Abstract

Terahertz technology offers solutions in nondestructive testing and spectroscopy for many scientific and industrial applications. While direct detection of photons in this frequency range is difficult to achieve, quantum optics provides a highly attractive alternative: it enables the characterization of materials in hardly accessible spectral ranges by measuring easily detectable photons of a different spectral range. Here we report on the application of this principle to terahertz spectroscopy, measuring absorption features of chemicals at sub-terahertz frequencies by detecting visible photons. To generate the needed correlated signal-idler photon pairs, a periodically poled lithium niobate crystal and a 660 nm continuous-wave pump source are used. After propagating through a single-crystal nonlinear interferometer, the pump photons are filtered by narrowband volume Bragg gratings. An uncooled scientific CMOS camera detects the frequency-angular spectra of the remaining visible signal and reveals terahertz-spectral information. Neither cooled detectors nor expensive pulsed lasers for coherent detection are required.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Quantum sensing [13] and imaging [46] based on induced coherence without induced emission [7,8] are highly interesting routes towards measurements in otherwise technological challenging spectral regions. First experimental demonstrations of quantum spectroscopy along these lines in the infrared spectral range [911] already point towards applications in gas sensing and material characterization. Extending this principle into the terahertz frequency is even more beneficial, as laser sources and highly efficient detectors for terahertz radiation are not as advanced as in the visible or infrared spectral region and applicability of terahertz radiation to numerous technologically relevant tasks has been shown in the last decades [1216]. While in first attempts towards quantum spectroscopy in the terahertz frequency region the terahertz radiation was not accessible outside the nonlinear crystals [17,18], this is a crucial requirement for measuring external samples. In our experiment, we generate correlated terahertz (idler) photons and visible (signal) photons propagating in free space (in contrast to [17,18]), which enables spectroscopic measurements of external samples using nonlinear interferometry. As a proof of concept, we determine the concentration-dependent extinction of $\alpha$-lactose monohydrate and para-aminobenzoic acid in the terahertz frequency range by only detecting visible photons.

The schematic of the experimental setup shown in Fig. 1 is an advanced version of our previously presented nonlinear interferometer [19]. As nonlinear media 1 mm long periodically poled lithium niobate (PPLN) crystals with a poling period of either 220 µm or 200 µm are used. The crystals are illuminated by a 660 nm continuous-wave pump laser generating correlated pairs of visible signal and terahertz idler photons. After the crystal, an off-axis parabolic mirror (OAP) with a through hole is placed, separating the terahertz photons from the pump and signal photons. Due to the high refractive index of lithium niobate in the terahertz frequency range [20], the scattering angles of the terahertz radiation are large, and even terahertz photons corresponding to collinearly emitted signal photons can have an angle with respect to its associated signal radiation [19]. This allows us to spectrally separate these wavelengths purely depending on the angle, having the additional advantage that no signal and pump losses occur at a beam splitter. After the second pass through the nonlinear crystal, the pump photons are efficiently filtered from the signal photons by volume Bragg gratings acting as highly efficient notch filters (filter section in Fig. 1). The remaining signal radiation is focused through a transmission grating to observe a frequency-angular spectrum on the scientific complementary metal–oxide–semiconductor (sCMOS) camera. To receive an interference of the signal radiation, the path-length difference is changed by moving the reflective mirror (${{\rm{M}}_i}$) with a piezoelectric linear stage.

 figure: Fig. 1.

Fig. 1. Experimental setup. The 1 mm long PPLN crystals are pumped by a continuous-wave laser with a wavelength of 660 nm, generating correlated pairs of signal and terahertz photons. After the crystal the terahertz radiation is separated by an OAP with a through hole and afterwards reflected at a moveable mirror Mi. Pump and generated signal photons are reflected at Ms directly back into the crystal. After the second pass the pump radiation is filtered from the signal radiation by three volume Bragg gratings (VBGs). To obtain a frequency-angular spectrum on the sCMOS camera, the signal radiation is focused through a transmission grating (TG).

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The acquired frequency-angular spectra show the characteristic tails for terahertz radiation in the Stokes and anti-Stokes region [see Fig. 2(a)]. These signal photons are either generated by spontaneous parametric down-conversion (SPDC) or conversion of thermal terahertz photons as reported earlier [2123]. As a consequence, the Stokes and the anti-Stokes parts only differ by count rate due to the contribution of SPDC in the Stokes part. Therefore, we limit the evaluation in this work to the Stokes part [see Fig. 2(b)]. To obtain interference, frequency-angular spectra are recorded for several path-length differences, and a fast Fourier transform (FFT) of the waveform measured of each individual pixel is carried out. In Fig. 2(c) the maximum amplitude of the individual FFT of each pixel is shown. The highest amplitudes can be observed for the collinear forward regions at about 0.52 THz. Due to the large scattering angle of the terahertz radiation out of lithium niobate, an interference can only be observed in the collinear forward regions corresponding to the highest amplitudes [19].

 figure: Fig. 2.

Fig. 2. Frequency-angular spectrum. (a) Frequency-angular spectrum for the used crystal with a poling period of $\Lambda = 220\;{{\unicode{x00B5}{\rm m}}}$. The image represents an averaging of 60 images with an exposure time of 500 ms each at a fixed delay of about 1 ps. (b) Enlargement of the dashed area (${{100}} \times {{100}}\;{\rm{pixels}}$) in (a). (c) Maximum amplitude of the FFT for each individual pixel and (d) corresponding frequency of the measured spectra [see (b)]. The highest amplitudes are achieved in the collinear forward region. For a better display, the frequency range in (d) is limited to 0.465–0.565 THz.

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Additionally, the frequency corresponding to the maximum amplitude in Fig. 2(c) is evaluated for each single pixel [see Fig. 2(d)]. The observed frequency of the interference increases with increasing frequency shift, leading to an accessible bandwidth of more than 100 GHz for a single crystal. While in the given experiment we only had access to crystal lengths of one millimeter, the bandwidth could be increased by shortening the crystal length. However, Fig. 2(d) shows, that pixel-wise spectral information is obtained from a measurement with a single crystal without varying external parameters and can be used to gain spectral information of samples in the terahertz frequency range.

To demonstrate the ability of quantum-inspired terahertz spectroscopy (QIS) by detecting only visible photons, well-characterized samples are measured. As samples, paraffin wax plates are manufactured in which $\alpha$-lactose monohydrate or para-aminobenzoic acid are dissolved (see Supplement 1). These substances are widely used for the demonstration of terahertz spectroscopy, as they show well-known characteristic absorption features [24,25]. Paraffin wax has proven to be an ideal carrier material, as it shows almost no absorption in the terahertz frequency range and has also a low refractive index of about 1.54 [26]. The amount of additives to the paraffin wax plate ranges between 0.0 and 2.1 g. By assuming a homogeneous distribution, this corresponds to concentrations between 0 and $0.25\;{{\rm mg/m}}{{\rm{m}}^2}$, respectively.

As one prominent absorption feature of $\alpha$-lactose monohydrate is at 0.53 THz and of para-aminobenzoic acid at 0.6 THz [27], we use two different poling periods of 220 µm for $\alpha$-lactose monohydrate and 200 µm for para-aminobenzoic acid, respectively. In Figs. 3(a) and 3(d) the measured waveforms in the collinear forward regions for both crystals are shown where plates with only paraffin wax are already inserted into the terahertz path. For both crystals the maximum relative visibility is about 1%, and some further interference after the main envelope is observable. This is mainly determined by the response behavior of water vapor in air having an absorption line at 0.56 THz. As this cannot be fully resolved by the rather small optical delay of 42.7 ps (corresponding to a frequency resolution of 23.4 GHz), the spectrum of the crystal used for para-aminobenzoic acid does not show a clear envelope (see Supplement 1 for details). Additionally, in Figs. 3(b) and 3(e) the measured waveforms of paraffin wax plates with an amount of 1.5 g of the additives are shown. In comparison, these waveforms show a decreased amplitude and a different response behavior due to the ingredient. In Figs. 3(c) and 3(f) the frequency spectra of the interference in the collinear forward region for both poling periods are shown for different amounts of additive. The obtained spectra with $\alpha$-lactose monohydrate added show a dip at 0.53 THz, and the depth of this dip increases with increasing amount of additive, as expected. As the absorption of para-aminobenzoic acid is near the observed spectral width of the interference, only a decrease of amplitude over almost the entire spectrum by an increased amount of additive is observed.

 figure: Fig. 3.

Fig. 3. Waveforms and spectra. Waveform of the used crystal with a poling period of (a), (b) $\Lambda = 220\;{{\unicode{x00B5}{\rm m}}}$ and (d), (e) $\Lambda = 200\;{{\unicode{x00B5}{\rm m}}}$ and a wax plate with an amount of (a), (c) 0.0 g and (b), (d) 1.5 g of the additive inserted in the terahertz path. The visibility of the measured waveforms without additive are about 1%, and after the interference envelope the response behavior of a water vapor absorption line at 0.56 THz is visible. Corresponding spectra of the used crystals with a poling period of (c) $\Lambda = 220\;{{\unicode{x00B5}{\rm m}}}$ and (f) $\Lambda = 200\;{{\unicode{x00B5}{\rm m}}}$ with wax plates of different amounts of (c) $\alpha$-lactose monohydrate and (f) para-aminobenzoic acid inserted in the terahertz beam path. For clarity, not all of the measured spectra are shown.

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For validation of the presented method, extinction measurements of the samples have been performed with a standard time-domain spectroscopy (TDS) system (bandwidth 4 THz, frequency resolution 10 GHz) by raster imaging the paraffin wax plates. Thus, the homogeneity of the additive distribution in the sample can be evaluated. Figures 4(b) and 4(d) show two exemplary imaging results of paraffin wax plates with an amount of 1.5 g $\alpha$-lactose monohydrate and para-aminobenzoic acid, respectively. For the sake of simplicity, only the peak-to-peak amplitude value of the time-domain waveform of each pixel is evaluated for imaging purposes. As can be seen, the distribution of the ingredient is not completely homogeneous.

 figure: Fig. 4.

Fig. 4. Comparison between QIS and conventional TDS. Comparison of the extinction measured at the absorption frequency in the experiment and by a standard TDS system for wax plates with different amounts of (a) $\alpha$-lactose monohydrate and (c) para-aminobenzoic acid. Raster image of a wax plate with an additive amount of 1.5 g (b) $\alpha$-lactose monohydrate and (d) para-aminobenzoic acid measured by a conventional TDS system. The dashed circles indicate the area that is illuminated by the terahertz radiation in the QIS experiment and therefore evaluated for extraction of extinction values.

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In order to be able to compare the TDS measurement with the QIS measurement, only the area of the sample that is penetrated by the terahertz radiation in the QIS experiment [indicated by the dashed circles in Figs. 4(b) and 4(d)] is considered for the evaluation of the extinction for both experiments. Additionally, the emission characteristics of the terahertz radiation and the angular density of the terahertz radiation that penetrates a given area are taken into account (see Supplement 1 for details). Considering both, the extinction at the evaluated absorption line was calculated. The extinction $K$ at the evaluated absorption line can then be calculated from

$$K = - \frac{2}{{n\Delta\! f}}\int_{\Delta\! f} \mathop {\log}\nolimits_{10} \frac{{\rm{A}}}{{{{\rm{A}}_0}}} {\rm{d}}f,$$
where $n$ is the number of passages through the object and $\Delta\! f$ is the considered frequency range of the absorption line. Furthermore, ${\rm{A}}$ and ${{\rm{A}}_0}$ are the field amplitudes of the corresponding sample measurement and the wax-only reference, respectively. As can be seen in Figs. 4(a) and 4(c) the measured extinctions by QIS show a good agreement with the extinctions measured with the standard TDS system, reaching a coefficient of determination of ${{\rm{R}}^2} = 0.91$ for $\alpha$-lactose monohydrate and ${{\rm{R}}^2} = 0.90$ for para-amino benzoic acid.

With a determination coefficient of the extinction of at least 0.9, a good agreement between the experimental results achieved with the nonlinear interferometer and the conventional TDS system is observed. The frequency of the observed absorption lines in the QIS experiment agree well with literature values [24,25,27]. One of the reasons for the remaining deviation between the two measurements is expected to be due to the limited displacement of the used translation stage. As a result, information from the sample or water vapor absorption that is delayed compared to the envelope of the origin waveform is lost. This causes a low resolution of the measured feature, which cannot be improved by simply zero filling before the FFT is performed. Additionally, the region that is penetrated by the terahertz radiation may differ from the evaluated area of the raster image, and the assumption of the angular density of the terahertz radiation is not precise enough. So far, the used lithium niobate crystals show a usable terahertz bandwidth of about 150 GHz and an interference visibility of more than 1%. The limited bandwidth will be widened in the future, e.g.,  by employing shorter crystals, while the effects on increasing the visibility are currently investigated. Despite all this, the experiment shown is a proof of principle for spectroscopy in the terahertz frequency range without using terahertz detectors by only measuring visible photons. It shows the potential of determining sample properties in the terahertz frequency range without using expensive femtosecond lasers by replacing them with rather cheap and highly developed lasers in the visible range and silicon-based cameras.

In conclusion, we have demonstrated spectroscopy in the terahertz frequency range by only detecting visible photons. For the first time to our knowledge, the spectral information of an external sample in the terahertz frequency range is obtained using the concept of nonlinear interferometry. As a first proof of concept, the concentrations of $\alpha$-lactose monohydrate and para-aminobenzoic acid dissolved in paraffin wax plates were determined. The estimated losses match the values measured by a standard TDS system fairly well. Although the achieved resolution and bandwidth are not yet comparable to classical terahertz measurement techniques, the presented demonstration of this concept is a first milestone toward multipixel terahertz spectral imaging.

Funding

Fraunhofer-Gesellschaft (Lighthouse project QUILT).

Acknowledgment

We thank P. Bickert for helpful discussions during this project.

Disclosures

The authors declare no conflicts of interest.

Supplemental document

See Supplement 1 for supporting content.

REFERENCES

1. A. V. Paterova, H. Yang, C. An, D. A. Kalashnikov, and L. A. Krivitsky, Quantum Sci. Technol. 3, 025008 (2018). [CrossRef]  

2. I. Kviatkovsky, H. M. Chrzanowski, E. G. Avery, H. Bartolomaeus, and S. Ramelow, Sci. Adv. 6, eabd0264 (2020). [CrossRef]  

3. A. V. Paterova, S. M. Maniam, H. Yang, G. Grenci, and L. A. Krivitsky, Sci. Adv. 6, eabd0460 (2020). [CrossRef]  

4. G. B. Lemos, V. Borish, G. D. Cole, S. Ramelow, R. Lapkiewicz, and A. Zeilinger, Nature 512, 409 (2014). [CrossRef]  

5. M. Genovese, J. Opt. 18, 073002 (2016). [CrossRef]  

6. M. Gilaberte Basset, F. Setzpfandt, F. Steinlechner, E. Beckert, T. Pertsch, and M. Gräfe, Laser Photon. Rev. 13, 1900097 (2019). [CrossRef]  

7. L. J. Wang, X. Y. Zou, and L. Mandel, Phys. Rev. A 44, 4614 (1991). [CrossRef]  

8. X. Y. Zou, L. J. Wang, and L. Mandel, Phys. Rev. Lett. 67, 318 (1991). [CrossRef]  

9. D. A. Kalashnikov, A. V. Paterova, S. P. Kulik, and L. A. Krivitsky, Nat. Photonics 10, 98 (2016). [CrossRef]  

10. A. Paterova, H. Yang, C. An, D. Kalashnikov, and L. Krivitsky, New J. Phys. 20, 043015 (2018). [CrossRef]  

11. C. Lindner, S. Wolf, J. Kiessling, and F. Kühnemann, Opt. Express 28, 4426 (2020). [CrossRef]  

12. P. U. Jepsen, D. G. Cooke, and M. Koch, Laser Photon. Rev. 5, 124 (2011). [CrossRef]  

13. B. B. Hu and M. C. Nuss, Opt. Lett. 20, 1716 (1995). [CrossRef]  

14. D. Molter, G. Torosyan, G. Ballon, L. Drigo, R. Beigang, and J. Léotin, Opt. Express 20, 5993 (2012). [CrossRef]  

15. T. Pfeiffer, S. Weber, J. Klier, S. Bachtler, D. Molter, J. Jonuscheit, and G. von Freymann, Opt. Express 26, 12558 (2018). [CrossRef]  

16. D. Grischkowsky, S. Keiding, M. Van Exter, and C. Fattinger, J. Opt. Soc. Am. B 7, 2006 (1990). [CrossRef]  

17. G. K. Kitaeva, S. P. Kovalev, A. N. Penin, A. N. Tuchak, and P. V. Yakunin, J. Infrared Millimeter Terahertz Waves 32, 1144 (2011). [CrossRef]  

18. K. A. Kuznetsov, E. I. Malkova, R. V. Zakharov, O. V. Tikhonova, and G. K. Kitaeva, Phys. Rev. A 101, 053843 (2020). [CrossRef]  

19. M. Kutas, B. Haase, P. Bickert, F. Riexinger, D. Molter, and G. von Freymann, Sci. Adv. 6, eaaz8065 (2020). [CrossRef]  

20. X. Wu, C. Zhou, W. R. Huang, F. Ahr, and F. X. Kärtner, Opt. Express 23, 29729 (2015). [CrossRef]  

21. G. K. Kitaeva, P. V. Yakunin, V. V. Kornienko, and A. N. Penin, Appl. Phys. B 116, 929 (2014). [CrossRef]  

22. B. Haase, M. Kutas, F. Riexinger, P. Bickert, A. Keil, D. Molter, M. Bortz, and G. von Freymann, Opt. Express 27, 7458 (2019). [CrossRef]  

23. V. V. Kornienko, G. K. Kitaeva, F. Sedlmeir, G. Leuchs, and H. G. Schwefel, APL Photon. 3, 051704 (2018). [CrossRef]  

24. E. R. Brown, J. E. Bjarnason, A. M. Fedor, and T. M. Korter, Appl. Phys. Lett. 90, 061908 (2007). [CrossRef]  

25. Q. Song, Y. Zhao, R. Zhang, X. Liu, L. Dong, and W. Xu, J. Infrared Millimeter Terahertz Waves 31, 310 (2010). [CrossRef]  

26. L. Tian and X. Xu, J. Infrared Millimeter Terahertz Waves 39, 302 (2018). [CrossRef]  

27. D. Molter, M. Kolano, and G. von Freymann, Opt. Express 27, 12659 (2019). [CrossRef]  

References

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  1. A. V. Paterova, H. Yang, C. An, D. A. Kalashnikov, and L. A. Krivitsky, Quantum Sci. Technol. 3, 025008 (2018).
    [Crossref]
  2. I. Kviatkovsky, H. M. Chrzanowski, E. G. Avery, H. Bartolomaeus, and S. Ramelow, Sci. Adv. 6, eabd0264 (2020).
    [Crossref]
  3. A. V. Paterova, S. M. Maniam, H. Yang, G. Grenci, and L. A. Krivitsky, Sci. Adv. 6, eabd0460 (2020).
    [Crossref]
  4. G. B. Lemos, V. Borish, G. D. Cole, S. Ramelow, R. Lapkiewicz, and A. Zeilinger, Nature 512, 409 (2014).
    [Crossref]
  5. M. Genovese, J. Opt. 18, 073002 (2016).
    [Crossref]
  6. M. Gilaberte Basset, F. Setzpfandt, F. Steinlechner, E. Beckert, T. Pertsch, and M. Gräfe, Laser Photon. Rev. 13, 1900097 (2019).
    [Crossref]
  7. L. J. Wang, X. Y. Zou, and L. Mandel, Phys. Rev. A 44, 4614 (1991).
    [Crossref]
  8. X. Y. Zou, L. J. Wang, and L. Mandel, Phys. Rev. Lett. 67, 318 (1991).
    [Crossref]
  9. D. A. Kalashnikov, A. V. Paterova, S. P. Kulik, and L. A. Krivitsky, Nat. Photonics 10, 98 (2016).
    [Crossref]
  10. A. Paterova, H. Yang, C. An, D. Kalashnikov, and L. Krivitsky, New J. Phys. 20, 043015 (2018).
    [Crossref]
  11. C. Lindner, S. Wolf, J. Kiessling, and F. Kühnemann, Opt. Express 28, 4426 (2020).
    [Crossref]
  12. P. U. Jepsen, D. G. Cooke, and M. Koch, Laser Photon. Rev. 5, 124 (2011).
    [Crossref]
  13. B. B. Hu and M. C. Nuss, Opt. Lett. 20, 1716 (1995).
    [Crossref]
  14. D. Molter, G. Torosyan, G. Ballon, L. Drigo, R. Beigang, and J. Léotin, Opt. Express 20, 5993 (2012).
    [Crossref]
  15. T. Pfeiffer, S. Weber, J. Klier, S. Bachtler, D. Molter, J. Jonuscheit, and G. von Freymann, Opt. Express 26, 12558 (2018).
    [Crossref]
  16. D. Grischkowsky, S. Keiding, M. Van Exter, and C. Fattinger, J. Opt. Soc. Am. B 7, 2006 (1990).
    [Crossref]
  17. G. K. Kitaeva, S. P. Kovalev, A. N. Penin, A. N. Tuchak, and P. V. Yakunin, J. Infrared Millimeter Terahertz Waves 32, 1144 (2011).
    [Crossref]
  18. K. A. Kuznetsov, E. I. Malkova, R. V. Zakharov, O. V. Tikhonova, and G. K. Kitaeva, Phys. Rev. A 101, 053843 (2020).
    [Crossref]
  19. M. Kutas, B. Haase, P. Bickert, F. Riexinger, D. Molter, and G. von Freymann, Sci. Adv. 6, eaaz8065 (2020).
    [Crossref]
  20. X. Wu, C. Zhou, W. R. Huang, F. Ahr, and F. X. Kärtner, Opt. Express 23, 29729 (2015).
    [Crossref]
  21. G. K. Kitaeva, P. V. Yakunin, V. V. Kornienko, and A. N. Penin, Appl. Phys. B 116, 929 (2014).
    [Crossref]
  22. B. Haase, M. Kutas, F. Riexinger, P. Bickert, A. Keil, D. Molter, M. Bortz, and G. von Freymann, Opt. Express 27, 7458 (2019).
    [Crossref]
  23. V. V. Kornienko, G. K. Kitaeva, F. Sedlmeir, G. Leuchs, and H. G. Schwefel, APL Photon. 3, 051704 (2018).
    [Crossref]
  24. E. R. Brown, J. E. Bjarnason, A. M. Fedor, and T. M. Korter, Appl. Phys. Lett. 90, 061908 (2007).
    [Crossref]
  25. Q. Song, Y. Zhao, R. Zhang, X. Liu, L. Dong, and W. Xu, J. Infrared Millimeter Terahertz Waves 31, 310 (2010).
    [Crossref]
  26. L. Tian and X. Xu, J. Infrared Millimeter Terahertz Waves 39, 302 (2018).
    [Crossref]
  27. D. Molter, M. Kolano, and G. von Freymann, Opt. Express 27, 12659 (2019).
    [Crossref]

2020 (5)

I. Kviatkovsky, H. M. Chrzanowski, E. G. Avery, H. Bartolomaeus, and S. Ramelow, Sci. Adv. 6, eabd0264 (2020).
[Crossref]

A. V. Paterova, S. M. Maniam, H. Yang, G. Grenci, and L. A. Krivitsky, Sci. Adv. 6, eabd0460 (2020).
[Crossref]

C. Lindner, S. Wolf, J. Kiessling, and F. Kühnemann, Opt. Express 28, 4426 (2020).
[Crossref]

K. A. Kuznetsov, E. I. Malkova, R. V. Zakharov, O. V. Tikhonova, and G. K. Kitaeva, Phys. Rev. A 101, 053843 (2020).
[Crossref]

M. Kutas, B. Haase, P. Bickert, F. Riexinger, D. Molter, and G. von Freymann, Sci. Adv. 6, eaaz8065 (2020).
[Crossref]

2019 (3)

2018 (5)

L. Tian and X. Xu, J. Infrared Millimeter Terahertz Waves 39, 302 (2018).
[Crossref]

V. V. Kornienko, G. K. Kitaeva, F. Sedlmeir, G. Leuchs, and H. G. Schwefel, APL Photon. 3, 051704 (2018).
[Crossref]

A. Paterova, H. Yang, C. An, D. Kalashnikov, and L. Krivitsky, New J. Phys. 20, 043015 (2018).
[Crossref]

A. V. Paterova, H. Yang, C. An, D. A. Kalashnikov, and L. A. Krivitsky, Quantum Sci. Technol. 3, 025008 (2018).
[Crossref]

T. Pfeiffer, S. Weber, J. Klier, S. Bachtler, D. Molter, J. Jonuscheit, and G. von Freymann, Opt. Express 26, 12558 (2018).
[Crossref]

2016 (2)

M. Genovese, J. Opt. 18, 073002 (2016).
[Crossref]

D. A. Kalashnikov, A. V. Paterova, S. P. Kulik, and L. A. Krivitsky, Nat. Photonics 10, 98 (2016).
[Crossref]

2015 (1)

2014 (2)

G. K. Kitaeva, P. V. Yakunin, V. V. Kornienko, and A. N. Penin, Appl. Phys. B 116, 929 (2014).
[Crossref]

G. B. Lemos, V. Borish, G. D. Cole, S. Ramelow, R. Lapkiewicz, and A. Zeilinger, Nature 512, 409 (2014).
[Crossref]

2012 (1)

2011 (2)

G. K. Kitaeva, S. P. Kovalev, A. N. Penin, A. N. Tuchak, and P. V. Yakunin, J. Infrared Millimeter Terahertz Waves 32, 1144 (2011).
[Crossref]

P. U. Jepsen, D. G. Cooke, and M. Koch, Laser Photon. Rev. 5, 124 (2011).
[Crossref]

2010 (1)

Q. Song, Y. Zhao, R. Zhang, X. Liu, L. Dong, and W. Xu, J. Infrared Millimeter Terahertz Waves 31, 310 (2010).
[Crossref]

2007 (1)

E. R. Brown, J. E. Bjarnason, A. M. Fedor, and T. M. Korter, Appl. Phys. Lett. 90, 061908 (2007).
[Crossref]

1995 (1)

1991 (2)

L. J. Wang, X. Y. Zou, and L. Mandel, Phys. Rev. A 44, 4614 (1991).
[Crossref]

X. Y. Zou, L. J. Wang, and L. Mandel, Phys. Rev. Lett. 67, 318 (1991).
[Crossref]

1990 (1)

Ahr, F.

An, C.

A. V. Paterova, H. Yang, C. An, D. A. Kalashnikov, and L. A. Krivitsky, Quantum Sci. Technol. 3, 025008 (2018).
[Crossref]

A. Paterova, H. Yang, C. An, D. Kalashnikov, and L. Krivitsky, New J. Phys. 20, 043015 (2018).
[Crossref]

Avery, E. G.

I. Kviatkovsky, H. M. Chrzanowski, E. G. Avery, H. Bartolomaeus, and S. Ramelow, Sci. Adv. 6, eabd0264 (2020).
[Crossref]

Bachtler, S.

Ballon, G.

Bartolomaeus, H.

I. Kviatkovsky, H. M. Chrzanowski, E. G. Avery, H. Bartolomaeus, and S. Ramelow, Sci. Adv. 6, eabd0264 (2020).
[Crossref]

Beckert, E.

M. Gilaberte Basset, F. Setzpfandt, F. Steinlechner, E. Beckert, T. Pertsch, and M. Gräfe, Laser Photon. Rev. 13, 1900097 (2019).
[Crossref]

Beigang, R.

Bickert, P.

M. Kutas, B. Haase, P. Bickert, F. Riexinger, D. Molter, and G. von Freymann, Sci. Adv. 6, eaaz8065 (2020).
[Crossref]

B. Haase, M. Kutas, F. Riexinger, P. Bickert, A. Keil, D. Molter, M. Bortz, and G. von Freymann, Opt. Express 27, 7458 (2019).
[Crossref]

Bjarnason, J. E.

E. R. Brown, J. E. Bjarnason, A. M. Fedor, and T. M. Korter, Appl. Phys. Lett. 90, 061908 (2007).
[Crossref]

Borish, V.

G. B. Lemos, V. Borish, G. D. Cole, S. Ramelow, R. Lapkiewicz, and A. Zeilinger, Nature 512, 409 (2014).
[Crossref]

Bortz, M.

Brown, E. R.

E. R. Brown, J. E. Bjarnason, A. M. Fedor, and T. M. Korter, Appl. Phys. Lett. 90, 061908 (2007).
[Crossref]

Chrzanowski, H. M.

I. Kviatkovsky, H. M. Chrzanowski, E. G. Avery, H. Bartolomaeus, and S. Ramelow, Sci. Adv. 6, eabd0264 (2020).
[Crossref]

Cole, G. D.

G. B. Lemos, V. Borish, G. D. Cole, S. Ramelow, R. Lapkiewicz, and A. Zeilinger, Nature 512, 409 (2014).
[Crossref]

Cooke, D. G.

P. U. Jepsen, D. G. Cooke, and M. Koch, Laser Photon. Rev. 5, 124 (2011).
[Crossref]

Dong, L.

Q. Song, Y. Zhao, R. Zhang, X. Liu, L. Dong, and W. Xu, J. Infrared Millimeter Terahertz Waves 31, 310 (2010).
[Crossref]

Drigo, L.

Fattinger, C.

Fedor, A. M.

E. R. Brown, J. E. Bjarnason, A. M. Fedor, and T. M. Korter, Appl. Phys. Lett. 90, 061908 (2007).
[Crossref]

Genovese, M.

M. Genovese, J. Opt. 18, 073002 (2016).
[Crossref]

Gilaberte Basset, M.

M. Gilaberte Basset, F. Setzpfandt, F. Steinlechner, E. Beckert, T. Pertsch, and M. Gräfe, Laser Photon. Rev. 13, 1900097 (2019).
[Crossref]

Gräfe, M.

M. Gilaberte Basset, F. Setzpfandt, F. Steinlechner, E. Beckert, T. Pertsch, and M. Gräfe, Laser Photon. Rev. 13, 1900097 (2019).
[Crossref]

Grenci, G.

A. V. Paterova, S. M. Maniam, H. Yang, G. Grenci, and L. A. Krivitsky, Sci. Adv. 6, eabd0460 (2020).
[Crossref]

Grischkowsky, D.

Haase, B.

M. Kutas, B. Haase, P. Bickert, F. Riexinger, D. Molter, and G. von Freymann, Sci. Adv. 6, eaaz8065 (2020).
[Crossref]

B. Haase, M. Kutas, F. Riexinger, P. Bickert, A. Keil, D. Molter, M. Bortz, and G. von Freymann, Opt. Express 27, 7458 (2019).
[Crossref]

Hu, B. B.

Huang, W. R.

Jepsen, P. U.

P. U. Jepsen, D. G. Cooke, and M. Koch, Laser Photon. Rev. 5, 124 (2011).
[Crossref]

Jonuscheit, J.

Kalashnikov, D.

A. Paterova, H. Yang, C. An, D. Kalashnikov, and L. Krivitsky, New J. Phys. 20, 043015 (2018).
[Crossref]

Kalashnikov, D. A.

A. V. Paterova, H. Yang, C. An, D. A. Kalashnikov, and L. A. Krivitsky, Quantum Sci. Technol. 3, 025008 (2018).
[Crossref]

D. A. Kalashnikov, A. V. Paterova, S. P. Kulik, and L. A. Krivitsky, Nat. Photonics 10, 98 (2016).
[Crossref]

Kärtner, F. X.

Keiding, S.

Keil, A.

Kiessling, J.

Kitaeva, G. K.

K. A. Kuznetsov, E. I. Malkova, R. V. Zakharov, O. V. Tikhonova, and G. K. Kitaeva, Phys. Rev. A 101, 053843 (2020).
[Crossref]

V. V. Kornienko, G. K. Kitaeva, F. Sedlmeir, G. Leuchs, and H. G. Schwefel, APL Photon. 3, 051704 (2018).
[Crossref]

G. K. Kitaeva, P. V. Yakunin, V. V. Kornienko, and A. N. Penin, Appl. Phys. B 116, 929 (2014).
[Crossref]

G. K. Kitaeva, S. P. Kovalev, A. N. Penin, A. N. Tuchak, and P. V. Yakunin, J. Infrared Millimeter Terahertz Waves 32, 1144 (2011).
[Crossref]

Klier, J.

Koch, M.

P. U. Jepsen, D. G. Cooke, and M. Koch, Laser Photon. Rev. 5, 124 (2011).
[Crossref]

Kolano, M.

Kornienko, V. V.

V. V. Kornienko, G. K. Kitaeva, F. Sedlmeir, G. Leuchs, and H. G. Schwefel, APL Photon. 3, 051704 (2018).
[Crossref]

G. K. Kitaeva, P. V. Yakunin, V. V. Kornienko, and A. N. Penin, Appl. Phys. B 116, 929 (2014).
[Crossref]

Korter, T. M.

E. R. Brown, J. E. Bjarnason, A. M. Fedor, and T. M. Korter, Appl. Phys. Lett. 90, 061908 (2007).
[Crossref]

Kovalev, S. P.

G. K. Kitaeva, S. P. Kovalev, A. N. Penin, A. N. Tuchak, and P. V. Yakunin, J. Infrared Millimeter Terahertz Waves 32, 1144 (2011).
[Crossref]

Krivitsky, L.

A. Paterova, H. Yang, C. An, D. Kalashnikov, and L. Krivitsky, New J. Phys. 20, 043015 (2018).
[Crossref]

Krivitsky, L. A.

A. V. Paterova, S. M. Maniam, H. Yang, G. Grenci, and L. A. Krivitsky, Sci. Adv. 6, eabd0460 (2020).
[Crossref]

A. V. Paterova, H. Yang, C. An, D. A. Kalashnikov, and L. A. Krivitsky, Quantum Sci. Technol. 3, 025008 (2018).
[Crossref]

D. A. Kalashnikov, A. V. Paterova, S. P. Kulik, and L. A. Krivitsky, Nat. Photonics 10, 98 (2016).
[Crossref]

Kühnemann, F.

Kulik, S. P.

D. A. Kalashnikov, A. V. Paterova, S. P. Kulik, and L. A. Krivitsky, Nat. Photonics 10, 98 (2016).
[Crossref]

Kutas, M.

M. Kutas, B. Haase, P. Bickert, F. Riexinger, D. Molter, and G. von Freymann, Sci. Adv. 6, eaaz8065 (2020).
[Crossref]

B. Haase, M. Kutas, F. Riexinger, P. Bickert, A. Keil, D. Molter, M. Bortz, and G. von Freymann, Opt. Express 27, 7458 (2019).
[Crossref]

Kuznetsov, K. A.

K. A. Kuznetsov, E. I. Malkova, R. V. Zakharov, O. V. Tikhonova, and G. K. Kitaeva, Phys. Rev. A 101, 053843 (2020).
[Crossref]

Kviatkovsky, I.

I. Kviatkovsky, H. M. Chrzanowski, E. G. Avery, H. Bartolomaeus, and S. Ramelow, Sci. Adv. 6, eabd0264 (2020).
[Crossref]

Lapkiewicz, R.

G. B. Lemos, V. Borish, G. D. Cole, S. Ramelow, R. Lapkiewicz, and A. Zeilinger, Nature 512, 409 (2014).
[Crossref]

Lemos, G. B.

G. B. Lemos, V. Borish, G. D. Cole, S. Ramelow, R. Lapkiewicz, and A. Zeilinger, Nature 512, 409 (2014).
[Crossref]

Léotin, J.

Leuchs, G.

V. V. Kornienko, G. K. Kitaeva, F. Sedlmeir, G. Leuchs, and H. G. Schwefel, APL Photon. 3, 051704 (2018).
[Crossref]

Lindner, C.

Liu, X.

Q. Song, Y. Zhao, R. Zhang, X. Liu, L. Dong, and W. Xu, J. Infrared Millimeter Terahertz Waves 31, 310 (2010).
[Crossref]

Malkova, E. I.

K. A. Kuznetsov, E. I. Malkova, R. V. Zakharov, O. V. Tikhonova, and G. K. Kitaeva, Phys. Rev. A 101, 053843 (2020).
[Crossref]

Mandel, L.

X. Y. Zou, L. J. Wang, and L. Mandel, Phys. Rev. Lett. 67, 318 (1991).
[Crossref]

L. J. Wang, X. Y. Zou, and L. Mandel, Phys. Rev. A 44, 4614 (1991).
[Crossref]

Maniam, S. M.

A. V. Paterova, S. M. Maniam, H. Yang, G. Grenci, and L. A. Krivitsky, Sci. Adv. 6, eabd0460 (2020).
[Crossref]

Molter, D.

Nuss, M. C.

Paterova, A.

A. Paterova, H. Yang, C. An, D. Kalashnikov, and L. Krivitsky, New J. Phys. 20, 043015 (2018).
[Crossref]

Paterova, A. V.

A. V. Paterova, S. M. Maniam, H. Yang, G. Grenci, and L. A. Krivitsky, Sci. Adv. 6, eabd0460 (2020).
[Crossref]

A. V. Paterova, H. Yang, C. An, D. A. Kalashnikov, and L. A. Krivitsky, Quantum Sci. Technol. 3, 025008 (2018).
[Crossref]

D. A. Kalashnikov, A. V. Paterova, S. P. Kulik, and L. A. Krivitsky, Nat. Photonics 10, 98 (2016).
[Crossref]

Penin, A. N.

G. K. Kitaeva, P. V. Yakunin, V. V. Kornienko, and A. N. Penin, Appl. Phys. B 116, 929 (2014).
[Crossref]

G. K. Kitaeva, S. P. Kovalev, A. N. Penin, A. N. Tuchak, and P. V. Yakunin, J. Infrared Millimeter Terahertz Waves 32, 1144 (2011).
[Crossref]

Pertsch, T.

M. Gilaberte Basset, F. Setzpfandt, F. Steinlechner, E. Beckert, T. Pertsch, and M. Gräfe, Laser Photon. Rev. 13, 1900097 (2019).
[Crossref]

Pfeiffer, T.

Ramelow, S.

I. Kviatkovsky, H. M. Chrzanowski, E. G. Avery, H. Bartolomaeus, and S. Ramelow, Sci. Adv. 6, eabd0264 (2020).
[Crossref]

G. B. Lemos, V. Borish, G. D. Cole, S. Ramelow, R. Lapkiewicz, and A. Zeilinger, Nature 512, 409 (2014).
[Crossref]

Riexinger, F.

M. Kutas, B. Haase, P. Bickert, F. Riexinger, D. Molter, and G. von Freymann, Sci. Adv. 6, eaaz8065 (2020).
[Crossref]

B. Haase, M. Kutas, F. Riexinger, P. Bickert, A. Keil, D. Molter, M. Bortz, and G. von Freymann, Opt. Express 27, 7458 (2019).
[Crossref]

Schwefel, H. G.

V. V. Kornienko, G. K. Kitaeva, F. Sedlmeir, G. Leuchs, and H. G. Schwefel, APL Photon. 3, 051704 (2018).
[Crossref]

Sedlmeir, F.

V. V. Kornienko, G. K. Kitaeva, F. Sedlmeir, G. Leuchs, and H. G. Schwefel, APL Photon. 3, 051704 (2018).
[Crossref]

Setzpfandt, F.

M. Gilaberte Basset, F. Setzpfandt, F. Steinlechner, E. Beckert, T. Pertsch, and M. Gräfe, Laser Photon. Rev. 13, 1900097 (2019).
[Crossref]

Song, Q.

Q. Song, Y. Zhao, R. Zhang, X. Liu, L. Dong, and W. Xu, J. Infrared Millimeter Terahertz Waves 31, 310 (2010).
[Crossref]

Steinlechner, F.

M. Gilaberte Basset, F. Setzpfandt, F. Steinlechner, E. Beckert, T. Pertsch, and M. Gräfe, Laser Photon. Rev. 13, 1900097 (2019).
[Crossref]

Tian, L.

L. Tian and X. Xu, J. Infrared Millimeter Terahertz Waves 39, 302 (2018).
[Crossref]

Tikhonova, O. V.

K. A. Kuznetsov, E. I. Malkova, R. V. Zakharov, O. V. Tikhonova, and G. K. Kitaeva, Phys. Rev. A 101, 053843 (2020).
[Crossref]

Torosyan, G.

Tuchak, A. N.

G. K. Kitaeva, S. P. Kovalev, A. N. Penin, A. N. Tuchak, and P. V. Yakunin, J. Infrared Millimeter Terahertz Waves 32, 1144 (2011).
[Crossref]

Van Exter, M.

von Freymann, G.

Wang, L. J.

X. Y. Zou, L. J. Wang, and L. Mandel, Phys. Rev. Lett. 67, 318 (1991).
[Crossref]

L. J. Wang, X. Y. Zou, and L. Mandel, Phys. Rev. A 44, 4614 (1991).
[Crossref]

Weber, S.

Wolf, S.

Wu, X.

Xu, W.

Q. Song, Y. Zhao, R. Zhang, X. Liu, L. Dong, and W. Xu, J. Infrared Millimeter Terahertz Waves 31, 310 (2010).
[Crossref]

Xu, X.

L. Tian and X. Xu, J. Infrared Millimeter Terahertz Waves 39, 302 (2018).
[Crossref]

Yakunin, P. V.

G. K. Kitaeva, P. V. Yakunin, V. V. Kornienko, and A. N. Penin, Appl. Phys. B 116, 929 (2014).
[Crossref]

G. K. Kitaeva, S. P. Kovalev, A. N. Penin, A. N. Tuchak, and P. V. Yakunin, J. Infrared Millimeter Terahertz Waves 32, 1144 (2011).
[Crossref]

Yang, H.

A. V. Paterova, S. M. Maniam, H. Yang, G. Grenci, and L. A. Krivitsky, Sci. Adv. 6, eabd0460 (2020).
[Crossref]

A. V. Paterova, H. Yang, C. An, D. A. Kalashnikov, and L. A. Krivitsky, Quantum Sci. Technol. 3, 025008 (2018).
[Crossref]

A. Paterova, H. Yang, C. An, D. Kalashnikov, and L. Krivitsky, New J. Phys. 20, 043015 (2018).
[Crossref]

Zakharov, R. V.

K. A. Kuznetsov, E. I. Malkova, R. V. Zakharov, O. V. Tikhonova, and G. K. Kitaeva, Phys. Rev. A 101, 053843 (2020).
[Crossref]

Zeilinger, A.

G. B. Lemos, V. Borish, G. D. Cole, S. Ramelow, R. Lapkiewicz, and A. Zeilinger, Nature 512, 409 (2014).
[Crossref]

Zhang, R.

Q. Song, Y. Zhao, R. Zhang, X. Liu, L. Dong, and W. Xu, J. Infrared Millimeter Terahertz Waves 31, 310 (2010).
[Crossref]

Zhao, Y.

Q. Song, Y. Zhao, R. Zhang, X. Liu, L. Dong, and W. Xu, J. Infrared Millimeter Terahertz Waves 31, 310 (2010).
[Crossref]

Zhou, C.

Zou, X. Y.

L. J. Wang, X. Y. Zou, and L. Mandel, Phys. Rev. A 44, 4614 (1991).
[Crossref]

X. Y. Zou, L. J. Wang, and L. Mandel, Phys. Rev. Lett. 67, 318 (1991).
[Crossref]

APL Photon. (1)

V. V. Kornienko, G. K. Kitaeva, F. Sedlmeir, G. Leuchs, and H. G. Schwefel, APL Photon. 3, 051704 (2018).
[Crossref]

Appl. Phys. B (1)

G. K. Kitaeva, P. V. Yakunin, V. V. Kornienko, and A. N. Penin, Appl. Phys. B 116, 929 (2014).
[Crossref]

Appl. Phys. Lett. (1)

E. R. Brown, J. E. Bjarnason, A. M. Fedor, and T. M. Korter, Appl. Phys. Lett. 90, 061908 (2007).
[Crossref]

J. Infrared Millimeter Terahertz Waves (3)

Q. Song, Y. Zhao, R. Zhang, X. Liu, L. Dong, and W. Xu, J. Infrared Millimeter Terahertz Waves 31, 310 (2010).
[Crossref]

L. Tian and X. Xu, J. Infrared Millimeter Terahertz Waves 39, 302 (2018).
[Crossref]

G. K. Kitaeva, S. P. Kovalev, A. N. Penin, A. N. Tuchak, and P. V. Yakunin, J. Infrared Millimeter Terahertz Waves 32, 1144 (2011).
[Crossref]

J. Opt. (1)

M. Genovese, J. Opt. 18, 073002 (2016).
[Crossref]

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

Laser Photon. Rev. (2)

P. U. Jepsen, D. G. Cooke, and M. Koch, Laser Photon. Rev. 5, 124 (2011).
[Crossref]

M. Gilaberte Basset, F. Setzpfandt, F. Steinlechner, E. Beckert, T. Pertsch, and M. Gräfe, Laser Photon. Rev. 13, 1900097 (2019).
[Crossref]

Nat. Photonics (1)

D. A. Kalashnikov, A. V. Paterova, S. P. Kulik, and L. A. Krivitsky, Nat. Photonics 10, 98 (2016).
[Crossref]

Nature (1)

G. B. Lemos, V. Borish, G. D. Cole, S. Ramelow, R. Lapkiewicz, and A. Zeilinger, Nature 512, 409 (2014).
[Crossref]

New J. Phys. (1)

A. Paterova, H. Yang, C. An, D. Kalashnikov, and L. Krivitsky, New J. Phys. 20, 043015 (2018).
[Crossref]

Opt. Express (6)

Opt. Lett. (1)

Phys. Rev. A (2)

K. A. Kuznetsov, E. I. Malkova, R. V. Zakharov, O. V. Tikhonova, and G. K. Kitaeva, Phys. Rev. A 101, 053843 (2020).
[Crossref]

L. J. Wang, X. Y. Zou, and L. Mandel, Phys. Rev. A 44, 4614 (1991).
[Crossref]

Phys. Rev. Lett. (1)

X. Y. Zou, L. J. Wang, and L. Mandel, Phys. Rev. Lett. 67, 318 (1991).
[Crossref]

Quantum Sci. Technol. (1)

A. V. Paterova, H. Yang, C. An, D. A. Kalashnikov, and L. A. Krivitsky, Quantum Sci. Technol. 3, 025008 (2018).
[Crossref]

Sci. Adv. (3)

I. Kviatkovsky, H. M. Chrzanowski, E. G. Avery, H. Bartolomaeus, and S. Ramelow, Sci. Adv. 6, eabd0264 (2020).
[Crossref]

A. V. Paterova, S. M. Maniam, H. Yang, G. Grenci, and L. A. Krivitsky, Sci. Adv. 6, eabd0460 (2020).
[Crossref]

M. Kutas, B. Haase, P. Bickert, F. Riexinger, D. Molter, and G. von Freymann, Sci. Adv. 6, eaaz8065 (2020).
[Crossref]

Supplementary Material (1)

NameDescription
» Supplement 1       Expanded descriptions of materials and methods

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Figures (4)

Fig. 1.
Fig. 1. Experimental setup. The 1 mm long PPLN crystals are pumped by a continuous-wave laser with a wavelength of 660 nm, generating correlated pairs of signal and terahertz photons. After the crystal the terahertz radiation is separated by an OAP with a through hole and afterwards reflected at a moveable mirror Mi. Pump and generated signal photons are reflected at Ms directly back into the crystal. After the second pass the pump radiation is filtered from the signal radiation by three volume Bragg gratings (VBGs). To obtain a frequency-angular spectrum on the sCMOS camera, the signal radiation is focused through a transmission grating (TG).
Fig. 2.
Fig. 2. Frequency-angular spectrum. (a) Frequency-angular spectrum for the used crystal with a poling period of $\Lambda = 220\;{{\unicode{x00B5}{\rm m}}}$. The image represents an averaging of 60 images with an exposure time of 500 ms each at a fixed delay of about 1 ps. (b) Enlargement of the dashed area (${{100}} \times {{100}}\;{\rm{pixels}}$) in (a). (c) Maximum amplitude of the FFT for each individual pixel and (d) corresponding frequency of the measured spectra [see (b)]. The highest amplitudes are achieved in the collinear forward region. For a better display, the frequency range in (d) is limited to 0.465–0.565 THz.
Fig. 3.
Fig. 3. Waveforms and spectra. Waveform of the used crystal with a poling period of (a), (b) $\Lambda = 220\;{{\unicode{x00B5}{\rm m}}}$ and (d), (e) $\Lambda = 200\;{{\unicode{x00B5}{\rm m}}}$ and a wax plate with an amount of (a), (c) 0.0 g and (b), (d) 1.5 g of the additive inserted in the terahertz path. The visibility of the measured waveforms without additive are about 1%, and after the interference envelope the response behavior of a water vapor absorption line at 0.56 THz is visible. Corresponding spectra of the used crystals with a poling period of (c) $\Lambda = 220\;{{\unicode{x00B5}{\rm m}}}$ and (f) $\Lambda = 200\;{{\unicode{x00B5}{\rm m}}}$ with wax plates of different amounts of (c) $\alpha$-lactose monohydrate and (f) para-aminobenzoic acid inserted in the terahertz beam path. For clarity, not all of the measured spectra are shown.
Fig. 4.
Fig. 4. Comparison between QIS and conventional TDS. Comparison of the extinction measured at the absorption frequency in the experiment and by a standard TDS system for wax plates with different amounts of (a) $\alpha$-lactose monohydrate and (c) para-aminobenzoic acid. Raster image of a wax plate with an additive amount of 1.5 g (b) $\alpha$-lactose monohydrate and (d) para-aminobenzoic acid measured by a conventional TDS system. The dashed circles indicate the area that is illuminated by the terahertz radiation in the QIS experiment and therefore evaluated for extraction of extinction values.

Equations (1)

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K = 2 n Δ f Δ f log 10 A A 0 d f ,