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Abstract
The foundation for polarization-based terahertz applications is the acquisition of polarization information. To develop an all-electronic terahertz straightforward polarization detection system, in this paper, a terahertz polarization detector based on three antenna-coupled AlGaN/GaN high-electron-mobility transistors (HEMTs) on a single chip is designed and fabricated. The function of the direct polarization detector is proven by measuring the polarization angle of linearly polarized continuous-wave terahertz radiation at 216 GHz. The average deviation and maximum deviation of the measured polarization angle are 3.7 degrees and 10 degrees, respectively. The error comes mainly from the disturbance of the local terahertz field by the interference effect. Simulations locate the sources of interference and guide the further device design and packaging of such kind of direct polarization detectors.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
As another degree of freedom which is independent of the amplitude and phase, polarization information is widely employed in imaging and material analysis to determine the birefringence of objects [1,2], identify the target [3,4], and provide additional information on anisotropic dielectric properties of materials [5,6]. Several strategies have been attempted to reach such goals. Rotating wire-grid polarizers is the most commonly used technique [7–9]. Relying on the precise micro-nano processing technology, the typical value of the extinction ratio of wire-grid polarizers reaches 1000:1 and the bandwidth is up to 3 THz. These rotating polarizers are widely implemented for acquiring complex constants of materials in terahertz ellipsometer [10–12] and continuous-wave imaging [13–15]. Another way to probe the polarization angle is electro-optic (EO) sampling which takes advantage of the anisotropic optical response of EO crystals [16–19]. Yasumatsu and Watanabe proposed a fast and precise method for polarization determination by mechanically rotating a GaP crystal and achieved a standard deviation of 0.56 degrees [19]. Both above two most typical methods of polarization angle detection rely on manual rotate of the polarizer or EO crystal placed in the terahertz beam path to reconstruct the polarization and obtain the polarization angle by detecting the two orthogonal polarization components of the terahertz waves through a single terahertz detector or a pair of photodetectors in optical region. Polarizers and crystals can be recognized as polarization modulators of terahertz waves. The ability to resolve the polarization angle of such modulator-detector mode is mainly dependent on the quality of modulators, as well as rotating accuracy. The terahertz detectors integrated in such systems usually only monitor the amplitude of the terahertz waves. It is possible to probe the polarization angle by the utilization of polarization-sensitive detectors [20–23] which do not rely on the rotation of polarizers or EO crystals. For example, a photoconductive antenna device with two orthogonal gaps or three contacts with 120 degrees spacing could gain the polarization angle of pulsed broadband terahertz waves generated by terahertz time-domain spectrometer (TDS). However, the three schemes of testing systems above are generally complex, costly, and difficult to operate. To satisfy the demand for a low-cost, efficient and portable terahertz polarization detection system, an all-electronic direct polarization detector is strongly desired.
Antenna-coupled AlGaN/GaN high-electron-mobility transistors (HEMTs) possess the inherent functional relationship between the response and the polarization angle of terahertz irradiation which can be continuous-wave or pulsed linearly polarized and circularly polarized [24,25]. The results indicated detection of terahertz-wave polarization angle is possible by utilizing such detectors. In this article, a prototype of an integrated terahertz polarization detector based on three antenna-coupled AlGaN/GaN HEMTs placed in an equilateral triangle on a single chip is designed and fabricated. Direct measurement of polarization angle with this detector for linearly polarized terahertz continuous waves at around 220 GHz is verified. The deviation of the measured polarization angle is evaluated. According to the simulation, the inaccuracy is mainly caused by interference from the metal plate under the transparent detector chip, as well as the metal filters on the chip. Subsequent proposals for eliminating such interference effect to improve the polarization angle resolution are proposed.
2. Device information and experimental implementations
The polarization detector is consisted of three antenna-coupled AlGaN/GaN HEMTs placed in an equilateral triangle on a single chip, as schematically shown in Fig. 1(a). The chip is fabricated based on AlGaN/GaN two-dimensional electron gas (2DEG) which is grown by metal-organic chemical vapor deposition (MOCVD) on a 2-inch silicon-carbide substrate. Each HEMT has three electrode pads (source, drain and gate): HEMT#1 ($\mathrm {S}_1$, $\mathrm {D}_1$ and $\mathrm {G}_1$), HEMT#2 ($\mathrm {S}_2$, $\mathrm {D}_2$ and $\mathrm {G}_2$), and HEMT#3 ($\mathrm {S}_3$, $\mathrm {D}_3$ and $\mathrm {G}_3$). The zoom-in view of polarization-sensitive antennas and the central active region are given in Fig. 1(b). The AlGaN/GaN heterostructure is similar to those reported previously in Ref. [24–27]. The antennas are fabricated on top of the active area and forms a capacitively coupled connection with the 2DEG. For each HEMT, the antenna is composed of three quarter-wavelength dipole antennas and designed for central resonance frequency of 220 GHz. G-antenna is connected to the gate electrode so that a bias voltage $V_\mathrm {G}$ can be applied to the gate. S-antenna and D-antenna placed on the opposite sides of the gate are connected to the source electrode and the drain electrode through 2DEG lead, respectively. The filters are placed between the G-antenna and the gate electrode. The filters are constructed from metal coils to lessen the effect of the metal connection line from the G-antenna to the lead electrode on the antenna’s resonant characteristics. The gate has a designed length of $L$=900 nm. The gaps on the source side and drain side are $D$=650 nm. The antenna length $AL$ and width $AW$ are $207\,\mathrm {\mu m}$ and $13\,\mathrm {\mu m}$, respectively. With the electron-beam evaporation process, the electrode pads, antennas and filters are all formed by the metal of nickel and gold (Ni/Au).
Fig. 1. (a) Terahertz polarization detector with three antenna-coupled AlGaN/GaN HEMTs placed in an equilateral triangle. (b) Enlarged view of the antennas and polarization characteristics of a single HEMT. Zoom-in view of the central active area.
Since the dipole antenna has the intrinsic ability of polarization resolution, the terahertz response is proportional to the square of cosine angle which is between the direction of the terahertz electric field and the long side of antenna, as shown in Fig. 1(b). The response signal is maximal when the antenna is parallel to the direction of the terahertz electric field while the signal is minimal when the antenna is perpendicular. Assuming a continuous-waves linearly polarized terahertz radiation beam is uniformly shone on the detector, the response photocurrents $i_1$, $i_2$ and $i_3$ (generated by HEMT#1, HEMT#2 and HEMT#3, respectively) can be expressed as
where $i_0$ is the maximum response photocurrent of HEMT#1 when its antenna is in parallel to the terahertz electric-field direction. $i_0$ can be stated as $i_0=R_\mathrm {i}P_\mathrm {THz}$, where $R_\mathrm {i}$ and $P_\mathrm {THz}$ are the current responsivity and the received terahertz power by HEMT#1, respectively. $\alpha$ and $\beta$ are ratio of HEMT#2 and HEMT#3’s maximum photocurrent to $i_0$, respectively. Also, $\alpha$ and $\beta$ are the responsivity ratio of HEMT#2 and HEMT#3, respectively, to HEMT#1. For the detector under uniform terahertz radiation, discrepancies in maximum photocurrents amongst the three HEMTs are mostly due to different current responsivity caused by fluctuations in process and material. Taking the direction perpendicular to HEMT#1 as the reference direction, $\theta$ represents the angle between the reference direction and the direction of terahertz electric field, and is defined as polarization angle. The unique polarization angle $\theta$ corresponding to a set of $i_1$, $i_2$ and $i_3$ can be solved by Eq.(1)(2)(3).To characterize the detector above, a detection system is setup as shown schematically in Fig. 2. The chip is packaged and assembled in $x-y$ plane at the center of a rotation stage, rotating with axis $z$ controlled by an automatic stepper motor. The three source electrodes $\mathrm {S}_1$, $\mathrm {S}_2$ and $\mathrm {S}_3$ are grounded, while three gates $\mathrm {G}_1$, $\mathrm {G}_2$ and $\mathrm {G}_3$ are connected to the same bias voltage source (Yokagawa GS200). A microwave signal is multiplied with a factor of 18 by a Schottky-barrier-diode frequency multiplier chain (VDI#AMC). The terahertz source creates linearly polarized continuous-wave radiation. In the experiment, the polarization direction of the incident terahertz waves is kept constant along the $y$-axis while rotating the detector. Therefore, the polarization angle defined above is also the angle at which the detector is rotated. The distance between the terahertz source and the detector is about 10 cm. The terahertz waves are uniformly radiated to the top of the chip. Three antennas induce strongly localized terahertz fields in the corresponding gated 2DEG channel. The localized terahertz fields contain a component in the source-drain direction and another component in the direction perpendicular to the 2DEG plane. Two electric fields with the same frequency are mixed in the channel, leading to a DC terahertz photocurrent along the source-drain direction. By on–off (50% duty cycle) modulating the microwave signal with modulation frequency $f_\mathrm {M}=3317$ Hz, the three photocurrents $i_1$, $i_2$ and $i_3$ exporting from three drains ($\mathrm {D}_1$, $\mathrm {D}_2$ and $\mathrm {D}_3$, respectively) are amplified by a current preamplifier (DL1211) with a transimpedance gain of 1 M$\Omega$ and then measured by a lock-in amplifier (Signal Recovery 7265). According to the self-mixing model of antenna-coupled HEMTs without source-drain bias, the terahertz photocurrent can be expressed as [24]
Fig. 2. Schematic setup for measurement of the polarization detecting. The inset is microscope image of the packaged detector chip.
3. Results and discussions
Prior to the realization of polarization detection, photo responses of three HEMTs are characterized so that $\alpha$ and $\beta$ are obtained. Turning rotation stage clockwise to 90 degrees, 150 degrees and 30 degrees, respectively. Irradiated by terahertz waves at a frequency of 216 GHz, the photocurrents of three HEMTs tuned by the gate voltage $V_\mathrm {G}$ are measured and shown in Fig. 3(a). Simultaneously, the max response photocurrent of each HEMT is available. After division calculation, coefficients $\alpha$=1.09 and $\beta$=2.10. In order to clearly read the information from the figure, the curves of HEMT#2 and HEMT#3 are horizontally offset by -0.5 V and -1.0 V, respectively. Rotating the rotary stage, the photocurrent of each HEMT as a function of polarization angle can be acquired. Considering the difference between three HEMTs, $i_2$ is divided by $\alpha$ and $i_3$ is divided by $\beta$, respectively. Figure 3(b) describes the such three compensated curves $i_1$, $i_2/\alpha$ and $i_3/\beta$ as open symbols. The curves of $i_1$, $i_2/\alpha$ and $i_3/\beta$ of experiment coincide with the corresponding theoretical curves. The three solid curves in Fig. 3(b) illustrate the normalized theoretical photocurrents $i_1$, $i_2$ and $i_3$ varying with polarization angle. $i_1$, $i_2$ and $i_3$ are 60 degrees apart in phase from each other, which is consistent with the geometrical relation between the three antennas. The experimental results reveal that the detector performs well in terms of polarization detection, as predicted by the design. Nevertheless, the measured values in Fig. 3(b)’s area highlighted by the dashed circles differ significantly from their theoretical values. The polarization angle can be calculated directly from a set of experimental data, but it will be far off from the true polarization angle. Furthermore, a set of photocurrents $i_1$, $i_2$ and $i_3$ must be normalized before solving the trigonometric functions to derive the corresponding polarization angle, which adds to the processing burden. Here, a concept of photocurrent ratio factors is proposed to fix the unique polarization angle more easily after a simple calculation. The photocurrent ratio factors $M$ and $N$ are defined as:
$M$ and $N$ are shown in Fig. 3(c). The solid lines and open symbols are calculated from the normalized theoretical photocurrents and the photocurrents experimentally detected from Fig. 3(b), respectively. The measured values are converted to unitless quantities and pulled to a level that is consistent with the theoretical values. The experimental $M$ and $N$ are closer to their theoretical values than the pre-processed photocurrents which have many locations with large departures from their related theoretical values. Points where the currents are close to 0 will generate a significant inaccuracy in the process of determining the polarization angle by the inverse solution of the three photocurrents. This formula, on the other hand, provides a minimum value of 0.25 for $M$ and $N$, eliminating this error.Fig. 3. (a) Measured photocurrents of three HEMTs as a function of the gate voltage $V_\mathrm {G}$ with $\vec {E}_\mathrm {THz}$ in parallel to the corresponding antenna. The curves of HEMT#2 and HEMT#3 are horizontally shifted by -0.5 V and -1.0 V, respectively. (b) Photocurrents as a function of the polarization angle. The solid lines corresponding to right $y$-axis are normalized theoretical photocurrents, and the open symbols corresponding to left $y$-axis are experimental data. (c) Photocurrents ratio factors as a function of the polarization angle. The open symbols are calculated from experimental data, and the solid curves are calculated from normalized theoretical photocurrents.
To evaluate the accuracy of the detector in detecting the polarization angle, angles of integer multiples of ten are selected for testing. The comparison of the measured polarization angle and the actual polarization angle is shown in Fig. 4. The solid lines in the diagram represent the actual polarization angle and the red solid circles represent the polarization angle of 216 GHz obtained by factors $M$ and $N$. The polarization angle obtained from the test is overall larger than the actual polarization angle, which may be due to angular errors in the chip package and interference effects. The average deviation and maximum deviation are respectively 3.7 degrees and 10 degrees, respectively. The results indicate that this integrated polarization detector can effectively detect linearly polarized terahertz continuous waves. However, the error of the measured polarization angle acquired at other frequencies is significantly larger than that at 216 GHz in the practical process. For example, the comparison of the measured polarization angle and the actual angle at 230.4 GHz is depicted as blue triangulars in Fig. 4. The values of $\alpha$ and $\beta$ are 0.20 and 2.34 at 230.4 GHz, respectively. The average deviation and maximum deviation are 16.8 degrees and 43 degrees, respectively. That means the feasibility of such an integrated polarization detector as a prototype is just proved. The sensitivity and detection frequency bandwidth need to be improved greatly.
Fig. 4. Comparison of the measured polarization angle and actual polarization angle at frequency of 216 GHz and 230.4 GHz.
In contrast to the polarization characteristics demonstrated in Ref. [24,25] with the same type of detector, the results show that the measured values agree well with the theory for the incoherent light generated by black-body radiation, while there is a relatively large error for the coherent light generated by backward-wave oscillator (BWO). It is interference effect that causes the experimental photocurrents to deviate from the theoretical values. In this system, metal electrode pads on the chip surface, filters, substrate, metal plate in the package and bonding wires might all be the sources of terahertz interference.
To determine the causes of errors and find the direction for optimization, simulations are conducted. In the simulation, irradiated by uniformly distributed terahertz wave at 220 GHz with a defined and varying polarization angle, the simulated antenna factors of the detector with a 200 $\mathrm {\mu }$m thick silicon carbide substrate can be gained. The three antenna factors as a function of the polarization angle lead to the three normalized photocurrents. By adopting the same procedure as before, the photocurrents ratio factors $M$ and $N$ are calculated, deriving to the simulated polarization angle. Figure 5 shows the results of simulated normalized photocurrents and simulated polarization angle for four cases. The simulation of the four cases shows that the interference effect led by the reflection of the metal plate in the package and the filters on the chip are the main causes of the measurement error. Despite the fact that the interference effect generates inaccuracy, the simulated polarization angle maintains high linearity. The deviation angle $\Delta \theta$ is defined as $\Delta \theta = \theta _\mathrm {sim}-\theta$, where $\theta _\mathrm {sim}$ and $\theta$ are simulated polarization angle and actual polarization angle, respectively. In the case of only three antennas, as shown in Fig. 5(a), the divergence from the theoretical polarization angle is slight. The simulated angle is overall 2 degrees larger than that of the actual, i.e., $\Delta \theta = 2^{\circ }$, which is mainly caused by substrate interference. The inaccuracy remains minor following the addition of the metal electrode pads, as illustrated in Fig. 5(b). The simulated angle is moved to the place of 1 degree smaller than the actual, i.e., $\Delta \theta = -1^{\circ }$. The interference induced by the electrode pads has a modest effect on the measurement due to sufficient distance from the electrodes to the gate-controlled 2DEG regions. The influence of the metal electrodes will be effectively eliminated by reducing the size of pads and pulling them away from the gated 2DEG regions.
Fig. 5. Simulated photocurrents $i_1$, $i_2$, $i_3$, and measured polarization angle at 220 GHz under the condition of: (a) three antennas only. (b) three antennas and electrode pads. (c) three antennas, electrode pads and filters. (d) three antennas, electrode pads, filters and metal plate.
With the addition of the filters to the antennas and electrode pads, as indicated in Fig. 5(c), the error increases significantly to 10 degrees. The polarization angle obtained from the simulation is 10 degrees larger than the actual polarization angle, i.e., $\Delta \theta = 10^{\circ }$. Since the filters are adjacent to gated 2DEG regions, interference reflected from the filters has a considerable impact on the measurement data. Replacing the metal filters by the resistive 2DEG interconnection could suppress such interference. Alternatively, removing the G-antenna and filter, the three-terminal HEMT structure is transformed into two terminals [26]. The source-drain bias voltage is applied to achieve the detector’s operating bias. Such a two-terminal design will effectively eliminate the effects of filters and G-antenna. Finally, after adding the metal plate in the package to the simulation model, the error is further increased to 19 degrees, i.e., $\Delta \theta = 19^{\circ }$. The next generation of the detector could be firmly attached to the silicon lens to eliminate the interference of the metal plate, as reported in Ref. [27]. The reflection of incident terahertz waves from the bottom of substrate is reduced due to that high-resistivity silicon has the similar dielectric constant with the substrate. Besides, covering the bottom surface of the substrate with a material absorbing terahertz waves can suppress the effects of substrate interference.
The polarization detection of the detector at other frequencies is simulated in the case of the simulation model containing the antennas, substrate, electrode pads, filters and metal plate. Relationship between the simulated polarization angle and the actual polarization angle is shown in Fig. 6(a). Although the simulation angle retains acceptable linearity at different frequencies, the deviations vary with frequency. Figure 6(b) depicts the deviation angle as a function of frequency. In the band from 180 GHz to 200 GHz, the overall simulation angle is less than the actual polarization angle, i.e. $\Delta \theta < 0^{\circ }$. The inaccuracy decreases as frequency increases. Error is minimized to less than 5 degrees at frequency from 200 GHz to 210 GHz. From 210 GHz to 240 GHz, the simulation reveals that the error increase with frequency increasing. At 240 GHz, the maximum deviation even reaches 41 degrees. The difference in interference intensity on the detector at various frequencies is the main cause of this error’s frequency-dependent fluctuation. The simulations help to partially explain the experiment’s phenomena of growing inaccuracy from 216 GHz to 230.4 GHz in Fig. 4.
Fig. 6. (a) Relationship between the simulated angle and the actual polarization angle at different frequencies. (b) Deviation angle $\Delta \theta$ as a function of the frequency.
However, the simulations above are unable to account for the increase in inaccuracy at certain polarization angles, as observed around polarization angles of $50^{\circ }$, $100^{\circ }$ and $150^{\circ }$ at 230.4 GHz. The package status of the detector is shown in the inset of Fig. 2. The detector is not at the center of the substrate, which is neglected in the simulation. The electromagnetic environment of the three HEMTs may change significantly when it is rotated to specific angles since they are situated at different substrate boundaries. Additionally, the irregular bonding wires make the reflection of terahertz waves vary at different angles, which might contribute to the variation of errors at different angles. It is challenging to implement such irregular bonding wires in simulation. Nevertheless, for practical reasons, the device’s packaging needs to be upgraded. For example, the flip chip method can be used instead of the gold wire bonding method, which will reduce the uncontrollable consequences. The final factor is that the terahertz waves released by the terahertz source are not completely uniform but instead are dispersed in a beam with a Gaussian distribution. As a result, the terahertz wave energy received by the detector changes during the rotation especially when the beam spot size is comparable to the overall area of the detector.
In addition, the noise of circuits also plays a role in disruption to the measured photocurrents. By optimizing the design of the detector (for example, utilizing electron beam lithography to minimize the gate length [28]), the signal-to-noise ratio of the detector can be improved to lessen the impact of the noise. The optimized direct polarization detector with increased precision, higher angle resolution and broad frequency bandwidth is promising for large arrays applied in terahertz real-time polarization imaging.
4. Conclusions
In conclusion, we propose and verify an approach of a terahertz direct polarization detector based on integrated antenna-coupled AlGaN/GaN high-electron-mobility transistors. The detector realizes polarization angle detection of linearly polarized continuous terahertz waves. The results indicate that the average error and maximum error of the measured polarization angle at 216 GHz are 3.7 degrees and 10 degrees, respectively. The simulations suggest that the major cause of the error is interference induced by the filters on the chip and the metal plate in the package. Elimination of interference effects could be expected by device design and packaging to boost the precision of the polarization detector. This work lays a foundation for the development of all-electronic terahertz straightforward polarization detector arrays for real-time polarization imaging.
Funding
National Natural Science Foundation of China (61927813, 61975227); Youth Innovation Promotion Association of the Chinese Academy of Sciences (Y2021089).
Disclosures
The authors declare no conflicts of interest.
Data Availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. L. L. Zhang, H. Zhong, D. Chao, C. L. Zhang, and Y. J. Zhao, “Polarization sensitive terahertz time-domain spectroscopy for birefringent materials,” Appl. Phys. Lett. 94(21), 211106–211109 (2009). [CrossRef]
2. S. Katletz, M. Pfleger, H. Pühringer, M. Mikulics, N. Vieweg, O. Peters, B. Scherger, M. Scheller, M. Koch, and K. Wiesauer, “Polarization sensitive terahertz imaging:detection of birefringence and optical axis,” Opt. Express 20(21), 23025–23035 (2012). [CrossRef]
3. W. Sparks, T. A. Germer, J. W. Mackenty, and F. Snik, “Compact and robust method for full Stokes spectropolarimetry,” Appl. Opt. 51(22), 5495–5511 (2012). [CrossRef]
4. Y. Aron and Y. Gronau, “Polarization in the LWIR: a method to improve target acquisition,” Infrared Technol. Appl. 5783, 653–661 (2005). [CrossRef]
5. D. M. Mittleman, J. Cunningham, M. C. Nuss, and M. Geva, “Noncontact semiconductor wafer characterization with the terahertz Hall effect,” Appl. Phys. Lett. 71(1), 16–18 (1997). [CrossRef]
6. T. Iwata, H. Uemura, Y. Mizutani, and T. Yasui, “Double-modulation reflection-type terahertz ellipsometer for measuring the thickness of a thin paint coating,” Opt. Express 22(17), 20595–20606 (2014). [CrossRef]
7. K. T. I. Yamada, M. Hangyo, M. Saito, and W. Watanabe, “Terahertz wire-grid polarizers with micrometer-pitch Al gratings,” Opt. Lett. 34(3), 274–276 (2009). [CrossRef]
8. L. Ren, C. L. Pint, T. Arikawa, K. Takeya, I. Kawayama, M. Tonouchi, R. H. Hauge, and J. Kono, “Broadband terahertz polarizers with ideal performance based on aligned carbon nanotube stacks,” Nano Lett. 12(2), 787–790 (2012). [CrossRef]
9. C. F. Hsieh, Y. C. Lai, R. P. Pan, and C. L. Pan, “Polarizing terahertz waves with nematic liquid crystals,” Opt. Lett. 33(11), 1174–1176 (2008). [CrossRef]
10. T. Nagashima and M. Hangyo, “Measurement of complex optical constants of a highly doped Si wafer using terahertz ellipsometry,” Appl. Phys. Lett. 79(24), 3917–3919 (2001). [CrossRef]
11. N. Matsumoto, T. Hosokura, T. Nagashima, and M. Hangyo, “Measurement of the dielectric constant of thin films by terahertz time-domain spectroscopic ellipsometry,” Opt. Lett. 36(2), 265–267 (2011). [CrossRef]
12. M. Neshat and N. P. Armitage, “Terahertz time-domain spectroscopic ellipsometry: instrumentation and calibration,” Opt. Express 20(27), 29063–29075 (2012). [CrossRef]
13. P. Doradla, K. Alavi, C. Joseph, and R. Gilesa, “Detection of colon cancer by continuous-wave terahertz polarization imaging technique,” J. Biomed. Opt. 18(9), 090504 (2013). [CrossRef]
14. Y. Liu, Y. C. Shen, and G. Z. Zhao, “Terahertz polarization imaging based on the continuous wave terahertz radiations,” International Conference on Optical Instruments and Technology 20159622, 962209–962217 (2015).
15. Y. Zhou and Q. Li, “Dual-axis reflective continuous-wave terahertz confocal scanning polarization imaging and image fusion,” Opt. Eng. 56(1), 013103 (2017). [CrossRef]
16. P. C. M. Planken, H. Nienhuys, H. J. Bakker, and T. Wenckebach, “Measurement and calculation of the orientation dependence of terahertz pulse detection in ZnTe,” J. Opt. Soc. Am. B 18(3), 313–317 (2001). [CrossRef]
17. N. C. J. Valk, T. Wenckebach, and P. C. M. Planken, “Full mathematical description of electro-optic detection in optically isotropic crystals,” J. Opt. Soc. Am. B 21(3), 622–631 (2004). [CrossRef]
18. N. Nemoto, T. Higuchi, N. Kanda, K. Konishi, and M. Kuwata-Gonokami, “Highly precise and accurate terahertz polarization measurements based on electro-optic sampling with polarization modulation of probe pulses,” Opt. Express 22(15), 17915–17929 (2014). [CrossRef]
19. N. Yasumatsua and S. Watanabe, “Precise real-time polarization measurement of terahertz electromagnetic waves by a spinning electro-optic sensor,” Rev. Sci. Instrum. 83(2), 023104 (2012). [CrossRef]
20. E. Castro-Camus, J. Lloyd-Hughes, B. M. Johnston, D. M. Fraser, and H. H. Tan, “Polarization-sensitive terahertz detection by multicontact photoconductive receivers,” Appl. Phys. Lett. 86(25), 254102–254105 (2005). [CrossRef]
21. H. Makabe, Y. Hirota, M. Tani, and M. Hangyo, “Polarization state measurement of terahertz electromagnetic radiation by three-contact photoconductive antenna,” Opt. Express 15(18), 11650–11657 (2007). [CrossRef]
22. G. Niehues, S. Funkner, D. S. Bulgarevich, S. Tsuzuki, and M. Tani, “A matter of symmetry: terahertz polarization detection properties of a multi-contact photoconductive antenna evaluated by a response matrix analysis,” Opt. Express 23(12), 16184–16195 (2015). [CrossRef]
23. A. Hussain and S. R. Andrews, “Ultrabroadband polarization analysis of terahertz pulses,” Opt. Express 16(10), 7251–7257 (2008). [CrossRef]
24. Y. F. Sun, J. D. Sun, Y. Zhou, R. B. Tan, C. H. Zeng, W. Xue, H. Qin, B. S. Zhang, and D. M. Wu, “Room temperature GaN/AlGaN self-mixing terahertz detector enhanced by resonant antennas,” Appl. Phys. Lett. 98(25), 252103–252106 (2011). [CrossRef]
25. J. D. Sun, Y. F. Zhu, W. Feng, Q. F. Ding, H. Qin, Y. F. Sun, Z. P. Zhang, X. Li, J. F. Zhang, X. X. Li, Y. Shangguan, and L. Jin, “Passive terahertz imaging detectors based on antenna-coupled high-electron-mobility transistors,” Opt. Express 28(4), 4911–4920 (2020). [CrossRef]
26. J. D. Sun, Z. P. Zhang, X. Li, H. Qin, Y. F. Sun, Y. Cai, G. H. Yu, Z. L. Zhang, J. F. Zhang, Y. Shangguan, L. Jin, X. X. Li, B. S. Zhang, and V. V. Popov, “Two-terminal terahertz detectors based on AlGaN/GaN high-electron-mobility transistors,” Appl. Phys. Lett. 115(11), 111101–111105 (2019). [CrossRef]
27. W. Feng, Y. F. Zhu, Q. F. Ding, K. Q. Zhu, J. D. Sun, J. F. Zhang, X. X. Li, Y. Shangguan, L. Jin, and H. Qin, “Heterodyne terahertz detection based on antenna-coupled AlGaN/GaN high-electron-mobility transistor,” Appl. Phys. Lett. 120(5), 051103–051110 (2022). [CrossRef]
28. J. D. Sun, W. Feng, Q. F. Ding, Y. F. Zhu, Z. P. Zhang, X. Li, H. Qin, J. F. Zhang, X. X. Li, Y. Shangguan, L. Jin, Y. F. Sun, and V. V. Popov, “Smaller antenna-gate gap for higher sensitivity of GaN/AlGaN HEMT terahertz detectors,” Appl. Phys. Lett. 116(16), 161109–161115 (2020). [CrossRef]
