Abstract

THz time-domain spectrometry (TDS) probes the complex polarization response of materials. Various analytical procedures are applied by many to extract the associated material optical constants. This has commonly been done by iteratively varying material parameters in order to achieve a match between experiment and a theoretical transfer function (TF). The poly root behavior of a TF is emphasized for measurements with reflections in the time domain. This study provides a comprehensive analysis of the influence of the initial guesses on the accuracy of extracted material parameters. In addition, various ways of representing multiple reflections inside the sample (a Fabry–Perot-like effect) are compared and their contribution to the uncertainty of material parameters is analyzed. Experimental evidence is provided where appropriate to support theoretical statements. Furthermore, this paper offers a basis for data comparison between different THz-TDS systems in transmission mode. Finally, a clear distinction is made between a commonly used basic analysis and an enhanced one, in terms of associated uncertainties in determination of the real and imaginary parts of the complex refractive index.

© 2013 Optical Society of America

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References

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  1. D. H. Auston, “Picosecond optoelectronic switching and gating in silicon,” Appl. Phys. Lett. 26, 101–103 (1975).
    [CrossRef]
  2. D. H. Auston and P. R. Smith, “Generation and detection of millimeter waves by picosecond photoconductivity,” Appl. Phys. Lett. 43, 631–633 (1983).
    [CrossRef]
  3. K. P. Cheung and D. H. Auston, “A novel technique for measuring far-infrared absorption and dispersion,” Infrared Phys. 26, 23–27 (1986).
    [CrossRef]
  4. D. Grischkowsky, S. Keiding, M. V. Exter, and C. Fattinger, “Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors,” J. Opt. Soc. Am. B 7, 2006–2015 (1990).
    [CrossRef]
  5. J. B. Baxter and G. W. Guglietta, “Terahertz spectroscopy,” Anal. Chem. 83, 4342–4368 (2011).
    [CrossRef]
  6. J. Dai, J. Zhang, W. Zhang, and D. Grischkowsky, “Terahertz time-domain spectroscopy characterization of the far-infrared absorption and index of refraction of high-resistivity, float-zone silicon,” J. Opt. Soc. Am. B 21, 1379–1386 (2004).
    [CrossRef]
  7. J. A. Zeitler, P. F. Taday, D. A. Newnham, M. Pepper, K. C. Gordon, and T. Rades, “Terahertz pulsed spectroscopy and imaging in the pharmaceutical setting—a review,” J. Pharm. Pharmacol. 59, 209–223 (2007).
    [CrossRef]
  8. B. Jin, C. Zhang, P. Wu, and S. Liu, “Recent progress of terahertz spectroscopy on medicine and biology in China,” Terahertz Sci. Tech. 3, 192–200 (2010).
  9. A. G. Markelz, “Terahertz dielectric sensitivity to biomolecular structure and function,” IEEE J. Sel. Top. Quantum Electron. 14, 180–190 (2008).
    [CrossRef]
  10. E. Castro-Camus and M. B. Johnston, “Conformational changes of photoactive yellow protein monitored by terahertz spectroscopy,” Chem. Phys. Lett. 455, 289–292 (2008).
    [CrossRef]
  11. I. Pupeza, R. Wilk, and M. Koch, “Highly accurate optical material parameter determination with THz time-domain spectroscopy,” Opt. Express 15, 4335–4350 (2007).
    [CrossRef]
  12. W. Withayachumnankul, B. M. Fischer, H. Lin, and D. Abbott, “Uncertainty in terahertz time-domain spectroscopy measurement,” J. Opt. Soc. Am. B 25, 1059–1072 (2008).
    [CrossRef]
  13. P. U. Jepsen and B. Fischer, “Dynamic range in terahertz time-domain transmission and reflection spectroscopy,” Opt. Lett. 30, 29–31 (2005).
    [CrossRef]
  14. M. Naftaly and R. E. Miles, “Terahertz time-domain spectroscopy for material characterization,” Proc. IEEE 95, 1658–1665 (2007).
    [CrossRef]
  15. W. X. Xie, J. Li, and J. H. Pei, “THz-TDS signal analysis and substance identification via the conformal split,” Sci. China Inf. Sci. 55, 49–63 (2012).
    [CrossRef]
  16. T. D. Dorney, R. G. Baraniuk, and D. M. Mittleman, “Material parameter estimation with terahertz time-domain spectroscopy,” J. Opt. Soc. Am. A 18, 1562–1571 (2001).
    [CrossRef]
  17. M. Krüger, S. Funkner, E. Bründermann, and M. Havenith, “Uncertainty and ambiguity in terahertz parameter extraction and data analysis,” Int. J. Infrared Millim. Waves 32, 699–715 (2011).
    [CrossRef]
  18. M. Naftaly and R. E. Miles, “A method for removing etalon oscillations from THz time-domain spectra,” Opt. Commun. 280, 291–295 (2007).
    [CrossRef]
  19. L. Duvillaret, F. Garet, and J. L. Coutaz, “A reliable method for extraction of material parameters in terahertz time-domain spectroscopy,” IEEE J. Sel. Top. Quantum Electron. 2, 739–746 (1996).
    [CrossRef]
  20. M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).
  21. 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, 409–415 (1999).
    [CrossRef]
  22. W. Withayachumnankul, B. Ferguson, T. Rainsford, S. P. Mickan, and D. Abbott, “Simple material parameter estimation via terahertz time-domain spectroscopy,” Electron. Lett. 41, 800–801 (2005).
    [CrossRef]
  23. L. Duvillaret, F. Garet, and J.-L. Coutaz, “Influence of noise on the characterization of materials by terahertz time-domain spectroscopy,” J. Opt. Soc. Am. B 17, 452–461 (2000).
    [CrossRef]
  24. W. Withayachumnankul, H. Lin, S. P. Mickan, B. M. Fischer, and D. Abbott, “Analysis of measurement uncertainty in THz-TDS,” Proc. SPIE 6593, 659326 (2007).
    [CrossRef]

2012

W. X. Xie, J. Li, and J. H. Pei, “THz-TDS signal analysis and substance identification via the conformal split,” Sci. China Inf. Sci. 55, 49–63 (2012).
[CrossRef]

2011

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

J. B. Baxter and G. W. Guglietta, “Terahertz spectroscopy,” Anal. Chem. 83, 4342–4368 (2011).
[CrossRef]

2010

B. Jin, C. Zhang, P. Wu, and S. Liu, “Recent progress of terahertz spectroscopy on medicine and biology in China,” Terahertz Sci. Tech. 3, 192–200 (2010).

2008

A. G. Markelz, “Terahertz dielectric sensitivity to biomolecular structure and function,” IEEE J. Sel. Top. Quantum Electron. 14, 180–190 (2008).
[CrossRef]

E. Castro-Camus and M. B. Johnston, “Conformational changes of photoactive yellow protein monitored by terahertz spectroscopy,” Chem. Phys. Lett. 455, 289–292 (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, 1059–1072 (2008).
[CrossRef]

2007

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

M. Naftaly and R. E. Miles, “Terahertz time-domain spectroscopy for material characterization,” Proc. IEEE 95, 1658–1665 (2007).
[CrossRef]

J. A. Zeitler, P. F. Taday, D. A. Newnham, M. Pepper, K. C. Gordon, and T. Rades, “Terahertz pulsed spectroscopy and imaging in the pharmaceutical setting—a review,” J. Pharm. Pharmacol. 59, 209–223 (2007).
[CrossRef]

M. Naftaly and R. E. Miles, “A method for removing etalon oscillations from THz time-domain spectra,” Opt. Commun. 280, 291–295 (2007).
[CrossRef]

W. Withayachumnankul, H. Lin, S. P. Mickan, B. M. Fischer, and D. Abbott, “Analysis of measurement uncertainty in THz-TDS,” Proc. SPIE 6593, 659326 (2007).
[CrossRef]

2005

W. Withayachumnankul, B. Ferguson, T. Rainsford, S. P. Mickan, and D. Abbott, “Simple material parameter estimation via terahertz time-domain spectroscopy,” Electron. Lett. 41, 800–801 (2005).
[CrossRef]

P. U. Jepsen and B. Fischer, “Dynamic range in terahertz time-domain transmission and reflection spectroscopy,” Opt. Lett. 30, 29–31 (2005).
[CrossRef]

2004

2001

2000

1999

1996

L. Duvillaret, F. Garet, and J. L. Coutaz, “A reliable method for extraction of material parameters in terahertz time-domain spectroscopy,” IEEE J. Sel. Top. Quantum Electron. 2, 739–746 (1996).
[CrossRef]

1990

1986

K. P. Cheung and D. H. Auston, “A novel technique for measuring far-infrared absorption and dispersion,” Infrared Phys. 26, 23–27 (1986).
[CrossRef]

1983

D. H. Auston and P. R. Smith, “Generation and detection of millimeter waves by picosecond photoconductivity,” Appl. Phys. Lett. 43, 631–633 (1983).
[CrossRef]

1975

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

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, 1059–1072 (2008).
[CrossRef]

W. Withayachumnankul, H. Lin, S. P. Mickan, B. M. Fischer, and D. Abbott, “Analysis of measurement uncertainty in THz-TDS,” Proc. SPIE 6593, 659326 (2007).
[CrossRef]

W. Withayachumnankul, B. Ferguson, T. Rainsford, S. P. Mickan, and D. Abbott, “Simple material parameter estimation via terahertz time-domain spectroscopy,” Electron. Lett. 41, 800–801 (2005).
[CrossRef]

Auston, D. H.

K. P. Cheung and D. H. Auston, “A novel technique for measuring far-infrared absorption and dispersion,” Infrared Phys. 26, 23–27 (1986).
[CrossRef]

D. H. Auston and P. R. Smith, “Generation and detection of millimeter waves by picosecond photoconductivity,” Appl. Phys. Lett. 43, 631–633 (1983).
[CrossRef]

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

Baraniuk, R. G.

Baxter, J. B.

J. B. Baxter and G. W. Guglietta, “Terahertz spectroscopy,” Anal. Chem. 83, 4342–4368 (2011).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).

Bründermann, E.

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

Castro-Camus, E.

E. Castro-Camus and M. B. Johnston, “Conformational changes of photoactive yellow protein monitored by terahertz spectroscopy,” Chem. Phys. Lett. 455, 289–292 (2008).
[CrossRef]

Cheung, K. P.

K. P. Cheung and D. H. Auston, “A novel technique for measuring far-infrared absorption and dispersion,” Infrared Phys. 26, 23–27 (1986).
[CrossRef]

Coutaz, J. L.

L. Duvillaret, F. Garet, and J. L. Coutaz, “A reliable method for extraction of material parameters in terahertz time-domain spectroscopy,” IEEE J. Sel. Top. Quantum Electron. 2, 739–746 (1996).
[CrossRef]

Coutaz, J.-L.

Dai, J.

Dorney, T. D.

Duvillaret, L.

Exter, M. V.

Fattinger, C.

Ferguson, B.

W. Withayachumnankul, B. Ferguson, T. Rainsford, S. P. Mickan, and D. Abbott, “Simple material parameter estimation via terahertz time-domain spectroscopy,” Electron. Lett. 41, 800–801 (2005).
[CrossRef]

Fischer, B.

Fischer, B. M.

W. Withayachumnankul, B. M. Fischer, H. Lin, and D. Abbott, “Uncertainty in terahertz time-domain spectroscopy measurement,” J. Opt. Soc. Am. B 25, 1059–1072 (2008).
[CrossRef]

W. Withayachumnankul, H. Lin, S. P. Mickan, B. M. Fischer, and D. Abbott, “Analysis of measurement uncertainty in THz-TDS,” Proc. SPIE 6593, 659326 (2007).
[CrossRef]

Funkner, S.

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

Garet, F.

Gordon, K. C.

J. A. Zeitler, P. F. Taday, D. A. Newnham, M. Pepper, K. C. Gordon, and T. Rades, “Terahertz pulsed spectroscopy and imaging in the pharmaceutical setting—a review,” J. Pharm. Pharmacol. 59, 209–223 (2007).
[CrossRef]

Grischkowsky, D.

Guglietta, G. W.

J. B. Baxter and G. W. Guglietta, “Terahertz spectroscopy,” Anal. Chem. 83, 4342–4368 (2011).
[CrossRef]

Havenith, M.

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

Jepsen, P. U.

Jin, B.

B. Jin, C. Zhang, P. Wu, and S. Liu, “Recent progress of terahertz spectroscopy on medicine and biology in China,” Terahertz Sci. Tech. 3, 192–200 (2010).

Johnston, M. B.

E. Castro-Camus and M. B. Johnston, “Conformational changes of photoactive yellow protein monitored by terahertz spectroscopy,” Chem. Phys. Lett. 455, 289–292 (2008).
[CrossRef]

Keiding, S.

Koch, M.

Krüger, M.

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

Li, J.

W. X. Xie, J. Li, and J. H. Pei, “THz-TDS signal analysis and substance identification via the conformal split,” Sci. China Inf. Sci. 55, 49–63 (2012).
[CrossRef]

Lin, H.

W. Withayachumnankul, B. M. Fischer, H. Lin, and D. Abbott, “Uncertainty in terahertz time-domain spectroscopy measurement,” J. Opt. Soc. Am. B 25, 1059–1072 (2008).
[CrossRef]

W. Withayachumnankul, H. Lin, S. P. Mickan, B. M. Fischer, and D. Abbott, “Analysis of measurement uncertainty in THz-TDS,” Proc. SPIE 6593, 659326 (2007).
[CrossRef]

Liu, S.

B. Jin, C. Zhang, P. Wu, and S. Liu, “Recent progress of terahertz spectroscopy on medicine and biology in China,” Terahertz Sci. Tech. 3, 192–200 (2010).

Markelz, A. G.

A. G. Markelz, “Terahertz dielectric sensitivity to biomolecular structure and function,” IEEE J. Sel. Top. Quantum Electron. 14, 180–190 (2008).
[CrossRef]

Mickan, S. P.

W. Withayachumnankul, H. Lin, S. P. Mickan, B. M. Fischer, and D. Abbott, “Analysis of measurement uncertainty in THz-TDS,” Proc. SPIE 6593, 659326 (2007).
[CrossRef]

W. Withayachumnankul, B. Ferguson, T. Rainsford, S. P. Mickan, and D. Abbott, “Simple material parameter estimation via terahertz time-domain spectroscopy,” Electron. Lett. 41, 800–801 (2005).
[CrossRef]

Miles, R. E.

M. Naftaly and R. E. Miles, “Terahertz time-domain spectroscopy for material characterization,” Proc. IEEE 95, 1658–1665 (2007).
[CrossRef]

M. Naftaly and R. E. Miles, “A method for removing etalon oscillations from THz time-domain spectra,” Opt. Commun. 280, 291–295 (2007).
[CrossRef]

Mittleman, D. M.

Naftaly, M.

M. Naftaly and R. E. Miles, “Terahertz time-domain spectroscopy for material characterization,” Proc. IEEE 95, 1658–1665 (2007).
[CrossRef]

M. Naftaly and R. E. Miles, “A method for removing etalon oscillations from THz time-domain spectra,” Opt. Commun. 280, 291–295 (2007).
[CrossRef]

Newnham, D. A.

J. A. Zeitler, P. F. Taday, D. A. Newnham, M. Pepper, K. C. Gordon, and T. Rades, “Terahertz pulsed spectroscopy and imaging in the pharmaceutical setting—a review,” J. Pharm. Pharmacol. 59, 209–223 (2007).
[CrossRef]

Pei, J. H.

W. X. Xie, J. Li, and J. H. Pei, “THz-TDS signal analysis and substance identification via the conformal split,” Sci. China Inf. Sci. 55, 49–63 (2012).
[CrossRef]

Pepper, M.

J. A. Zeitler, P. F. Taday, D. A. Newnham, M. Pepper, K. C. Gordon, and T. Rades, “Terahertz pulsed spectroscopy and imaging in the pharmaceutical setting—a review,” J. Pharm. Pharmacol. 59, 209–223 (2007).
[CrossRef]

Pupeza, I.

Rades, T.

J. A. Zeitler, P. F. Taday, D. A. Newnham, M. Pepper, K. C. Gordon, and T. Rades, “Terahertz pulsed spectroscopy and imaging in the pharmaceutical setting—a review,” J. Pharm. Pharmacol. 59, 209–223 (2007).
[CrossRef]

Rainsford, T.

W. Withayachumnankul, B. Ferguson, T. Rainsford, S. P. Mickan, and D. Abbott, “Simple material parameter estimation via terahertz time-domain spectroscopy,” Electron. Lett. 41, 800–801 (2005).
[CrossRef]

Smith, P. R.

D. H. Auston and P. R. Smith, “Generation and detection of millimeter waves by picosecond photoconductivity,” Appl. Phys. Lett. 43, 631–633 (1983).
[CrossRef]

Taday, P. F.

J. A. Zeitler, P. F. Taday, D. A. Newnham, M. Pepper, K. C. Gordon, and T. Rades, “Terahertz pulsed spectroscopy and imaging in the pharmaceutical setting—a review,” J. Pharm. Pharmacol. 59, 209–223 (2007).
[CrossRef]

Wilk, R.

Withayachumnankul, W.

W. Withayachumnankul, B. M. Fischer, H. Lin, and D. Abbott, “Uncertainty in terahertz time-domain spectroscopy measurement,” J. Opt. Soc. Am. B 25, 1059–1072 (2008).
[CrossRef]

W. Withayachumnankul, H. Lin, S. P. Mickan, B. M. Fischer, and D. Abbott, “Analysis of measurement uncertainty in THz-TDS,” Proc. SPIE 6593, 659326 (2007).
[CrossRef]

W. Withayachumnankul, B. Ferguson, T. Rainsford, S. P. Mickan, and D. Abbott, “Simple material parameter estimation via terahertz time-domain spectroscopy,” Electron. Lett. 41, 800–801 (2005).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).

Wu, P.

B. Jin, C. Zhang, P. Wu, and S. Liu, “Recent progress of terahertz spectroscopy on medicine and biology in China,” Terahertz Sci. Tech. 3, 192–200 (2010).

Xie, W. X.

W. X. Xie, J. Li, and J. H. Pei, “THz-TDS signal analysis and substance identification via the conformal split,” Sci. China Inf. Sci. 55, 49–63 (2012).
[CrossRef]

Zeitler, J. A.

J. A. Zeitler, P. F. Taday, D. A. Newnham, M. Pepper, K. C. Gordon, and T. Rades, “Terahertz pulsed spectroscopy and imaging in the pharmaceutical setting—a review,” J. Pharm. Pharmacol. 59, 209–223 (2007).
[CrossRef]

Zhang, C.

B. Jin, C. Zhang, P. Wu, and S. Liu, “Recent progress of terahertz spectroscopy on medicine and biology in China,” Terahertz Sci. Tech. 3, 192–200 (2010).

Zhang, J.

Zhang, W.

Anal. Chem.

J. B. Baxter and G. W. Guglietta, “Terahertz spectroscopy,” Anal. Chem. 83, 4342–4368 (2011).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

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

D. H. Auston and P. R. Smith, “Generation and detection of millimeter waves by picosecond photoconductivity,” Appl. Phys. Lett. 43, 631–633 (1983).
[CrossRef]

Chem. Phys. Lett.

E. Castro-Camus and M. B. Johnston, “Conformational changes of photoactive yellow protein monitored by terahertz spectroscopy,” Chem. Phys. Lett. 455, 289–292 (2008).
[CrossRef]

Electron. Lett.

W. Withayachumnankul, B. Ferguson, T. Rainsford, S. P. Mickan, and D. Abbott, “Simple material parameter estimation via terahertz time-domain spectroscopy,” Electron. Lett. 41, 800–801 (2005).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

L. Duvillaret, F. Garet, and J. L. Coutaz, “A reliable method for extraction of material parameters in terahertz time-domain spectroscopy,” IEEE J. Sel. Top. Quantum Electron. 2, 739–746 (1996).
[CrossRef]

A. G. Markelz, “Terahertz dielectric sensitivity to biomolecular structure and function,” IEEE J. Sel. Top. Quantum Electron. 14, 180–190 (2008).
[CrossRef]

Infrared Phys.

K. P. Cheung and D. H. Auston, “A novel technique for measuring far-infrared absorption and dispersion,” Infrared Phys. 26, 23–27 (1986).
[CrossRef]

Int. J. Infrared Millim. Waves

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

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

J. Pharm. Pharmacol.

J. A. Zeitler, P. F. Taday, D. A. Newnham, M. Pepper, K. C. Gordon, and T. Rades, “Terahertz pulsed spectroscopy and imaging in the pharmaceutical setting—a review,” J. Pharm. Pharmacol. 59, 209–223 (2007).
[CrossRef]

Opt. Commun.

M. Naftaly and R. E. Miles, “A method for removing etalon oscillations from THz time-domain spectra,” Opt. Commun. 280, 291–295 (2007).
[CrossRef]

Opt. Express

Opt. Lett.

Proc. IEEE

M. Naftaly and R. E. Miles, “Terahertz time-domain spectroscopy for material characterization,” Proc. IEEE 95, 1658–1665 (2007).
[CrossRef]

Proc. SPIE

W. Withayachumnankul, H. Lin, S. P. Mickan, B. M. Fischer, and D. Abbott, “Analysis of measurement uncertainty in THz-TDS,” Proc. SPIE 6593, 659326 (2007).
[CrossRef]

Sci. China Inf. Sci.

W. X. Xie, J. Li, and J. H. Pei, “THz-TDS signal analysis and substance identification via the conformal split,” Sci. China Inf. Sci. 55, 49–63 (2012).
[CrossRef]

Terahertz Sci. Tech.

B. Jin, C. Zhang, P. Wu, and S. Liu, “Recent progress of terahertz spectroscopy on medicine and biology in China,” Terahertz Sci. Tech. 3, 192–200 (2010).

Other

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).

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Figures (10)

Fig. 1.
Fig. 1.

Refractive index calculation for a 3 mm thick z-cut quartz sample. The graph shows estimation of n(ν) using the simple TF [Eq. (2)] and the more rigorous TF [Eq. (5)]. The initial guess for estimating n(ν) by Eq. (5) is shown as an intermediate straight line.

Fig. 2.
Fig. 2.

Possible values of n(ν) are shown (gray circles) for a 3 mm thick sample of z-cut quartz when real and imaginary parts of HTheory(ν) and HExp(ν) are, respectively equated. Both traces were generated at 1 THz.

Fig. 3.
Fig. 3.

For a 3 mm thick z-cut sample of quartz: dependence of the OF modulus (oscillatory trace) (scaled by 50 times for clarity) and unwrapped phase (straight line) of refractive index. Both traces were generated at 1 THz.

Fig. 4.
Fig. 4.

(a) Shows estimates of n(ν) for LiNbO3 using (1) the basic approach [Eq. (2)], (2) the more rigorous approach of Eq. (5) that accounts for multiple internal reflections, the black trace by equating modulus and argument between theory and experiment and the light gray, by equating real and imaginary parts, and (3) the gray dotted trace shows the initial guess used during the rigorous approach. A lithium niobate sample of 0.5 mm thickness was used for these measurements. (b) Shows the same but for k(ν).

Fig. 5.
Fig. 5.

TD response of the reference path (black trace) and the path when filled with a 1 mm thick plate of silicon plate (gray trace). Silicon values are offset by +0.025 for clarity. Measurements were done under normal conditions of atmosphere and temperature. Two internal reflections are circled.

Fig. 6.
Fig. 6.

Additional errors in estimation of n(ν) resulting from the analysis procedure of Eq. (12) when the sample response contains (1) no ringing (dark gray), (2) one reflection (gray), and (3) two internal reflections (light gray). The black solid-curve represents uncertainty in the refractive index when Eq. (5) is used for analysis.

Fig. 7.
Fig. 7.

Additional errors in estimation of k(ν) resulting from the analysis procedure of Eq. (12) when the sample response contains (1) no ringing (dark gray curve), (2) one reflection (gray), and (3) two internal reflections (light gray). The black solid-curve represents uncertainty in the refractive index when Eq. (5) is used for analysis.

Fig. 8.
Fig. 8.

(a) Shows the contribution of each error part to the total uncertainty in n(ν) for the simplified extraction procedure. (b) Shows the same for k(ν).

Fig. 9.
Fig. 9.

(a) Shows the contribution of each error term to the total uncertainty in n(ν) for the advanced extraction procedure. (b) Shows the same for k(ν).

Fig. 10.
Fig. 10.

This graph shows the total uncertainty in n(ν) for general [Fig. 8(a)] and enhanced [Fig. 9(a)] analyses. The same applies for k(ν) [Figs. 8(b) and 9(b), respectively]. The black heavy curve shows values of k(ν) for comparison purposes.

Tables (1)

Tables Icon

Table 1. Use of Error Terms

Equations (20)

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

HExp(ν)=Esample(ν)Ereference(ν).
H(ν)=t12(ν)t21(ν)exp(i2πνd(n˜(ν)nair)c),
n(ν)=1+c2πνd(φsampleφreference),
k(ν)=c2πνdln[EsampleEreference(1+n)24n].
HTheory(ν)=t12(ν)t21(ν)exp(i2πνd(n˜(ν)nair)c)·l=0m[r2(ν)exp(i4dπνn˜(ν)c)]l,
Tosc=cνd.
nactual±Tosc/2.
n=nair+cΔt/d
k=c2πνdln(|Esample,max||Ereference,max|(1+n)24n).
A(ν)=exp(i2πνn˜(ν)dc).
FP(ν)={1+r2(ν)A2(ν)+r4(ν)A4(ν)+}=i=0[r2(ν)A2(ν)]i=[1r2(ν)A2(ν)]1.
FP0(ν)=i=0m[r2(ν)A2(ν)]i,
HApprox.(ν)=t12(ν)t21(ν)exp(i2πνd(n˜(ν)nair)c)1r2(ν)exp(i4dπνn˜(ν)c).
fn(ν)=c2πνd|farg(ν)|
fk(ν)=c2πνd[|fmod(ν)|+1n(ν)n(ν)nairn(ν)+nair|fn(ν)|],
farg(ν)=arg(Happrox(ν))arg(Hexact(ν))
fmod(ν)=ln|Happrox(ν)|ln|Hexact(ν)|.
un,k(ν)=sn,k_samp2+sn,k_ref2,
un,k(ν)=sn,k_samp2Nsamp+sn,k_ref2Nref,
un,k(ν)=sn,k2Nmeas1+(sn,kd2Nd2+sn,kδ22a)+fn,kTFA3+fn,k_align4+fn,k_n05+fn,k_FP6+fn,k_FPE7.

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