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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 20 — Sep. 28, 2009
  • pp: 17723–17733
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Terahertz quasi time domain spectroscopy

Maik Scheller and Martin Koch  »View Author Affiliations


Optics Express, Vol. 17, Issue 20, pp. 17723-17733 (2009)
http://dx.doi.org/10.1364/OE.17.017723


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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

The development of systems working in the terahertz (THz) frequency range is a subject of active research due to the plethora of potential application fields for THz technology. Applications include non-destructive test of industrial processes and products [1

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. 85(22), 5194–5196 (2004).

4

4. C. Jördens and M. Koch, “Detection of foreign bodies in chocolate with pulsed terahertz spectroscopy,” Opt. Eng. 47(3), 037003 (2008).

], of cultural heritage [5

5. K. Fukunaga, Y. Ogawa, S. Hayashi, and I. Hosako, “Terahertz spectroscopy for art conservation,” IEICE Electronics Express 4(8), 258–263 (2007).

7

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]

], and the detection of hazardous materials [8

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. 20(7), S266–280 (2005).

,9

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]

] and THz near-field imaging [10

10. 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).

13

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]

]. Two different system approaches exist. Firstly, THz time domain spectroscopy (TDS), where femtosecond lasers are employed to generate broadband THz pulses [14

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 7(10), 2006–2015 (1990).

] (see [15

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

] for a comprehensive review). The overall advantage of TDS systems is that a single measurement contains the information on the complete THz frequency window, only restricted by the systems bandwidth. Due to the enormous amount of information obtained by every measurement, TDS systems are discussed for industrial and real world applications. Yet, their core component, the femtosecond laser, is still rather expensive and often not reliable and stable enough for long term industrial operation. Hence, photomixing systems are investigated for their practical applicability due to their potentially lower price. Here, two continuous wave (cw) single mode lasers with slightly different center wavelength are heterodyned onto a photomixer to generate cw THz radiation [16

16. 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).

20

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 In0.53Ga0.47As at 1.55 μm wavelengths,” Appl. Phys. Lett. 91(24), 241102 (2007).

]. But the measurements of this system type provide only a limited amount of information since only a single frequency component is detected. Furthermore, the thickness determination is complicated because of the 2π ambiguity of the detected phase [21

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]

]. In addition a precise and sophisticated frequency stabilization of the laser diodes is essential to preserve the phase information [22

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]

].

In this paper, we present an alternative system approach which provides quasi TDS (QTDS) like signals. It is based upon a low cost commercial multimode laser diode. Thus, the proposed system approach bears the potential to be used in real world applications of THz technology.

While multimode laser diodes with three or more oscillating modes have been employed to drive THz spectrometers [23

23. 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).

25

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. 90(16), 161127 (2007).

], a comprehensive analytical discussion of this generation and detection scheme is essential to fully explore the potential of multi-frequency THz systems and especially of the QTDS approach [26

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

] which we introduce here. The paper is organized as follows: First, the theory of cw multi-frequency THz systems is discussed in general. This includes the most promising case of QTDS. Afterwards, the theoretical deductions are validated by measurements obtained with a QTDS system. Finally, the system is utilized for typical THz application scenarios to highlight its practical applicability.

2. Theory

While the theory of continuous wave THz systems based on photoconductive antennas gated with two laser modes has been deeply discussed e.g. in [27

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. 73(26), 3824–3826 (1998).

], we will analyze here the system properties for the general case of multi-frequency excitation. After calculating the emitted THz field we derive the resulting photocurrent in the detector antenna. We will conclude by discussing the specific case of equidistant mode spacing.

If a laser beam, consisting of multiple frequency components, is focused onto the emitter antenna, the incident photons excite free carriers in the semiconductor material. These carriers are accelerated by the bias voltage which leads to a photocurrent. Due to the fact that the carrier generation is proportional to the laser power, a frequency mixing of the differing laser modes occurs and the photocurrent is modulated by the various mixing products.

However, the free carrier lifetime of the semiconductor material in the range of hundreds of femtoseconds induces a low pass characteristic and hence, the effective current modulation just consists of the difference frequencies between the laser modes. These difference frequencies lie in the THz range. According to [28

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. 73(3), 1480–1484 (1993).

] the emitted steady state THz field is proportional to time derivative of the photocurrent IE, which itself depends linearly on the antennas conductance GE and thus on the amount of optically excited free carriers nE, which is a function of the optical excitation power POpt,E.

ETHz(t)δδtIE(t)δδtGE(t)δδtnE(t,POpt,E(t)).
(1)

The density of the photo carriers can be determined as the solution of the differential equation [28

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. 73(3), 1480–1484 (1993).

]
nE(t)dt=ΩEPOpt,E(t)nE(t)τ,
(2)
where ΩE 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

nE(t)=ΩEτPOpt,E(t)¯(1+sin(ωt)1+ω2τ2).
(3)

Yet, it can be concluded from the equation, that the carrier lifetime induces a low pass characteristics. Due to the fact that the optical power POpt,E is given by the squared sum of the electrical field of the M different laser modes, each of them oscillating with the angular frequency ωi:
POpt,E(t)[m=1M(Em(t))]2,
(4)
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.

For clarity, we will first specify the problem to the case of three laser modes (M = 3). Then the optical power at the emitter antenna is:

POpt,E(t)[E1sin(ω1t+ϕ1)+E2sin(ω2t+ϕ2)+E3sin(ω3t+ϕ3)]2.
(5)

Here we account for the amplitude Ei and the time varying phase ϕi of the different laser modes, oscillating with the angular frequencies ωi. By employing Eq. (1) and 3, the THz field can be calculated as:
ETHz(t)Δω12AE(Δω12)E1E2cos(Δω12t+ϕ1ϕ2)+Δω13AE(Δω13)E1E3cos(Δω23t+ϕ1ϕ3)+Δω23AE(Δω23)E2E3cos(Δω23t+ϕ2ϕ3),
(6)
where AE(ω) is the spectral emitter antenna characteristics, including the low pass characteristics and the metallization caused radiation efficiency and Δωij is the THz frequency, defined by:

Δωij:=ωiωj.
(7)

ID(ΔX)=Δω12A(Δω12)P1P2cos(ΔXc0Δω12+ϕ12)+Δω13A(Δω13)P1P3cos(ΔXc0Δω13+ϕ13)+Δω23A(Δω23)P2P3cos(ΔXc0Δω23+ϕ23).
(10)

Analogue to the deductions above, the more general case of M laser mode mixing can be calculated. Here, the photocurrent is given by:

ID(ΔX)=m=1M1n=m+1MΔωmnA(Δωmn)PmPncos(ΔXc0Δωmn+ϕmn).
(11)

The last point that will be generally discussed concerns the power efficiency. As can be seen from Eq. (11), the detected signal is a function of the individual power Pi of the laser modes. Thus by assuming an equal power spreading over the M laser modes, i.e. Pi = P/M, with P being the total power of the laser, the amplitude of the resulting THz frequency components ID(ω) are proportional to
ID(Δω)P2M2,
(12)
and 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.

The theoretical waveforms for the case of three and multiple modes and identical total power are shown Fig. 1
Fig. 1 The theoretical waveforms for the case of three THz frequencies (50, 350 and 450GHz) (left) and multiple frequencies (25 to 375GHz in 25GHz steps) (right).
: An equidistant frequency spacing of the laser modes leads to TDS-like pulses, which occur with a repetition rate determined by the mode spacing. A frequency difference of 25GHz for instance induces an effective pulse repetition time of 40ps. This is especially interesting, since here the elaborate signal processing known from THz TDS can be utilized to analyze the measured data. Consequently, this specific case will be referred in the following as quasi time domain spectroscopy (QTDS).

The equidistant mode spacing Δf induces a constructive enhancement of the individual frequency components, which is illustrated in the Fig. 2
Fig. 2 The generated difference frequencies Δf interfere constructively in the case of equidistant mode spacing of the laser modes. For this example, the frequency component at 100GHz exhibits an amplification of three and the one at 200 GHz is two times amplified.
. Therefore, in the case of a QTDS system, the detected signal is given by

ID(ΔX)=m=1M1(Mm)M2(2πmΔf)A(2πmΔf)P2cos(ΔXc02πmΔf+ϕm).
(13)

As a consequence, the signals peak-to-peak amplitude is theoretically only weakly dependent on the number of oscillating modes. On the one hand the lower frequency components are enhanced by the constructive superposition of the modes with the factor (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
Fig. 3 Simulated waveforms for a different number of modes M. The equidistant frequency spacing is 25GHz and the free carrier lifetime 250fs.
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.

However, the metallization structures of the utilized photoconductive antennas affect the resulting waveform. Consequently, the antennas resonances can be optimized with respect to the employed laser diodes emission bandwidth.

3. System & Experiment

To experimentally verify the above conclusions, we employ a commercial multi mode laser diode operating at a center wavelength of 660nm. Instead of using a custom-tailored laser diode, we utilized an inexpensive device that was produced for the consumer electronic industry. The diode emits multiple laser lines, spaced by a constant difference frequency Δf of about 24GHz. The diodes spectrum which is shown in Fig. 4
Fig. 4 The spectrum of the multi mode cw laser diode utilized to gate the antennas. The frequency difference between the modes of 1THz is visualized.
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.

The laser beam is spitted by a beam splitter into two paths with equal powers. Afterwards, one of the beams is focused onto the emitter antenna. The other one is focused onto the detector antenna after being guided over a linear stage which is utilized as optical delay line. The antennas comprise a 100µm dipole and a 5µm gap without interdigital structures [21

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]

]. They are made of standard low temperature (LT)-gallium arsenide (GaAs). This material provides fast recombination times of the optically exited free carriers and is consequently suitable for cw THz systems [29

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. 66(3), 285–287 (1995).

] as well as for the QTDS system discussed there. The emitter antenna is biased with 35V at 4.6kHz and a lock-in amplifier is utilized to enhance the signal-to-noise ratio. The integration time is set to 50ms. Four parabolic off-axis parabolic mirrors are employed for collimating and focusing the THz beam. The Fig. 5
Fig. 5 Schematic of the quasi time domain spectrometer: The laser beam is guided over the Mirrors M1 to M3 and focused onto the emitter and detector antenna. The THz wave are collimated and focused by four off axis parabolic mirrors P1 to P4.
shows a schematic of the setup.

4. Results

In the beginning of this section, we will discuss the experimentally obtained THz waveform and its Fourier spectrum. Afterwards, we will highlight the broad applicability of the QTDS approach by demonstrating its suitability for a few practical application scenarios.

The signal obtained with the system is shown in Fig. 6
Fig. 6 The time domain waveform obtained from the system. The signals period TR is 41ps. The dashed lines indicate the time window exploited to determine the spectrum in Fig. 7 (right).
. As can be seen from the figure, the resulting pulse repetition time is 41ps, which is given by the inverse mode spacing of the utilized diode laser. Please note that this time constant can be optimized for the specific application scenario by choosing a laser diode with the preferred mode spacing. The Fig. 7
Fig. 7 The THz spectrum of the system for a time window of 82ps (left) and 41ps (right).
shows the corresponding THz spectra for a time window of 82ps and for one of only 41ps. For the latter, the second pulse is not considered within the time window of the measurement. This leads to a smooth spectrum. However, the frequency resolution is determined by the oscillation laser modes. In this case the mode spacing is 24.1GHz. As can be further seen from the spectra, the signal-to-noise ratio of this demonstrator system is in the range of 50 dB and the bandwidth is on the order of 600GHz. The latter is determined by the restricted spectral bandwidth of the employed laser diode and the antenna characteristic, which exhibits its constructive resonance at 500GHz. The second maximum in the pulse shape originates from the back reflections from the dipole ends [30

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. 09001, 4 (2009).

]. The ringing of the ground level is caused by water absorption lines and by back reflections from the contact pads.

In analogy to THz TDS measurements, a sample inserted into the THz path induces a delay of the pulses and reduces their amplitude due to reflection and absorption losses. Furthermore, Fabry Pérot (FP) echo pulses occur caused by the multiple reflections within the sample [31

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. 38(2), 409–415 (1999).

,32

32. 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).

]. By comparing the reference and the sample measurement, the optical parameters of the sample can be determined.

To demonstrate the applicability of the QTDS approach for material characterization as well as thickness determination, we conduct measurements on a high resistive silicon wafer. The results are presented in Fig. 8
Fig. 8 The waveform from the measurement on a HR Si wafer. The pulse is delayed and its amplitudes is reduced compared to the reference signal. In addition, FP echo pulses occur.
. The figure shows the delayed pulse and two clearly observable echo pulses. This signal can be exploited to analyze the sample by a time domain algorithm recently presented in [33

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 30(7), 762–769 (2009).

]. By numerically shifting the time axis and by amplitude scaling of the reference pulse to optimally overlap with the samples pulse, the refractive index and the absolute thickness of the sample under investigation can be determined simultaneously.

Figure 9
Fig. 9 Left: Experimental THz signal for the HR SI measurement together with the simulation based on a time domain algorithm to determine the thickness and the refractive index simultaneously. Right: The refractive index of HR Si extracted with a frequency domain algorithm from the measured data.
shows on the left the measured waveform compared to the results of the time domain algorithm. A very good agreement is observed. The derived spectrally averaged refractive index of 3.418 and the thickness of 531µm are in accordance to the literate value [14

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 7(10), 2006–2015 (1990).

] and the values obtained by a micrometer screw, respectively. Additionally, a frequency domain based algorithm, proposed in [34

34. M. Scheller, C. Jansen, and M. Koch, “Analyzing Sub-100µm Samples with Transmission Terahertz Time Domain Spectroscopy,” Opt. Commun. 282(7), 1304–1306 (2009).

], was employed to extract the refractive index of the sample from a single measurement over a broad frequency range. The extracted data are shown on the right side of Fig. 9.

These results clearly demonstrate that the QTDS approach is suitable to determine the thickness and the dielectric THz properties of samples analogous to TDS systems with both, time domain and frequency domain parameter extraction.

A second potential application of THz systems is the monitoring of the water status of plants [35

35. D. M. Mittleman, R. H. Jacobsen, and M. C. Nuss,“T-ray imaging,” IEEE J. Sel. Top. Quantum Electron. 2(3), 679–692 (1996).

,36

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]

]. A leaf of coffea arabica was detached from the plant and afterwards measured in the system for 6 hours. With time the leaf looses water by evaporation. Consequently, the thickness of the leaf decreases and its THz transmittance increases. Figure 10
Fig. 10 Measurements results of the detached leafs monitoring: The water loss of the leaf induces an increase of the pulses amplitude (left) and a reduced delay of the pulses maxima (right).
shows on the left hand side the amplitude of the transmitted THz pulse (100% corresponds to the pulse amplitude without the leaf in the beam path) which rises with time as the water evaporates. On the right hand side we plot the temporal evolution of the position of the pulse maximum. Both measurands can be exploited to monitor the plant water status.

A third promising application of THz spectroscopy systems is the orientation analysis of birefringent samples such as fiber enforced polymers, liquid crystal polymers, paper tissue or optical crystals [37

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

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]

]. As one example, a 4mm thick LCP sample is measured at different orientation angles. This sample exhibits a distinctive birefringence as shown by the measured refractive index presented on the left side of Fig. 11
Fig. 11 Left: The measured refractive index of the LCP sample for the fast and the slow axis. Right: The waveform of the LCP measurements parallel and perpendicular to the slow axis.
. This birefringence induces an extended pulse delay if the THz wave is polarized along the slow axis of the sample. The waveforms for the signals parallel and perpendicular to the slow axis are shown in Fig. 11.

After the samples THz properties have been determined using the procedure described in [34

34. M. Scheller, C. Jansen, and M. Koch, “Analyzing Sub-100µm Samples with Transmission Terahertz Time Domain Spectroscopy,” Opt. Commun. 282(7), 1304–1306 (2009).

], we use the algorithm presented in [40

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]

] to analyze its orientation angle with respect to the slow axis. Figure 12
Fig. 12 The measured and simulated waveform for an orientation of 38° (left) and 62° (right).
shows the waveforms for two arbitrarily adjusted orientations together with the simulated signals. A very good agreement allows for a precise orientation analysis.

Overall, the results of theses selective examples suggest that the QTDS approach combines the practically applicability of THz TDS with an unrivaled cost-effectiveness.

5. Conclusion

A new approach for THz spectroscopy systems based on inexpensive, commercially available multimode laser diodes has been proposed. This approach provides signals similar to that of THz TDS systems and is consequently referred to quasi time domain spectroscopy (QTDS). A demonstration system was presented, which exhibits a bandwidth of 600GHz and a signal-to-noise ratio of about 50 dB. The potential of QTDS was demonstrated by means of three examples.

While the presented system performance already allows for a broad applicability, the THz bandwidth could be extended by employing antenna structures with different resonance behavior and laser diodes with broader spectral emission. In conclusion, the QTDS approach carries the potential to foster real world applications of THz technology.

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. 85(22), 5194–5196 (2004).

2.

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3.

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4.

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5.

K. Fukunaga, Y. Ogawa, S. Hayashi, and I. Hosako, “Terahertz spectroscopy for art conservation,” IEICE Electronics Express 4(8), 258–263 (2007).

6.

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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]

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. 20(7), S266–280 (2005).

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]

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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 7(10), 2006–2015 (1990).

15.

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

16.

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).

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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).

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 79(6), 725–729 (2004).

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 In0.53Ga0.47As at 1.55 μm wavelengths,” Appl. Phys. Lett. 91(24), 241102 (2007).

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]

23.

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).

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. 87(3), 034106 (2005).

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. 90(16), 161127 (2007).

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. 73(26), 3824–3826 (1998).

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. 73(3), 1480–1484 (1993).

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. 66(3), 285–287 (1995).

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. 09001, 4 (2009).

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. 38(2), 409–415 (1999).

32.

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).

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 30(7), 762–769 (2009).

34.

M. Scheller, C. Jansen, and M. Koch, “Analyzing Sub-100µm Samples with Transmission Terahertz Time Domain Spectroscopy,” Opt. Commun. 282(7), 1304–1306 (2009).

35.

D. M. Mittleman, R. H. Jacobsen, and M. C. Nuss,“T-ray imaging,” IEEE J. Sel. Top. Quantum Electron. 2(3), 679–692 (1996).

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]

38.

M. Reid and R. Fedosejevs, “Terahertz birefringence and attenuation properties of wood and paper,” Appl. Opt. 45(12), 2766–2772 (2006). [PubMed]

39.

F. Rutz, T. Hasek, M. Koch, H. Richter, and U. Ewert, “Terahertz birefringence of liquid crystal polymers,” Appl. Phys. Lett. 89(22), 221911 (2006).

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]

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

  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. 85(22), 5194–5196 (2004).
  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. 44(32), 6849–6856 (2005). [PubMed]
  3. 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]
  4. C. Jördens and M. Koch, “Detection of foreign bodies in chocolate with pulsed terahertz spectroscopy,” Opt. Eng. 47(3), 037003 (2008).
  5. K. Fukunaga, Y. Ogawa, S. Hayashi, and I. Hosako, “Terahertz spectroscopy for art conservation,” IEICE Electronics Express 4(8), 258–263 (2007).
  6. 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).
  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]
  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. 20(7), S266–280 (2005).
  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]
  10. 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).
  11. H.-T. Chen, R. Kersting, and G. C. Cho, “Terahertz imaging with nanometer resolution,” Appl. Phys. Lett. 83(15), 3009–3011 (2003).
  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. 8(11), 3766–3770 (2008). [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]
  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 7(10), 2006–2015 (1990).
  15. W. L. Chan, J. Deibel, and D. M. Mittleman, “Imaging with terahertz radiation,” Rep. Prog. Phys. 70(8), 1325–1379 (2007).
  16. 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).
  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. 80(16), 3003–3005 (2002).
  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. 48(10-11), 2041–2045 (2004).
  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 79(6), 725–729 (2004).
  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 In0.53Ga0.47As at 1.55 μm wavelengths,” Appl. Phys. Lett. 91(24), 241102 (2007).
  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]
  23. 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).
  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. 87(3), 034106 (2005).
  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. 90(16), 161127 (2007).
  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. 73(26), 3824–3826 (1998).
  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. 73(3), 1480–1484 (1993).
  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. 66(3), 285–287 (1995).
  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. 09001, 4 (2009).
  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. 38(2), 409–415 (1999).
  32. 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).
  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 30(7), 762–769 (2009).
  34. M. Scheller, C. Jansen, and M. Koch, “Analyzing Sub-100µm Samples with Transmission Terahertz Time Domain Spectroscopy,” Opt. Commun. 282(7), 1304–1306 (2009).
  35. D. M. Mittleman, R. H. Jacobsen, and M. C. Nuss,“T-ray imaging,” IEEE J. Sel. Top. Quantum Electron. 2(3), 679–692 (1996).
  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]
  38. M. Reid and R. Fedosejevs, “Terahertz birefringence and attenuation properties of wood and paper,” Appl. Opt. 45(12), 2766–2772 (2006). [PubMed]
  39. F. Rutz, T. Hasek, M. Koch, H. Richter, and U. Ewert, “Terahertz birefringence of liquid crystal polymers,” Appl. Phys. Lett. 89(22), 221911 (2006).
  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]

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