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Abstract
In this paper, we demonstrate a phase-sensitive photonic terahertz imaging system, based on two-tone square-law detection with a record-low phase noise. The system comprises a high-frequency photodiode (PD) for THz generation and a square-law detector (SLD) for THz detection. Two terahertz of approximately 300 GHz tones, separated by an intermediate frequency (IF) (7 GHz–15 GHz), are generated in the PD by optical heterodyning and radiated into free-space. After transmission through a device-under-test, the two-tones are self-mixed inside the SLD. The mixing results in an IF-signal, which still contains the phase information of the terahertz tones. To achieve ultra-low phase-noise, we developed a new mixing scheme using a reference PD and a low-frequency electrical local oscillator (LO) to get rid of additional phase-noise terms. In combination with a second reference PD, the output signal of the SLD can be down-converted to the kHz region to realize lock-in detection with ultra-low phase noise. The evaluation of the phase-noise shows the to-date lowest reported value of phase deviation in a frequency domain photonic terahertz imaging and spectroscopy system of 0.034°. Consequently, we also attain a low minimum detectable path difference of 2 µm for a terahertz difference frequency of 15 GHz. This is in the same range as in coherent single-tone THz systems. At the same time, it lacks their complexity and restrictions caused by the necessary optical LOs, photoconductive antennas, temperature control and delay lines.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Currently, many THz applications leave the labs and become commercialized, due to continuous costs reductions, decreases in size and weight vis a vis increasing the mobility and portability of these systems and devices [1,2]. The high transparency of non-conductive materials like plastics and ceramics for THz waves (300 GHz - 10 THz), the fact that THz waves are non-ionizing but can excite specific rotational and vibrational resonances in numerous molecules, as well as high THz absorption in water are the foundation of many THz-based applications [1–7]. Further, according to the current state of scientific knowledge, THz waves do not harm the human body while penetrating and cannot pass the skin barrier in contrast to X-rays [8]. These beneficial properties and high capabilities of THz-waves have led to increases in the study of THz applications and number of related scientific publications. Yet, their full potential is not completely exploited yet.
Several photonic solutions for THz generation and detection have been established in the last years [9]. These are based on mature and relatively low-cost C-band fiber-optics components. High-frequency photodiodes (PDs) like pin-PDs, uni-traveling carrier PDs (UTC-PDs) or triple-transit-region PDs (TTR-PDs) [10–13], provide high RF-power in a frequency range of up to a few THz, whereas photoconductive antennas or square-law detectors (SLDs) are used for THz detection.
Besides THz communication [14,15], spectroscopy and imaging systems are among the most promising candidates for successful commercialization [16]. By using fingerprint absorption spectra, terahertz spectroscopy is a suitable solution for the identification of various chemical compounds such as medicines, drugs, and explosives [17,18]. Usually, for THz imaging the same setups are employed as for spectroscopy, but with a constant frequency. In order to get the THz picture, sequential scanning approaches and parallel array-solutions are reported [19,20]. Recently, THz imaging: has been applied for quality inspection or process monitoring in the food industry [21] and for security checks [22]. Furthermore, medical applications like breast or skin cancer diagnostics could play a major role in commercializing THz related products [23].
For simple amplitude measurements with frequency domain systems, incoherent direct detection with square-law detectors is a common solution [24,25]. In contrast, coherent detection is capable of revealing additional phase information about the device-under-test (DUT). Coherent THz detection can be implemented using different detection schemes like homodyning [26] or self-heterodyning [27]. Usually, in these coherent systems, a pair of optical coupled photomixers is used for THz generation and detection. Mostly, the setup contains a high-speed photodiode and a photoconductive antenna as THz emitter and THz receiver, respectively. Coherent systems can reach a much higher signal-to-noise ratio (SNR) and lower phase-noise as compared to incoherent THz systems and time domain THz systems. Yet, they are highly complex, have a high dependency on the environment temperature and require an equal optical path lengths. Hence, to achieve a high accuracy for measuring small variations of thicknesses or refractive indices, a low phase-noise is required. This is demonstrated by [28] who achieve low phase deviation of 0.18° with a coherent single-tone THz system resulting in a minimum detectable path difference of 0.7 µm.
Besides standard single-tone continuous wave THz spectroscopy, multi-tone techniques add additional abilities to THz frequency domain spectroscopy systems. Terahertz quasi time-domain spectroscopy (QTDS) combines a low cost continuous wave setup with pulse-like signal detection [29]. Other coherent approaches using a simple SLD also allow for a very sensitive THz phase detection [12,30–32]. In [30], a phase-sensitive THz system with low phase noise was realized via self-mixing of two THz tones within a square-law Schottky barrier diode (SBD). Here, the difference frequency between the two THz tones determines the minimum detectable path difference instead of the THz carrier frequency itself. This results in a larger minimum detectable path difference as in coherent single-tone systems, despite the relative low phase noise. We presented a THz system based on two-tone square-law detection with in-house TTR-PDs used as THz emitters [12].
In this article, we report on the systematic characterization of our two-tone THz system with respect to achievable SNR, phase noise and minimum detectable path difference. In the photonic THz two-tone system, a high-speed PD is used as a THz emitter and a SLD as a receiver. The THz detection is based on the mixing of two THz tones in the SLD which generates an intermediate frequency containing the THz phase information. By using an additional reference photodiode and electrical down-converter (mixer), the developed THz two-tone system has been optimized to provide, to the best of our knowledge, the lowest reported phase deviation of a photonic terahertz frequency domain system to date. In addition, as compared to the two-tone system reported in [30], the difference frequency between the two THz tones can be easily tuned over a wide frequency range. On account of both, a very low phase noise and a comparably high THz difference frequency up to 15 GHz, the minimum detectable path difference δx is comparable to the best values achieved with coherent single-tone systems.
This paper is organized as follows: In section 2 we first present the concept and principles of the proposed imaging system. Afterwards, we evaluate the phase noise characteristics and classify the performance in the current state-of-art in photonic CW THz systems. Following, in section 3, THz amplitude and phase-difference images of different samples are presented, to prove the predicted system capability.
2. Ultra-low phase-noise THz two-tone system
In this section, the developed phase sensitive continuous wave THz imaging system based on square-law detection is introduced. Low phase noise is achieved by self-mixing two optically generated THz tones, using a SBD envelope detector. In Fig. 1, the system is schematically illustrated, including the optical as well as the electrical and THz free-space paths.
Fig. 1. Schematic of the photonic THz two-tone system including the optical (red), electrical (blue) and THz free-space path (green). (Abbreviations: TLD: Tunable laser diode; MZM: Mach-Zehnder modulator; THz-PD: Terahertz photodiode; Ref. PD: Reference photodiode; SBD: Schottky barrier diode; LIA: Lock-in detector)
2.1 Basic system setup
All optical components are commercial devices operating at the telecom wavelength of 1.55 µm. Two optical C-band signals, with the frequencies f1 and f2 (see ① in Fig. 1), are generated by two free-running external cavity tunable laser diodes (PurePhotonics PPCL200). The electric fields ${\overrightarrow {\underline{{E} }} _\textrm{1}}$ and ${\overrightarrow {\underline{{E} }} _2}$ of the laser signals are expressed by
Typically, in standard single-tone optical heterodyne systems, the difference frequency f1 – f2 represents the frequency of the resulting monochromatic THz signal. In our approach two THz tones are generated optically. To achieve this, one optical carrier is modulated using a Mach Zehnder modulator (MZM) (Fujitsu FTM7936EKA) operated at its minimum transmission point. By applying a RF modulation signal to the MZM with the frequency fmod an optical double sideband with suppressed carrier (DSB-CS) is generated. This leads to a suppression of the optical carrier at f2, while two sidebands with the frequencies f2 - fmod and f2 + fmod are generated (see ② in Fig. 1). Assuming no additional phase fluctuations the electric fields E2+ and E2- of the sidebands are
Fig. 2. a) Optical spectrum before photomixing in THz PD and b) electrical output spectrum of the SBD after selfmixing fTH1 and fTHZ2 to intermediate frequency fIF.
Afterwards, the combined optical signals are amplified again by a second EDFA (IPG Laser EAD-500-CL) and illuminate a THz-PD (commercial NTT/NEL J-band photomixer module or in-house triple transit region PD-chip). Inside the THz-PD, the absorption of the optical C-band signals produces an alternating density of free-carriers. This leads to a photocurrent with AC components frequencies equal to the two beat frequencies. This RF-generation process is known as photomixing or optical heterodyning. In detail, the RF-signal is proportional to the intensity of the C-band signals Itotal, which depends on the squared sums of the electric fields:
After passing the DUT, the two THz tones are detected and mixed via the SBD. This process is also known as self-mixing or self-heterodyning. Analogue to the optical heterodyning in the THz PD, the resulting output signal is the mixing product between the two THz tones, i.e., the frequency fIF = 2fmod is generated (see ⑤ in Fig. 1). The advantage of this approach is, that the origins of both optical beats are the same laser sources, i.e., the frequency and phase noise of each free-running laser is incorporated in both THz tones. Therefore, the cross-correlation between the two THz tones which is achieved by the self-heterodyning process in the SBD, leads to a complete cancelation of these phase noise components in the IF signal. The resulting IF signal only depends on the difference of the additional phase rotations in the THz path ΔϕTHz. If one assumes that the refractive index n is equal for the two closely spaced THz frequencies, then the difference phase ΔϕTHz relates only to n and the thickness d of a homogeneous DUT [32]:
Here, c0 is the speed of light. The detailed output voltage of the square-law detector VSLD is shown in (9):In our setup, a commercial SBD module (Virginia Diodes WR3.4ZBD) was used for the self-mixing detection. Figure 2(b) shows the resulting electrical output spectrum after self-mixing in the SBD, with an intermediate frequency fIF = 2fmod. To measure the phase information with low phase-noise a lock-in technique was used, which will be presented in the next sub-section.
2.2 Lock-in detection approach for low phase noise measurements
In order to enable lock-in detection, fIF must be down-converted to the lock-in frequency fLIA, which can be at most the maximum frequency of the used lock-in amplifier (LIA). Typically, fLIA lies in the kHz or MHz range. Furthermore, a reference signal is needed for the homodyne-based detection of the LIA.
In [30], Song et al. used a frequency doubler to generate 2fmod which they required as reference signal for the LIA. Additionally, they used an electrical oscillator operating at fLO = 2fmod – fLIA generated from an additional reference oscillator. By mixing fLO with the detected signal from the SBD they were able to finally detect the down-converted THz signal using an LIA. A similar approach has recently also been published in [32]. The disadvantage of this approach is that the second LO required for generating fLO is the main source of phase noise in the system. In addition, it is necessary to tune this oscillator depending on the THz difference frequency 2fmod. This is quite a disadvantage as a tunable oscillator has significantly higher phase noise than a fixed frequency reference LO. Both facts directly impact the system’s phase noise deviation and thus have a negative impact on the minimum path difference that can be detected with the system.
To overcome this restriction, we suggest a different approach for down-mixing of 2fmod to fLIA which allows to decouple the local oscillator frequency fLO from the THz difference frequency 2fmod. In our proposed setup, a second photodiode (reference PD) is used for generating a reference signal with the same frequency as the SBD output, i.e. 2fmod. To obtain this, the DSB-CS modulated signal f2 with the beat frequency 2fmod is split by a 3dB-coupler and feed to the reference PD (see ⑥ in Fig. 1). After amplification, the electrical output signal from the reference PD is mixed with the LO signal which in our case is directly the lock-in frequency fLO = fLIA. The mixing leads to 2fmod - fLO and 2fmod + fLO (see ⑦ in Fig. 1). Figure 3(a) shows the resulting electrical spectrum after the mixer.
Fig. 3. a) Electrical spectrum after mixing the reference PD output signal (fIF) with the LO (fLO = fLIA) and b) spectrum around the lock-in frequency fLo before lock-in detection, with and without active THz input signal.
To down-convert the detected signal, which contains the phase information about the DUT, the output signal of the SBD at 2fmod is mixed with the reference signal at 2fmod - fLO and 2fmod + fLO. This transfers amplitude and phase information of the THz channel to fLO (see ⑧ in Fig. 1) which is finally detected using the LIA (Stanford Research SR530) triggered directly from the reference output of the reference oscillator (see ⑨ in Fig. 1). Figure 3(b) shows the finally detected signal at fIF, when switching the THz signal on and off, while keeping the reference PD constantly illuminated. The noise floor depends on the displayed average noise level of the spectrum analyzer (Agilent 8563E). The resulting low phase-noise and high signal-to-noise ratios are investigated in the following subsection in more detail. Besides a low phase noise, this approach allows to tune the THz difference frequency without the necessity to also tune the frequency of the reference oscillator.
2.3 Phase-noise evaluation
To illustrate the noise characteristics of the presented two-tone system, the fluctuation of amplitude and phase within a certain time span were investigated. For this measurement, commercial J-band photomixer and SBD modules have been coupled back-to-back via their rectangular waveguide-ports, without any THz free-space path.
For the sake of a reasonable measurement time and to allow for comparison, the lock-in time constant was set to 100 µs for all following measurements. Figure 4(a) illustrates an exemplary measurement of the amplitude and phase variation within 15 s. As can be seen, a low noise is observed for phase and amplitude. To determine the SNR, the measured mean amplitude value Amean was divided by the amplitude standard deviation σA:
Fig. 4. a) Low fluctuation of amplitude and phase values within a period of 15 seconds at 2fmod = 8 GHz and f1 – f2 = 300 GHz and b) mean SNR and phase deviation values of five measurements, at fIF = 2fmod and f1 - f2 = 300 GHz. The error bars indicate the 95% confidence interval of student`s t-distribution [Student, 1908 #30]. The highest SNR of 49 dB was achieved at 8 GHz, while at 15 GHz, the lowest phase deviation of 0.034° was attained.
To estimate the system’s phase-noise, we analyzed the standard deviation of the measured phase σφ. It is worse mentioning again that in our case, σφ represents the deviation of the phase-difference of the two THz-tones. In Fig. 4(b), the SNR and σφ dependency on the THz difference frequency 2fmod are shown in a frequency range from 7 GHz to 14 GHz. The upper and lower frequency limits are depending on the RF mixers and amplifiers. During this measurement, fLO was set to 100 kHz, while the central THz frequency f1 - f2 was set to 300 GHz. Moreover, to consider the uncertainty of the measurement, every depicted datapoint represents a mean value of five measurements while the error bars indicate the 95% confidence interval of the student’s t-distributions [33].
In detail, the SNRs vary between 29 dB and 49 dB, with a maximum at 8 GHz, while the phase deviations have very low values of <0.2°. Especially the latter show the high quality of the system performance. Depending on σφ and the used frequency, the minimum detectable path difference δx can be calculated by [34]:
One origin of the variation of the SNRs can be traced back to the frequency-dependency of the resonant J-band photomixer and the SBD. Therefore, the difference in the RF-output power levels leads to a variation of the detected amplitude values and therefore to a SNR variance. Also, the used RF amplifiers and mixers show a strong frequency dependency. Due to high conversion losses of the RF-mixer (Minicircuit ZX05-153+) at 13 GHz no stable signal could be attained. It is worth mentioning that improved IF components (LO, mixer) will likely further improve the system performance.
Figure 5(a) proves the dependency of the SNR from the detected amplitude level. The phase deviation shows a decrease with rising SNR, as depicted in Fig. 5(b). Consequently, the origin of the σa variation can be traced back mostly in the difference of the SNRs. Through an additional increase of the SNR, e.g., via an enhancement of the radiated THz power or the square-law detector’s responsivity, σa should be further decreased.
Fig. 5. a) Rising signal-to-noise ratio with increasing amplitude of the detected signal and b) decreasing phase deviation with increasing SNR for 2fmod ≥ 7 GHz.
2.4 Classification of system performance in state-of-the-art
In contrast to coherent homodyne systems, the presented photonic THz two-tone setup allows phase detection without any bulky delay line in the optical or THz path. This yields a much more compact setup that can potentially be employed for mobile applications. Moreover, due to the square-law detection, there is no need for an optical LO connection to the receiver. Consequently, an equal optical path length in emitter and receiving arm for phase-noise reduction is not necessary. Therefore, controlling the temperature of the optical fiber setup for reducing excess losses is not necessary.
To classify the phase stability, phase deviation values of various reported continuous wave terahertz systems are summarized in Table 1 together with the related SNRs and δx. Previous to this work, the lowest phase deviation in a coherent single-tone THz system of 0.18° was achieved in [28], by using balanced self-heterodyne detection. To realize this, the phases of two receiving photomixers were subtracted to eliminate noise terms.
Table 1. Lowest reported phase deviations in photonic continuous wave terahertz systems
In the aforementioned two-tone system, published by Song et al. a phase deviation of 0.18° at 323 ± 5 GHz was attained [30]. By adding the low frequency LO in our system, we could increase the phase stability. Despite that the achieved SNR of 41 dB is lower than in other reported values, we realize a superior phase deviation of 0.034° at a central frequency of 300 GHz. To the best of our knowledge, this is the lowest reported phase deviation in a photonic continuous wave terahertz system to date.
2.5 System abilities and potentials
Due to the demonstrated phase sensitivity, the proposed system could ideally be used for thickness or refractive index measurements, which will be demonstrated in section 3. Another possible approach is the use of the system for time-of-flight measurements in air. If the system is used in reflection mode, a detection of path length differences for e.g., 3D-imaging or sensing should be possible. Furthermore, by tuning the modulation frequency and therefore by shifting the 2π phase ambiguity, our system should be able to measure small as well as long distances.
The system also allows spectroscopic measurements. Due to the achieved decoupling of fLO and fLIA, the THz center frequency can easily be changed without any need of additionally modifications to the setup, simply by tuning f1. A change of the complex refractive index for one of the THz tones results in a direct change of the difference phase signal. Depending on the direction of frequency tuning, the change could be allocated to the lower or higher THz frequency. In [38], we already used a similar system setup to measure the phase delay inside a silicon wafer for different frequencies, which occurred due to the Fabry-Perot effect.
For a planned future integration on a photonic integrated circuit (PIC), the tunable laser diodes and both PDs could be hybrid integrated e.g., on a low loss photonic platform, on which the MZM and the optical couplers could easily be fabricated. Additionally, a constant low frequency oscillator for down-mixing to fLIA could also be integrated on a hybrid electric/photonic chip. Even a monolithic integration of both photodiodes as well as the square-law detector, could be realized in the future which then may pave the way towards a fully-integrated mobile THz image sensor.
3. Measurement examples
To demonstrate the capabilities of the proposed system, we present proof-of-concept THz-images in this section. The images were taken with in-house fabricated triple transit region photodiodes [12,13] for THz generation. In Fig. 6(a) depicts the THz free-space setup, comprising the emitting TTR-PD, the receiving SBD, THz lenses and a DUT.
Fig. 6. a) THz free-space setup, b) vertical fiber-chip coupling with lensed fiber and c) total measurement setup
The TTR-PD was illuminated via a lensed fiber, as is shown in Fig. 6(b). The generated electrical power was received by a RF probe with WR3 rectangular waveguide output, amplified by a THz amplifier (Radiometer Physic H-LNA 260-350) and radiated into free-space via a horn antenna. The total radiated THz power was set to -15 dBm at a center frequency of f1 - f2 = 300 GHz. The THz two-tone signal was focused on the device under test (DUT) utilizing a set of Teflon lenses. By using lenses with a diameter of 50 mm and a focus length of 10 mm (Thorlabs LAT100) the calculated minimum spot radius (gaussian beam waist) at 300 GHz is < 1.5 mm. To keep the setup as simple and compact as possible, and to test the system under a realistic real-life scenario, the THz setup was built up without an additionally enclosed purge box filled with nitrogen to reduce THz absorption. The complete setup is shown in Fig. 6(c).
Different DUTs, comprising different materials were investigated using the photonic THz two-tone system: a paper sheet, a 4 mm thick plate formed from polymethyl methacrylate (PMMA) covered with protecting foil also known as acrylic glass, a metal structure, two types of highly resistive silicon objects, a 1.3 mm thick plate and a hemispherical lens with a diameter of 3 mm. All DUTs were placed on one side of a double-sided adhesive tape, while the tape-cover was still on the other side of the tape. In Fig. 7, all objects are shown.
Within the measurement, 2fmod was set to 15 GHz. THz images were taken by an automated setup with a scanning speed in x-direction of 1.8 mm/s and a step size of 1 mm in y-direction. The total number of measurement points was 4535 and the LIA integration time was set to 100 µs. The resulting amplitude and phase-difference images of all devices are presented in Fig. 8.
It is shown that the amplitude decreases strongly while transmitting through the PMMA. This effect should be caused by the protecting foil. By neglecting the phase-impact of the foil, the phase-difference measurements give a refractive index of 1.61 for the PMMA-sample by using Eq. (13), which is close to the reported values in [39] and [40]. In Fig. 9, the corresponding phase-difference profile is depicted. The figure also demonstrates the stability of the system.
Fig. 9. Longitudinal phase-difference profile corresponding to PMMA sample (Inset: PMMA sample with cutline).
It is worth mentioning, that the fluctuation of amplitude and phase values within the HR-Si plate, which can be seen in Fig. 8, should be based on standing waves within these devices, known as the Fabry-Perot effect [38]. As a result of a slightly non perpendicular incident of the THz waves, different effective lengths in the plate lead to different phases and amplitudes. Without any additional signal processing, the Fabry-Perot effect inside the HR-Si object prevents the use of Eq. (8) for refractive index determination due to the deviation of the phase values.
4. Conclusion
We report a phase-sensitive photonic terahertz two-tone imaging system, based on square-law detection. Record low phase noise is achieved by cross-correlating two THz tones in the 300 GHz range to an IF-signal which is independent of the frequency and phase noise of the lasers used to generate the THz tones. In addition, a reference photodiode and a low-frequency LO are used to down-convert and detect the received IF-signal with a lock-in amplifier. To the best of our knowledge, we achieve the lowest phase deviation reported in any photonic continuous wave THz system of σφ = 0.034° to date. Also, the minimum detectable path difference of δx = 2 µm is in the range of the best coherent single-tone systems reported but without their complexity and restrictions. Further, the decoupling of fLO from the difference frequency of the THz tones, adds additional tuning capabilities to the system and by tuning the frequency of one the lasers, the system can also be employed for frequency-domain spectroscopy. To demonstrate the capabilities of the system, proof-of-concept terahertz images of various devices were taken and the refractive index of PMMA was successful characterized.
Funding
Deutsche Forschungsgemeinschaft (Project-ID 287022738 – TRR 196).
Disclosures
The authors declare no conflicts of interest.
References
1. M. Naftaly, N. Vieweg, and A. Deninger, “Industrial Applications of Terahertz Sensing: State of Play,” Sensors 19(19), 4203 (2019). [CrossRef]
2. S. S. Dhillon, M. S. Vitiello, E. H. Linfield, A. G. Davies, M. C. Hoffmann, J. Booske, C. Paoloni, M. Gensch, P. Weightman, G. P. Williams, E. Castro-Camus, D. R. S. Cumming, F. Simoens, I. Escorcia-Carranza, J. Grant, S. Lucyszyn, M. Kuwata-Gonokami, K. Konishi, M. Koch, C. A. Schmuttenmaer, T. L. Cocker, R. Huber, A. G. Markelz, Z. D. Taylor, V. P. Wallace, J. Axel Zeitler, J. Sibik, T. M. Korter, B. Ellison, S. Rea, P. Goldsmith, K. B. Cooper, R. Appleby, D. Pardo, P. G. Huggard, V. Krozer, H. Shams, M. Fice, C. Renaud, A. Seeds, A. Stöhr, M. Naftaly, N. Ridler, R. Clarke, J. E. Cunningham, and M. B. Johnston, “The 2017 terahertz science and technology roadmap,” J. Phys. D: Appl. Phys. 50(4), 043001 (2017). [CrossRef]
3. A. Ahmadivand, B. Gerislioglu, R. Ahuja, and Y. Kumar Mishra, “Terahertz plasmonics: The rise of toroidal metadevices towards immunobiosensings,” Mater. Today 32, 108–130 (2020). [CrossRef]
4. D. M. Mittleman, “Perspective: Terahertz science and technology,” J. Appl. Phys. 122(23), 230901 (2017). [CrossRef]
5. D. A. Bandurin, D. Svintsov, I. Gayduchenko, S. G. Xu, A. Principi, M. Moskotin, I. Tretyakov, D. Yagodkin, S. Zhukov, T. Taniguchi, K. Watanabe, I. V. Grigorieva, M. Polini, G. N. Goltsman, A. K. Geim, and G. Fedorov, “Resonant terahertz detection using graphene plasmons,” Nat. Commun. 9(1), 5392 (2018). [CrossRef]
6. B. Gerislioglu, A. Ahmadivand, and N. Pala, “Tunable plasmonic toroidal terahertz metamodulator,” Phys. Rev. B 97(16), 161405 (2018). [CrossRef]
7. K. Sengupta, T. Nagatsuma, and D. M. Mittleman, “Terahertz integrated electronic and hybrid electronic–photonic systems,” Nat. Electron. 1(12), 622–635 (2018). [CrossRef]
8. Y. Hwang, J. Ahn, J. Mun, S. Bae, Y. U. Jeong, N. A. Vinokurov, and P. Kim, “In vivo analysis of THz wave irradiation induced acute inflammatory response in skin by laser-scanning confocal microscopy,” Opt. Express 22(10), 11465–11475 (2014). [CrossRef]
9. T. Nagatsuma, S. Hisatake, M. Fujita, H. H. N. Pham, K. Tsuruda, S. Kuwano, and J. Terada, “Millimeter-Wave and Terahertz-Wave Applications Enabled by Photonics,” IEEE J. Quantum Electron. 52(1), 1–12 (2016). [CrossRef]
10. S. Nellen, T. Ishibashi, A. Deninger, R. B. Kohlhaas, L. Liebermeister, M. Schell, and B. Globisch, “Experimental Comparison of UTC- and PIN-Photodiodes for Continuous-Wave Terahertz Generation,” J. Infrared, Millimeter, Terahertz Waves 41(4), 343–354 (2020). [CrossRef]
11. T. Ishibashi and H. Ito, “Uni-traveling-carrier photodiodes,” J. Appl. Phys. 127(3), 031101 (2020). [CrossRef]
12. S. Dülme, M. Grzeslo, J. Morgan, M. Steeg, M. Lange, J. Tebart, N. Schrinski, I. Mohammad, T. Neerfeld, P. Lu, A. Beling, and A. Stöhr, “300 GHz Photonic Self-Mixing Imaging-System with vertical illuminated Triple-Transit-Region Photodiode Terahertz Emitters,” in 2019 International Topical Meeting on Microwave Photonics (MWP), 2019), 1–4.
13. V. Rymanov, A. Stöhr, S. Dülme, and T. Tekin, “Triple transit region photodiodes (TTR-PDs) providing high millimeter wave output power,” Opt. Express 22(7), 7550–7558 (2014). [CrossRef]
14. T. Nagatsuma, G. Ducournau, and C. C. Renaud, “Advances in terahertz communications accelerated by photonics,” Nat. Photonics 10(6), 371–379 (2016). [CrossRef]
15. A. A. Boulogeorgos, A. Alexiou, T. Merkle, C. Schubert, R. Elschner, A. Katsiotis, P. Stavrianos, D. Kritharidis, P. Chartsias, J. Kokkoniemi, M. Juntti, J. Lehtomaki, A. Teixeira, and F. Rodrigues, “Terahertz Technologies to Deliver Optical Network Quality of Experience in Wireless Systems Beyond 5G,” IEEE Commun. Mag. 56(6), 144–151 (2018). [CrossRef]
16. A. Deninger, “11 - State-of-the-art in terahertz continuous-wave photomixer systems,” in Handbook of Terahertz Technology for Imaging, Sensing and Communications, D. Saeedkia, ed. (Woodhead Publishing, 2013), pp. 327-373.
17. D. Mittleman, “Sensing With Terahertz Radiation,” AIP Conference Proceedings 760 (2005).
18. Y.-S. Lee, Principles of Terahertz Science and Technology (Springer, Boston, MA, 2009).
19. D. M. Mittleman, “Twenty years of terahertz imaging [Invited],” Opt. Express 26(8), 9417–9431 (2018). [CrossRef]
20. H. Guerboukha, K. Nallappan, and M. Skorobogatiy, “Toward real-time terahertz imaging,” Adv. Opt. Photonics 10(4), 843–938 (2018). [CrossRef]
21. L. Afsah-Hejri, P. Hajeb, P. Ara, and R. J. Ehsani, “A Comprehensive Review on Food Applications of Terahertz Spectroscopy and Imaging,” Compr. Rev. Food Sci. Food Saf. 18, 1563–1621 (2019). [CrossRef]
22. 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,” Semiconductor Sci. Technol. 20, S266–S280 (2005).
23. J.-H. Son, S. J. Oh, and H. Cheon, “Potential clinical applications of terahertz radiation,” J. Appl. Phys. 125(19), 190901 (2019). [CrossRef]
24. M. Yahyapour, N. Vieweg, A. Roggenbuck, F. Rettich, O. Cojocari, and A. Deninger, “A Flexible Phase-Insensitive System for Broadband CW-Terahertz Spectroscopy and Imaging,” IEEE Trans. THz Sci. Technol. 6(5), 670–673 (2016). [CrossRef]
25. E. S. Lee, M. Kim, K. Moon, I. Lee, D. W. Park, S. J. H. Kim, D. Choi, K. S. Choi, D. H. Lee, and K. H. Park, “High-Speed and Cost-effective Reflective Terahertz Imaging System using a Novel 2D Beam Scanner,” J. Lightwave Technol. 38(16), 4237–4243 (2020). [CrossRef]
26. B. Sartorius, M. Schlak, D. Stanze, H. Roehle, H. Künzel, D. Schmidt, H. G. Bach, R. Kunkel, and M. Schell, “Continuous wave terahertz systems exploiting 1.5 µm telecom technologies,” Opt. Express 17(17), 15001–15007 (2009). [CrossRef]
27. S. Hisatake, G. Kitahara, K. Ajito, Y. Fukada, N. Yoshimoto, and T. Nagatsuma, “Phase-Sensitive Terahertz Self-Heterodyne System Based on Photodiode and Low-Temperature-Grown GaAs Photoconductor at 1.55,” IEEE Sens. J. 13(1), 31–36 (2013). [CrossRef]
28. S. Hisatake, Y. Koda, R. Nakamura, N. Hamada, and T. Nagatsuma, “Terahertz balanced self-heterodyne spectrometer with SNR-limited phase-measurement sensitivity,” Opt. Express 23(20), 26689–26695 (2015). [CrossRef]
29. M. Scheller and M. Koch, “Terahertz quasi time domain spectroscopy,” Opt. Express 17(20), 17723–17733 (2009). [CrossRef]
30. H. Song, S. Hwang, H. An, H.-J. Song, and J.-I. Song, “Continuous-wave THz vector imaging system utilizing two-tone signal generation and self-mixing detection,” Opt. Express 25(17), 20718–20726 (2017). [CrossRef]
31. S. Hisatake and T. Nagatsuma, “Continuous-wave terahertz field imaging based on photonics-based self-heterodyne electro-optic detection,” Opt. Lett. 38(13), 2307–2310 (2013). [CrossRef]
32. X. Cao, X. Gao, L. Zhang, L. Zhang, S. Wang, W. Li, M. Qiao, Z. Lu, H. Zhang, M. Saqlain, M. Nazar Idrees, and X. Yu, 300 GHz vector imaging system based on self-mixing detection, Sixth Symposium on Novel Photoelectronic Detection Technology and Application (SPIE, 2020), Vol. 11455.
33. Student, “The Probable Error of a Mean,” Biometrika 6(1), 1–25 (1908). [CrossRef]
34. 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]
35. J.-Y. Kim, H.-J. Song, M. Yaita, A. Hirata, and K. Ajito, “CW-THz vector spectroscopy and imaging system based on 1.55-µm fiber-optics,” Opt. Express 22(2), 1735–1741 (2014). [CrossRef]
36. S. Hisatake, J. Kim, K. Ajito, and T. Nagatsuma, “Self-Heterodyne Spectrometer Using Uni-Traveling-Carrier Photodiodes for Terahertz-Wave Generators and Optoelectronic Mixers,” J. Lightwave Technol. 32(20), 3683–3689 (2014). [CrossRef]
37. H. Song and J.-I. Song, “Robust terahertz self-heterodyne system using a phase noise compensation technique,” Opt. Express 23(16), 21181–21192 (2015). [CrossRef]
38. S. Dülme, N. Schrinski, M. Steeg, P. Lu, B. Khani, C. Brenner, M. R. Hofmann, and A. Stöhr, “Phase Delay of Terahertz Fabry-Perot Resonator characterized by a Photonic Two-Tone Spectroscopy System with Self-Heterodyne Receiver,” in 2018 43rd International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz), 2018), 1–2.
39. P. D. Cunningham, N. N. Valdes, F. A. Vallejo, L. M. Hayden, B. Polishak, X.-H. Zhou, J. Luo, A. K.-Y. Jen, J. C. Williams, and R. J. Twieg, “Broadband terahertz characterization of the refractive index and absorption of some important polymeric and organic electro-optic materials,” J. Appl. Phys. 109(4), 043505 (2011). [CrossRef]
40. T. Chang, X. Zhang, C. Yang, Z. Sun, and H.-L. Cui, “Measurement of complex terahertz dielectric properties of polymers using an improved free-space technique,” Meas. Sci. Technol. 28(4), 045002 (2017). [CrossRef]
