## Terahertz quasi time domain spectroscopy

Optics Express, Vol. 17, Issue 20, pp. 17723-17733 (2009)

http://dx.doi.org/10.1364/OE.17.017723

Acrobat PDF (342 KB)

### Abstract

It is shown theoretically and experimentally that for the specific case of an equidistant frequency spacing of semiconductor laser modes, signals similar to terahertz (THz) time domain spectroscopy (TDS) can be detected in a standard photomixer setup. This quasi TDS system approach enables for both, time and frequency domain data processing. Measurements with a THz system which is based on a low cost multimode laser diode are presented. The system exhibits a bandwidth of 600 GHz and can be applied to the classical THz TDS application scenarios.

© 2009 OSA

## 1. Introduction

7. A. J. L. Adam, P. C. M. Planken, S. Meloni, and J. Dik, “TeraHertz imaging of hidden paint layers on canvas,” Opt. Express **17**(5), 3407–3416 (2009). [PubMed]

9. H. B. Liu, Y. Chen, G. J. Bastiaans, and X.-C. Zhang, “Detection and identification of explosive RDX by THz diffuse reflection spectroscopy,” Opt. Express **14**(1), 415–423 (2006). [PubMed]

13. M. A. Seo, A. J. Adam, J. H. Kang, J. W. Lee, K. J. Ahn, Q. H. Park, P. C. Planken, and D. S. Kim, “Near field imaging of terahertz focusing onto rectangular apertures,” Opt. Express **16**(25), 20484–20489 (2008). [PubMed]

21. 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). [PubMed]

22. 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). [PubMed]

## 2. Theory

*I*, which itself depends linearly on the antennas conductance

_{E}*G*and thus on the amount of optically excited free carriers

_{E}*n*, which is a function of the optical excitation power

_{E}*P*

_{Opt,E}._{E}is a constant depending of the antenna material and structure and τ is the free carrier lifetime. It can be shown that a steady state solution of Eq. (2) in the case of a sinusoidal excitation with the angular frequency

*ω*is given by

*P*is given by the squared sum of the electrical field of the

_{Opt,E}*M*different laser modes, each of them oscillating with the angular frequency

*ω*a nonlinear mixing of the modes occurs within the antenna and a plethora of mixture products are created theoretically. However, the free carrier lifetime induced low pass characteristics eliminates the fast oscillating components and thus, only the frequency components up to THz frequencies remain.

_{i}:*M*= 3). Then the optical power at the emitter antenna is:

*E*and the time varying phase

_{i}*ϕ*of the different laser modes, oscillating with the angular frequencies

_{i}*ω*. By employing Eq. (1) and 3, the THz field can be calculated as:

_{i}*A*is the spectral emitter antenna characteristics, including the low pass characteristics and the metallization caused radiation efficiency and

_{E}(ω)*Δω*is the THz frequency, defined by:

_{ij}*M*laser mode mixing can be calculated. Here, the photocurrent is given by:

*P*of the laser modes. Thus by assuming an equal power spreading over the M laser modes, i.e.

_{i}*P*with

_{i}= P/M,*P*being the total power of the laser, the amplitude of the resulting THz frequency components

*I*are proportional toand hence their amplitude decreases quadratically with the number of modes. Consequently, an increasing of the number of THz frequencies induces a decreasing spectral signal-to-noise ratio per frequency as a price for the enhanced frequency information.

_{D}(ω)*Δf*induces a constructive enhancement of the individual frequency components, which is illustrated in the Fig. 2 . Therefore, in the case of a QTDS system, the detected signal is given by

*M-m*). On the other hand the signal is also proportional to the factor (

*2πmΔf*

**. Thus, the higher frequencies are amplified as well. Yet, the low pass characteristics induced by the free carriers, which is considered in the spectral efficiency of the system**

*)**A(2πmΔf)*, effectively lower the pulses amplitude for higher bandwidths, since the higher frequency components have smaller amplitudes than the lower ones. The Fig. 3 shows simulated signals based on Eq. (13) for a different number of laser modes

*M*, and identical total power and a resonance free antenna structure.

## 3. System & Experiment

*Δf*of about 24GHz. The diodes spectrum which is shown in Fig. 4 exhibits an emission bandwidth of several hundreds of GHz. The total output power is 100mW with an electrical power consumption of 400mW. The laser beam is collimated by a standard low cost polymeric lens. The overall laser device including the driver electronics consumes the space of a laser pointer.

21. 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). [PubMed]

## 4. Results

36. 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). [PubMed]

37. N. C. van der Valk, W. A. M. van der Marel, and P. C. M. Planken, “Terahertz polarization imaging,” Opt. Lett. **30**(20), 2802–2804 (2005). [PubMed]

40. C. Jördens, M. Scheller, M. Wichmann, M. Mikulics, K. Wiesauer, and M. Koch, “Terahertz birefringence for orientation analysis,” Appl. Opt. **48**(11), 2037–2044 (2009). [PubMed]

40. C. Jördens, M. Scheller, M. Wichmann, M. Mikulics, K. Wiesauer, and M. Koch, “Terahertz birefringence for orientation analysis,” Appl. Opt. **48**(11), 2037–2044 (2009). [PubMed]

## 5. Conclusion

## References and links

1. | 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. |

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

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

4. | C. Jördens and M. Koch, “Detection of foreign bodies in chocolate with pulsed terahertz spectroscopy,” Opt. Eng. |

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

6. | 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. |

7. | A. J. L. Adam, P. C. M. Planken, S. Meloni, and J. Dik, “TeraHertz imaging of hidden paint layers on canvas,” Opt. Express |

8. | J. F. Federici, B. Schulkin, F. Huang, D. Gary, R. Barat, F. Oliveira, and D. Zimdars, “THz imaging and sensing for security applications - explosives, weapons and drugs,” Semicond. Sci. Technol. |

9. | H. B. Liu, Y. Chen, G. J. Bastiaans, and X.-C. Zhang, “Detection and identification of explosive RDX by THz diffuse reflection spectroscopy,” Opt. Express |

10. | S. Hunsche, D. M. Mittelman, M. Koch, and M. C. Nuss, “New Dimensions in T-Ray Imaging,” IEICE Trans. Electron. |

11. | H.-T. Chen, R. Kersting, and G. C. Cho, “Terahertz imaging with nanometer resolution,” Appl. Phys. Lett. |

12. | A. J. Huber, F. Keilmann, J. Wittborn, J. Aizpurua, and R. Hillenbrand, “Terahertz near-field nanoscopy of mobile carriers in single semiconductor nanodevices,” Nano Lett. |

13. | M. A. Seo, A. J. Adam, J. H. Kang, J. W. Lee, K. J. Ahn, Q. H. Park, P. C. Planken, and D. S. Kim, “Near field imaging of terahertz focusing onto rectangular apertures,” Opt. Express |

14. | D. Grischkowsky, S. Keiding, M. Exter, and C. Fattinger, “Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors,” J. Opt. Soc. Am. B |

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

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

17. | 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. |

18. | R. Mendis, C. Sydlo, J. Sigmund, M. Feiginov, P. Meissner, and H. L. Hartnagel, “Tunable CW-THz system with a log-periodic photoconductive emitter,” Solid-State Electron. |

19. | G. Mouret, S. Matton, R. Bocquet, F. Hindle, E. Peytavit, J. F. Lampin, and D. Lippens, “Far-infrared cw difference-frequency generation using vertically integrated and planar low temperature grown GaAs photomixers: application to H2S rotational spectrum up to 3 THz,” Appl. Phys. B |

20. | J. Mangeney, A. Merigault, N. Zerounian, P. Crozat, K. Blary, and J. F. Lampin, “Continuous wave terahertz generation up to 2 THz by photomixing on ion-irradiated In |

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

22. | 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. |

23. | O. Morikawa, M. Tonouchi, and M. Hangyo, “Sub-THz spectroscopic system using a multimode laser diode and photoconductive antenna,” Appl. Phys. Lett. |

24. | I. S. Gregory, W. R. Tribe, M. J. Evans, T. D. Drysdale, D. R. S. Cumming, and M. Missous, “Multi-channel homodyne detection of continuous-wave terahertz radiation,” Appl. Phys. Lett. |

25. | K. Shibuya, M. Tani, M. Hangyo, O. Morikawa, and H. Kan, “Compact and inexpensive continuous-wave subterahertz imaging system with a fiber-coupled multimode laser diode,” Appl. Phys. Lett. |

26. | German patent application, Nr. 10 2009 036 111.1. |

27. | 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. |

28. | 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. |

29. | E. R. Brown, K. A. McIntosh, K. B. Nichols, and C. L. Dennis, “Photomixing up to 3.8 THz in low-temperature-grown GaAs,” Appl. Phys. Lett. |

30. | K. Ezdi, B. Heinen, C. Jördens, N. Vieweg, N. Krumbholz, R. Wilk, M. Mikulics, and M. Koch, “A hybrid time-domain model for pulsed terahertz dipole antennas,” J. Europ. Opt. Soc. Rap. Public. |

31. | L. Duvillaret, F. Garet, and J. L. Coutaz, “Highly precise determination of optical constants and sample thickness in terahertz time-domain spectroscopy,” Appl. Opt. |

32. | T. D. Dorney, R. G. Baraniuk, and D. M. Mittleman, “Material parameter estimation with terahertz time-domain spectroscopy,” J. Opt. Soc. Am. A |

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

34. | M. Scheller, C. Jansen, and M. Koch, “Analyzing Sub-100µm Samples with Transmission Terahertz Time Domain Spectroscopy,” Opt. Commun. |

35. | D. M. Mittleman, R. H. Jacobsen, and M. C. Nuss,“T-ray imaging,” IEEE J. Sel. Top. Quantum Electron. |

36. | 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. |

37. | N. C. van der Valk, W. A. M. van der Marel, and P. C. M. Planken, “Terahertz polarization imaging,” Opt. Lett. |

38. | M. Reid and R. Fedosejevs, “Terahertz birefringence and attenuation properties of wood and paper,” Appl. Opt. |

39. | F. Rutz, T. Hasek, M. Koch, H. Richter, and U. Ewert, “Terahertz birefringence of liquid crystal polymers,” Appl. Phys. Lett. |

40. | C. Jördens, M. Scheller, M. Wichmann, M. Mikulics, K. Wiesauer, and M. Koch, “Terahertz birefringence for orientation analysis,” Appl. Opt. |

**OCIS Codes**

(120.3180) Instrumentation, measurement, and metrology : Interferometry

(150.3045) Machine vision : Industrial optical metrology

(300.6495) Spectroscopy : Spectroscopy, teraherz

(250.5960) Optoelectronics : Semiconductor lasers

**ToC Category:**

Spectroscopy

**History**

Original Manuscript: August 14, 2009

Revised Manuscript: September 14, 2009

Manuscript Accepted: September 14, 2009

Published: September 18, 2009

**Citation**

Maik Scheller and Martin Koch, "Terahertz quasi time domain spectroscopy," Opt. Express **17**, 17723-17733 (2009)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-20-17723

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### References

- 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), 5194–5196 (2004).
- 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). [PubMed]
- 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). [PubMed]
- C. Jördens and M. Koch, “Detection of foreign bodies in chocolate with pulsed terahertz spectroscopy,” Opt. Eng. 47(3), 037003 (2008).
- K. Fukunaga, Y. Ogawa, S. Hayashi, and I. Hosako, “Terahertz spectroscopy for art conservation,” IEICE Electronics Express 4(8), 258–263 (2007).
- 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).
- A. J. L. Adam, P. C. M. Planken, S. Meloni, and J. Dik, “TeraHertz imaging of hidden paint layers on canvas,” Opt. Express 17(5), 3407–3416 (2009). [PubMed]
- J. F. Federici, B. Schulkin, F. Huang, D. Gary, R. Barat, F. Oliveira, and D. Zimdars, “THz imaging and sensing for security applications - explosives, weapons and drugs,” Semicond. Sci. Technol. 20(7), S266–280 (2005).
- H. B. Liu, Y. Chen, G. J. Bastiaans, and X.-C. Zhang, “Detection and identification of explosive RDX by THz diffuse reflection spectroscopy,” Opt. Express 14(1), 415–423 (2006). [PubMed]
- S. Hunsche, D. M. Mittelman, M. Koch, and M. C. Nuss, “New Dimensions in T-Ray Imaging,” IEICE Trans. Electron. 81-C(2), 269–276 (1998).
- H.-T. Chen, R. Kersting, and G. C. Cho, “Terahertz imaging with nanometer resolution,” Appl. Phys. Lett. 83(15), 3009–3011 (2003).
- A. J. Huber, F. Keilmann, J. Wittborn, J. Aizpurua, and R. Hillenbrand, “Terahertz near-field nanoscopy of mobile carriers in single semiconductor nanodevices,” Nano Lett. 8(11), 3766–3770 (2008). [PubMed]
- M. A. Seo, A. J. Adam, J. H. Kang, J. W. Lee, K. J. Ahn, Q. H. Park, P. C. Planken, and D. S. Kim, “Near field imaging of terahertz focusing onto rectangular apertures,” Opt. Express 16(25), 20484–20489 (2008). [PubMed]
- D. Grischkowsky, S. Keiding, M. Exter, and C. Fattinger, “Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors,” J. Opt. Soc. Am. B 7(10), 2006–2015 (1990).
- W. L. Chan, J. Deibel, and D. M. Mittleman, “Imaging with terahertz radiation,” Rep. Prog. Phys. 70(8), 1325–1379 (2007).
- 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).
- 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).
- R. Mendis, C. Sydlo, J. Sigmund, M. Feiginov, P. Meissner, and H. L. Hartnagel, “Tunable CW-THz system with a log-periodic photoconductive emitter,” Solid-State Electron. 48(10-11), 2041–2045 (2004).
- G. Mouret, S. Matton, R. Bocquet, F. Hindle, E. Peytavit, J. F. Lampin, and D. Lippens, “Far-infrared cw difference-frequency generation using vertically integrated and planar low temperature grown GaAs photomixers: application to H2S rotational spectrum up to 3 THz,” Appl. Phys. B 79(6), 725–729 (2004).
- J. Mangeney, A. Merigault, N. Zerounian, P. Crozat, K. Blary, and J. F. Lampin, “Continuous wave terahertz generation up to 2 THz by photomixing on ion-irradiated In0.53Ga0.47As at 1.55 μm wavelengths,” Appl. Phys. Lett. 91(24), 241102 (2007).
- 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). [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). [PubMed]
- O. Morikawa, M. Tonouchi, and M. Hangyo, “Sub-THz spectroscopic system using a multimode laser diode and photoconductive antenna,” Appl. Phys. Lett. 75(24), 3772–3774 (1999).
- I. S. Gregory, W. R. Tribe, M. J. Evans, T. D. Drysdale, D. R. S. Cumming, and M. Missous, “Multi-channel homodyne detection of continuous-wave terahertz radiation,” Appl. Phys. Lett. 87(3), 034106 (2005).
- K. Shibuya, M. Tani, M. Hangyo, O. Morikawa, and H. Kan, “Compact and inexpensive continuous-wave subterahertz imaging system with a fiber-coupled multimode laser diode,” Appl. Phys. Lett. 90(16), 161127 (2007).
- German patent application, Nr. 10 2009 036 111.1.
- 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).
- 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).
- E. R. Brown, K. A. McIntosh, K. B. Nichols, and C. L. Dennis, “Photomixing up to 3.8 THz in low-temperature-grown GaAs,” Appl. Phys. Lett. 66(3), 285–287 (1995).
- K. Ezdi, B. Heinen, C. Jördens, N. Vieweg, N. Krumbholz, R. Wilk, M. Mikulics, and M. Koch, “A hybrid time-domain model for pulsed terahertz dipole antennas,” J. Europ. Opt. Soc. Rap. Public. 09001, 4 (2009).
- 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).
- 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).
- M. Scheller and M. Koch, “Fast and accurate thickness determination of unknown materials using terahertz time domain spectroscopy,” J. of Infrared, Millimeter, and Terahertz Waves 30(7), 762–769 (2009).
- M. Scheller, C. Jansen, and M. Koch, “Analyzing Sub-100µm Samples with Transmission Terahertz Time Domain Spectroscopy,” Opt. Commun. 282(7), 1304–1306 (2009).
- D. M. Mittleman, R. H. Jacobsen, and M. C. Nuss,“T-ray imaging,” IEEE J. Sel. Top. Quantum Electron. 2(3), 679–692 (1996).
- 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). [PubMed]
- N. C. van der Valk, W. A. M. van der Marel, and P. C. M. Planken, “Terahertz polarization imaging,” Opt. Lett. 30(20), 2802–2804 (2005). [PubMed]
- M. Reid and R. Fedosejevs, “Terahertz birefringence and attenuation properties of wood and paper,” Appl. Opt. 45(12), 2766–2772 (2006). [PubMed]
- F. Rutz, T. Hasek, M. Koch, H. Richter, and U. Ewert, “Terahertz birefringence of liquid crystal polymers,” Appl. Phys. Lett. 89(22), 221911 (2006).
- C. Jördens, M. Scheller, M. Wichmann, M. Mikulics, K. Wiesauer, and M. Koch, “Terahertz birefringence for orientation analysis,” Appl. Opt. 48(11), 2037–2044 (2009). [PubMed]

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