and P. U. Jepsen, “Far-infrared vibrational spectra of all-trans, 9-cis and 13-cis retinal measured by THz time-domain spectroscopy,” Chem. Phys. Lett. 332(3), 389–395 (2000).
[Crossref]

Keiding, S.

Kindt, J. T.

J. T. Kindt and C. A. Schmuttenmaer, “Far-infrared dielectric properties of polar liquids probed by femtosecond terahertz pulse spectroscopy,” J. Phys. Chem. 100(24), 10373–10379 (1996).
[Crossref]

Koch, M.

M. Scheller, C. Jansen, and M. Koch, “Analyzing sub-100-μm samples with transmission terahertz time domain spectroscopy,” Opt. Commun. 282(7), 1304–1306 (2009).
[Crossref]

R. Piesiewicz, C. Jansen, S. Wietzke, D. Mittleman, M. Koch, and T. Kürner, “Properties of building and plastic materials in the THz range,” Int. J. Infrared Millieter Waves 28(5), 363–371 (2007).
[Crossref]

I. Pupeza, R. Wilk, and M. Koch, “Highly accurate optical material parameter determination with THz time-domain spectroscopy,” Opt. Express 15(7), 4335–4350 (2007).
[Crossref] [PubMed]

Kronig, R. D. L.

Krüger, M.

M. Krüger, S. Funkner, E. Bründermann, and M. Havenith, “Uncertainty and ambiguity in terahertz parameter extraction and data analysis,” J. Infrared Millim. Terahertz Waves 32(5), 699–715 (2011).
[Crossref]

Kürner, T.

R. Piesiewicz, C. Jansen, S. Wietzke, D. Mittleman, M. Koch, and T. Kürner, “Properties of building and plastic materials in the THz range,” Int. J. Infrared Millieter Waves 28(5), 363–371 (2007).
[Crossref]

Kuwata-Gonokami, M.

V. Lucarini, Y. Ino, K.-E. Peiponen, and M. Kuwata-Gonokami, “Detection and correction of the misplacement error in terahertz spectroscopy by application of singly subtractive Kramers–Kronig relations,” Phys. Rev. B 72(12), 125107 (2005).
[Crossref]

Lin, H.

Liu, L.

F. Yang, L. Liu, M. Song, F. Han, L. Shen, P. Hu, and F. Zhang, “Uncertainty in terahertz time-domain spectroscopy measurement of liquids,” J. Infrared Millim. Terahertz Waves 38, 1–19 (2016).

Lucarini, V.

V. Lucarini, Y. Ino, K.-E. Peiponen, and M. Kuwata-Gonokami, “Detection and correction of the misplacement error in terahertz spectroscopy by application of singly subtractive Kramers–Kronig relations,” Phys. Rev. B 72(12), 125107 (2005).
[Crossref]

V. Lucarini, J. J. Saarinen, and K.-E. Peiponen, “Multiply subtractive Kramers–Krönig relations for arbitrary-order harmonic generation susceptibilities,” Opt. Commun. 218(4), 409–414 (2003).
[Crossref]

Mickan, S. P.

S. P. Mickan, R. Shvartsman, J. Munch, X. C. Zhang, and D. Abbott, “Low noise laser-based T-ray spectroscopy of liquids using double-modulated differential time-domain spectroscopy,” J. Opt. B Quantum Semiclassical Opt. 6(8), S786–S795 (2004).
[Crossref]

Minamide, H.

M. Bernier, F. Garet, J. L. Coutaz, H. Minamide, and A. Sato, “Accurate characterization of resonant samples in the terahertz regime through a technique combining time-domain spectroscopy and Kramers–Kronig analysis,” IEEE Trans. Terahertz Sci. Technol. 6(3), 442–450 (2016).
[Crossref]

Mittleman, D.

R. Piesiewicz, C. Jansen, S. Wietzke, D. Mittleman, M. Koch, and T. Kürner, “Properties of building and plastic materials in the THz range,” Int. J. Infrared Millieter Waves 28(5), 363–371 (2007).
[Crossref]

Mittleman, D. M.

T. D. Dorney, R. G. Baraniuk, and D. M. Mittleman, “Material parameter estimation with terahertz time-domain spectroscopy,” J. Opt. Soc. Am. A 18(7), 1562–1571 (2001).
[Crossref] [PubMed]

D. M. Mittleman, R. H. Jacobsen, R. Neelamani, R. G. Baraniuk, and M. C. Nuss, “Gas sensing using terahertz time-domain spectroscopy,” Appl. Phys. B 67(3), 379–390 (1998).
[Crossref]

Munch, J.

S. P. Mickan, R. Shvartsman, J. Munch, X. C. Zhang, and D. Abbott, “Low noise laser-based T-ray spectroscopy of liquids using double-modulated differential time-domain spectroscopy,” J. Opt. B Quantum Semiclassical Opt. 6(8), S786–S795 (2004).
[Crossref]

Neelamani, R.

D. M. Mittleman, R. H. Jacobsen, R. Neelamani, R. G. Baraniuk, and M. C. Nuss, “Gas sensing using terahertz time-domain spectroscopy,” Appl. Phys. B 67(3), 379–390 (1998).
[Crossref]

Nuss, M. C.

D. M. Mittleman, R. H. Jacobsen, R. Neelamani, R. G. Baraniuk, and M. C. Nuss, “Gas sensing using terahertz time-domain spectroscopy,” Appl. Phys. B 67(3), 379–390 (1998).
[Crossref]

Peiponen, K.-E.

V. Lucarini, Y. Ino, K.-E. Peiponen, and M. Kuwata-Gonokami, “Detection and correction of the misplacement error in terahertz spectroscopy by application of singly subtractive Kramers–Kronig relations,” Phys. Rev. B 72(12), 125107 (2005).
[Crossref]

V. Lucarini, J. J. Saarinen, and K.-E. Peiponen, “Multiply subtractive Kramers–Krönig relations for arbitrary-order harmonic generation susceptibilities,” Opt. Commun. 218(4), 409–414 (2003).
[Crossref]

Piesiewicz, R.

R. Piesiewicz, C. Jansen, S. Wietzke, D. Mittleman, M. Koch, and T. Kürner, “Properties of building and plastic materials in the THz range,” Int. J. Infrared Millieter Waves 28(5), 363–371 (2007).
[Crossref]

Plaxco, K. W.

J. Xu, K. W. Plaxco, and S. J. Allen, “Absorption spectra of liquid water and aqueous buffers between 0.3 and 3.72 THz,” J. Chem. Phys. 124(3), 036101 (2006).
[Crossref] [PubMed]

Pupeza, I.

Saarinen, J. J.

V. Lucarini, J. J. Saarinen, and K.-E. Peiponen, “Multiply subtractive Kramers–Krönig relations for arbitrary-order harmonic generation susceptibilities,” Opt. Commun. 218(4), 409–414 (2003).
[Crossref]

Sato, A.

M. Bernier, F. Garet, J. L. Coutaz, H. Minamide, and A. Sato, “Accurate characterization of resonant samples in the terahertz regime through a technique combining time-domain spectroscopy and Kramers–Kronig analysis,” IEEE Trans. Terahertz Sci. Technol. 6(3), 442–450 (2016).
[Crossref]

Schall, M.

M. Walther, B. Fischer, M. Schall, H. Helm, and P. U. Jepsen, “Far-infrared vibrational spectra of all-trans, 9-cis and 13-cis retinal measured by THz time-domain spectroscopy,” Chem. Phys. Lett. 332(3), 389–395 (2000).
[Crossref]

Scheller, M.

M. Scheller, C. Jansen, and M. Koch, “Analyzing sub-100-μm samples with transmission terahertz time domain spectroscopy,” Opt. Commun. 282(7), 1304–1306 (2009).
[Crossref]

Schmuttenmaer, C. A.

J. T. Kindt and C. A. Schmuttenmaer, “Far-infrared dielectric properties of polar liquids probed by femtosecond terahertz pulse spectroscopy,” J. Phys. Chem. 100(24), 10373–10379 (1996).
[Crossref]

Shen, L.

F. Yang, L. Liu, M. Song, F. Han, L. Shen, P. Hu, and F. Zhang, “Uncertainty in terahertz time-domain spectroscopy measurement of liquids,” J. Infrared Millim. Terahertz Waves 38, 1–19 (2016).

Shvartsman, R.

S. P. Mickan, R. Shvartsman, J. Munch, X. C. Zhang, and D. Abbott, “Low noise laser-based T-ray spectroscopy of liquids using double-modulated differential time-domain spectroscopy,” J. Opt. B Quantum Semiclassical Opt. 6(8), S786–S795 (2004).
[Crossref]

Song, M.

F. Yang, L. Liu, M. Song, F. Han, L. Shen, P. Hu, and F. Zhang, “Uncertainty in terahertz time-domain spectroscopy measurement of liquids,” J. Infrared Millim. Terahertz Waves 38, 1–19 (2016).

Van Exter, M.

Walther, M.

M. Walther, B. Fischer, M. Schall, H. Helm, and P. U. Jepsen, “Far-infrared vibrational spectra of all-trans, 9-cis and 13-cis retinal measured by THz time-domain spectroscopy,” Chem. Phys. Lett. 332(3), 389–395 (2000).
[Crossref]

Weingärtner, H.

B. Born, H. Weingärtner, E. Bründermann, and M. Havenith, “Solvation dynamics of model peptides probed by terahertz spectroscopy. Observation of the onset of collective network motions,” J. Am. Chem. Soc. 131(10), 3752–3755 (2009).
[Crossref] [PubMed]

Wietzke, S.

R. Piesiewicz, C. Jansen, S. Wietzke, D. Mittleman, M. Koch, and T. Kürner, “Properties of building and plastic materials in the THz range,” Int. J. Infrared Millieter Waves 28(5), 363–371 (2007).
[Crossref]

Wilk, R.

Withayachumnankul, W.

Woutersen, S.

S. Woutersen and H. J. Bakker, “Ultrafast vibrational and structural dynamics of the proton in liquid water,” Phys. Rev. Lett. 96(13), 138305 (2006).
[Crossref] [PubMed]

Xu, J.

J. Xu, K. W. Plaxco, and S. J. Allen, “Absorption spectra of liquid water and aqueous buffers between 0.3 and 3.72 THz,” J. Chem. Phys. 124(3), 036101 (2006).
[Crossref] [PubMed]

Yang, F.

F. Yang, L. Liu, M. Song, F. Han, L. Shen, P. Hu, and F. Zhang, “Uncertainty in terahertz time-domain spectroscopy measurement of liquids,” J. Infrared Millim. Terahertz Waves 38, 1–19 (2016).

Zhang, F.

F. Yang, L. Liu, M. Song, F. Han, L. Shen, P. Hu, and F. Zhang, “Uncertainty in terahertz time-domain spectroscopy measurement of liquids,” J. Infrared Millim. Terahertz Waves 38, 1–19 (2016).

Zhang, X. C.

S. P. Mickan, R. Shvartsman, J. Munch, X. C. Zhang, and D. Abbott, “Low noise laser-based T-ray spectroscopy of liquids using double-modulated differential time-domain spectroscopy,” J. Opt. B Quantum Semiclassical Opt. 6(8), S786–S795 (2004).
[Crossref]

Appl. Opt. (1)

Appl. Phys. B (1)

D. M. Mittleman, R. H. Jacobsen, R. Neelamani, R. G. Baraniuk, and M. C. Nuss, “Gas sensing using terahertz time-domain spectroscopy,” Appl. Phys. B 67(3), 379–390 (1998).
[Crossref]

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[Crossref]

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[Crossref]

Chem. Phys. Lett. (1)

M. Walther, B. Fischer, M. Schall, H. Helm, and P. U. Jepsen, “Far-infrared vibrational spectra of all-trans, 9-cis and 13-cis retinal measured by THz time-domain spectroscopy,” Chem. Phys. Lett. 332(3), 389–395 (2000).
[Crossref]

IEEE Trans. Terahertz Sci. Technol. (1)

M. Bernier, F. Garet, J. L. Coutaz, H. Minamide, and A. Sato, “Accurate characterization of resonant samples in the terahertz regime through a technique combining time-domain spectroscopy and Kramers–Kronig analysis,” IEEE Trans. Terahertz Sci. Technol. 6(3), 442–450 (2016).
[Crossref]

Int. J. Infrared Millieter Waves (1)

R. Piesiewicz, C. Jansen, S. Wietzke, D. Mittleman, M. Koch, and T. Kürner, “Properties of building and plastic materials in the THz range,” Int. J. Infrared Millieter Waves 28(5), 363–371 (2007).
[Crossref]

J. Am. Chem. Soc. (1)

B. Born, H. Weingärtner, E. Bründermann, and M. Havenith, “Solvation dynamics of model peptides probed by terahertz spectroscopy. Observation of the onset of collective network motions,” J. Am. Chem. Soc. 131(10), 3752–3755 (2009).
[Crossref] [PubMed]

J. Chem. Phys. (1)

J. Xu, K. W. Plaxco, and S. J. Allen, “Absorption spectra of liquid water and aqueous buffers between 0.3 and 3.72 THz,” J. Chem. Phys. 124(3), 036101 (2006).
[Crossref] [PubMed]

J. Infrared Millim. Terahertz Waves (2)

F. Yang, L. Liu, M. Song, F. Han, L. Shen, P. Hu, and F. Zhang, “Uncertainty in terahertz time-domain spectroscopy measurement of liquids,” J. Infrared Millim. Terahertz Waves 38, 1–19 (2016).

M. Krüger, S. Funkner, E. Bründermann, and M. Havenith, “Uncertainty and ambiguity in terahertz parameter extraction and data analysis,” J. Infrared Millim. Terahertz Waves 32(5), 699–715 (2011).
[Crossref]

J. Opt. B Quantum Semiclassical Opt. (1)

S. P. Mickan, R. Shvartsman, J. Munch, X. C. Zhang, and D. Abbott, “Low noise laser-based T-ray spectroscopy of liquids using double-modulated differential time-domain spectroscopy,” J. Opt. B Quantum Semiclassical Opt. 6(8), S786–S795 (2004).
[Crossref]

J. Opt. Soc. Am. (1)

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

J. Opt. Soc. Am. B (2)

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W. J. Ellison, “Permittivity of pure water, at standard atmospheric pressure, over the frequency range 0–25 THz and the temperature range 0–100 C,” J. Phys. Chem. Ref. Data 36(1), 1–18 (2007).
[Crossref]

Opt. Commun. (2)

M. Scheller, C. Jansen, and M. Koch, “Analyzing sub-100-μm samples with transmission terahertz time domain spectroscopy,” Opt. Commun. 282(7), 1304–1306 (2009).
[Crossref]

V. Lucarini, J. J. Saarinen, and K.-E. Peiponen, “Multiply subtractive Kramers–Krönig relations for arbitrary-order harmonic generation susceptibilities,” Opt. Commun. 218(4), 409–414 (2003).
[Crossref]

Opt. Express (2)

Phys. Rev. B (1)

V. Lucarini, Y. Ino, K.-E. Peiponen, and M. Kuwata-Gonokami, “Detection and correction of the misplacement error in terahertz spectroscopy by application of singly subtractive Kramers–Kronig relations,” Phys. Rev. B 72(12), 125107 (2005).
[Crossref]

Phys. Rev. Lett. (1)

S. Woutersen and H. J. Bakker, “Ultrafast vibrational and structural dynamics of the proton in liquid water,” Phys. Rev. Lett. 96(13), 138305 (2006).
[Crossref] [PubMed]

Other (1)

V. Lucarini, J. J. Saarinen, K.-E. Peiponen, and E. M. Vartiainen, Kramers–Kronig relations in optical materials research (Springer Science & Business Media, 2005).

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Figures (8)

Fig. 1
Fig. 1 Block diagram of the optimization procedure.
Fig. 2
Fig. 2 Schematic diagram of transmitted THz wave through the liquid sample (not to scale).
Fig. 3
Fig. 3 Material parameter extraction of liquid water with a 50 μm-thick aluminum spacer (errors are within the linewidth)
Fig. 4
Fig. 4 Sample thickness and frequency dependence of (a) refractive index and (b) absorption coefficient of liquid water with a 50 μm-thick aluminum spacer
Fig. 5
Fig. 5 Optimized thickness of (a) 25, (b) 56 and (c) 100 μm Teflon spacers.
Fig. 6
Fig. 6 Optical parameters of liquid water measured with Teflon spacers before ((a), (b)) and after ((c), (d)) thickness optimization.
Fig. 7
Fig. 7 Optimized thickness (a) and optical parameters ((b), (c)) of a z-cut quartz window.
Fig. 8
Fig. 8 Optimized thickness (a) and optical parameters ((b), (c)) of a HDPE window.

Equations (9)

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T(ω)= E sam (ω)/ E ref (ω)
E sam(ref) = E i P win (ω,L) P sam(ref) (ω,l)F C sam(ref) (ω)M R sam(ref) (ω,l), where P win (ω,L)=exp(iω n win * L/c), P sam(ref) (ω,l)=exp(iω n sam(air) * l/c), F C sam(ref) (ω)= 2 n air * n air * + n win * 2 n win * n win * + n sam(air) * 2 n sam(air) * n sam(air) * + n win * 2 n win * n win * + n air * , M R sam(ref) (ω,l)= j=0 m sam(ref) [ ( n win * n sam(air) * n win * + n sam(air) * )exp( iω n sam(air) * l/c ) ] 2j .
1+2 m sam(ref) cW n ini(air) l , where n ini = n air + cΔt l .
T exp (ω,l)=| T exp |exp(i T exp ), T theory (ω,l)= F C sam (ω,l) P sam (ω,l)M R sam (ω,l) F C ref (ω,l) P ref (ω,l)M R ref (ω,l) .
Δ(ω,l)= [δA(ω,l)] 2 + [δϕ(ω,l)] 2 , where δA(ω,l)=| T theory (ω,l) || T exp (ω,l) | δϕ(ω,l)= T theory (ω,l) T exp (ω,l).
n(ω)=n()+ 2 π P 0 ω'κ(ω') ω ' 2 ω 2 dω' , κ(ω)= 2 π ωP 0 n(ω')n() ω ' 2 ω 2 dω'
n KK (ω,l)= n exp ( ω 0 , l ini )+ 2 π ( ω 2 ω 0 2 ) ω' ω'κ(ω',l)Δω' ( ω ' 2 ω 2 )( ω ' 2 ω 0 2 ) κ KK (ω,l) ω = κ exp ( ω 0 , l ini ) ω 0 2 π ( ω 2 ω 0 2 ) ω' [ n(ω',l)n() ]Δω' ( ω ' 2 ω 2 )( ω ' 2 ω 0 2 )
e(ω)= 2 π ω( ω 2 ω 0 2 )[ ω'=0 ω min [ n(ω')n() ]Δω' ( ω ' 2 ω 2 )( ω ' 2 ω 0 2 ) + ω'= ω max [ n(ω')n() ]Δω' ( ω ' 2 ω 2 )( ω ' 2 ω 0 2 ) ]
Dif f KK (l)= ω [ κ KK (ω,l) κ exp (ω,l)] 2

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