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Abstract
We report a sub-terahertz scattering-type scanning near-field microscope (sub-THz s-SNOM) which uses a 6 mm long metallic tip driven by a quartz tuning fork as the near-field probe. Under continuous-wave illumination by a 94 GHz Gunn diode oscillator, terahertz near-field images are obtained by demodulating the scattered wave at both the fundamental and the second harmonic of the tuning fork oscillation frequency together with the atomic-force-microscope (AFM) image. The terahertz near-field image of a gold grating with a period of 2.3 µm obtained at the fundamental modulation frequency agrees well with the AFM image. The experimental relationship between the signal demodulated at the fundamental frequency and the tip-sample distance is well fitted with the coupled dipole model indicating that the scattered signal from the long probe is mainly contributed by the near-field interaction between the tip and the sample. This near-filed probe scheme using quartz tuning fork can adjust the tip length flexibly to match the wavelength over the entire terahertz frequency range and allows for operation in cryogenic environment.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Owing to the advantages such as non-ionizing and hence biologically safer than ionizing X-rays, many elementary excitations in solids and bio molecules are found in the terahertz electromagnetic spectrum range. Terahertz technology shows great application prospects in the fields of imaging [1–4] and spectroscopy [5,6]. However, unlike infrared and visible fields, imaging and spectroscopy with terahertz radiation propagating in free space suffer from poor spatial resolution, which is a consequence of the comparatively large wavelength and the Abbe diffraction limit. To meet the demand for high spatial resolution imaging and spectroscopy at terahertz frequencies, there is a continuous and urgent need for instrumentation with a high spatial resolution to break through the diffraction limit. Terahertz near-field imaging techniques, such as aperture-based scanning terahertz microscopy, terahertz scattering-type scanning near-field microscope (THz s-SNOM), and lightwave-driven terahertz scanning tunneling microscopy (THz-STM) [7] have been developed for such purpose. Aperture-based scanning terahertz microscopies are pioneer works to break the diffraction limit [8,9], but the resolution is limited to the order of microns because the transmittance of the apertures and hence the signal-to-noise ratio (SNR) decreases with the sixth power of the aperture diameter [10]. THz-STM achieves excellent spatial resolution independent of the wavelength of incident light by detecting the tunneling current through the tunneling barrier between the tip and the sample generated by the near-field terahertz electric field. THz-STM is a very promising technique that makes terahertz spectroscopy access to the atomic length scale for the first time [11,12]. However, the mandatory requirement of conducting and ‘clean’ samples in high-vacuum working environment limits its applications. Amongst these near-field instruments, THz s-SNOM is another outstanding representative which can achieve sub-100-nm spatial resolution independent of the wavelength. THz s-SNOMs have been successfully demonstrated in imaging carrier distribution in silicon transistors [13], compositional analysis of lactose crystals [14], study of modal field distribution in micro-resonators [15], and applied to the study of micro/nano structures [16–18] and novel materials such as graphene [19], Dirac semimetals [20], and topological insulators [21,22].
A THz s-SNOM is usually based on an atomic force microscope (AFM) and employs terahertz time-domain spectroscopy (THz TDS). In these cases, commercially available cantilever-type AFM probes with a typical tip length of 4–80 µm are commonly used to enhance and confine the incident terahertz light at the fine tips like short antennas. When entering the sub-terahertz (sub-THz) and millimeter wave (mmW) region, it is difficult to realize this type of THz s-SNOM due to the serious mismatch between the incident wavelength and the tip length [23,24]. Besides, a customized cantilever probe with a longer tip length will bring instability. Other solutions besides s-SNOM have also been tried, such as a metal-coated optical fiber serving as a tapered waveguide [25], probes with resonant microstrip lines [26], or other customized probes. However, none of these have achieved a spatial resolution better than 1 µm in the mmW range. Another approach named scanning near-field microwave microscopy (SMM) at the microwave region uses the cantilever of the probe tip as a waveguide for injection and the return of the microwave signal. This solution has been promoted into commercial products by Keysight Technologies and has achieved extremely high spatial resolution better than hundreds of nanometers [27,28]. However, complex calibration and measurement procedures are required for SMM. The probe with the waveguide and resonant cavity structure is also difficult to realize in the terahertz region. Researchers have recently begun to develop THz s-SNOM by employing tips attached to quartz tuning forks [16,29,17]. Using a quartz tuning fork instead of a cantilever, the length of the tip can be adjusted flexibly to match the terahertz frequency in the whole terahertz bands. At the same time, the tuning fork can be easily applied to a vacuum or cryogenic environment [30] without the additional laser feedback required for a cantilever. However, most of these works have not entered the sub-THz and mmW regions because they are commonly excited by terahertz pulses, e.g., from a THz TDS. In addition, the spatial resolution in some of these works is also limited by the so-called constant-height mode which lacks of precise control of the tip-sample distance [31].
In this article, we report a sub-terahertz scattering-type scanning near-field microscope (sub-THz s-SNOM) which operates with a long probe driven by a quartz tuning fork and a 94 GHz continuous-wave Gunn diode oscillator as the illumination source. The setup was built based on the homodyne scheme, and the scattered signal is demodulated at both the fundamental and the second harmonic of the tuning fork oscillation frequency. We have used this sub-THz s-SNOM to map a gold grating sample with a period of 2.3 µm. The relationship between field intensity enhancement factor at the tip apex and tip length under the consideration of the size of light spot was calculated with finite-difference time-domain (FDTD) electromagnetic method. The experimental relationship between the signal demodulated at the fundamental frequency and the tip-sample distance is well fitted with the coupled dipole model indicate that the scattered signal from the long probe is mainly contributed by the near-field interaction between the tip and the sample. This near-field probe using quartz tuning fork scheme is able to cover the entire terahertz frequency range and allows for operation in cryogenic environment.
2. Experiment setup and FDTD simulation
The detection technique that enhances the near-field signal and extracts it from the collected scattered signal is the primary work in designing a THz s-SNOM, among which heterodyne, homodyne, and pseudo-heterodyne are the most common schemes used [32]. Unlike the use of an acousto-optic frequency shifter to manipulate the incident light to a reference beam in the pulse terahertz field, for measurement at sub-THz region, two sets of radiation sources with a slight frequency difference and one heterodyne receiver such as Schottky-barrier diode mixer is required by the heterodyne scheme [33,18]. For homodyne and pseudo-heterodyne schemes only one radiation source and one direct detection detector are required. Pseudo-heterodyne is the state-of-art technology developed in the infrared and visible region and has been introduced into the terahertz field by terahertz pulse and time-domain spectrometers [34,35]. However, in the sub-THz and mmW region, the larger displacement required for periodic modulation of the mirror becomes impractical due to the larger wavelength. As shown in Fig. 1, we employ the homodyne scheme to build the sub-THz s-SNOM, which provides the same level of interferometric signal enhancement as the pseudo-heterodyne scheme, but requires two measurements at two different mirror positions to obtain the phase information. In this homodyne scheme, the radiation emitted by the source, propagating along the signal arm of the interferometer, is focused on the probe tip of the AFM. After interacting with the tip and sample, the scattered light is collected and directed onto the detector. The reference light reflected by the movable mirror interferes with the scattered light. When the movable mirror is at the position of constructive interference, the signal level output from the detector can be effectively enhanced. Phase changes by the sample are identified by measurements at different mirror positions. The sample mounted on an XYZ scanner is scanned under the tip and the scattered light is recorded as a function of the tip position. The topography of the sample surface is obtained by the function of AFM. In order to realize the distance control of the probe, the quartz tuning fork needs to vibrate at a certain resonant frequency (Ω). This periodic vibration modulates the interaction between the tip and the sample. Using a lock-in amplifier to read out the detector signal can effectively filter other background signals that are not modulated by the probe. Extracting the signal at a higher harmonic of the tip oscillation frequency is very helpful in obtaining a pure near-filed signal and suppressing the unwanted, and usually non-trivial far-field signal. Hence suppressing far-field signal by demodulating the scattered signal at higher harmonics is the commonly adopted technique, especially in THz s-SNOMs using cantilever probes [32,36].
Fig. 1. Configuration of the sub-THz s-SNOM using a metallic probe driven by a quartz tuning fork. The right side shows the interferometric setup for the homodyne near-filed measurements. Radiation from the Gunn diode oscillator propagating along the signal arm is focused onto the tip. The backscattered light is directed onto the HEMT detector and demodulated by a lock-in amplifier. The reference arm with the moveable mirror enhances the signal level and allows for relative phase measurement by setting the mirror at two different positions. The left side shows a tip attached to a quartz tuning fork scanning the sample mounted on an AFM scanning stage.
The setup we built is shown in Fig. 1. The radiation source is a linearly polarized Gunn diode oscillator with an output power of 30 mW at 94 GHz. The radiation is collimated and focused by three off-axis parabolic mirrors (OAP). A 2 mm thick high-resistivity silicon wafer is used as the beam splitter to generate two beams for interferometric detection. The detector is a homemade terahertz detector based on an antenna-coupled AlGaN/GaN high-electron-mobility transistor (HEMT). As a sensitive direct detection detector operated either at room temperature or at 77 K, this type of detectors has been successfully implemented in active [37] and passive [38] imaging in far-field region. By using different antenna design, the central detection frequency can be set from 110 GHz to 4.2 THz. The detector used in this setup is optimized at 110 GHz with a noise-equivalent power (NEP) about 15 pW/Hz1/2. A high-resistivity silicon lens with a diameter of 12 mm is integrated in front of the detector chip. Before being converted to the readout voltage by the amplifier, the self-mixing current (i) of the HEMT detector is proportional to the product of a horizontal (Ex) and a perpendicular (Ez) electric field induced in the electron channel under the terahertz irradiation. (i${\propto} $<Ex ·Ez >) [39]. Both the Ex and Ez are induced by compose of the scattered signal (Esca) from the signal arm and the reference signal (Eref) of the interferometer. The current can be expressed as
Figure 2(a) shows the assembled near-field probe. The metallic probe is glued with epoxy resin to the side wall of one of the tuning fork prongs. The quartz tuning fork is obtained by carefully removing the metal encapsulation of the crystal oscillator used in conventional quartz watches. The curvature radius of the tip is about 1 µm. The probe length is about 6 mm, and the diameter is 0.5 mm. The length of the probe extending out of the tuning fork is about 4 mm, and only the tip of the probe is immersed in the light during the test. A high-frequency signal applied to the tuning fork drives the fork to oscillate with an amplitude proportional to the magnitude of the driving current which is measured by the lock-in amplifier build-in the AFM controller. With the base retained after the removal of metal case, the resonant frequency of the bare quartz tuning fork remains at the factory-tuned frequency of 32.76 kHz. Once the metallic probe is loaded, the resonance shifts to a lower frequency and the quality factor of the resonance decreases. The resonant frequency and quality factor are sensitive to the weight and dimension of the metallic probe, the amount and the location of the glue. In this work, the resonant frequency of the tuning fork probe is 28.68 kHz and the quality factor is about 920.
Fig. 2. (a) A metallic probe attached to a quartz tuning fork. (b) Scanning-electron-microscope image of the tip. (c) Resonance of the tuning fork loaded with the metallic probe.
Due to the low scattering efficiency of the tip, it is always the challenge to build a THz s-SNOM arises from the unfavorable ratio between the tip diameter and the diameter of the focal spot of the terahertz beam. To evaluate the spot size at the focus of the OAP that converges the signal to the tip in the s-SNOM system, we tried to obtain the spot image directly by mechanical scanning at the focal point. The setup is shown in Fig. 3(b). In order to improve the imaging resolution, a 110 GHz HEMT detector chip without silicon lens is mounted on a motorized XY stage. Figure 3(c) shows the scanning image of the intensity at the focal point, the step size is 0.4 mm. It can be clearly seen from the FWHM (full width at half maximum) of the intensity distribution pattern that the diameter of the spot at the focal point is greater than 4 mm, which is much larger than the size of the commercial cantilever probes and comparable to the length of the metallic probe we use.
Fig. 3. (a) Schematic of different near-field probes under illuminate of focused light beam with the same spot size. For cantilever-type probe, the incident light approximates a plane wave due to the tip size is much smaller than the spot size. (b) Setup for spot size measurement at the OAP’s focal point of the s-SNOM, a HEMT THz detector is placed directly at the original tip position. (c) Intensity of the beam at the focal point.
For THz s-SNOM, terahertz fields are enhanced and confined at the tip apex due to the lightning rod and antenna effect. Adjusting the tip length to reach geometric antenna resonances can strongly enhance the terahertz near-field signal. Many models and electromagnetic simulations have been published [40–42]. Here, we carry out FDTD electromagnetic simulations to evaluate the field enhancement affected by the probe length in tuning fork scheme. Since the tip length of the commercially available cantilever-type probes is much smaller than the diameter of the spot, the light source is usually set as a plane wave in the electromagnetic simulation. But for the long metallic probe assembled on the tuning fork, the finite spot size should be considered in the simulation, as the situation shown in Fig. 3(a). Three sets of simulations were carried out by setting the source as a normal plane wave or a source with a specific size considering the spot size. For the simulation with finite-spot size, the excitation was set as Gaussian beam. Different probe lengths were chosen in the simulations, including relatively long commercially available cantilever-type probes (80 ∼ 200 µm) and other longer lengths. The curvature radius of the tip was set to 50 nm, while the radius of the probe body was set to 15 µm. The tip material in the simulation was selected as gold (Drude). No cantilevers or tuning forks were included in the simulation because only the tip was immersed in the light during the test. The frequency of incident light was 100 GHz and tip-sample distance was fixed at 100 nm. The boundary conditions were set as PML (perfectly matched layer). All parameter settings were kept same except for the probe length. The simulation results are shown in Fig. 4. It is evident that the cantilever probes have a serious mismatch between the length and the wavelength, resulting in poor field enhancement. This mismatch gradually disappears as the probe length increases. The terahertz field is well enhanced when the probe length is close to the incident wavelength and further enhanced as it reaches the resonant length (about half a wavelength). When the probe length exceeds the spot diameter, the antenna resonance effect of the probe is suppressed. The longer probes are less effective in field enhancement compared to the probe with resonance length. But for a constant vibrating amplitude, a longer probe has a larger swing amplitude, which means a deeper modulation for the scattered light. Considering both field enhancement and signal modulation, a longer probe or a probe with resonant length has comparable performance in reading scattered signal. Besides, a longer probe does not require the precise control of probe length and is easier to mount with the tuning fork. For applications at 100 GHz, a probe of approximately 6 mm in length was chosen.
Fig. 4. FDTD electromagnetic simulation of the field enhancement factor as a function of the probe length.
The sample we used to verify the function of sub-THz s-SNOM, as shown in Fig. 5(a), is a periodic gold grating fabricated on sapphire substrate. Figure 5(b) is a scanning-electron-microscope image of the graphic structure in the central of the device. The thickness of the gold strips is 150 nm and the structures are arranged at a period of 2.32 µm while the width of a single strip is about 980 nm. The quartz tuning fork was excited at its resonant frequency, shown in Fig. 2(c), and the excitation voltage was 0.2 V. The near-field probe worked in shear force mode. The sample was scanned in a range of 20 µm × 20 µm with a step size of 200 nm. The sampling time for each point is 300 ms, limited by the integration time of the lock-in amplifier used to read the detector signal.
Fig. 5. (a) Optical image of the sample. (b) Scanning-electron-microscope image of the periodic structure in the center of the sample. (c) Topography mapped by the tuning fork probe. (d) sub-THz s-SNOM image demodulated at fundamental frequency Ω. (e) sub-THz s-SNOM image demodulated at the second harmonic frequency 2Ω.
3. Results and discussions
The topography of the sample and the sub-THz s-SNOM signal were acquired simultaneously. Figure 5(c) is the topography mapped by the tuning fork probe, while Fig. 5(d) and (e) are the terahertz near-filed image demodulated by lock-in amplifier at the fundamental frequency (Ω) and the second harmonic of the tuning fork vibration frequency (2Ω), respectively. Clear grating stripes can be seen in the images, the contrast of the THz s-SNOM signal is higher than the topography image. Both signal amplitude and signal-to-noise ratio of the near-field image demodulated at the fundamental frequency are stronger than those from the second harmonic signal. Figure 6 shows the curves of the single row scan data from the topography and terahertz near-field images. Three curves have obvious correlations. However, limited by the sharpness and taper of the tip, the tip can’t fully access the corners of the grooves between the gold-strips. This effect due to the blunt tip can be observed from the topography curve in Fig. 6. This is the reason why the resolution of the topography is limited and it is difficult to distinguish the different widths of the grooves. However, the obtained average grating period of 2.3 µm is in agree with the sample. It has to be noted that the width of the grating expands from left to right as shown in Fig. 5 and Fig. 6. This is due to the fact that our piezo calibration data was lost due to a previous repair of the controller. The conversion of the voltage-distance relationship was only performed by the controller according to the model of the piezos and was not calibrated to the specific ones [43]. Although this resulted in imprecise positional data with slight deviations from the scanning-electron-microscope image, however, considering the strong correlation between the terahertz near-field signal and the topography, we still consider the results to be compelling. Based on the lightning rod effect and other corresponding experimental evidences, the enhanced terahertz field is mainly confined to the region around the tip apex on a scale of the radius of curvature of the tip. Since the radius of curvature of the tip in our current setup was larger than the sampling interval, the tip averaged the terahertz near-field signals of the adjacent points, i.e., the terahertz near-field image or curve in Fig. 5 and Fig. 6 are smoothed.
Figure 7(b) display the so-called approach curve at the fundamental demodulation frequency of the scattered signal. The experimental data was obtained by sampling at different distances from the Au film sample. The coupled dipoles theory is often used to model the near-field enhancement in a tip-sample interaction problem, as schematically shown in Fig. 7(a). The tip and sample are usually approximated as two spheres of radius a, with polarizabilities αt and αs. Δα stands for the polarizability modulation resulting from the modulated coupling between the tip and sample, and can be expressed by Eq. (2) [44]. The scattered field Es is caused by the polarizability α and the scattered electric-field modulation ΔEs is proportional to Δα. Therefore, ΔEs attenuates sharply with the decrease of the coupling dipole effect when the tip-sample distance r increases. Correspondingly, the background scattered signal generated by other parts of the probe, such as cantilever or needle rod, does not contain any near-field information and this signal is independent of the tip-sample distance.
Fig. 7. (a) Schematic of the coupled tip-sample dipole model. (b) Approach curve obtained by sampling at different tip-sample (Au) distance. The data points were the detector signal demodulated at the fundamental oscillation frequency Ω. The curve was obtained by fitting the data using Eq. (2).
A fitted approach curve obtained from Eq. (2) is shown in Fig. 7. A strong decrease in the scattered signal can be observed beyond a distance corresponding to the tip diameter, 80 nm in this case. In THz s-SNOM systems built with cantilever-type AFM, the approach curve at the fundamental frequency decays slowly while the curves at higher harmonics decay rapidly, revealing the strong background contribution at the fundamental signal and the effective background suppression at harmonic frequencies. Unlike the situation mentioned above, the approach curve we sampled at the fundamental demodulation frequency of the scattered signal decays rapidly indicating that it is a relatively pure near-field signal without strong background contribution. We suspect that this is mainly due to the fact that the vibration amplitude of the tuning fork is much smaller than that of the cantilever-type probes [45,46]. Furthermore, compared with the irregular shape of the cantilever, the metallic tip of in our tuning fork scheme immersed in the incident light spot is simpler, as shown in Fig. 3(a). The smaller vibration amplitude and the simpler configuration ensure a weaker background signal and hence imaging with a high SNR at the fundamental frequency.
4. Conclusion
In conclusion, we built a sub-THz s-SNOM which used a 6 mm long tip driven by a quartz tuning fork as the near-field probe. This scheme avoids the serious antenna mismatch between the cantilever-type AFM probes and the long wavelength in sub-THz region. Terahertz near-field images of a 2.3 µm period gold grating were obtained by demodulating the scattered wave at both the fundamental and the second harmonic of the tuning fork oscillation frequency together with the AFM image. The experimental relationship between the signal demodulated at the fundamental frequency and the tip-sample distance infers the scattered signal from the long probe is mainly contributed by the near-field interaction between the tip and the sample. The SNR of the system can be further improved by 1-2 orders of magnitude by introducing the heterodyne scheme, and the resolution can be improved by sharpening the tips. At that time, the sub-THz SNOM is expected to realize the measurement of carrier concentration in our HEMT field effect transistor. Our scheme with a long metallic probe driven by quartz tuning fork can be applied in the entire terahertz frequency range and allows for operation in cryogenic environment as well.
Funding
National Natural Science Foundation of China (11403084, 61927813, 61975227); Youth Innovation Promotion Association of the Chinese Academy of Sciences (Y2021089); Suzhou Science and Technology Plan Project (SYC2022090).
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. K. Kawase, Y. Ogawa, Y. Watanabe, and H. Inoue, “Non-destructive terahertz imaging of illicit drugs using spectral fingerprints,” Opt. Express 11(20), 2549–2554 (2003). [CrossRef]
2. D. M. Mittleman, M. Gupta, R. Neelamani, R. G. Baraniuk, J. V. Rudd, and M. Koch, “Recent advances in terahertz imaging,” Appl. Phys. B: Lasers Opt. 68(6), 1085–1094 (1999). [CrossRef]
3. D. M. Mittleman, “Twenty years of terahertz imaging [Invited],” Opt. Express 26(8), 9417–9431 (2018). [CrossRef]
4. C. Jansen, S. Wietzke, O. Peters, M. Scheller, N. Vieweg, M. Salhi, N. Krumbholz, C. Jördens, T. Hochrein, and M. Koch, “Terahertz imaging: applications and perspectives,” Appl. Opt. 49(19), E48–E57 (2010). [CrossRef]
5. P. U. Jepsen, D. G. Cooke, and M. Koch, “Terahertz spectroscopy and imaging – Modern techniques and applications,” Laser & Photon. Rev. 5(1), 124–166 (2011). [CrossRef]
6. J. B. Baxter and G. W. Guglietta, “Terahertz spectroscopy,” Anal. Chem. 83(12), 4342–4368 (2011). [CrossRef]
7. T. L. Cocker, V. Jelic, R. Hillenbrand, and F. A. Hegmann, “Nanoscale terahertz scanning probe microscopy,” Nat. Photon. 15(8), 558–569 (2021). [CrossRef]
8. S. Hunsche, M. Koch, I. Brener, and M. C. Nuss, “THz near-field imaging,” Opt. Commun. 150(1-6), 22–26 (1998). [CrossRef]
9. Q. Chen, Z. Jiang, G. X. Xu, and X.-C. Zhang, “Near-field terahertz imaging with a dynamic aperture,” Opt. Lett. 25(15), 1122–1124 (2000). [CrossRef]
10. H. A. Bethe, “Theory of diffraction by small holes,” Phys. Rev. 66(7-8), 163–182 (1944). [CrossRef]
11. T. L. Cocker, V. Jelic, M. Gupta, S. J. Molesky, J. A. J. Burgess, G. Reyes, L. V. Titova, Y. Y. Tsui, M. R. Freeman, and F. A. Hegmann, “An ultrafast terahertz scanning tunnelling microscope,” Nat. Photonics 7(8), 620–625 (2013). [CrossRef]
12. K. Yoshioka, I. Katayama, Y. Minami, M. Kitajima, S. Yoshida, H. Shigekawa, and J. Takeda, “Real-space coherent manipulation of electrons in a single tunnel junction by single-cycle terahertz electric fields,” Nat. Photonics 10(12), 762–765 (2016). [CrossRef]
13. 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]
14. K. Moon, Y. Do, H. Park, J. Kim, H. Kang, G. Lee, J.-H. Lim, J.-W. Kim, and H. Han, “Computed terahertz near-field mapping of molecular resonances of lactose stereo-isomer impurities with sub-attomole sensitivity,” Sci. Rep. 9(1), 16915 (2019). [CrossRef]
15. N. Sulollari, J. Keeley, S. Park, P. Rubino, A. D. Burnett, L. Li, M. C. Rosamond, E. H. Linfield, A. G. Davies, J. E. Cunningham, and P. Dean, “Coherent terahertz microscopy of modal field distributions in micro-resonators,” APL Photonics 6(6), 066104 (2021). [CrossRef]
16. K. Moon, H. Park, J. Kim, Y. Do, S. Lee, G. Lee, H. Kang, and H. Han, “Subsurface nanoimaging by broadband terahertz pulse near-field microscopy,” Nano Lett. 15(1), 549–552 (2015). [CrossRef]
17. R. Degl’Innocenti, R. Wallis, B. Wei, L. Xiao, S. J. Kindness, O. Mitrofanov, P. Braeuninger-Weimer, S. Hofmann, H. E. Beere, and D. A. Ritchie, “Terahertz nanoscopy of plasmonic resonances with a quantum cascade laser,” ACS Photonics 4(9), 2150–2157 (2017). [CrossRef]
18. X. Chen, X. Liu, X. Guo, S. Chen, H. Hu, E. Nikulina, X. Ye, Z. Yao, H. A. Bechtel, M. C. Martin, G. L. Carr, Q. Dai, S. Zhuang, Q. Hu, Y. Zhu, R. Hillenbrand, M. Liu, and G. You, “THz Near-Field Imaging of Extreme Subwavelength Metal Structures,” ACS Photonics 7(3), 687–694 (2020). [CrossRef]
19. J. Zhang, X. Chen, S. Mills, T. Ciavatti, Z. Yao, R. Mescall, H. Hu, V. Semenenko, Z. Fei, H. Li, V. Perebeinos, H. Tao, Q. Dai, X. DuM, and M. Liu, “Terahertz Nanoimaging of Graphene,” ACS Photonics 5(7), 2645–2651 (2018). [CrossRef]
20. R. H. J. Kim, C. Huang, Y. Luan, L.-L. Wang, Z. Liu, J.-M. Park, L. Luo, P. M. Lozano, G. Gu, D. Turan, N. T. Yardimci, M. Jarrahi, I. E. Perakis, Z. Fei, Q. Li, and J. Wang, “Terahertz Nano-Imaging of Electronic Strip Heterogeneity in a Dirac Semimetal,” ACS Photonics 8(7), 1873–1880 (2021). [CrossRef]
21. E. A. A. Pogna, L. Viti, A. Politano, M. Brambilla, G. Scamarcio, and M. S. Vitiello, “Mapping propagation of collective modes in Bi2Se3 and Bi2Te2.2Se0.8 topological insulators by near-field terahertz nanoscopy,” Nat. Commun. 12(1), 6672 (2021). [CrossRef]
22. S. Chen, A. Bylinkin, Z. Wang, M. Schnell, G. Chandan, P. Li, A. Y. Nikitin, S. Law, and R. Hillenbrand, “Real-space nanoimaging of THz polaritons in the topological insulator Bi2Se3,” Nat. Commun. 13(1), 1374 (2022). [CrossRef]
23. A. Alù and N. Engheta, “Input impedance, nanocircuit loading, and radiation tuning of optical nanoantennas,” Phys. Rev. Lett. 101(4), 043901 (2008). [CrossRef]
24. A. Alù and N. Engheta, “Tuning the scattering response of optical nanoantennas with nanocircuit loads,” Nat. Photonics 2(5), 307–310 (2008). [CrossRef]
25. D. W. Pohl, W. Denk, and M. Lanz, “Optical stethoscopy: Image recording with resolution λ/20,” Appl. Phys. Lett. 44(7), 651–653 (1984). [CrossRef]
26. O. Benzaim, K. Haddadi, M. M. Wang, A. Maazi, D. Glay, and T. Lasri, “Scanning near-field millimeter-wave microscope: Application to a vector-coding technique,” IEEE Trans. Instrum. Meas. 57(11), 2392–2397 (2008). [CrossRef]
27. S.-S. Tuca, M. Kasper, F. Kienberger, and G. Gramse, “Interferometer scanning microwave microscopy: performance evaluation,” IEEE Trans. Nanotechnology 16(6), 991–998 (2017). [CrossRef]
28. A. Baskakova, G. Stella, and K. Hoffmann, “An interferometric sensor for scanning microwave microscopy application,” Asia-Pacific Microwave Conference (APMC) 2018, 1232–1234 (2018). [CrossRef]
29. T. Siday, L. L. Hale, R. I. Hermans, and O. Mitrofanov, “Resonance-enhanced terahertz nanoscopy probes,” ACS Photonics 7(3), 596–601 (2020). [CrossRef]
30. I. C. Moldovan-Doyen, G. Xu, L. Greusard, G. Sevin, E. Strupiechonski, G. Beaudoin, I. Sagnes, S. P. Khanna, E. H. Linfield, A. G. Davies, R. Colombelli, and Y. De Wilde, “Low temperature near-field scanning optical microscopy on infrared and terahertz photonic-crystal quantum cascade lasers,” Appl. Phys. Lett. 98(23), 231112 (2011). [CrossRef]
31. F. Buersgens and G. Acuna, “Shear force control for a terahertz near field microscope,” Rev. Sci. Instrum. 78(11), 113701 (2007). [CrossRef]
32. G. B. Dai, Z. B. Yang, G. S. Geng, M. L. Li, T. Y. Chang, D. S. Wei, C. L. Du, H. L. Cui, and H. W. Wang, “Signal detection techniques for scattering-type scanning near-field optical microscopy,” Appl. Spectrosc. Rev. 53(10), 806–835 (2018). [CrossRef]
33. C. Liewald, S. Mastel, J. Hesler, A. J. Huber, R. Hillenbrand, and F. Keilmann, “All-electronic terahertz nanoscopy,” Optica 5(2), 159–163 (2018). [CrossRef]
34. N. Ocelic, A. Huber, and R. Hillenbrand, “Pseudoheterodyne detection for background-free near-field spectroscopy,” Appl. Phys. Lett. 89(10), 101124 (2006). [CrossRef]
35. F. Walla, M. Wiecha, N. Mecklenbeck, S. Beldi, F. Keilmann, M. Thomson, and H. Roskos, “Anisotropic excitation of surface plasmon polaritons on a metal film by a scattering-type scanning near-field microscope with a non-rotationally-symmetric probe tip,” Nanophotonics 7(1), 269–276 (2018). [CrossRef]
36. K. Fritz and H. Rainer, “Near-field microscopy by elastic light scattering from a tip,” Philos. Trans. R. Soc., A 362(1817), 787–805 (2004). [CrossRef]
37. 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]
38. 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]
39. J. D. Sun, Y. F. Sun, D. M. Wu, Y. Cai, H. Qin, and B. S. Zhang, “High-responsivity, low-noise, room-temperature, self-mixing terahertz detector realized using floating antennas on a GaN-based field-effect transistor,” Appl. Phys. Lett. 100(1), 013506 (2012). [CrossRef]
40. G. B. Dai, G. S. Geng, X. X. Zhang, J. Wang, T. Y. Chang, and H.-L. Cui, “W-Band Near-Field Microscope,” IEEE Access 7, 48060–48067 (2019). [CrossRef]
41. X. Chen, C. F. B. Lo, W. Zheng, H. Hu, Q. Dai, and M. Liu, “Rigorous numerical modeling of scattering-type scanning near-field optical microscopy and spectroscopy,” Appl. Phys. Lett. 111(22), 223110 (2017). [CrossRef]
42. C. Maissen, S. Chen, E. Nikulina, A. Govyadinov, and R. Hillenbrand, “Probes for Ultrasensitive THz Nanoscopy,” ACS Photonics 6(5), 1279–1288 (2019). [CrossRef]
43. attocube systems AG, www.attocube.com.
44. F. Zenhausern, Y. Martin, and H. K. Wickramasinghe, “Scanning interferometric apertureless microscopy: optical imaging at 10 angstrom resolution,” Science 269(5227), 1083–1085 (1995). [CrossRef]
45. L. Schwab, P. E. Allain, N. Mauran, X. Dollat, L. Mazenq, D. Lagrange, M. Gély, S. Hentz, G. Jourdan, I. Favero, and B. Legrandet, “Very-high-frequency probes for atomic force microscopy with silicon optomechanics,” Microsyst. Nanoeng. 8(1), 32 (2022). [CrossRef]
46. P. Sandoz, J.-M. Friedt, and É. Carry, “Vibration amplitude of a tip-loaded quartz tuning fork during shear force microscopy scanning,” Rev. Sci. Instrum. 79(8), 086102 (2008). [CrossRef]
