Abstract

An extensive investigation of the origin and the impact of periodic sampling errors of terahertz time-domain spectroscopy systems is given. We present experimental findings and compare them to a theoretical model which is developed in this work. Special attention is given to the influence on the extraction of the refractive index from measurements. It can be shown that even distortions of the spectrum at frequencies higher than the used bandwidth can have a significant impact on the extracted refractive index.

© 2017 Optical Society of America

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  1. M. Walther, P. Plochocka, B. Fischer, H. Helm, and P. Uhd Jepsen, “Collective vibrational modes in biological molecules investigated by terahertz time-domain spectroscopy,” Biopolymers 67, 310–313 (2002).
    [Crossref] [PubMed]
  2. N. Vieweg, B. M. Fischer, M. Reuter, P. Kula, R. Dabrowski, M. a. Celik, G. Frenking, M. Koch, and P. U. Jepsen, “Ultrabroadband terahertz spectroscopy of a liquid crystal,” Opt. Express 20, 28249–56 (2012).
    [Crossref] [PubMed]
  3. R. H. Jacobsen, D. M. Mittleman, and M. C. Nuss, “Chemical recognition of gases and gas mixtures with terahertz waves,” Opt. Lett. 21, 2011 (1996).
    [Crossref] [PubMed]
  4. J. B. Baxter and C. A. Schmuttenmaer, “Carrier dynamics in bulk ZnO. I. Intrinsic conductivity measured by terahertz time-domain spectroscopy,” Phys. Rev. B 80, 235205 (2009).
    [Crossref]
  5. M. J. Drexler, R. Woscholski, S. Lippert, W. Stolz, A. Rahimi-Iman, and M. Koch, “Disturbing the coherent dynamics of an excitonic polarization with strong terahertz fields,” Phys. Rev. B 90, 195304 (2014).
    [Crossref]
  6. S. Hunsche, D. M. Mittleman, M. Koch, and M. C. Nuss, “New dimensions in t-ray imaging,” IEICE Trans. Electron. 81, 269–276 (1998).
  7. P. U. Jepsen, D. G. Cooke, and M. Koch, “Terahertz spectroscopy and imaging - modern techniques and applications,” Laser Photon. Rev. 5, 124–166 (2011).
    [Crossref]
  8. 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, 409 (1999).
    [Crossref]
  9. T. D. Dorney, R. G. Baraniuk, and D. M. Mittleman, “Material parameter estimation with terahertz time-domain spectroscopy,” J. Opt. Soc. Am. A 18, 1562 (2001).
    [Crossref]
  10. 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. Semiclass. Opt. 6, S786–S795 (2004).
    [Crossref]
  11. R. Wilk, I. Pupeza, R. Cernat, and M. Koch, “Highly Accurate THz Time-Domain Spectroscopy of Multilayer Structures,” IEEE J. Sel. Top. Quantum Electron. 14, 392–398 (2008).
    [Crossref]
  12. M. Scheller, C. Jansen, and M. Koch, “Analyzing sub-100-µm samples with transmission terahertz time domain spectroscopy,” Opt. Commun. 282, 1304–1306 (2009).
    [Crossref]
  13. M. Krüger, S. Funkner, E. Bründermann, and M. Havenith, “Uncertainty and Ambiguity in Terahertz Parameter Extraction and Data Analysis,” J. Infra. Millim. THz Waves 32, 699–715 (2011).
    [Crossref]
  14. W. Withayachumnankul, B. M. Fischer, H. Lin, and D. Abbott, “Uncertainty in terahertz time-domain spectroscopy measurement,” J. Opt. Soc. Am. B 25, 1059 (2008).
    [Crossref]
  15. W. Withayachumnankul and M. Naftaly, “Fundamentals of measurement in terahertz time-domain spectroscopy,” J. Infrared, Millimeter, and Terahertz Waves 35, 610–637 (2014).
    [Crossref]
  16. D. Jahn, S. Lippert, M. Bisi, L. Oberto, J. C. Balzer, and M. Koch, “On the Influence of Delay Line Uncertainty in THz Time-Domain Spectroscopy,” J. Infra. Millim. THz Waves 37, 605–613 (2016).
    [Crossref]
  17. A. Soltani, D. Jahn, L. Duschek, E. Castro-Camus, M. Koch, and W. Withayachumnankul, “Attenuated Total Reflection Terahertz Time-Domain Spectroscopy: Uncertainty Analysis and Reduction Scheme,” IEEE Trans. THz Sci. Technol. 6, 32–39 (2016).
    [Crossref]
  18. M. Naftaly, R. A. Dudley, J. R. Fletcher, F. Bernard, C. Thomson, and Z. Tian, “Frequency calibration of terahertz time-domain spectrometers,” J. Opt. Soc. Am. B 26, 1357–1362 (2009).
    [Crossref]
  19. M. Kinoshita, H. Iida, and Y. Shimada, “Frequency calibration of terahertz time-domain spectrometer using air-gap etalon,” IEEE Trans. THz Sci. Technol. 4, 756–759 (2014).
    [Crossref]
  20. T. Probst, A. Rehn, and M. Koch, “Compact and low-cost THz QTDS system,” Opt. Express 23, 21972 (2015).
    [Crossref] [PubMed]
  21. J. Xu, T. Yuan, S. Mickan, and X. C. Zhang, “Limit of Spectral Resolution in Terahertz Time-Domain Spectroscopy,” Chinese Physics Letters 20, 1266–1268 (2003).
    [Crossref]
  22. R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, and D. E. Knuth, “On the Lambert W function,” Adv. Comput. Math. 5, 329–359 (1996).
    [Crossref]
  23. N. Vieweg, F. Rettich, A. Deninger, H. Roehle, R. Dietz, T. Göbel, and M. Schell, “Terahertz-time domain spectrometer with 90 dB peak dynamic range,” J. Infra. Millim. THz Waves 35, 823–832 (2014).
    [Crossref]
  24. S. F. Busch, M. Weidenbach, M. Fey, F. Schäfer, T. Probst, and M. Koch, “Optical Properties of 3D Printable Plastics in the THz Regime and their Application for 3D Printed THz Optics,” J. Infra. Millim. THz Waves 35, 993–997 (2014).
    [Crossref]
  25. P. D. Cunningham, N. N. Valdes, F. A. Vallejo, L. M. Hayden, B. Polishak, X.-H. Zhou, J. Luo, A. K.-Y. Jen, J. C. Williams, and R. J. Twieg, “Broadband terahertz characterization of the refractive index and absorption of some important polymeric and organic electro-optic materials,” J. Appl. Phys. 109, 043505 (2011).
    [Crossref]
  26. M. Naftaly and R. E. Miles, “Terahertz time-domain spectroscopy for material characterization,” Proc. IEEE 95, 1658 (2007).
    [Crossref]
  27. A. M. Abdul-Munaim, M. Reuter, O. M. Abdulmunem, J. C. Balzer, M. Koch, and D. G. Watson, “Using Terahertz Time-Domain Spectroscopy to Discriminate among Water Contamination Levels in Diesel Engine Oil,” Trans. Am. Soc. Agr. Bio. Eng. 59, 795–801 (2016).
  28. P. Kužel, H. Němec, F. Kadlec, and C. Kadlec, “Gouy shift correction for highly accurate refractive index retrieval in time-domain terahertz spectroscopy,” Opt. Express 18, 15338–15348 (2010).
    [Crossref]
  29. S. Ahmed, J. Savolainen, and P. Hamm, “The effect of the Gouy phase in optical-pump-THz-probe spectroscopy,” Opt. Express 22, 4256–4266 (2014).
    [Crossref] [PubMed]

2016 (3)

D. Jahn, S. Lippert, M. Bisi, L. Oberto, J. C. Balzer, and M. Koch, “On the Influence of Delay Line Uncertainty in THz Time-Domain Spectroscopy,” J. Infra. Millim. THz Waves 37, 605–613 (2016).
[Crossref]

A. Soltani, D. Jahn, L. Duschek, E. Castro-Camus, M. Koch, and W. Withayachumnankul, “Attenuated Total Reflection Terahertz Time-Domain Spectroscopy: Uncertainty Analysis and Reduction Scheme,” IEEE Trans. THz Sci. Technol. 6, 32–39 (2016).
[Crossref]

A. M. Abdul-Munaim, M. Reuter, O. M. Abdulmunem, J. C. Balzer, M. Koch, and D. G. Watson, “Using Terahertz Time-Domain Spectroscopy to Discriminate among Water Contamination Levels in Diesel Engine Oil,” Trans. Am. Soc. Agr. Bio. Eng. 59, 795–801 (2016).

2015 (1)

2014 (6)

S. Ahmed, J. Savolainen, and P. Hamm, “The effect of the Gouy phase in optical-pump-THz-probe spectroscopy,” Opt. Express 22, 4256–4266 (2014).
[Crossref] [PubMed]

W. Withayachumnankul and M. Naftaly, “Fundamentals of measurement in terahertz time-domain spectroscopy,” J. Infrared, Millimeter, and Terahertz Waves 35, 610–637 (2014).
[Crossref]

M. Kinoshita, H. Iida, and Y. Shimada, “Frequency calibration of terahertz time-domain spectrometer using air-gap etalon,” IEEE Trans. THz Sci. Technol. 4, 756–759 (2014).
[Crossref]

N. Vieweg, F. Rettich, A. Deninger, H. Roehle, R. Dietz, T. Göbel, and M. Schell, “Terahertz-time domain spectrometer with 90 dB peak dynamic range,” J. Infra. Millim. THz Waves 35, 823–832 (2014).
[Crossref]

S. F. Busch, M. Weidenbach, M. Fey, F. Schäfer, T. Probst, and M. Koch, “Optical Properties of 3D Printable Plastics in the THz Regime and their Application for 3D Printed THz Optics,” J. Infra. Millim. THz Waves 35, 993–997 (2014).
[Crossref]

M. J. Drexler, R. Woscholski, S. Lippert, W. Stolz, A. Rahimi-Iman, and M. Koch, “Disturbing the coherent dynamics of an excitonic polarization with strong terahertz fields,” Phys. Rev. B 90, 195304 (2014).
[Crossref]

2012 (1)

2011 (3)

P. U. Jepsen, D. G. Cooke, and M. Koch, “Terahertz spectroscopy and imaging - modern techniques and applications,” Laser Photon. Rev. 5, 124–166 (2011).
[Crossref]

M. Krüger, S. Funkner, E. Bründermann, and M. Havenith, “Uncertainty and Ambiguity in Terahertz Parameter Extraction and Data Analysis,” J. Infra. Millim. THz Waves 32, 699–715 (2011).
[Crossref]

P. D. Cunningham, N. N. Valdes, F. A. Vallejo, L. M. Hayden, B. Polishak, X.-H. Zhou, J. Luo, A. K.-Y. Jen, J. C. Williams, and R. J. Twieg, “Broadband terahertz characterization of the refractive index and absorption of some important polymeric and organic electro-optic materials,” J. Appl. Phys. 109, 043505 (2011).
[Crossref]

2010 (1)

2009 (3)

M. Naftaly, R. A. Dudley, J. R. Fletcher, F. Bernard, C. Thomson, and Z. Tian, “Frequency calibration of terahertz time-domain spectrometers,” J. Opt. Soc. Am. B 26, 1357–1362 (2009).
[Crossref]

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

J. B. Baxter and C. A. Schmuttenmaer, “Carrier dynamics in bulk ZnO. I. Intrinsic conductivity measured by terahertz time-domain spectroscopy,” Phys. Rev. B 80, 235205 (2009).
[Crossref]

2008 (2)

R. Wilk, I. Pupeza, R. Cernat, and M. Koch, “Highly Accurate THz Time-Domain Spectroscopy of Multilayer Structures,” IEEE J. Sel. Top. Quantum Electron. 14, 392–398 (2008).
[Crossref]

W. Withayachumnankul, B. M. Fischer, H. Lin, and D. Abbott, “Uncertainty in terahertz time-domain spectroscopy measurement,” J. Opt. Soc. Am. B 25, 1059 (2008).
[Crossref]

2007 (1)

M. Naftaly and R. E. Miles, “Terahertz time-domain spectroscopy for material characterization,” Proc. IEEE 95, 1658 (2007).
[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. Semiclass. Opt. 6, S786–S795 (2004).
[Crossref]

2003 (1)

J. Xu, T. Yuan, S. Mickan, and X. C. Zhang, “Limit of Spectral Resolution in Terahertz Time-Domain Spectroscopy,” Chinese Physics Letters 20, 1266–1268 (2003).
[Crossref]

2002 (1)

M. Walther, P. Plochocka, B. Fischer, H. Helm, and P. Uhd Jepsen, “Collective vibrational modes in biological molecules investigated by terahertz time-domain spectroscopy,” Biopolymers 67, 310–313 (2002).
[Crossref] [PubMed]

2001 (1)

1999 (1)

1998 (1)

S. Hunsche, D. M. Mittleman, M. Koch, and M. C. Nuss, “New dimensions in t-ray imaging,” IEICE Trans. Electron. 81, 269–276 (1998).

1996 (2)

R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, and D. E. Knuth, “On the Lambert W function,” Adv. Comput. Math. 5, 329–359 (1996).
[Crossref]

R. H. Jacobsen, D. M. Mittleman, and M. C. Nuss, “Chemical recognition of gases and gas mixtures with terahertz waves,” Opt. Lett. 21, 2011 (1996).
[Crossref] [PubMed]

Abbott, D.

W. Withayachumnankul, B. M. Fischer, H. Lin, and D. Abbott, “Uncertainty in terahertz time-domain spectroscopy measurement,” J. Opt. Soc. Am. B 25, 1059 (2008).
[Crossref]

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. Semiclass. Opt. 6, S786–S795 (2004).
[Crossref]

Abdul-Munaim, A. M.

A. M. Abdul-Munaim, M. Reuter, O. M. Abdulmunem, J. C. Balzer, M. Koch, and D. G. Watson, “Using Terahertz Time-Domain Spectroscopy to Discriminate among Water Contamination Levels in Diesel Engine Oil,” Trans. Am. Soc. Agr. Bio. Eng. 59, 795–801 (2016).

Abdulmunem, O. M.

A. M. Abdul-Munaim, M. Reuter, O. M. Abdulmunem, J. C. Balzer, M. Koch, and D. G. Watson, “Using Terahertz Time-Domain Spectroscopy to Discriminate among Water Contamination Levels in Diesel Engine Oil,” Trans. Am. Soc. Agr. Bio. Eng. 59, 795–801 (2016).

Ahmed, S.

Balzer, J. C.

D. Jahn, S. Lippert, M. Bisi, L. Oberto, J. C. Balzer, and M. Koch, “On the Influence of Delay Line Uncertainty in THz Time-Domain Spectroscopy,” J. Infra. Millim. THz Waves 37, 605–613 (2016).
[Crossref]

A. M. Abdul-Munaim, M. Reuter, O. M. Abdulmunem, J. C. Balzer, M. Koch, and D. G. Watson, “Using Terahertz Time-Domain Spectroscopy to Discriminate among Water Contamination Levels in Diesel Engine Oil,” Trans. Am. Soc. Agr. Bio. Eng. 59, 795–801 (2016).

Baraniuk, R. G.

Baxter, J. B.

J. B. Baxter and C. A. Schmuttenmaer, “Carrier dynamics in bulk ZnO. I. Intrinsic conductivity measured by terahertz time-domain spectroscopy,” Phys. Rev. B 80, 235205 (2009).
[Crossref]

Bernard, F.

Bisi, M.

D. Jahn, S. Lippert, M. Bisi, L. Oberto, J. C. Balzer, and M. Koch, “On the Influence of Delay Line Uncertainty in THz Time-Domain Spectroscopy,” J. Infra. Millim. THz Waves 37, 605–613 (2016).
[Crossref]

Bründermann, E.

M. Krüger, S. Funkner, E. Bründermann, and M. Havenith, “Uncertainty and Ambiguity in Terahertz Parameter Extraction and Data Analysis,” J. Infra. Millim. THz Waves 32, 699–715 (2011).
[Crossref]

Busch, S. F.

S. F. Busch, M. Weidenbach, M. Fey, F. Schäfer, T. Probst, and M. Koch, “Optical Properties of 3D Printable Plastics in the THz Regime and their Application for 3D Printed THz Optics,” J. Infra. Millim. THz Waves 35, 993–997 (2014).
[Crossref]

Castro-Camus, E.

A. Soltani, D. Jahn, L. Duschek, E. Castro-Camus, M. Koch, and W. Withayachumnankul, “Attenuated Total Reflection Terahertz Time-Domain Spectroscopy: Uncertainty Analysis and Reduction Scheme,” IEEE Trans. THz Sci. Technol. 6, 32–39 (2016).
[Crossref]

Celik, M. a.

Cernat, R.

R. Wilk, I. Pupeza, R. Cernat, and M. Koch, “Highly Accurate THz Time-Domain Spectroscopy of Multilayer Structures,” IEEE J. Sel. Top. Quantum Electron. 14, 392–398 (2008).
[Crossref]

Cooke, D. G.

P. U. Jepsen, D. G. Cooke, and M. Koch, “Terahertz spectroscopy and imaging - modern techniques and applications,” Laser Photon. Rev. 5, 124–166 (2011).
[Crossref]

Corless, R. M.

R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, and D. E. Knuth, “On the Lambert W function,” Adv. Comput. Math. 5, 329–359 (1996).
[Crossref]

Coutaz, J.-L.

Cunningham, P. D.

P. D. Cunningham, N. N. Valdes, F. A. Vallejo, L. M. Hayden, B. Polishak, X.-H. Zhou, J. Luo, A. K.-Y. Jen, J. C. Williams, and R. J. Twieg, “Broadband terahertz characterization of the refractive index and absorption of some important polymeric and organic electro-optic materials,” J. Appl. Phys. 109, 043505 (2011).
[Crossref]

Dabrowski, R.

Deninger, A.

N. Vieweg, F. Rettich, A. Deninger, H. Roehle, R. Dietz, T. Göbel, and M. Schell, “Terahertz-time domain spectrometer with 90 dB peak dynamic range,” J. Infra. Millim. THz Waves 35, 823–832 (2014).
[Crossref]

Dietz, R.

N. Vieweg, F. Rettich, A. Deninger, H. Roehle, R. Dietz, T. Göbel, and M. Schell, “Terahertz-time domain spectrometer with 90 dB peak dynamic range,” J. Infra. Millim. THz Waves 35, 823–832 (2014).
[Crossref]

Dorney, T. D.

Drexler, M. J.

M. J. Drexler, R. Woscholski, S. Lippert, W. Stolz, A. Rahimi-Iman, and M. Koch, “Disturbing the coherent dynamics of an excitonic polarization with strong terahertz fields,” Phys. Rev. B 90, 195304 (2014).
[Crossref]

Dudley, R. A.

Duschek, L.

A. Soltani, D. Jahn, L. Duschek, E. Castro-Camus, M. Koch, and W. Withayachumnankul, “Attenuated Total Reflection Terahertz Time-Domain Spectroscopy: Uncertainty Analysis and Reduction Scheme,” IEEE Trans. THz Sci. Technol. 6, 32–39 (2016).
[Crossref]

Duvillaret, L.

Fey, M.

S. F. Busch, M. Weidenbach, M. Fey, F. Schäfer, T. Probst, and M. Koch, “Optical Properties of 3D Printable Plastics in the THz Regime and their Application for 3D Printed THz Optics,” J. Infra. Millim. THz Waves 35, 993–997 (2014).
[Crossref]

Fischer, B.

M. Walther, P. Plochocka, B. Fischer, H. Helm, and P. Uhd Jepsen, “Collective vibrational modes in biological molecules investigated by terahertz time-domain spectroscopy,” Biopolymers 67, 310–313 (2002).
[Crossref] [PubMed]

Fischer, B. M.

Fletcher, J. R.

Frenking, G.

Funkner, S.

M. Krüger, S. Funkner, E. Bründermann, and M. Havenith, “Uncertainty and Ambiguity in Terahertz Parameter Extraction and Data Analysis,” J. Infra. Millim. THz Waves 32, 699–715 (2011).
[Crossref]

Garet, F.

Göbel, T.

N. Vieweg, F. Rettich, A. Deninger, H. Roehle, R. Dietz, T. Göbel, and M. Schell, “Terahertz-time domain spectrometer with 90 dB peak dynamic range,” J. Infra. Millim. THz Waves 35, 823–832 (2014).
[Crossref]

Gonnet, G. H.

R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, and D. E. Knuth, “On the Lambert W function,” Adv. Comput. Math. 5, 329–359 (1996).
[Crossref]

Hamm, P.

Hare, D. E. G.

R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, and D. E. Knuth, “On the Lambert W function,” Adv. Comput. Math. 5, 329–359 (1996).
[Crossref]

Havenith, M.

M. Krüger, S. Funkner, E. Bründermann, and M. Havenith, “Uncertainty and Ambiguity in Terahertz Parameter Extraction and Data Analysis,” J. Infra. Millim. THz Waves 32, 699–715 (2011).
[Crossref]

Hayden, L. M.

P. D. Cunningham, N. N. Valdes, F. A. Vallejo, L. M. Hayden, B. Polishak, X.-H. Zhou, J. Luo, A. K.-Y. Jen, J. C. Williams, and R. J. Twieg, “Broadband terahertz characterization of the refractive index and absorption of some important polymeric and organic electro-optic materials,” J. Appl. Phys. 109, 043505 (2011).
[Crossref]

Helm, H.

M. Walther, P. Plochocka, B. Fischer, H. Helm, and P. Uhd Jepsen, “Collective vibrational modes in biological molecules investigated by terahertz time-domain spectroscopy,” Biopolymers 67, 310–313 (2002).
[Crossref] [PubMed]

Hunsche, S.

S. Hunsche, D. M. Mittleman, M. Koch, and M. C. Nuss, “New dimensions in t-ray imaging,” IEICE Trans. Electron. 81, 269–276 (1998).

Iida, H.

M. Kinoshita, H. Iida, and Y. Shimada, “Frequency calibration of terahertz time-domain spectrometer using air-gap etalon,” IEEE Trans. THz Sci. Technol. 4, 756–759 (2014).
[Crossref]

Jacobsen, R. H.

Jahn, D.

D. Jahn, S. Lippert, M. Bisi, L. Oberto, J. C. Balzer, and M. Koch, “On the Influence of Delay Line Uncertainty in THz Time-Domain Spectroscopy,” J. Infra. Millim. THz Waves 37, 605–613 (2016).
[Crossref]

A. Soltani, D. Jahn, L. Duschek, E. Castro-Camus, M. Koch, and W. Withayachumnankul, “Attenuated Total Reflection Terahertz Time-Domain Spectroscopy: Uncertainty Analysis and Reduction Scheme,” IEEE Trans. THz Sci. Technol. 6, 32–39 (2016).
[Crossref]

Jansen, C.

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

Jeffrey, D. J.

R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, and D. E. Knuth, “On the Lambert W function,” Adv. Comput. Math. 5, 329–359 (1996).
[Crossref]

Jen, A. K.-Y.

P. D. Cunningham, N. N. Valdes, F. A. Vallejo, L. M. Hayden, B. Polishak, X.-H. Zhou, J. Luo, A. K.-Y. Jen, J. C. Williams, and R. J. Twieg, “Broadband terahertz characterization of the refractive index and absorption of some important polymeric and organic electro-optic materials,” J. Appl. Phys. 109, 043505 (2011).
[Crossref]

Jepsen, P. U.

Kadlec, C.

Kadlec, F.

Kinoshita, M.

M. Kinoshita, H. Iida, and Y. Shimada, “Frequency calibration of terahertz time-domain spectrometer using air-gap etalon,” IEEE Trans. THz Sci. Technol. 4, 756–759 (2014).
[Crossref]

Knuth, D. E.

R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, and D. E. Knuth, “On the Lambert W function,” Adv. Comput. Math. 5, 329–359 (1996).
[Crossref]

Koch, M.

D. Jahn, S. Lippert, M. Bisi, L. Oberto, J. C. Balzer, and M. Koch, “On the Influence of Delay Line Uncertainty in THz Time-Domain Spectroscopy,” J. Infra. Millim. THz Waves 37, 605–613 (2016).
[Crossref]

A. Soltani, D. Jahn, L. Duschek, E. Castro-Camus, M. Koch, and W. Withayachumnankul, “Attenuated Total Reflection Terahertz Time-Domain Spectroscopy: Uncertainty Analysis and Reduction Scheme,” IEEE Trans. THz Sci. Technol. 6, 32–39 (2016).
[Crossref]

A. M. Abdul-Munaim, M. Reuter, O. M. Abdulmunem, J. C. Balzer, M. Koch, and D. G. Watson, “Using Terahertz Time-Domain Spectroscopy to Discriminate among Water Contamination Levels in Diesel Engine Oil,” Trans. Am. Soc. Agr. Bio. Eng. 59, 795–801 (2016).

T. Probst, A. Rehn, and M. Koch, “Compact and low-cost THz QTDS system,” Opt. Express 23, 21972 (2015).
[Crossref] [PubMed]

M. J. Drexler, R. Woscholski, S. Lippert, W. Stolz, A. Rahimi-Iman, and M. Koch, “Disturbing the coherent dynamics of an excitonic polarization with strong terahertz fields,” Phys. Rev. B 90, 195304 (2014).
[Crossref]

S. F. Busch, M. Weidenbach, M. Fey, F. Schäfer, T. Probst, and M. Koch, “Optical Properties of 3D Printable Plastics in the THz Regime and their Application for 3D Printed THz Optics,” J. Infra. Millim. THz Waves 35, 993–997 (2014).
[Crossref]

N. Vieweg, B. M. Fischer, M. Reuter, P. Kula, R. Dabrowski, M. a. Celik, G. Frenking, M. Koch, and P. U. Jepsen, “Ultrabroadband terahertz spectroscopy of a liquid crystal,” Opt. Express 20, 28249–56 (2012).
[Crossref] [PubMed]

P. U. Jepsen, D. G. Cooke, and M. Koch, “Terahertz spectroscopy and imaging - modern techniques and applications,” Laser Photon. Rev. 5, 124–166 (2011).
[Crossref]

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

R. Wilk, I. Pupeza, R. Cernat, and M. Koch, “Highly Accurate THz Time-Domain Spectroscopy of Multilayer Structures,” IEEE J. Sel. Top. Quantum Electron. 14, 392–398 (2008).
[Crossref]

S. Hunsche, D. M. Mittleman, M. Koch, and M. C. Nuss, “New dimensions in t-ray imaging,” IEICE Trans. Electron. 81, 269–276 (1998).

Krüger, M.

M. Krüger, S. Funkner, E. Bründermann, and M. Havenith, “Uncertainty and Ambiguity in Terahertz Parameter Extraction and Data Analysis,” J. Infra. Millim. THz Waves 32, 699–715 (2011).
[Crossref]

Kula, P.

Kužel, P.

Lin, H.

Lippert, S.

D. Jahn, S. Lippert, M. Bisi, L. Oberto, J. C. Balzer, and M. Koch, “On the Influence of Delay Line Uncertainty in THz Time-Domain Spectroscopy,” J. Infra. Millim. THz Waves 37, 605–613 (2016).
[Crossref]

M. J. Drexler, R. Woscholski, S. Lippert, W. Stolz, A. Rahimi-Iman, and M. Koch, “Disturbing the coherent dynamics of an excitonic polarization with strong terahertz fields,” Phys. Rev. B 90, 195304 (2014).
[Crossref]

Luo, J.

P. D. Cunningham, N. N. Valdes, F. A. Vallejo, L. M. Hayden, B. Polishak, X.-H. Zhou, J. Luo, A. K.-Y. Jen, J. C. Williams, and R. J. Twieg, “Broadband terahertz characterization of the refractive index and absorption of some important polymeric and organic electro-optic materials,” J. Appl. Phys. 109, 043505 (2011).
[Crossref]

Mickan, S.

J. Xu, T. Yuan, S. Mickan, and X. C. Zhang, “Limit of Spectral Resolution in Terahertz Time-Domain Spectroscopy,” Chinese Physics Letters 20, 1266–1268 (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. Semiclass. Opt. 6, S786–S795 (2004).
[Crossref]

Miles, R. E.

M. Naftaly and R. E. Miles, “Terahertz time-domain spectroscopy for material characterization,” Proc. IEEE 95, 1658 (2007).
[Crossref]

Mittleman, D. M.

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. Semiclass. Opt. 6, S786–S795 (2004).
[Crossref]

Naftaly, M.

W. Withayachumnankul and M. Naftaly, “Fundamentals of measurement in terahertz time-domain spectroscopy,” J. Infrared, Millimeter, and Terahertz Waves 35, 610–637 (2014).
[Crossref]

M. Naftaly, R. A. Dudley, J. R. Fletcher, F. Bernard, C. Thomson, and Z. Tian, “Frequency calibration of terahertz time-domain spectrometers,” J. Opt. Soc. Am. B 26, 1357–1362 (2009).
[Crossref]

M. Naftaly and R. E. Miles, “Terahertz time-domain spectroscopy for material characterization,” Proc. IEEE 95, 1658 (2007).
[Crossref]

Nemec, H.

Nuss, M. C.

S. Hunsche, D. M. Mittleman, M. Koch, and M. C. Nuss, “New dimensions in t-ray imaging,” IEICE Trans. Electron. 81, 269–276 (1998).

R. H. Jacobsen, D. M. Mittleman, and M. C. Nuss, “Chemical recognition of gases and gas mixtures with terahertz waves,” Opt. Lett. 21, 2011 (1996).
[Crossref] [PubMed]

Oberto, L.

D. Jahn, S. Lippert, M. Bisi, L. Oberto, J. C. Balzer, and M. Koch, “On the Influence of Delay Line Uncertainty in THz Time-Domain Spectroscopy,” J. Infra. Millim. THz Waves 37, 605–613 (2016).
[Crossref]

Plochocka, P.

M. Walther, P. Plochocka, B. Fischer, H. Helm, and P. Uhd Jepsen, “Collective vibrational modes in biological molecules investigated by terahertz time-domain spectroscopy,” Biopolymers 67, 310–313 (2002).
[Crossref] [PubMed]

Polishak, B.

P. D. Cunningham, N. N. Valdes, F. A. Vallejo, L. M. Hayden, B. Polishak, X.-H. Zhou, J. Luo, A. K.-Y. Jen, J. C. Williams, and R. J. Twieg, “Broadband terahertz characterization of the refractive index and absorption of some important polymeric and organic electro-optic materials,” J. Appl. Phys. 109, 043505 (2011).
[Crossref]

Probst, T.

T. Probst, A. Rehn, and M. Koch, “Compact and low-cost THz QTDS system,” Opt. Express 23, 21972 (2015).
[Crossref] [PubMed]

S. F. Busch, M. Weidenbach, M. Fey, F. Schäfer, T. Probst, and M. Koch, “Optical Properties of 3D Printable Plastics in the THz Regime and their Application for 3D Printed THz Optics,” J. Infra. Millim. THz Waves 35, 993–997 (2014).
[Crossref]

Pupeza, I.

R. Wilk, I. Pupeza, R. Cernat, and M. Koch, “Highly Accurate THz Time-Domain Spectroscopy of Multilayer Structures,” IEEE J. Sel. Top. Quantum Electron. 14, 392–398 (2008).
[Crossref]

Rahimi-Iman, A.

M. J. Drexler, R. Woscholski, S. Lippert, W. Stolz, A. Rahimi-Iman, and M. Koch, “Disturbing the coherent dynamics of an excitonic polarization with strong terahertz fields,” Phys. Rev. B 90, 195304 (2014).
[Crossref]

Rehn, A.

Rettich, F.

N. Vieweg, F. Rettich, A. Deninger, H. Roehle, R. Dietz, T. Göbel, and M. Schell, “Terahertz-time domain spectrometer with 90 dB peak dynamic range,” J. Infra. Millim. THz Waves 35, 823–832 (2014).
[Crossref]

Reuter, M.

A. M. Abdul-Munaim, M. Reuter, O. M. Abdulmunem, J. C. Balzer, M. Koch, and D. G. Watson, “Using Terahertz Time-Domain Spectroscopy to Discriminate among Water Contamination Levels in Diesel Engine Oil,” Trans. Am. Soc. Agr. Bio. Eng. 59, 795–801 (2016).

N. Vieweg, B. M. Fischer, M. Reuter, P. Kula, R. Dabrowski, M. a. Celik, G. Frenking, M. Koch, and P. U. Jepsen, “Ultrabroadband terahertz spectroscopy of a liquid crystal,” Opt. Express 20, 28249–56 (2012).
[Crossref] [PubMed]

Roehle, H.

N. Vieweg, F. Rettich, A. Deninger, H. Roehle, R. Dietz, T. Göbel, and M. Schell, “Terahertz-time domain spectrometer with 90 dB peak dynamic range,” J. Infra. Millim. THz Waves 35, 823–832 (2014).
[Crossref]

Savolainen, J.

Schäfer, F.

S. F. Busch, M. Weidenbach, M. Fey, F. Schäfer, T. Probst, and M. Koch, “Optical Properties of 3D Printable Plastics in the THz Regime and their Application for 3D Printed THz Optics,” J. Infra. Millim. THz Waves 35, 993–997 (2014).
[Crossref]

Schell, M.

N. Vieweg, F. Rettich, A. Deninger, H. Roehle, R. Dietz, T. Göbel, and M. Schell, “Terahertz-time domain spectrometer with 90 dB peak dynamic range,” J. Infra. Millim. THz Waves 35, 823–832 (2014).
[Crossref]

Scheller, M.

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

Schmuttenmaer, C. A.

J. B. Baxter and C. A. Schmuttenmaer, “Carrier dynamics in bulk ZnO. I. Intrinsic conductivity measured by terahertz time-domain spectroscopy,” Phys. Rev. B 80, 235205 (2009).
[Crossref]

Shimada, Y.

M. Kinoshita, H. Iida, and Y. Shimada, “Frequency calibration of terahertz time-domain spectrometer using air-gap etalon,” IEEE Trans. THz Sci. Technol. 4, 756–759 (2014).
[Crossref]

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. Semiclass. Opt. 6, S786–S795 (2004).
[Crossref]

Soltani, A.

A. Soltani, D. Jahn, L. Duschek, E. Castro-Camus, M. Koch, and W. Withayachumnankul, “Attenuated Total Reflection Terahertz Time-Domain Spectroscopy: Uncertainty Analysis and Reduction Scheme,” IEEE Trans. THz Sci. Technol. 6, 32–39 (2016).
[Crossref]

Stolz, W.

M. J. Drexler, R. Woscholski, S. Lippert, W. Stolz, A. Rahimi-Iman, and M. Koch, “Disturbing the coherent dynamics of an excitonic polarization with strong terahertz fields,” Phys. Rev. B 90, 195304 (2014).
[Crossref]

Thomson, C.

Tian, Z.

Twieg, R. J.

P. D. Cunningham, N. N. Valdes, F. A. Vallejo, L. M. Hayden, B. Polishak, X.-H. Zhou, J. Luo, A. K.-Y. Jen, J. C. Williams, and R. J. Twieg, “Broadband terahertz characterization of the refractive index and absorption of some important polymeric and organic electro-optic materials,” J. Appl. Phys. 109, 043505 (2011).
[Crossref]

Uhd Jepsen, P.

M. Walther, P. Plochocka, B. Fischer, H. Helm, and P. Uhd Jepsen, “Collective vibrational modes in biological molecules investigated by terahertz time-domain spectroscopy,” Biopolymers 67, 310–313 (2002).
[Crossref] [PubMed]

Valdes, N. N.

P. D. Cunningham, N. N. Valdes, F. A. Vallejo, L. M. Hayden, B. Polishak, X.-H. Zhou, J. Luo, A. K.-Y. Jen, J. C. Williams, and R. J. Twieg, “Broadband terahertz characterization of the refractive index and absorption of some important polymeric and organic electro-optic materials,” J. Appl. Phys. 109, 043505 (2011).
[Crossref]

Vallejo, F. A.

P. D. Cunningham, N. N. Valdes, F. A. Vallejo, L. M. Hayden, B. Polishak, X.-H. Zhou, J. Luo, A. K.-Y. Jen, J. C. Williams, and R. J. Twieg, “Broadband terahertz characterization of the refractive index and absorption of some important polymeric and organic electro-optic materials,” J. Appl. Phys. 109, 043505 (2011).
[Crossref]

Vieweg, N.

N. Vieweg, F. Rettich, A. Deninger, H. Roehle, R. Dietz, T. Göbel, and M. Schell, “Terahertz-time domain spectrometer with 90 dB peak dynamic range,” J. Infra. Millim. THz Waves 35, 823–832 (2014).
[Crossref]

N. Vieweg, B. M. Fischer, M. Reuter, P. Kula, R. Dabrowski, M. a. Celik, G. Frenking, M. Koch, and P. U. Jepsen, “Ultrabroadband terahertz spectroscopy of a liquid crystal,” Opt. Express 20, 28249–56 (2012).
[Crossref] [PubMed]

Walther, M.

M. Walther, P. Plochocka, B. Fischer, H. Helm, and P. Uhd Jepsen, “Collective vibrational modes in biological molecules investigated by terahertz time-domain spectroscopy,” Biopolymers 67, 310–313 (2002).
[Crossref] [PubMed]

Watson, D. G.

A. M. Abdul-Munaim, M. Reuter, O. M. Abdulmunem, J. C. Balzer, M. Koch, and D. G. Watson, “Using Terahertz Time-Domain Spectroscopy to Discriminate among Water Contamination Levels in Diesel Engine Oil,” Trans. Am. Soc. Agr. Bio. Eng. 59, 795–801 (2016).

Weidenbach, M.

S. F. Busch, M. Weidenbach, M. Fey, F. Schäfer, T. Probst, and M. Koch, “Optical Properties of 3D Printable Plastics in the THz Regime and their Application for 3D Printed THz Optics,” J. Infra. Millim. THz Waves 35, 993–997 (2014).
[Crossref]

Wilk, R.

R. Wilk, I. Pupeza, R. Cernat, and M. Koch, “Highly Accurate THz Time-Domain Spectroscopy of Multilayer Structures,” IEEE J. Sel. Top. Quantum Electron. 14, 392–398 (2008).
[Crossref]

Williams, J. C.

P. D. Cunningham, N. N. Valdes, F. A. Vallejo, L. M. Hayden, B. Polishak, X.-H. Zhou, J. Luo, A. K.-Y. Jen, J. C. Williams, and R. J. Twieg, “Broadband terahertz characterization of the refractive index and absorption of some important polymeric and organic electro-optic materials,” J. Appl. Phys. 109, 043505 (2011).
[Crossref]

Withayachumnankul, W.

A. Soltani, D. Jahn, L. Duschek, E. Castro-Camus, M. Koch, and W. Withayachumnankul, “Attenuated Total Reflection Terahertz Time-Domain Spectroscopy: Uncertainty Analysis and Reduction Scheme,” IEEE Trans. THz Sci. Technol. 6, 32–39 (2016).
[Crossref]

W. Withayachumnankul and M. Naftaly, “Fundamentals of measurement in terahertz time-domain spectroscopy,” J. Infrared, Millimeter, and Terahertz Waves 35, 610–637 (2014).
[Crossref]

W. Withayachumnankul, B. M. Fischer, H. Lin, and D. Abbott, “Uncertainty in terahertz time-domain spectroscopy measurement,” J. Opt. Soc. Am. B 25, 1059 (2008).
[Crossref]

Woscholski, R.

M. J. Drexler, R. Woscholski, S. Lippert, W. Stolz, A. Rahimi-Iman, and M. Koch, “Disturbing the coherent dynamics of an excitonic polarization with strong terahertz fields,” Phys. Rev. B 90, 195304 (2014).
[Crossref]

Xu, J.

J. Xu, T. Yuan, S. Mickan, and X. C. Zhang, “Limit of Spectral Resolution in Terahertz Time-Domain Spectroscopy,” Chinese Physics Letters 20, 1266–1268 (2003).
[Crossref]

Yuan, T.

J. Xu, T. Yuan, S. Mickan, and X. C. Zhang, “Limit of Spectral Resolution in Terahertz Time-Domain Spectroscopy,” Chinese Physics Letters 20, 1266–1268 (2003).
[Crossref]

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. Semiclass. Opt. 6, S786–S795 (2004).
[Crossref]

J. Xu, T. Yuan, S. Mickan, and X. C. Zhang, “Limit of Spectral Resolution in Terahertz Time-Domain Spectroscopy,” Chinese Physics Letters 20, 1266–1268 (2003).
[Crossref]

Zhou, X.-H.

P. D. Cunningham, N. N. Valdes, F. A. Vallejo, L. M. Hayden, B. Polishak, X.-H. Zhou, J. Luo, A. K.-Y. Jen, J. C. Williams, and R. J. Twieg, “Broadband terahertz characterization of the refractive index and absorption of some important polymeric and organic electro-optic materials,” J. Appl. Phys. 109, 043505 (2011).
[Crossref]

Adv. Comput. Math. (1)

R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, and D. E. Knuth, “On the Lambert W function,” Adv. Comput. Math. 5, 329–359 (1996).
[Crossref]

Appl. Opt. (1)

Biopolymers (1)

M. Walther, P. Plochocka, B. Fischer, H. Helm, and P. Uhd Jepsen, “Collective vibrational modes in biological molecules investigated by terahertz time-domain spectroscopy,” Biopolymers 67, 310–313 (2002).
[Crossref] [PubMed]

Chinese Physics Letters (1)

J. Xu, T. Yuan, S. Mickan, and X. C. Zhang, “Limit of Spectral Resolution in Terahertz Time-Domain Spectroscopy,” Chinese Physics Letters 20, 1266–1268 (2003).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

R. Wilk, I. Pupeza, R. Cernat, and M. Koch, “Highly Accurate THz Time-Domain Spectroscopy of Multilayer Structures,” IEEE J. Sel. Top. Quantum Electron. 14, 392–398 (2008).
[Crossref]

IEEE Trans. THz Sci. Technol. (2)

A. Soltani, D. Jahn, L. Duschek, E. Castro-Camus, M. Koch, and W. Withayachumnankul, “Attenuated Total Reflection Terahertz Time-Domain Spectroscopy: Uncertainty Analysis and Reduction Scheme,” IEEE Trans. THz Sci. Technol. 6, 32–39 (2016).
[Crossref]

M. Kinoshita, H. Iida, and Y. Shimada, “Frequency calibration of terahertz time-domain spectrometer using air-gap etalon,” IEEE Trans. THz Sci. Technol. 4, 756–759 (2014).
[Crossref]

IEICE Trans. Electron. (1)

S. Hunsche, D. M. Mittleman, M. Koch, and M. C. Nuss, “New dimensions in t-ray imaging,” IEICE Trans. Electron. 81, 269–276 (1998).

J. Appl. Phys. (1)

P. D. Cunningham, N. N. Valdes, F. A. Vallejo, L. M. Hayden, B. Polishak, X.-H. Zhou, J. Luo, A. K.-Y. Jen, J. C. Williams, and R. J. Twieg, “Broadband terahertz characterization of the refractive index and absorption of some important polymeric and organic electro-optic materials,” J. Appl. Phys. 109, 043505 (2011).
[Crossref]

J. Infra. Millim. THz Waves (4)

M. Krüger, S. Funkner, E. Bründermann, and M. Havenith, “Uncertainty and Ambiguity in Terahertz Parameter Extraction and Data Analysis,” J. Infra. Millim. THz Waves 32, 699–715 (2011).
[Crossref]

D. Jahn, S. Lippert, M. Bisi, L. Oberto, J. C. Balzer, and M. Koch, “On the Influence of Delay Line Uncertainty in THz Time-Domain Spectroscopy,” J. Infra. Millim. THz Waves 37, 605–613 (2016).
[Crossref]

N. Vieweg, F. Rettich, A. Deninger, H. Roehle, R. Dietz, T. Göbel, and M. Schell, “Terahertz-time domain spectrometer with 90 dB peak dynamic range,” J. Infra. Millim. THz Waves 35, 823–832 (2014).
[Crossref]

S. F. Busch, M. Weidenbach, M. Fey, F. Schäfer, T. Probst, and M. Koch, “Optical Properties of 3D Printable Plastics in the THz Regime and their Application for 3D Printed THz Optics,” J. Infra. Millim. THz Waves 35, 993–997 (2014).
[Crossref]

J. Infrared, Millimeter, and Terahertz Waves (1)

W. Withayachumnankul and M. Naftaly, “Fundamentals of measurement in terahertz time-domain spectroscopy,” J. Infrared, Millimeter, and Terahertz Waves 35, 610–637 (2014).
[Crossref]

J. Opt. B-Quantum. Semiclass. 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. Semiclass. Opt. 6, S786–S795 (2004).
[Crossref]

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

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

Laser Photon. Rev. (1)

P. U. Jepsen, D. G. Cooke, and M. Koch, “Terahertz spectroscopy and imaging - modern techniques and applications,” Laser Photon. Rev. 5, 124–166 (2011).
[Crossref]

Opt. Commun. (1)

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

Opt. Express (4)

Opt. Lett. (1)

Phys. Rev. B (2)

J. B. Baxter and C. A. Schmuttenmaer, “Carrier dynamics in bulk ZnO. I. Intrinsic conductivity measured by terahertz time-domain spectroscopy,” Phys. Rev. B 80, 235205 (2009).
[Crossref]

M. J. Drexler, R. Woscholski, S. Lippert, W. Stolz, A. Rahimi-Iman, and M. Koch, “Disturbing the coherent dynamics of an excitonic polarization with strong terahertz fields,” Phys. Rev. B 90, 195304 (2014).
[Crossref]

Proc. IEEE (1)

M. Naftaly and R. E. Miles, “Terahertz time-domain spectroscopy for material characterization,” Proc. IEEE 95, 1658 (2007).
[Crossref]

Trans. Am. Soc. Agr. Bio. Eng. (1)

A. M. Abdul-Munaim, M. Reuter, O. M. Abdulmunem, J. C. Balzer, M. Koch, and D. G. Watson, “Using Terahertz Time-Domain Spectroscopy to Discriminate among Water Contamination Levels in Diesel Engine Oil,” Trans. Am. Soc. Agr. Bio. Eng. 59, 795–801 (2016).

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Figures (7)

Fig. 1
Fig. 1 This figure shows a sketch of a typical THz TDS setup. The delay line changes the optical path lengths of the emitter and/or detector paths. The sampling of the THz pulse is thus controlled by the delay line position and trigger pulses are generated by the controller, acting as a clock. The actual time of acquisition is, however, determined by the lock-in amplifier’s clock.

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Fig. 2
Fig. 2 These graphs show the deviations τ(t) of the correct time axis to an unsynchronised second time axis for different movement speeds. The shape of the deviation τ(t) appears to be sawtooth-like. In the context of optical sampling, the error’s amplitude scales linearly with the movement speed of the translation stage and can lead to complex periodic structures.

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Fig. 3
Fig. 3 The effects of the unsynchronised clocks are evident: If each acquisition of a sample is triggered individually (green), the signal never fully drops to the noise floor. Instead, some kind of “wobbles” dominate most of the frequency range. It is very likely that the actual THz spectrum at around 1.5 to 2 THz is influenced by these artefacts, even though it is not apparent in which way. These effects do not occur when only the scan’s start is triggered and samples are acquired continuously afterwards (orange). Here, the sampling rate is solely determined by the lock-in amplifier’s internal clock.

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Fig. 4
Fig. 4 Non-linear movement of the delay line effectively amount to periodic sampling time errors in optical sampling systems. a) shows the deviation from linear movement for two investigated delay lines. b) displays the resulting THz spectra. Due to the pronounced non-linearity of the re-purposed CD drive, spectral artefacts at around 1 THz appear.

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Fig. 5
Fig. 5 Comparing the original spectrum with the spectrum under the influence of a periodic sampling error, “mirror spectra” appear at integer multiples of the error frequency ν. The first order approximation only describes the most intense mirror spectrum at ν.

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Fig. 6
Fig. 6 Depending on the parameters, a periodic sampling error can have a significant impact on the spectrum. In this figure, the effects of a very weak error (with regard to it’s amplitude, compared to typical THz time scales) with a frequency within the bandwidth of the original THz spectrum are shown. The spectrum affected by the sampling error has a higher, but fake, bandwidth and mirrors some of the original absorption features. The error is not readily discernible as such and the fake spectral features might be taken for real.

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Fig. 7
Fig. 7 Top left: Deviation of the the transfer function’s magnitude |H| from the proper transfer function’s magnitude |H0| in logarithmic scale. Top right: The resulting refractive index error Δn. Bottom: Zoom of the refractive index error to the region of main interest. The THz frequency ω/(2π) and error frequency ν/(2π) are in the region 0 THz ≤ ω/(2π), ν/(2π) ≤ 4 THz. Errors in the magnitude of the transfer function as well as in the calculated refractive index appear dominantly on the high-frequency side of the equi-power line.

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Tables (1)

Tables Icon

Table 1 This table shows the birefringence ΔnLCP of an LCP sample as extracted by Probst et al. The periodic error exhibited by the CD drive creates inconsistent data, leading to results which depend on the used evaluation method.

View Table

Equations (30)

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

σ LIA ( n ) = n ⋅ Δ t mod v move 512 Hz ,
σ CD ( t ) ≈ ∑ i = 1 3 A i sin ( 2 π f i t + ϕ i )
f s ( t ) = f ( t + σ ( t ) ) .
f s ( t ) = ∑ n = 0 ∞ 1 n ! ∂ n f ∂ t n σ n ( t ) .
f ^ s ( ω ) = ∑ n = 0 ∞ 1 n ! ℱ t [ ∂ n f ∂ t n σ n ] ( ω ) .
f ^ s ( ω ) = ∑ n = 0 ∞ 1 ( 2 π ) n n ! { ℱ t [ ∂ n f ∂ t n ] * ℱ t [ σ ] * n } ( ω )
= ∑ n = 0 ∞ 1 ( 2 π ) n n ! ( ( i ω ) n f ^ ( ω ) ) * σ ^ * n ( ω )
σ ( t ) = A cos ( v t + ϕ )
σ ^ ( ω ) = A π [ e i ϕ δ ( ω − ν ) + e − i ϕ δ ( ω + ν ) ] .
σ ^ * n ( ω ) = ( A π ) n [ e i ϕ δ ( ω − ν ) + e − i ϕ δ ( ω + ν ) ] * n
= ( A π ) n ∑ k = 0 n ( n k ) e i ( n − 2 k ) ϕ δ ( ω − ( n − 2 k ) ν )
≡ ( A π ) n ∑ k = 0 n ( n k ) e i Φ k n δ ( Ω k n ( ω ) ) .
Ω k n ( ω ) ≡ ω − ( n − 2 k ) ν ,
Φ k n ( ω ) ≡ ( n − 2 k ) ϕ
f ^ s ( ω ) = ∑ n = 0 ∞ ∑ k = 0 n ( n k ) ( A π ) n ( 2 π ) n n ! e i Φ k n ( ( i ω ) n f ^ ( ω ) ) * δ ( Ω k n ( ω ) )
= ∑ n = 0 ∞ ∑ k = 0 n ( i A Ω k n ( ω ) ) n 2 n k ! ( n − k ) ! e i Φ k n f ^ ( Ω k n ( ω ) )
= f ^ ( ω ) + ∑ n = 0 ∞ ∑ k = 0 n ( i A Ω k n ( ω ) ) n 2 n k ! ( n − k ) ! e i Φ k n f ^ ( Ω k n ( ω ) ) .
f ^ s ( ω ) = f ^ ( ω ) + i A 2 e i Φ 0 1 Ω 0 1 f ^ ( Ω 0 1 ) + i A 2 e i Φ 1 1 Ω 1 1 f ^ ( Ω 1 1 )
= f ^ ( ω ) + i A 2 [ e i ϕ ( ω − ν ) f ^ ( ω − ν ) + e − i ϕ ( ω + ν ) f ^ ( ω + ν ) ] .
H s ( ω ) = f ^ s samp ( ω ) f ^ s ref ( ω ) = f ^ samp ( ω ) + ∑ ( f ^ samp , ω , ν , ϕ ) f ^ ref ( ω ) + ∑ ( f ^ ref , ω , ν , ϕ ) .
f ( t ) ∝ t 2 π τ 2 exp ( − t 2 2 τ 2 )
f ^ ( ω ) ∝ − i ω τ 2 exp ( − 1 2 τ 2 ω 2 ) .
| f ( ω ) | 2 = | i A 2 exp ( i ϕ ) ⋅ ( ω − ν ) ⋅ f ( ω − ν ) | 2
⇒ ( 22 ) ω = A 2 ⋅ ( ω − ν ) 2 ⋅ exp ( ω ν τ 2 ) exp ( − 1 2 ν 2 τ 2 )
⇒ 2 A exp ( 1 2 ν 2 τ 2 ) ≡ C = ( ω − ν ) 2 ω exp ( ω ν τ 2 )
( ω − ν ) 2 ω ≈ ω 2 ν
⇒ ω ≈ − 1 ν τ 2 W n ( − ν 3 τ 2 C )
( ω − ν ) 2 ω ≈ ω
⇒ ω ≈ − 1 ν τ 2 W n ( C ν τ 2 )
| Δ n max | ≈ 0.003 for ν / ( 2 π ) ∈ [ 0 THz , 3 THz ] , ω / ( 2 π ) ∈ [ 0.25 THz , 3 THz ] .

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