Open Access
Add to BibSonomy
Abstract
The detection of terahertz photons by using silicon-based devices enabled by visible photons is one of the fundamental ideas of quantum optics. Here, we present a classical detection principle using optical upconversion of terahertz photons to the near-infrared spectral range in the picosecond pulse regime, which finally enables the detection with a conventional sCMOS camera. By superimposing terahertz and optical pump pulses in a periodically poled lithium-niobate crystal, terahertz photons at 0.87 THz are converted to optical photons with wavelengths close to the central pump wavelength of 776 nm. A tunable delay between the pulses helps overlap the pulses and enables time-of-flight measurements. Using a sCMOS camera, we achieve a dynamic range of 47.8 dB with a signal to noise ratio of 23.5 dB at a measurement time of one second, in our current setup.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Corrections
8 October 2020: A correction was made to the author listing.
1. Introduction
With a growing number of applications for terahertz measurements in industry and science [1–8], the demand for fast and reliable detection methods is increasing. While sensors for visible light are cheap and readily available, the detection of terahertz radiation still is a much more difficult task. In an effort to combine the beneficial measurement characteristics of terahertz radiation with the advantages of detecting optical light, Kutas et al. utilized correlated photons to separate detection and measurement, achieving terahertz quantum sensing [9]. While the methodology of quantum sensing enables a wide range of possibilities, at the current stage the measurements are very time-consuming, as the experiment so far relies on thermal and vacuum fluctuation photons. In this manuscript, the classical approach of nonlinear optical upconversion is used, which also benefits from detection in the optical regime while reducing the measurement duration compared to quantum sensing. Using a medium with high optical nonlinearity, it is possible to create the sum and difference frequency between an optical pump and a terahertz signal by superimposing both inside the material. In a process called upconversion or downconversion respectively, a single terahertz photon and a single optical photon are converted to one new photon with a frequency close to that of the optical pump, due to the low photon energy of terahertz. This detection principle was sucessfully demonstrated in the past, utilizing different materials as nonlinear medium, such as lithium niobate ($\mathrm {LiNbO_3}$) [10–15], gallium arsenide [16,17], gallium selenide [18], zinc-germanium diphosphide [19], or organic materials such as DAST [20,21]. However, while the achieved results in these works are very promising, most of the measurements were driven by Nd:YAG-laser sources [10,13,14,18,19] and other sources with central wavelengths beyond 1000 nm, where silicon-based detection is not feasible and detectors based on indium gallium arsenide and the like are required. Also, the terahertz sources either provided continuous wave [16,20,21] or nanosecond pulsed radiation. In contrast to that, in our work the terahertz and the pump source provide synchronized pulses in the picosecond range, which increases peak power at equal pulse energy and optimizes the timing overlap between pump and signal. Due to the short pulses in the terahertz and optical regime, precise information about the relative timing between the pulses can be retrieved, which can then be used for optical runtime measurements. By using a frequency-doubled erbium-doped fiber laser as pump source, the experiment operates at a center wavelength of 776 nm, which allows the use of standard sCMOS equipment for signal detection and enables the concurrent and spectrally resolved detection of the upconverted and downconverted signal. Although a titanium-sapphire laser could be used as a source for picosecond laser pulses in the 800 nm range, using ultrafast laser components in the well-established 1550 nm telecom range simplifies the setup drastically and provides a high degree of flexibility due to the inherent fiber-based delivery compared to the standard 800 nm sources.
2. Experimental setup
As shown in Fig. 1, the experiment is driven by an erbium-doped fiber laser, with a pulse duration of 80 fs at a repetition rate of 100 MHz and a center wavelength of about 1550 nm. The laser light is then split into two separate paths with identical pulses, displayed in orange. The pulse on the first path pumps a periodically poled $\mathrm {LiNbO_3}$ crystal which is quasi-phase-matched for second-harmonic generation (SHG PPLN) of the incoming pump at a center wavelength of about 1550 nm. The SHG process provides a pulse in the near-infrared (NIR) range at a center wavelength of 776 nm, which is shown in red. Since the length of the PPLN crystal directly influences its spectral selectivity, the crystal used in this setup is 50 mm in length, resulting in a picosecond pulse with a spectral full width at half maximum of 0.14 nm. The frequency-doubled pulse is further narrowed down spectrally using high-precision volume Bragg gratings as reflective bandpass filter (RBP), with a designed acceptance bandwidth of 0.1 nm. To achieve sufficiently narrow spectra, three RBPs are used in series, where the filtered beam is reflected at each one. While every additional filter also reduces the available pump power, the filtering is required to allow a clean separation of the pump and signal in later steps.Using a lens with a focal length $\mathrm {f_1}$ of 125 mm, the beam is focussed into a second PPLN acting as nonlinear medium for the upconversion process. This PPLN is phase matched for 0.87 THz and provides an aperture of $1 \times 5~\mathrm {mm^{2}}$ at a length of 7 mm. The terahertz radiation for the upconversion is provided by a photoconductive antenna (PCA), which is pumped by the 1550 nm pulse of the second path. The PCA emits a terahertz pulse with a bandwidth of 4.5 THz and a duration in the picosecond range. The terahertz radiation is guided using two off-axis parabolic mirrors for collimation and focussing, respectively. Terahertz and optical pump photons are superimposed before entering the PPLN using a glass substrate with an indium-tin-oxide (ITO) coating, which is transparent for the pump beam but reflects the terahertz radiation. Both terahertz and optical beams are e-polarized to access the highest nonlinear coefficient (type-0 phase matching). After passing the crystal, the optical beam is collimated and passes through the filter section, where a different set of RBPs filters the remaining pump light while transmitting the converted signal. A transmission grating is used afterwards to spectrally resolve the signal components, before detecting the photons with a silicon-based sCMOS camera.
Fig. 1. Schematic of the experimental setup. A pulsed laser at about 1550 nm (orange) is used to pump the terahertz source and a frequency-doubling crystal to generate the NIR pump beam (red). Reflective bandpass filters are used to narrow the spectrum before the pump enters the nonlinear medium together with the terahertz radiation (green). SHG: second harmonics generation, PPLN: periodically poled lithium niobate crystal, RBP: reflective bandpass, M: mirror, ITO: indium-tin-oxide coated glass, PCA: photoconductive antenna, $\mathrm {f_1, f_2}$: lenses (focal lengths of $\mathrm {f_1}$: 125 mm, $\mathrm {f_2}$: 400 mm).
3. Results
3.1 Discussion of captured data
The image from the sCMOS camera is used to evaluate the conversion processes. To describe the visible features of the signal detected by the camera, Fig. 2 shows the camera image with the terahertz source turned off on top and the source turned on in the bottom image. The horizontal position of the signal is specified as frequency shift with respect to the pump photons. With no external terahertz radiation present in the crystal, the conversion signal originates from the interaction between the optical pump photons and thermal photons in the crystal. While the influence of thermal photons in the visible range is negligible in comparable setups, the low photon energy of the terahertz photons results in high thermal radiation in this spectral range, creating a clearly visible signal. For a better understanding of this signal, the k-vector diagrams for all of the possible conversion processes are displayed in Fig. 3. The pump photon is represented in red by $\mathrm {\textbf {k}_{Pump}}$, shown in black is the k-vector $\mathrm {\textbf {k}_{\Lambda }}$ of the periodic poling of the crystal. $\mathrm {\textbf {k}_{\Lambda }}$ is necessary to achieve phase matching between optical and terahertz photons, due to their large difference in refractive index. $\mathrm {\textbf {k}_{THz}}$ represents the thermal terahertz photon as green vector and $\mathrm {\textbf {k}_{Signal}}$ is the resulting signal photon, which is detected by the camera, also shown in red. The camera image shows a symmetrical signal, which is divided into downconversion on the left side and upconversion on the right side. The k-vector diagrams are divided accordingly for convenience. Since the thermal terahertz photons have statistical directions, as indicated by the green circles in both k-vector diagrams, they can either travel in forward direction like the pump photons, resulting in the more significant outer trails in the signal image, or travelling in backward direction, which creates the inner trails. In the case of collinear phase matching, in which pump and terahertz photons are parallel, the energy difference between the pump and signal photon is minimal and well-defined by the phase-matching condition of the crystal, forming the bend of the trails. Different angles are possible for conversion as long as both energy and momentum are conserved in the process, which is called noncollinear phase matching and leads to the remaining trail. The grey curves in the vector diagram indicate the intersections of terahertz and signal vectors for which the conservation criteria hold. In addition to that, a process called spontaneous parametric downconversion contributes to the trail generated by the difference frequency (left), making it stronger than the upconversion side. The process describes the spontaneous emission of two individual photons with the combined energy of a single pump photon [22]. The bottom half of Fig. 2 shows the same signal with external terahertz seeding. The additional signal appears on the bend of the forward-generated trail. This is due to the fact that the direction of the external terahertz photons is given as forward, with only small angles to the pump. The horizontal spread of the seeded signal originates from the bandwidth of the phase matching of the nonlinear medium, the additional small dots in line with the conversion signal stem from higher-order phase matching. The first order signal provides immense magnitudes compared to the thermal signal, which makes it well suited for absorption measurements in the terahertz regime. In theory, the higher order signal allows absorption measurements at the corresponding terahertz frequencies as well, but was not evaluated further due to the low signal strength. A comparison of the measured signal with the signal of the continuous wave (CW) pumped setup used by Haase et al. [22] will be given in the next section, which provides a better perspective on the magnitude of the seed influence and demonstrates the potential of this setup.
Fig. 2. Camera image of the conversion signal after the transmission grating. The top image shows the sum and difference frequency of the pump with thermal terahertz photons, which are present without external seeding. The bottom image shows the additional seed signal, including higher-order phase matching. In both cases, the pump has an average power of 5.8 mW. For better comparability, the color scale is identical for both images.
Fig. 3. Vector diagrams for the possible spontaneous conversion processes. For downconversion (left), the energy of the signal and terahertz photons add up to the pump-photon energy. For upconversion (right), the signal photon has the combined energy of the pump and the terahertz photon. Due to the high dispersion, additional phase matching is needed which is introduced by the periodic poling of the lithium-niobate crystal and represented by the $\mathrm {\textbf {k}_{\Lambda }}$-vector. Because of the large difference in energy between the optical and the terahertz photon, the vectors are not to scale.
3.2 Comparison with CW setup
To quantify the benefit of using a pulsed pump source over a CW source, the setup as demonstrated in this paper is compared to a similar setup with a CW optical pump. It is worth noting that for this comparison, a different crystal is used to match the crystal in the CW setup. For the CW setup, an exposure time of 2000 ms was used, whereas in the pulsed case the exposure time was set to 400 ms to prevent overexposure. The data were multiplied by the respective factor to normalize the measurements to an exposure of one second, which is the reference exposure time throughout this paper.Figure 4 shows the camera image of the downconversion signal for the pulsed setup at the top and for the CW setup at the bottom. The signal on the left side shows the unseeded signal only while the signal on the right also includes external terahertz seed. In contrast to Fig. 2 which shows the raw camera data, a dark image has been subtracted from the captured data to remove hotpixels and reduce the noise floor in Fig. 4. The line plot in the foreground shows the maximum value of the corresponding image row. The black curve shows the row maximum for the unseeded signal only, while the red curve shows also the seed influence. This allows an easy comparison of the signal strength of both unseeded and seeded signal simultaneously. A more precise method of determining the performance is found in the following section. It is clearly seen that the effect of external seeding is several orders of magnitude higher for the setup utilizing the pulsed pump source, while the unseeded signal is stronger overall for the CW setup. As the spontaneous upconversion signal is only dependent on average pump power, the signal from the CW source is expected to exceed the pulsed signal by two orders of magnitude, as the average power of the pulsed laser is 5.8 mW compared to 500 mW CW power. This result is verified by the measurement. Since the terahertz source is pulsed with a pulse duration of about 1 ps and a repetition rate of 100 MHz in both setups, only 0.01 % of the CW pump has temporal overlap with the terahertz pulse and can therefore contribute to the seeded upconversion. In the pulsed case, the optical pulses with a measured full width at half maximum of 26 ps have about 4 % of temporal overlap with the terahertz pulse, ignoring the temporal pulse form. Despite the significantly lower average power of the pulsed pump, the seeded signal for the pulsed pump surpasses the CW signal by a factor of four, in theory as well as in the measurement as shown in Fig. 4. For a more accurate evaluation of the system performance, the measurement system is characterized adequately in the following section.
3.3 System characterization
As previously shown, the setup which is pumped by a pulsed laser source shows more total counts when seeded. More importantly, the difference between the seeded and the unseeded signal level is much larger, which directly translates to the dynamic range (DR) of the measurement. This is one of the key parameters to characterize a measurement system, together with the signal-to-noise ratio (SNR). Here, we define the DR as the ratio between the average signal and the standard deviation of the noise floor, according to [23]. SNR describes the ratio between the average signal and its standard deviation:
The signal is defined as the integral of a square area of the camera image, surrounding the maximum count rate. The highest dynamic range is achieved when integrating an area of 13x13 pixels, as shown in Fig. 5, marked in red. Since the camera is limited to 16 bits of DR, images were taken at 100 ms exposure time to prevent saturation and possible nonlinear response of the camera. To reproduce a measurement of one second, ten consecutive images are added up and evaluated afterwards. To achieve sufficient statistical accuracy, 1000 images were captured from the camera at 100 ms exposure, which were added up to provide the equivalent of a one-second exposure for evaluation. For a blocked terahertz beam, the spontaneous signal is still visible, establishing the noise floor. The noise data is measured and evaluated with the same methods as the signal data. The sum of the marked area for each of the images is displayed on the right side of Fig. 5, with the mean and standard deviation shown in red. For the seeded data, it is clearly seen that the sum values drift over time which results in an increased standard deviation. This has a negative effect on the SNR but does not affect DR. The drift of the noise floor is much less severe, which indicates that the terahertz emitter is the source of the drift, rather than the optical pump. While it could be argued that drifting over the shown time scale of 100 seconds does not affect the single measurement and can therefore be corrected to yield smaller standard deviations, the data were evaluated as presented, resulting in a measured SNR of 23.5 dB and a DR of 47.8 dB for a measurement time of one second. While the DR is hugely dependent on the hardware used for detection, the next section will estimate the efficiency of the physical conversion process itself.Fig. 4. Comparing the signal for spontaneous (left) and seeded (right) downconversion for pulsed (top) and CW (bottom) pumped setups. The spontaneous signal is stronger for a CW pump, as it is dependent on the total number of pump photons only, while the seeded signal in the pulsed case exceeds the CW signal by a factor of four.
Fig. 5. Characterization of the measurement setup. Left: Captured image with no terahertz seed on the bottom and seeded on top, with the marked area to be integrated for the signal measurements. The plot on the right shows the according integral for consecutive measurements, together with the average in solid red and the standard deviations as dashed red lines.
3.4 Detection efficiency
To estimate the efficiency of the conversion process, the number of terahertz photons which are available to be converted has to be considered first. The upper limit of available terahertz radiation is determined by measuring the total terahertz power in the focus. Using a calibrated pyroelectric detector, the terahertz power is measured to be 13.1 µW $\pm$ 1.1 µW. As the terahertz pulses are in the picosecond range, the spectrum spans 4.5 THz, as seen in Fig. 6.Since the crystal is periodically poled in favor of a specific spectral range, only a fraction of the emitted terahertz radiation is converted due to the the phase-matching condition
Using the Sellmeier coefficients of LiNbO3 for the terahertz range [24] to calculate the wavelength dependent refractive index $n_{\mathrm {THz}}$, the given poling period of $\Lambda$ = 123.6 µm results in optimal phase matching for 0.87 THz. Even though the emitted terahertz radiation offers a broad spectrum, the bandwidth of the measured signal is currently limited by the upconversion process. As described in chapter 2, the crystal length influences the acceptance bandwidth of the crystal. A shorter crystal would result in a broader upconversion spectrum which would be beneficial for spectroscopic measurements but would simultaneously reduce signal strength. The central terahertz frequency of the upconversion process is defined by the physical characteristics of the crystal. Thermal tuning has negligible influence for this process due to the large difference in photon energy between pump and signal wave. Better tunability could be achieved using methods such as circular crystals [25]. The spectral width of the conversion was estimated using the measured upconversion signal to be 60 GHz, as shown in Fig. 6 as red curve in the spectrum. This results in approximately 5 % of usable terahertz radiation compared to the total available radiation. With the photon energy the number of photons with sufficient energy to be converted equals $1.13 \times 10^{15}$ per second. Since the photons can only be converted when superimposed with an optical photon, the beam width of both pump and terahertz beam have to be considered as well. The beam widths at the entry facet of the crystal were measured using a knife-edge measurement. The resulting Gaussian profiles are shown in Fig. 6 as inset. The green curve represents the much broader terahertz beam with $\sigma _{\mathrm {THz}}=1683$ µm, while the red curve represents the optical pump beam with $\sigma _{\mathrm {Pump}}=105$ µm. The dashed vertical lines symbolize the $3 \sigma _{\mathrm {Pump}}$ interval of the pump beam, indicating the fraction of the terahertz profile which is superimposing the pump beam. To calculate the amount of terahertz photons in this area, the integral of the two-dimensional Gaussian function is used:Fig. 6. Limiting factors of the usable terahertz power. The diagram shows the emitted spectrum together with a Gaussian curve indicating the frequency range for which the crystal is phase matched. All of the other components are not upconverted in the crystal. Shown as inset is the beam profile of the terahertz beam in green and the pump beam in red at the crystal facet. Only the overlapping volume, defined by the $3\sigma$ interval of the pump beam is considered.
3.5 Sample measurements
To measure the absorption of material inserted into the parallel terahertz beam, the additional optical path length of the radiation originating from the higher refractive index of the material has to be considered as well. Because the terahertz pulse must overlap with the optical pump pulse in time, the delay cannot be ignored. To measure the additional delay and also the absorption of the material, the delay line shown in Fig. 1 is used to manipulate the timing relation between the terahertz and the pump pulse. The delay of the terahertz pulse can be tuned over a sufficient range to measure the cross correlation between the terahertz pulse and the optical pulse. This method allows an easy determination of the position and magnitude of the signal maximum.Fig. 7 shows cross correlation measurements for a different number of paper sheets in the terahertz beam in the left diagram. By using logarithmic scaling on the y-axis, the curves of the individual cross correlations have nearly equal distance to each other, showing the exponential absorption of the paper as expected. The data are normalized to the reference curve without sample to better show the DR of the measurement. The red horizontal line indicates the calculated dynamic range of 47.8 dB. The curve measured with 40 sheets still shows distinguishable signal and a noise floor in accordance to the calculated DR. The vertical line in the figure shows the delay shift from the added paper layers, connecting the maxima of the individual curves. While the shift can be seen clearly, a measurement without shift correction would still yield usable results. To better show the signal shift, a 10-mm-thick high-resistivity silicon wafer was used, since it is highly refractive but less absorbing in the terahertz range. The diagram on the right of Fig. 7 shows the cross-correlation for the signal without any obstacle in red and the corresponding signal transmitted through the silicon in blue. The time delay between the main maxima is 80.0 ps, which is equal to 23.98 mm additional optical length. With a refractive index of $n_{\mathrm {s}} = 3.42$ [27], the expected shift introduced by 10 mm of silicon is 24.2 mm, which resembles the measurement. According to the Fresnel equations, the amount of reflected radiation on an interface is given by
For the given material, 30 % of the intensity is reflected on each interface, resulting in an intensity loss of 51% for a single pass through the material. The fraction of the radiation which is reflected on the Si-air interface leads to multireflections in the material. The first multireflection, resulting from the beam entering the silicon, reflecting on the inner interface, then reflecting on the rear interface and exiting the medium in forward direction forms the second peak in the diagram. As the radiation runs through the material for an extra two passes, the additional travel distance equals $2 n_{\mathrm {s}} \times 10~\mathrm {mm} = 68.4~\mathrm {mm}$, which is equal to 229.7 ps, with a remaining intensity of 4.4 %. All of the above mentioned numbers are according to the measurement.Fig. 7. Measuring cross correlation between terahertz and optical pulse by tuning the timing relation between both. On the left, the cross correlations for different amounts of paper in the terahertz beam is shown. The radiation is steadily absorbed and the shift of the pulse is visible. On the right, the delay introduced by a 10-mm-thick high-resistivity silicon wafer is measured using the maxima positions.
4. Conclusions
We were able to utilize an upconversion process to convert terahertz photons to the optical range, to accomplish the goal of detecting terahertz measurements using silicon-based optical detectors. We characterized the system performance and validated the dynamic range of 48 dB for a one second measurement period in two measurements. The measurements showed the effect of high material absorption and high refraction. The relative timing control of the used picosecond terahertz and pump pulses enabled an accurate thickness determination. All measurements showed the expected behavior. Finally, the efficiency of the measurement setup was estimated to be 7.5 detected signal photons per one million. All of the results look promising and demonstrate the potential of this approach, which makes the step towards interferometric measurements in accordance to [9] plausible in the future.
Funding
Fraunhofer-Gesellschaft.
Acknowledgements
This project was funded by the Fraunhofer-Gesellschaft within the Fraunhofer Lighthouse Project Quantum Methods for Advanced Imaging Solutions (QUILT).
Disclosures
The authors declare no conflicts of interest..
References
1. T. Nagatsuma, G. Ducournau, and C. C. Renaud, “Advances in terahertz communications accelerated by photonics,” Nat. Photonics 10(6), 371–379 (2016). [CrossRef]
2. A. Redo-Sanchez, B. Heshmat, A. Aghasi, S. Naqvi, M. Zhang, J. Romberg, and R. Raskar, “Terahertz time-gated spectral imaging for content extraction through layered structures,” Nat. Commun. 7(1), 12665 (2016). [CrossRef]
3. 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). [CrossRef]
4. T. Pfeiffer, S. Weber, J. Klier, S. Bachtler, D. Molter, J. Jonuscheit, and G. von Freymann, “Terahertz thickness determination with interferometric vibration correction for industrial applications,” Opt. Express 26(10), 12558–12568 (2018). [CrossRef]
5. H. Merbold, D. J. H. C. Maas, and J. L. M. van Mechelen, “Multiparameter sensing of paper sheets using terahertz time-domain spectroscopy: Caliper, fiber orientation, moisture, and the role of spatial inhomogeneity,” in 2016 IEEE SENSORS, pp. 1–3 (IEEE, 2016).
6. S. Weber, J. Klier, F. Ellrich, S. Paustian, N. Güttler, O. Tiedje, J. Jonuscheit, and G. von Freymann, “Thickness determination of wet coatings using self-calibration method,” in 2017 42nd International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz), pp. 1–2 (IEEE, 2017).
7. D. Molter, G. Torosyan, G. Ballon, L. Drigo, R. Beigang, and J. Léotin, “Step-scan time-domain terahertz magneto-spectroscopy,” Opt. Express 20(6), 5993–6002 (2012). [CrossRef]
8. J. Klier, D. Kharik, W. Zwetow, D. Gundacker, S. Weber, D. Molter, F. Ellrich, J. Jonuscheit, and G. von Freymann, “Four-channel terahertz time-domain spectroscopy system for industrial pipe inspection,” in 2018 43rd International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz), pp. 1–2 (IEEE, 2018).
9. M. Kutas, B. Haase, P. Bickert, F. Riexinger, D. Molter, and G. von Freymann, “Terahertz quantum sensing,” Sci. Adv. 6(11), eaaz8065 (2020). [CrossRef]
10. R. Guo, S. Ohno, H. Minamide, T. Ikari, and H. Ito, “Highly sensitive coherent detection of terahertz waves at room temperature using a parametric process,” Appl. Phys. Lett. 93(2), 021106 (2008). [CrossRef]
11. R. Guo, T. Ikari, J. Zhang, H. Minamide, and H. Ito, “Frequency-agile THz-wave generation and detection system using nonlinear frequency conversion at room temperature,” Opt. Express 18(16), 16430–16436 (2010). [CrossRef]
12. H. Minamide, S. Hayashi, K. Nawata, T. Taira, J.-I. Shikata, and K. Kawase, “Kilowatt-peak terahertz-wave generation and sub-femtojoule terahertz-wave pulse detection based on nonlinear optical wavelength-conversion at room temperature,” J. Infrared, Millimeter, Terahertz Waves 35(1), 25–37 (2014). [CrossRef]
13. K. Nawata, T. Notake, H. Ishizuki, F. Qi, Y. Takida, S. Fan, S. Hayashi, T. Taira, and H. Minamide, “Effective terahertz-to-near-infrared photon conversion in slant-stripe-type periodically poled LiNbO3,” Appl. Phys. Lett. 104(9), 091125 (2014). [CrossRef]
14. Y. Takida, K. Nawata, S. Suzuki, M. Asada, and H. Minamide, “Nonlinear optical detection of terahertz-wave radiation from resonant tunneling diodes,” Opt. Express 25(5), 5389–5396 (2017). [CrossRef]
15. V. V. Kornienko, S. A. Savinov, Y. A. Mityagin, and G. K. Kitaeva, “Terahertz continuous wave nonlinear-optical detection without phase-locking between a source and the detector,” Opt. Lett. 41(17), 4075–4078 (2016). [CrossRef]
16. M. J. Khan, J. C. Chen, and S. Kaushik, “Optical detection of terahertz using nonlinear parametric upconversion,” Opt. Lett. 33(23), 2725–2727 (2008). [CrossRef]
17. M. J. Khan, J. C. Chen, and S. Kaushik, “Optical detection of terahertz radiation by using nonlinear parametric upconversion,” Opt. Lett. 32(22), 3248–3250 (2007). [CrossRef]
18. W. Shi, Y. J. Ding, N. Fernelius, and F. K. Hopkins, “Observation of difference-frequency generation by mixing of terahertz and near-infrared laser beams in a GaSe crystal,” Appl. Phys. Lett. 88(10), 101101 (2006). [CrossRef]
19. Y. J. Ding and W. Shi, “Observation of THz to near-infrared parametric conversion in ZnGeP 2 crystal,” Opt. Express 14(18), 8311–8316 (2006). [CrossRef]
20. F. Qi, S. Fan, T. Notake, K. Nawata, T. Matsukawa, Y. Takida, and H. Minamide, “An ultra-broadband frequency-domain terahertz measurement system based on frequency conversion via DAST crystal with an optimized phase-matching condition,” Laser Phys. Lett. 11(8), 085403 (2014). [CrossRef]
21. H. Minamide, J. Zhang, R. Guo, K. Miyamoto, S. Ohno, and H. Ito, “High-sensitivity detection of terahertz waves using nonlinear up-conversion in an organic 4-dimethylamino-N-methyl-4-stilbazolium tosylate crystal,” Appl. Phys. Lett. 97(12), 121106 (2010). [CrossRef]
22. B. Haase, M. Kutas, F. Riexinger, P. Bickert, A. Keil, D. Molter, M. Bortz, and G. von Freymann, “Spontaneous parametric down-conversion of photons at 660 nm to the terahertz and sub-terahertz frequency range,” Opt. Express 27(5), 7458–7468 (2019). [CrossRef]
23. M. Naftaly and R. Dudley, “Methodologies for determining the dynamic ranges and signal-to-noise ratios of terahertz time-domain spectrometers,” Opt. Lett. 34(8), 1213–1215 (2009). [CrossRef]
24. J. Kiessling, K. Buse, and I. Breunig, “Temperature-dependent Sellmeier equation for the extraordinary refractive index of 5 mol.% MgO-doped LiNbO 3 in the terahertz range,” J. Opt. Soc. Am. B 30(4), 950–952 (2013). [CrossRef]
25. C. Weiss, G. Torosyan, J.-P. Meyn, R. Wallenstein, R. Beigang, and Y. Avetisyan, “Tuning characteristics of narrowband THz radiation generated via optical rectification in periodically poled lithium niobate,” Opt. Express 8(9), 497–502 (2001). [CrossRef]
26. F. F. Sizov, V. P. Reva, A. G. Golenkov, and V. V. Zabudsky, “Uncooled detectors challenges for THz/sub-THz arrays imaging,” J. Infrared, Millimeter, Terahertz Waves 32(10), 1192–1206 (2011). [CrossRef]
27. J. Dai, J. Zhang, W. Zhang, and D. Grischkowsky, “Terahertz time-domain spectroscopy characterization of the far-infrared absorption and index of refraction of high-resistivity, float-zone silicon,” J. Opt. Soc. Am. B 21(7), 1379–1386 (2004). [CrossRef]
