## Hybrid continuous wave terahertz spectroscopy |

Optics Express, Vol. 18, Issue 15, pp. 15887-15892 (2010)

http://dx.doi.org/10.1364/OE.18.015887

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### Abstract

We propose a hybrid architecture for continuous wave terahertz spectroscopy employing a conventional two color photomixing system combined with a quasi time domain spectrometer, driven by a multimode laser diode. This approach fuses high spectral intensity with broadband frequency information and overcomes the ambiguity of standard continuous wave thickness measurements.

© 2010 OSA

## 1. Introduction

13. W. L. Chan, J. Deibel, and D. M. Mittleman, “Imaging with terahertz radiation,” Rep. Prog. Phys. **70**(8), 1325–1379 (2007). [CrossRef]

14. S. Matsuura, M. Tani, and K. Sakai, “Generation of coherent terahertz radiation by photomixing in dipole photoconductive antennas,” Appl. Phys. Lett. **70**(5), 559 (1997). [CrossRef]

16. S. Verghese, K. A. McIntosh, S. Calawa, W. F. Dinatale, E. K. Duerr, and K. A. Molvar, “Generation and detection of coherent terahertz waves using two photomixers,” Appl. Phys. Lett. **73**(26), 3824–3826 (1998). [CrossRef]

17. R. Wilk, F. Breitfeld, M. Mikulics, and M. Koch, “Continuous wave terahertz spectrometer as a noncontact thickness measuring device,” Appl. Opt. **47**(16), 3023–3026 (2008). [CrossRef] [PubMed]

## 2. Theory

16. S. Verghese, K. A. McIntosh, S. Calawa, W. F. Dinatale, E. K. Duerr, and K. A. Molvar, “Generation and detection of coherent terahertz waves using two photomixers,” Appl. Phys. Lett. **73**(26), 3824–3826 (1998). [CrossRef]

*Δf*, the resulting THz signal

*I*is a function of the path length difference between emitter and detector path,

_{D}*ΔX*, and exhibits a sinusoidal like shape:where

*A(Δf)*is the spectral system efficiency,

*P*and

_{1}*P*are the optical powers of the two laser modes and

_{2}*c*is the speed of light.

_{0}18. M. Scheller and M. Koch, “Terahertz quasi time domain spectroscopy,” Opt. Express **17**(20), 17723–17733 (2009). [CrossRef] [PubMed]

*δf*, the resulting THz signal can be described by:Here,

*M*denotes the amount of modes and

*P*the total power of the laser radiation that is assumed to be uniformly spread over the multiple laser modes. Since the THz signal is not a function of the random phase relation between the individual laser modes, the signal exhibit a pulse like shape [18

18. M. Scheller and M. Koch, “Terahertz quasi time domain spectroscopy,” Opt. Express **17**(20), 17723–17733 (2009). [CrossRef] [PubMed]

18. M. Scheller and M. Koch, “Terahertz quasi time domain spectroscopy,” Opt. Express **17**(20), 17723–17733 (2009). [CrossRef] [PubMed]

21. E. R. Brown, F. W. Smith, and K. A. McIntosh, “Coherent millimeter-wave generation by heterodyne conversion in low-temperature-grown GaAs photoconductors,” J. Appl. Phys. **73**(3), 1480–1484 (1993). [CrossRef]

*τ*as the carrier lifetime in the range of 100 fs [22

22. N. Vieweg, M. Mikulics, M. Scheller, K. Ezdi, R. Wilk, H. W. Hübers, and M. Koch, “Impact of the contact metallization on the performance of photoconductive THz antennas,” Opt. Express **16**(24), 19695–19705 (2008). [CrossRef] [PubMed]

_{0}as resonance frequency.

## 3. Measurements and results

23. A. J. Deninger, T. Göbel, D. Schönherr, T. Kinder, A. Roggenbuck, M. Köberle, F. Lison, T. Müller-Wirts, and P. Meissner, “Precisely tunable continuous-wave terahertz source with interferometric frequency control,” Rev. Sci. Instrum. **79**(4), 044702 (2008). [CrossRef] [PubMed]

23. A. J. Deninger, T. Göbel, D. Schönherr, T. Kinder, A. Roggenbuck, M. Köberle, F. Lison, T. Müller-Wirts, and P. Meissner, “Precisely tunable continuous-wave terahertz source with interferometric frequency control,” Rev. Sci. Instrum. **79**(4), 044702 (2008). [CrossRef] [PubMed]

*Δt*between the sample and the reference measurement. Then we obtain the phase difference

_{p}*Δφ*at the frequency

_{cw}*f*of the cw component with a Fourier transformation of the detected THz signal. Latter one is affected by the 2π ambiguity in the case of thicker samples. The corrected phase shift

_{cw}*Δφ*can then be calculated by:where the operation

_{cw,cor}*RD*denotes for round down to the nearest integer of the argument. Since

*Δφ*is the absolute phase shift induced by the sample, the absolute sample thickness

_{cw,cor}*T*can be identified knowing its index of refraction n at the frequency

*f*:Considering the corresponding refractive indices of the materials, the thicknesses of the investigated samples were determined from the measurements using EqS. (5-6) to be 6.25 mm (glass) and 550 µm (Si) which agrees with the values obtained by micrometer screw measurements.

_{cw}*Δφ*as illustrated in Fig. 4(c). A linear interpolation trough the discrete phase values of the QTDS signal and the intersection at (

_{cw,cor}*f = 0, Δφ = 0*) allows for correcting the 2π ambiguity at the cw frequency component in the case of low dispersive samples. Here, the integer

*N*is determined so that the value of

*Δφ*is closest to the linear interpolation trough the QTDS components.

_{cw,cor}= Δφ_{cw}- 2π N## 4. Conclusion

## References and links

1. | K. Fukunaga, Y. Ogawa, S. Hayashi, and I. Hosako, “Terahertz spectroscopy for art conservation,” IEICE Electron. Express |

2. | J. B. Jackson, M. Mourou, J. F. Whitaker, I. N. Duling III, S. L. Williamson, M. Menu, and G. A. Mourou, “Terahertz imaging for non-destructive evaluation of mural paintings,” Opt. Commun. |

3. | K. Fukunaga, N. Sekine, I. Hosako, N. Oda, H. Yoneyama, and T. Sudoh, “Real-time terahertz imaging for art conservation science,” J. Eur. Opt. Soc. Rapid Publ. |

4. | K. Yamamoto, M. Yamaguchi, M. Tani, M. Hangyo, S. Teramura, T. Isu, and N. Tomita, “Degradation diagnosis of ultrahigh-molecular weight polyethylene with terahertz-time-domain spectroscopy,” Appl. Phys. Lett. |

5. | C. D. Stoik, M. J. Bohn, and J. L. Blackshire, “Nondestructive evaluation of aircraft composites using transmissive terahertz time domain spectroscopy,” Opt. Express |

6. | N. Krumbholz, T. Hochrein, N. Vieweg, T. Hasek, K. Kretschmer, M. Bastian, M. Mikulics, and M. Koch, “Monitoring polymeric compounding processes in line with THz time-domain spectroscopy,” Polym. Test. |

7. | M. Nagai, H. Yada, T. Arikawa, and K. Tanaka, “Terahertz time-domain attenuated total reflection spectroscopy in water and biological solution,” Int. J. Infrared Millim. Waves |

8. | C. Jördens, M. Scheller, B. Breitenstein, D. Selmar, and M. Koch, “Evaluation of leaf water status by means of permittivity at terahertz frequencies,” J. Biol. Phys. |

9. | M. Walther, B. M. Fischer, A. Ortner, A. Bitzer, A. Thoman, and H. Helm, “Chemical sensing and imaging with pulsed terahertz radiation,” Anal. Bioanal. Chem. |

10. | E. Knoesel, M. Bonn, J. Shan, and T. F. Heinz, “Charge transport and carrier dynamics in liquids probed by THz time-domain spectroscopy,” Phys. Rev. Lett. |

11. | G. Segschneider, F. Jacob, T. Löffler, H. G. Roskos, S. Tautz, P. Kiesel, and G. Döhler, “Free-carrier dynamics in low-temperature-grown GaAs at high excitation densities investigated by time-domain terahertz spectroscopy,” Phys. Rev. B |

12. | H. B. Liu, G. Plopper, S. Earley, Y.-J. Chen, B. S. Ferguson, and X. C. Zhang, “Sensing minute changes in biological cell monolayers with THz differential time-domain spectroscopy,” Biosens. Bioelectron. |

13. | W. L. Chan, J. Deibel, and D. M. Mittleman, “Imaging with terahertz radiation,” Rep. Prog. Phys. |

14. | S. Matsuura, M. Tani, and K. Sakai, “Generation of coherent terahertz radiation by photomixing in dipole photoconductive antennas,” Appl. Phys. Lett. |

15. | K. J. Siebert, H. Quast, R. Leonhardt, T. Löffler, M. Thomson, T. Bauer, H. G. Roskos, and S. Czasch, “Continuous-wave all-optoelectronic terahertz imaging,” Appl. Phys. Lett. |

16. | S. Verghese, K. A. McIntosh, S. Calawa, W. F. Dinatale, E. K. Duerr, and K. A. Molvar, “Generation and detection of coherent terahertz waves using two photomixers,” Appl. Phys. Lett. |

17. | R. Wilk, F. Breitfeld, M. Mikulics, and M. Koch, “Continuous wave terahertz spectrometer as a noncontact thickness measuring device,” Appl. Opt. |

18. | M. Scheller and M. Koch, “Terahertz quasi time domain spectroscopy,” Opt. Express |

19. | T. Yasui, T. Yasuda, K. Sawanaka, and T. Araki, “Terahertz paintmeter for noncontact monitoring of thickness and drying progress in paint film,” Appl. Opt. |

20. | M. Scheller and M. Koch, “Fast and accurate thickness determination of unknown materials using terahertz time domain spectroscopy,” J. Infrared, Millim, Terahertz Waves |

21. | E. R. Brown, F. W. Smith, and K. A. McIntosh, “Coherent millimeter-wave generation by heterodyne conversion in low-temperature-grown GaAs photoconductors,” J. Appl. Phys. |

22. | N. Vieweg, M. Mikulics, M. Scheller, K. Ezdi, R. Wilk, H. W. Hübers, and M. Koch, “Impact of the contact metallization on the performance of photoconductive THz antennas,” Opt. Express |

23. | A. J. Deninger, T. Göbel, D. Schönherr, T. Kinder, A. Roggenbuck, M. Köberle, F. Lison, T. Müller-Wirts, and P. Meissner, “Precisely tunable continuous-wave terahertz source with interferometric frequency control,” Rev. Sci. Instrum. |

**OCIS Codes**

(120.3180) Instrumentation, measurement, and metrology : Interferometry

(150.3045) Machine vision : Industrial optical metrology

(300.6495) Spectroscopy : Spectroscopy, teraherz

**ToC Category:**

Spectroscopy

**History**

Original Manuscript: May 27, 2010

Revised Manuscript: July 2, 2010

Manuscript Accepted: July 2, 2010

Published: July 12, 2010

**Citation**

Maik Scheller, Matthias Stecher, Marina Gerhard, and Martin Koch, "Hybrid continuous wave terahertz spectroscopy," Opt. Express **18**, 15887-15892 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-15-15887

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### References

- K. Fukunaga, Y. Ogawa, S. Hayashi, and I. Hosako, “Terahertz spectroscopy for art conservation,” IEICE Electron. Express 4(8), 258–263 (2007). [CrossRef]
- J. B. Jackson, M. Mourou, J. F. Whitaker, I. N. Duling, S. L. Williamson, M. Menu, and G. A. Mourou, “Terahertz imaging for non-destructive evaluation of mural paintings,” Opt. Commun. 281(4), 527–532 (2008). [CrossRef]
- K. Fukunaga, N. Sekine, I. Hosako, N. Oda, H. Yoneyama, and T. Sudoh, “Real-time terahertz imaging for art conservation science,” J. Eur. Opt. Soc. Rapid Publ. 3, 08027 (2008). [CrossRef]
- K. Yamamoto, M. Yamaguchi, M. Tani, M. Hangyo, S. Teramura, T. Isu, and N. Tomita, “Degradation diagnosis of ultrahigh-molecular weight polyethylene with terahertz-time-domain spectroscopy,” Appl. Phys. Lett. 85(22), 5194 (2004). [CrossRef]
- C. D. Stoik, M. J. Bohn, and J. L. Blackshire, “Nondestructive evaluation of aircraft composites using transmissive terahertz time domain spectroscopy,” Opt. Express 16(21), 17039–17051 (2008). [CrossRef] [PubMed]
- N. Krumbholz, T. Hochrein, N. Vieweg, T. Hasek, K. Kretschmer, M. Bastian, M. Mikulics, and M. Koch, “Monitoring polymeric compounding processes in line with THz time-domain spectroscopy,” Polym. Test. 28(1), 30–35 (2009). [CrossRef]
- M. Nagai, H. Yada, T. Arikawa, and K. Tanaka, “Terahertz time-domain attenuated total reflection spectroscopy in water and biological solution,” Int. J. Infrared Millim. Waves 27, 1572–9559 (2006).
- C. Jördens, M. Scheller, B. Breitenstein, D. Selmar, and M. Koch, “Evaluation of leaf water status by means of permittivity at terahertz frequencies,” J. Biol. Phys. 35(3), 255–264 (2009). [CrossRef] [PubMed]
- M. Walther, B. M. Fischer, A. Ortner, A. Bitzer, A. Thoman, and H. Helm, “Chemical sensing and imaging with pulsed terahertz radiation,” Anal. Bioanal. Chem. 397(3), 1009–1017 (2010). [CrossRef] [PubMed]
- E. Knoesel, M. Bonn, J. Shan, and T. F. Heinz, “Charge transport and carrier dynamics in liquids probed by THz time-domain spectroscopy,” Phys. Rev. Lett. 86(2), 340–343 (2001). [CrossRef] [PubMed]
- G. Segschneider, F. Jacob, T. Löffler, H. G. Roskos, S. Tautz, P. Kiesel, and G. Döhler, “Free-carrier dynamics in low-temperature-grown GaAs at high excitation densities investigated by time-domain terahertz spectroscopy,” Phys. Rev. B 65(12), 125205 (2002). [CrossRef]
- H. B. Liu, G. Plopper, S. Earley, Y.-J. Chen, B. S. Ferguson, and X. C. Zhang, “Sensing minute changes in biological cell monolayers with THz differential time-domain spectroscopy,” Biosens. Bioelectron. 22(6), 1075–1080 (2007). [CrossRef]
- W. L. Chan, J. Deibel, and D. M. Mittleman, “Imaging with terahertz radiation,” Rep. Prog. Phys. 70(8), 1325–1379 (2007). [CrossRef]
- S. Matsuura, M. Tani, and K. Sakai, “Generation of coherent terahertz radiation by photomixing in dipole photoconductive antennas,” Appl. Phys. Lett. 70(5), 559 (1997). [CrossRef]
- K. J. Siebert, H. Quast, R. Leonhardt, T. Löffler, M. Thomson, T. Bauer, H. G. Roskos, and S. Czasch, “Continuous-wave all-optoelectronic terahertz imaging,” Appl. Phys. Lett. 80(16), 3003–3005 (2002). [CrossRef]
- S. Verghese, K. A. McIntosh, S. Calawa, W. F. Dinatale, E. K. Duerr, and K. A. Molvar, “Generation and detection of coherent terahertz waves using two photomixers,” Appl. Phys. Lett. 73(26), 3824–3826 (1998). [CrossRef]
- R. Wilk, F. Breitfeld, M. Mikulics, and M. Koch, “Continuous wave terahertz spectrometer as a noncontact thickness measuring device,” Appl. Opt. 47(16), 3023–3026 (2008). [CrossRef] [PubMed]
- M. Scheller and M. Koch, “Terahertz quasi time domain spectroscopy,” Opt. Express 17(20), 17723–17733 (2009). [CrossRef] [PubMed]
- T. Yasui, T. Yasuda, K. Sawanaka, and T. Araki, “Terahertz paintmeter for noncontact monitoring of thickness and drying progress in paint film,” Appl. Opt. 44(32), 6849–6856 (2005). [CrossRef] [PubMed]
- M. Scheller and M. Koch, “Fast and accurate thickness determination of unknown materials using terahertz time domain spectroscopy,” J. Infrared, Millim, Terahertz Waves 30(7), 762–769 (2009). [CrossRef]
- E. R. Brown, F. W. Smith, and K. A. McIntosh, “Coherent millimeter-wave generation by heterodyne conversion in low-temperature-grown GaAs photoconductors,” J. Appl. Phys. 73(3), 1480–1484 (1993). [CrossRef]
- N. Vieweg, M. Mikulics, M. Scheller, K. Ezdi, R. Wilk, H. W. Hübers, and M. Koch, “Impact of the contact metallization on the performance of photoconductive THz antennas,” Opt. Express 16(24), 19695–19705 (2008). [CrossRef] [PubMed]
- A. J. Deninger, T. Göbel, D. Schönherr, T. Kinder, A. Roggenbuck, M. Köberle, F. Lison, T. Müller-Wirts, and P. Meissner, “Precisely tunable continuous-wave terahertz source with interferometric frequency control,” Rev. Sci. Instrum. 79(4), 044702 (2008). [CrossRef] [PubMed]

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