Recent Developments in Terahertz Nanosensors

Terahertz (THz) waves occupy the electromagnetic spectrum between microwave and infrared radiation, with frequencies typically ranging from 0.1 to 10 THz. Compared with other optic and electronic tools, this frequency range allows for unique sensing applications such as nondestructive, label‐free, and fast detection. Despite the promising features of THz sensing applications, the dimensional mismatch between THz wavelength and nanoscale agents hinders practical applications, especially in biosensing and chemical sensing. Several recent studies propose that engineered THz resonators, such as split ring resonators, linear dipole and slot antennas, and nanogap loop antennas, enhance the sensitivity for detecting trace amounts of target molecules, such as viruses and explosives. When combined with near‐field imaging techniques in the THz range, these THz nanosensors may revolutionize our understanding of complex nanoscale systems, including 2D materials, as researchers can observe quantum dynamics directly in molecules, mobile carriers in semiconductors, THz quantum nonlocal effects, and dynamics of excitons and polaritons at THz frequencies. Additionally, THz biomolecular sensors are also discussed, where the sensor platforms will lead to a great impact in the advancement of ultrasmall‐quantity characterization of proteins, label‐free diagnosis of Alzheimer's disease, and conformational dynamics of biomolecules in their aqueous environment.


Introduction
[18][19][20][21][22] However, THz sensing encounters challenges in efficiently coupling with agents ranging in size from nanometers to microns due to the disparity in wavelength.This mismatch between the THz wavelength and the size of target molecules becomes more pronounced in the underexplored THz regime.Nevertheless, exploring strong coupling between THz waves and nanosized agents holds the potential for developing innovative THz nanosensors, which encompass the capability to sense nanoparticles via THz electromagnetic (EM) wave.

Principles of Sensing Materials in General
In general, sensing materials are pursued by measuring the EM wave transmitted through a targeted substance with respect to the propagation of the wave in bare space.For simplicity, we consider a plane wave passing normally through a substance with a dielectric constant ε and a thickness d, as presented at the left illustration in Figure 1a.
The wave propagating along the z-direction and passing through the substance can be expressed as E tr ðt þ ΔtÞ $E 0 exp ½Àiωðt þ ΔtÞ, where E 0 is the field amplitude and ω is the angular frequency.Additionally, we assume a negligibly small value of d compared to wavelength λ in so much as kd % 0 where k is the wave number ðk ¼ 2π=λÞ.Then, using ffiffi ffi where c 0 denotes speed of light in vacuum.Next, we classify ε into two different cases: 1) nonresonant (absorptive) material with κ ¼ 0 leads to where δω ¼ ωdðn À 1Þ=c 0 : Compared to the bare propagation E 0 exp ½Àiωðt þ d=c 0 Þ for n = 1, the Fourier-transformed transmitted wave through the substance experiences the resonance frequency shift by δω. 2) For resonant (absorptive) materials with κ 6 ¼ 0, besides the frequency shift caused by δn ¼ n À 1, the transmitted field intensity is decreased by exp ½Àαd where the absorption coefficient is defined as α ¼ 2κd=c 0 (see the right illustration in Figure 1a).In any case, the frequency shift by δn and the absorption by αd are hardly measurable when d is very small with respect to wavelength λ.
In special, the above expression for ensemble average of atoms or molecules is not adequate for single molecular detection.The absorption cross section σ of single molecule with a dipole moment μ is given by σ ¼ 2πωμ 2 ρðℏωÞE 2 =S where ρðℏωÞ is the density of state, E is the EF at the molecule position, and S ¼ jE Â Hj is the incident energy.In free space, since E 2 =S ¼ Z 0 corresponds to free space impedance, σ is determined only by molecular properties.However, the EF funneled inside THz nanoresonators can be strongly enhanced by orders of magnitude, but the enhancement of the magnetic field (MF) is little compared to the incident wave as explained in the next section.Thus, E 2 =S 6 ¼ Z 0 and the ratio E 2 =S are another factor to increase the absorption cross-section of single molecules. [3]he widely accepted quantitative metrics for sensing is the sensitivity defined as Σ f ¼ δf =δn for a resonance frequency shift δf with respect to a refractive index change δn and Σ a ¼ δA=δκ for an amplitude variation with respect to extinction coefficient change δκ.Together with quality factor (Q = resonance frequency/full width at half maximum) of resonators, figure of merit (FOM) defined by FOM ¼ Q Â Σ f =a is adopted to quantify sensing performance. [59]For 2D samples, δn in Σ f =a can be replaced by areal density of molecules or the product of the thickness and the refractive index of substance. [60]2.Rectangular Slot Antennas in a Thin Layer of PEC Since wireless communication and radio detection and ranging (RADAR) have been introduced in the mid-20th century, radiation and scattering of EM wave from half-wavelength linear dipole antennas have been intensively investigated.In special, according to Babinet's principle, [61] the complementary structure of a linear dipole antenna has exactly same EM response when the polarization directions of the incident EF and MF are exchanged, rectangular slots punctured in thin metal films have been widely used as negative linear dipole antennas for airplane and spacecraft.
Recently, subwavelength holes fabricated in noble metals have renewedly focused as efficient surface plasmon launchers. [62]ransmission of EM plane wave through a single rectangular hole (see the upper figure in Figure 1b) has been rigorously derived in the previous studies. [28,63]Here, the EM fields in input and output aperture regions are expressed in terms of plane wave in free space, but the EM field inside hole is expanded by rectangular waveguide (WG) eigenmodes.By matching the boundary conditions at two interfaces, the transmitted as well as reflected fields from the rectangular hole could be obtained as a function of the projection onto the WG eigenmodes.
From the analytically derived transmittance and numerical calculations, several important optical properties of single rectangular hole could be known.For the polarization direction of the incident field parallel to the slit width (a x ) and both sides of aperture regions filled with the same material, the transmittance at resonance wavelength can be approximated to T r % 3λ 2 r 4πa y a x ¼ 3a y πa x .The transmission maximum appears at around the cut-off wavelength λ r ¼ 2a y , and increasing peak value and decreasing linewidth can be observed by the increasing aspect ratio between the length and the width ða y =a x Þ, while the transmittance spectrum has no dependence on the incident angle.Furthermore, the enhancement of the EF at the output aperture plane is governed by λ 4 r =ða y a x Þ 2 which is much larger than the transmittance enhancement and enables even single molecular sensing using THz nanoantennas, as explained in the previous section.
The resonance behavior and EF enhancement of single slot antennas are substantially changed when input and output aperture regions are filled with different media, such as slot antennas on a dielectric substrate.J. H. Kang et al. studied theoretically the effect of half-infinite substrates on resonance properties of single slot antennas in thin PEC, as depicted at the upper figure in Figure 1c. [30]By approximating the analytically solved model for the EM wave at the output aperture plane, the EF at the center of the output aperture and the normalized Poynting vector are obtained as , where the effective wavenumber at the resonant WG mode is given as and n i denote the refractive indices in each region ði ¼ 1, 2, 3Þ. [64]Additionally, the numerical calculations demonstrate that the amplitude of the E II y component at the substrate interface is reduced, and its spatial occupation is more pushed into the substrate region due to the presence of a substrate.On the contrary, the MF Reproduced with permission. [28]Copyright 2005, American Physical Society.https://doi.org/10.1103/PhysRevLett.95.103901.c) (top) Single rectangular slot antenna on a dielectric substrate with thickness t.Reproduced with permission. [30]Copyright 2009, Optical Society of America.(Bottom) The calculated electric field (EF) enhancement at the center of the output aperture as a function of frequency for different values of t.Reproduced with permission. [34]Copyright 2010, AIP Publishing.d) 1D array of THz nanoresonators with period d on a Si substrate (upper) and the calculated transmitted amplitude of THz wave, normalized by aperture area and plotted as a function of frequency, for different values of d and the number of nanoresonators in a fixed sample area (bottom).Reproduced with permission. [67]Copyright 2011, American Physical Society.https://doi.org/10.1103/PhysRevLett.106.013902.e) A unit cell of ultrabroadband THz nanoresonators mimicking log-periodic antennas (upper) and the calculated normalized-to-area amplitudes of the transmitted THz wave as a function of frequency for two different values of d x (bottom).Reproduced with permission. [33]opyright 2010, AIP Publishing.
component H II x is increased.As a consequence, the Poynting vector does not change significantly as long as n 3 is not so large.
Park et al. investigated the resonance peak position shift depending on the thickness of finite substrate, [34] as shown at the bottom figures in Figure 1c.Furthermore, they argued that noble metal with a thickness smaller than skin depth should not be regarded as PEC but as a real metal for determining the resonance peak position of THz slot antennas.In general, a redshift of the resonance peak position can be expected when the width of a slot antenna is increased while its length is fixed because of the increased effective length of the antenna.The opposite tendency has been reported in near-infrared (IR) and visible frequency range, caused by Ohmic loss in metals. [29]Similar to the self-consistency of optical properties of low-dimensional semiconductor excitons interacting with their environments, [65] the substrate thickness together with the slot antenna width is responsible for determining the effective refractive index of a finite substrate and, eventually, the resonance peak position of slot antennas on it.
Ultrasensitive absorption sensing of molecules embedded in the WG region of slot antennas has been theoretically investigated in the study of Ahn et al. [66] The authors provided an analytical expression for the transmission T with target material with respect to that of an empty WG T 0 as T=T 0 ¼ j hk 0 2G r ε i þ 1j À2 .Here, the self-energy at the input W 1 and output aperture W 3 are assumed to be same and replaced by a complex value and the slot WG with thickness h is filled by a material of dielectric constant ε 2 ¼ ε r þ iε i .The normalized transmission shows that the peak height is substantially decreased when the attenuation length of the EM wave propagating in the WG is the same order of magnitude of the spectral width at the resonance wavelength of the slot antenna.
To improve signal-to-noise ratio and to manipulate the spectral width, diverse arrangements of THz slot antenna arrays have been suggested.Bahk et al. [67] studied systematically EM field band formation by varying the distance d and number N of 1D slot arrays in a given sample area while other parameters were fixed (see the upper figure in Figure 1d).As the lower part in Figure 1d shows, the maximum value of the transmitted amplitude increases as d decreases and N increases.In special, the transmission spectrum of the slot array with d ¼ 2 μm and N ¼ 500 spans over an ultrawide spectral band from 0.2 to 2 THz while maintaining almost uniform normalized transmission amplitude of 80% and the corresponding field enhancement of over 30.For d ¼ l ¼ 100 μm, the transmission spectrum of the array shows close resemblance at the peak position and spectral width to those of single slot antennas.The non-negligible EM field coupled between THz nanoantennas causes them to exhibit oscillatory behaviors as d further increases.
By using the concept of log-periodic antennas, a flat and ultrabroad transmission spectrum spanning over one decade could be achieved in Park et al. [33] A unit cell consists of ten THz nanoslot antennas with four different lengths l 1 ¼ 200 μm, l 2 ¼ l 1 2 , l 3 ¼ l 1 3 , and l 4 ¼ l 1 =4, a same width of w ¼ 250 nm, and spacing s 1 ¼ 2s 2 ¼ 4s 3 (see the upper figure in Figure 1e).Two different samples at the bottom figure in Figure 1e (sample 1 with d x ¼ 110 μm and s 1 ¼ 40 μm, and sample 2 with d x ¼ 40 μm and s 1 ¼ 15 μm) present commonly transmission spectra over three octaves from 0.2 THz to 2.0 THz, which are enabled by pushing the Rayleigh minima (anomalies) where destructive interferences between the direct transmission and scattering of light from periodic slits occur in the spectrum out of the spectral range.

SRRs with Nanogaps
In THz frequency regime, rectangular SRR is one of preferred resonators for sensing purpose.Since its introduction by Pendry et al., [68] different shapes and resonance behaviors of SRR have been suggested.In Figure 2a, SRR unit cell with definitions of geometries, the corresponding transmission line (TL) RLC-model, and a comparison of the transmission spectrum between theory and experiment are presented (refer caption for the detailed description). [69]The resonance properties of SRR can be described by a lower frequency LC resonance (R 1 , L 1 , and C 1 ) caused by oscillating current loop at the rings and accumulated charges at the gaps and a higher frequency electric dipole resonance (R 2 , L 2 , and C 2 ) produced at metal components parallel to the polarization direction of the incident EF, and the coupling between two resonances (M).In addition, Z 0 and Z G denoting the intrinsic impedances of air and the substrate, respectively, are also responsible for the resonance properties of SRR.
The resonance feature and field enhancement depending on nanogap width g were systematically compared between 2D SRR and 1D slit arrays (see Figure 2b). [38]Two resonances at f L % 0.25 THz and f H % 1.2 THz shown by the SRR with g = 10 nm are shifted by 0.1 THz when the gap size is reduced to g = 5 nm, meanwhile the EF enhancement is decreased to 11 300 from 22 100.These values are one order of magnitude higher than those in slits for the same gap sizes but demonstrate the opposite tendency for the decreasing gap.In slit structures, a narrower gap width induces stronger capacitive coupling of charges accumulated on two facing metal surfaces and leads to higher field enhancement at around the gap.On the contrary, SRRs with a broader gap width can have a higher excitation efficiency and field enhancement, because the fundamental lower frequency f L belongs to the magnetic resonance and depends on the broken symmetry at the gap.
By actively controlling the gap width, electrically tunable SRRs operating in a THz frequency band have been suggested by Ma et al., as shown at the left figures in Figure 2c. [70]The authors used bimorph cantilevers in the unit cell of SRR where bimorph cantilevers bend upward due to the tensile stress caused by the thermal expansion mismatch between the Al and Al 2 O 3 layers fabricated using vapor hydrofluoric acid.When a DC voltage is applied between the cantilever and the substrate, the cantilever is attracted downward to the substrate until to the critical voltage (V pull-in ).Because the capacitance of the gap is changed by the cantilever height, the low-frequency resonance of the SRR, , can be continuously varied by the biased voltage below V pull-in as demonstrated at the right figure in Figure 2c.
As already mentioned in Section 1, the quality factor Q of resonators is a crucial element for quantifying sensing performance.The Q-factor is determined by nonradiative (Ohmic) and radiative losses.The former can be neglected in .Reproduced with permission. [69]Copyright 2008, AIP Publishing.b) SRR with single nanogap unit cell.Calculated transmission spectra for 5 and 10 nm gap SRRs are compared to that of a square ring array with no gap.Reproduced with permission. [38]Copyright 2018, American Chemical Society.c) Reconfigurable SRR depending on applied bias V (left).The cantilever height h determined by the radius R of the curvature and the angle θ (top middle) is controlled by the driving volage V (bottom left).The LC resonance frequencies of SRR as a function of h are compared between experiment (exp) and theory (sim) for three different locations of the gap in SRRs.Reproduced with permission. [70]Copyright 2014, Springer Nature.d) Calculated current distributions for the dipole resonance of independent SRR at f 1 and JSRR at f 2 and new resonance appearing only in JSRR at f 3 (left).Transmission amplitude (left vertical axis) and Q-factor (right vertical axis) as a function of the length of microstrip line d x (bottom right).Reproduced with permission. [71]Copyright 2014, American Physical Society.https:// doi.org/10.1103/PhysRevLett.112.183903.e) Schematics of the THz unit cell at oblique angle (top left) and top views with geometries (bottom left).The refractive index sensitivity of the THz sensor at three different resonance frequencies f 1 , f 2 , and f 3 (right).Reproduced with permission. [72]Copyright 2020, IOP Publishing.f ) 3D schematic illustration of three different shapes of vertical SRR (VSRR) unit cells (left) depending on gap positions.Refractive index sensing with a constant thickness of analyte (right).Reproduced with permission. [73]Copyright 2017, Optical Society of America.
THz frequency regime because most metals are considered as PEC beyond far IR wavelength region.Thus, reducing the radiative loss is the main challenge to tailor highly sensitive resonators.Asymmetric double SRRs connected by a microstrip line have been proposed to substantially reduce the radiative loss, as presented in Figure 2d. [71]The unit cell of this structure has an antisymmetric resonance of two coupled nonradiating dark modes (see the left panel in Figure 2d).As a result, it possesses the resonance with highly reduced radiative losses, correspondingly, a highly enhanced Q-factor.At an optimized length of the connecting line, the authors could achieve one order of magnitude larger Q-factor compared to that of isolated SRRs.
Another approach to improve Q-factor and FOM has been suggested by using electromagnetically induced transparency occurring in metamaterial structures where four gaps are fabricated asymmetrically only in the outer rectangle in nested SRRs, as shown in Figure 2e. [72]In their transmission spectrum, two resonance dips f 1 and f 3 and, additionally, f 2 caused by the destructive interference peak between two resonances appear at the right figure of Figure 2e.Furthermore, the insensitivity of transmission spectrum on the polarization direction of the incident field has been considered to be an additional strong point.For example, using an optimized geometries listed in the Table 1 of the Ref. [72], Q = 30.5 and FOM = 8.54 were obtained at f 2 = 1.335THz.
THz vertical sensors with a double slot have been introduced by Wang et al. [73] Compared to traditional SRR fabricated in the plane normal to the incident field propagation direction, VSRRs standing on the substrate should have enhanced interaction with the incident MF perpendicular to the SRR structure plane, leading increased magnetic dipole resonance.At the left figure in Figure 2f, three different types of VSRRs are defined, only single slot either on the top (TVSRR) or the bottom (BVSRR) and double-slot SRR (DVSRR).The normal incidence of plane wave was considered with the electric field polarized along the gap width of VSRRs.For the same geometrical values (p ¼ 70μm, g ¼ 2μm, a ¼ 50μm, andb ¼ 12μm), the DVSRR shows Q = 20 at the resonance frequency ω res ¼ 1.51THz, while Q = 4.38 at ω res ¼ 0.98THz by TVSRR and Q = 2.61 at ω res ¼ 0.73THz by BVSRR, respectively.Compared to TVSRR and BVSRR with the broken symmetry along the normal axis, the inversion symmetry of the DVSRR is preserved.Thus, the DVSRR has an electric quadrupole (two electric and one magnetic dipole resonances).Anyway, due to the canceled electric excitation, the magnetic resonance mainly contributed to the LC resonance of DVSRR.Because the radiation damping of electric quadrupole is relatively low, the Q-factor of DVSRR is usually higher than those of TVSRR and BVSRR.The right figure in Figure 2f demonstrates refractive index sensing by the DVSRR in comparison with TVSRR and BVSRR.Since the gap at the bottom is interfaced with the substrate, substantial electric energy loss can be expected.Therefore, the gap located at the top plays a decisive role in determining the sensitivity of DVSRR.

THz Resonator-Based Nanosensing
THz spectroscopy has advantages regarding sensing applications for biological and chemical materials because of its label-free, noncontact, and nondestructive nature.As sensing can be achieved by changing physical parameters in more general terms, THz time-domain spectroscopy provides an appropriate platform: from the field amplitude and phase information of a measured time trace, basic optical parameters like complex refractive index, dielectric constant, and absorption coefficient can be extracted.As a result, various target systems with/without resonance phenomena can be probed, which includes molecules (or intermolecular structure) with resonances in THz frequency regime, free/bound charge dynamics, and low energy quasiparticles.
Despite those advantages, the scaling mismatch related with the diffraction limit still needs to be overcome.In the case of nanomaterials such as nanoparticles, nanowires, and nanothin films, whose size is much smaller than the wavelength even if they have an absorption resonance in THz region, they have low scattering cross-sections and small interactive absorption lengths.This leads that the sensitive detection is limited.In other words, target materials with tiny size and small amount are unlikely to be detected by THz wave itself.
In this aspect, THz nanoresonators, such as metallic nano slot antenna and nanogap loop antenna, can play a role in terms of strong light-matter interaction.Well-established formalism for the EF confinement and enhancement using meta-surfaces provides fundamental basis to understand interaction between THz wave and various materials and consequently can be utilized for sensing applications.In particular, the recent state-of-the-art technique to fabricate nm-sized nanoantennas leads to ultimate sensing performance. [41]For example, THz nanoresonators can be an ideal platform for the sensitive detection of nanomaterials because the size of metal gaps embedded in the resonators is compatible with the target materials. [10]A strongly localized and enhanced EF in the vicinity of the metal nanogap enables sensitive detection of extremely small amounts of molecules.This strong near-field light-matter interaction results in dramatic far-field spectrum changes in terms of frequency shift and transmission/reflection change.
In 2013, Park et al. reported that the significant transmission reduction is observed in the far-field spectrum when the molecules resonantly interact with THz nanoslot antenna (Figure 3a, left). [3]This result shows the detection of only a few tens to hundreds of femtograms of 1,3,5-trinitroperhydro-1,3,5triazine (RDX) molecules having the absorption resonance near 0.8 THz attributed to molecular conformations or a weak hydrogen bond between two RDX molecules. [74,75]The extreme small amount of molecular detection results from the strongly enhanced absorption coefficient and cross-section enabled by an asymmetric EM environment in the near-field of the nanoslot antenna (Figure 3a, right).It should be noted that the molecular crosssection can be enhanced by over 1,000 accompanied by a colossal absorption coefficient of about 170 000 cm À1 .Also, the strong resonant interaction of THz waves with monolayer molecules such as quantum dot having a phonon resonance in THz frequency regime results in the sensitive frequency shift (Figure 3b). [76]rom the imaging of THz nanoresonator-based molecular sensing, the selective enhancement of the absorption cross-section can be visualized, which leads to the screening and identification of various bio-and chemical-molecules in the application.For example, the distinguishable absorption features of various sugar molecules in THz frequency regime are addressed, where the frequency-dependent absorption coefficient can be listed up to drive fingerprinting (Figure 3c, left). [36]he dataset can be considered as an identification (ID) card.Center panel of Figure 3c exhibits the corresponding demonstration for detecting a specific molecule using the ID card.When two different sugar molecules such as D-glucose and fructose are dropped on an array of nanoslot antennas with a resonant frequency matched for fructose, distinct transmittances are apparently obtained.The representative example using one criterion implies that the accuracy for specifying unknown molecules can be further improved by constructing the ID card with more various physical parameters such as frequency shift and amplitude/phase change.Also, since a distinguished lightmatter interaction can be achieved depending on the structure of metallic antennas, designing antennas can contribute to enhanced sensing performance.
The resonance of nanoantennas can be affected by changes of surrounding dielectric properties, where the target molecules only act as a dielectric surrounding.Even though the molecules nonresonantly interact with THz nanoresonators because of their transparent characteristics in THz frequency regime, a sensitive molecular detection is possible by changing the dielectric environment of the metal nanogap.The resonance of THz metamaterials such as slot antenna, dipole antenna, bowtie antenna, and SRR is highly sensitive to the dielectric environment in the metal gap.Therefore, the presence of the molecules in the gap changes the resonance frequency, and the resonance frequency shift can be an evaluation index for the sensing performance.Since a spectral overlapping between the localized EM wave and the molecules is of the essence, quantitative understanding and deliberate engineering of THz nanoresonators and target molecules are highly required to improve sensing performance.Park et al. (2017) showed the resonance frequency shift versus surface density of virus molecules with respect to the size of nanogap in a SRR, called THz nanometamaterial (Figure 4a). [1]ith an increasing amount of viruses, resonant frequency shift increases and finally saturates.The frequency shift can be attributed to a change of resonance in THz nanoresonators due to different dielectric circumstance. [30,34,77,78]Considering the fact that the confinement size of the transmitted EM wave is comparable with the gap size, the saturation of frequency shift can take place when the viruses cover a similar thickness with the size of nanogap.Therefore, the smaller nanogap, a faster saturation can occur.The magnitude of frequency shift also depends on the size of nanogaps, which can be explained by the enhancement of the transmitted EM wave.As a result, the sensitivity that obeys a 1/w behavior, as shown in Figure 4a, can be employed.
The sensitive change can similarly occur in extremely narrow gap regime (a few nm scale).Figure 4b exhibits a schematic of THz nanoresonators with 2 nm-wide gap and an insulating layer with 1-nm-thick Al 2 O 3 . [42]When the Al 2 O 3 layer is initially The fitted line (dashed line) shows a 1/w dependence.Reproduced with permission. [3]Copyright 2013, American Chemical Society.b) A schematic (left, top) and scanning electron microscope (SEM) images (left, middle, and bottom) of gap region of terahertz dipole nanoantenna covered with a cadmium selenide (CdSe) quantum dot (QD) monolayer.The QD has a phonon resonance around 5.6 THz.Terahertz transmission spectra of dipole antenna arrays covered with a CdSe monolayer for four different structures.Reproduced with permission. [76]Copyright 2015, American Chemical Society.c) A photograph (center) and THz transmittance image (right) of two kinds of sugar molecules (D-glucose (left, bottom) and fructose (right, top)) dropped down onto an array of nanoslot antennas.The antenna resonance is matched with the absorption resonance of fructose, which leads to a larger transmission reduction for fructose.Reproduced with permission. [36]Copyright 2015, Springer Nature.
deposited with a thickness of 1 nm, THz nanoresonators exhibit a common response regardless of size of nanogap.This abrupt change indicates that the dielectric property of surrounding environment sensitively affects the transmittance trend.After the initial change, a negligible change of transmitted amplitude is obtained in case of the 2 nm-wide gap as the thickness of Al 2 O 3 varies from 0 to 15 nm.Meanwhile, the transmitted amplitude of THz nanoresonators with 10 nm-wide gap is significantly modified with a different thickness of Al 2 O 3 from 0 to 15 nm.The results imply that the confinement scale originating from the size of the nanogap is directly related to the interacting scale of dielectric environment.
As the gap size decreases, the aforementioned sensitivity with 1/w behavior has a trade-off in sensing performance.Namely, even though the sensitivity can be enhanced in case of nm-sized gaps, mounting target molecules on desired positions is rarely achievable.Furthermore, since the enhancement region is limited to a few nanometers, metallic nanoantennas should be deliberately fabricated.Ji et al., for example, reported that metallic nanoantenna design strongly affected the sensing performance (Figure 4c). [19]Two THz nanoresonators with differently treated insulating layers show distinct frequency shifts with a factor of two.According to the results, a slight change in design of metallic nanoantennas has a significant effect on the overlapping configuration between the confined waves and target molecules (viruses in this case).A large overlapping region can result from direct contact between nanogaps and viruses when the insulating layer is etched.When the virus particle was attached on the etched nanogap, its sensitivity was doubled compared to the unetched nanogap, which resulted in 400% more resonance frequency shift per single virus particle than the previous work, [1] as shown in Figure 4c.
Another approach to improve sensing performance is to increase the hosting rate of target materials.In the vicinity of a gap where the EM is strongly localized, a functionalization can be utilized to attach target materials effectively.For example, antibody molecules as a linker can be hosted prior to locating target biochemical molecules. [4,79]Also, graphene with defective carbon structure can be employed because the surplus electrons in the defect site increase the chemical binding and, consequently, promote the hosting efficiency. [80]Furthermore, an electric tweezing technique [21] allows to trap target particles in optical hotspots with a nanoscale spatial resolution and monitor their steady-state kinetic evolution in liquid.

THz Near-Field Measurement Methods
The tip-based near-field measurements are one of most common methods for measuring the interaction of the light and matters with a subwavelength spatial resolution.][83][84][85][86][87] For example, Figure 5a shows the scanning near-field optical microscopy (SNOM) in the mid-IR wavelength regime. [48]The IR light was shined into the end of the tip and then the scattered light was collected into the detectors.The scattered light from the plasmon-enhanced near-field coupling between metallic nanostructures carries the information on the optical properties from the enhanced optical near-field coupling.In the mid-IR wavelength regime, the lattice vibrations of polar dielectrics such as SiC were analyzed by using scattering SNOM (s-SNOM), showing distinct spectral responses in the near-field imaging with the nanometer scale spatial resolution attributed to the phonon-enhanced near-field coupling (Figure 5a).
The tip-enhanced near-field measurement method also has been developed in the THz frequency regime with various .Reproduced with permission. [1]Copyright 2017, Optical Society of America.b) Schematic image of annual-nanogap-loop-shaped metasurface covered by insulating layer, Al 2 O 3 , where the thickness of cover layer is comparable with the size of nanogap (left).Frequency-dependent transmitted amplitude of the annual-nanogap-loop nanoresonator with nanogap size of 2, 5, and 10 nm, where THz transmittance is sensitively affected by relative scale between enhancement region and thickness of covering insulating layer (right).Reproduced with permission. [42]Copyright 2015, American Chemical Society.c) Schematic and SEM image for THz nanoresonators with nm-sized gap (left, top).Frequency-dependent transmitted amplitude of two-types of nanogap for detecting viruses: unetched and etched nanogap result in accuracy difference for locating target molecules on desired position (left, bottom).Resonance frequency shift, Δf versus surface density of viruses with unetched (red circles) and etched (blue circles) nanogap (right), where improved resonance frequency shift for etched case is obtained due to complete overlapping of THz wave and viruses.Reproduced with permission. [19]Copyright 2023, De Gruyter.
][84][85][86][87] Chen et al. developed the tip-based THz near-field optical microscopy for the first time. [82]In their approach, they achieved the spatial resolution of 150 nm at 2 THz pulse light, which is about 1000 times smaller than the incident light wavelength.With this high spatial resolution, the s-SNOM provides the route to access the evanescent field on the surface of the sample.Zhang et al. demonstrated the near-unity reflection for the high in-plane momentum on a graphene at ambient environment by using s-SNOM (Figure 5b). [45]n their THz nanoimaging of graphene, they measured the scattering signal from the graphene surface and analyzed the nonlocal graphene optical conductivity with the change of the doping level, temperature and the substrate materials at the frequency range from 0.2 to 1.0 THz with a spatial resolution smaller than 100 nm.Their results clearly revealed that single-layer graphene can become a perfect reflector comparable to the gold film in THz frequency regime for the high in-plane momentum light although the thickness of graphene is atomically thin.
One other interesting method is the integration of the near-field THz pulse illumination and the scanning tunneling microscope (STM). [49,88,89]The THz-STM was developed by applying the THz pulse illumination to the tip of the existing STM system, facilitating the ultrafast pump-probe imaging with I (current)-V (voltage) curve dynamics in the STM compatible samples (Figure 5c).Cocker et al. demonstrated the THz pulse-induced tunneling in an STM with the spatial resolution of 2 nm and the temporal resolution <500 fs for imaging the carrier dynamics in an InAs nanodot. [49]The ultrafast tunneling measurement with the atomic resolution has facilitated the observations of the molecular orbitals and the quantum coherent measurements in a single molecule level. [88,89]n addition, the improved THz light sources such as synchrotron radiation, quantum cascade lasers (QCL), and free-electron lasers (FEL) were employed in s-SNOM system. [50,83,86,90]Due to the low scattering signal from the tip in s-SNOM, the advanced THz light source is one possible breakthrough for enhancing the signal-to-noise ratio in hyperspectral THz nanoimaging.Pistore et al. demonstrated the self-mixing intermode-beatnote spectroscopy system composed of THz QCL frequency combs (FC) and the s-SNOM (Figure 5d). [50]The chip-scale electrically-pumped THz QCL allows nonlinear four-wave-mixing processes, resulting in the self-induced phase locking of THz FC.In the stable phase-locked condition, the FC-based hyperspectral THz s-SNOM nanoscopy was demonstrated with 160 nm spatial resolution in the THz frequency range up to 3.5 THz, allowing the coherent detection of multiple phase-locked modes.Furthermore, they demonstrated the manipulation of the amplitude, linewidth, and central frequency of the FC intermodebeatnotes and analyzed the optical response of a thin flake of  [48] Copyright 2002, Springer Nature.b) The s-SNOM in THz frequency regime for characterization of the optical properties of the graphene shows near-perfect THz light reflection with high in-plane momentum.Reproduced with permission. [45]Copyright 2018, American Chemical Society.c) The ultrafast THz pulse-integrated STM with the spatial resolution of 2 nm and the temporal resolution of <500 fs.Reproduced with permission. [49]Copyright 2013, Springer Nature.d) The self-mixing intermode-beatnote spectroscopy composed of the THz QCL FCs and the s-SNOM.Reproduced with permission. [50]Copyright 2022, Wiley-VCH GmbH.e) The THz near-field vectorial imaging of subwavelength apertures.The full-vectorial electric fields near the subwavelength apertures were extracted and reconstructed to visualize the evanescent fields.Reproduced with permission. [51]Copyright 2009, Optical Society of America.
Bi 2 Se 3 by using their developed highly sensitive hyperspectral THz nanoimaging.
The enhanced signal-to-noise is crucial for detecting weak THz optical signals from samples such as molecules because of the huge difference of the wavelength and the size of molecules.With the spatially resolved imaging with the near-field THz nanosensors, the resonant cavities have been employed to increase the interaction between THz wave and the molecules. [51,91]Knab et al. demonstrated the THz near-field vectorial imaging of subwavelength apertures measuring the THz nearfield distributions in both the time and frequency domains (Figure 5e). [51]In general, it is difficult to analyze the fullvectorial EF in subwavelength structurers because of the diffractions near the scattering structures.They developed the method to measure the THz EF distribution near the subwavelength apertures.They demonstrated the direct visualization of the direction of EF near the apertures with the subwavelength spatial resolution and revealed the near-field interactions in the metallic aperture geometries.In addition, the contribution of the longitudinal electric component, which is not measurable in far-field measurement, to the resonant transmission in the array of the apertures was demonstrated in the full-vectorial near-field measurements.These measurements extract detailed information on the light-matter interactions from subwavelength apertures, facilitating the THz sensor applications with the resonant process.Furthermore, with the resonant feature enhancing the lightmatter interaction, Ha et al. employed coaxial nanogap ring resonators for detecting the biomolecules by the distinct measurement of α-lactose and maltose monohydrates. [91]2.THz Near-Field Applications

Quantum Dynamics in Molecules
[93][94] Figure 6a shows the single molecule orbital imaging by using the ultrafast THz STM.Cocker et al. developed the ultrafast tracking method for the observation of the motion of the single molecule orbital by accessing a state-selective tunneling regime through the transient THz EF. [88] By using ultrafast THz-STM, they measured the orbital structure snapshot images with a sub-Å spatial resolution and directly observed the coherent molecular vibrations in THz frequencies through pump-probe measurements.In this submolecular resolution imaging, they provided the way to observe the dynamics of the electrons and phonons in a single molecule, enabling visualization of molecular electronics in the femtosecond photochemistry of well-defined quantum states with the atomic resolution.Furthermore, the ultrafast THz-STM has been used to observe single diatomic molecules.Wang et al. demonstrated the coherence measurements of the single H 2 molecules in the cavity by using ultrafast THz-STM in low temperature (Figure 6b). [89]he optical cavity was defined by the Cu 2 N island on the Cu(100) surface and the Ag tip, and then the THz pulse was illuminated on the cavity to perform THz rectification spectroscopy and THz pump-probe measurements.The two states of H 2 molecules in a double-well potential can couple to the incident THz pulse through the cavity, resulting in the periodic oscillation with a frequency corresponding to the energy separation of the two states (Δε).By measuring the damping of this oscillation, the decoherence time for the interaction of the two-level system can be characterized with varying the surrounding environment of the molecules (position 1, 2, 3).The coherent oscillation is highly sensitive to the measurement condition such as the applying EF and cavity condition including substrate materials, enabling the direct visualization of the chemical environment in the atomic-scale spatial resolution and the femtosecond temporal resolution.The development of the ultrafast THz-STM enables the direct visualization of the molecular level quantum dynamics, accessing a new route to build molecular quantum sensors in chemistry and biology.

Mobile Carriers in Semiconductors
The near-field THz nanoscopy has been employed for the characterization of the carrier dynamics in semiconductor materials. [92,93,95]Huber et al. exploited the near-field THz nanoscopy to measure the mobile carriers in a single transistor (Figure 6c). [92]To achieve high-resolution imaging, the THz light from the continuous-wave CH 3 OH gas laser with the frequency of 2.54 THz was illuminated to the tip, and the scattered light from the tip was collected to the bolometer detector integrated with the Michelson interferometer.The interferometer was introduced to enhance the signal-to-noise ratio with the reasonable detection speed.With the spatial resolution of %40 nm in their near-field THz nanoimaging, distinct feature of the mobile carrier concentration in the range of 10 17 -10 18 cm À3 was demonstrated in a single transistor, indicating that %100 electrons were probed in the minimal spatial volume of the measurements.In addition, they revealed that the nonuniform THz response showing a contrast map in the same material, is attributed to the plasmon-assisted near-field interaction between THz light and the doped semiconductor materials with a high concentration of mobile carriers.Furthermore, Pogna et al. demonstrated the detection of the carrier dynamics in a semiconductor nanowire and the THz photoresponse of an InAs nanowire by using the near-field THz photocurrent nanoscopy with the spatial resolution of 35 nm (Figure 6d). [93]By using s-SNOM with a THz QCL, they illuminated the continuous-wave THz light with the frequency of 2.7 THz to the tip and placed the tip near to the surface of the nanowire.Simultaneously, they measured the electrical current along an InAs nanowire via the electric read-out.In the spatially resolved electrical signal measurements with the scanning of the tip on the nanowire, it was demonstrated the distinct contributions of the photo-thermoelectric (PTE) and bolometric currents to the electric current.They revealed that the different electric current flow mechanism depending on the THz photon flux and the material doping condition can be resolved, enabling the engineered photoresponse for the photons in tens of meV energy.Through the mobile carrier sensing by near-field THz nanoscopy, it would pave the way for the quantitative studies of carrier concentration and mobility also in superconductors, low-dimensional electron systems, or conducting biopolymers at nanoscale.

THz Near-Field Biomolecular Sensors
The tip-based THz nanosensors can be used to detect biomolecules. [91,94,96]Ha et al. developed the subwavelength THz resonance imaging for biomolecular materials (Figure 6e). [91]To demonstrate the highly sensitive molecular detection, the ringshaped coaxial resonators with nanogaps were introduced for enhancing local field enhancement near the resonator.With the microprobe antenna detector, the near-field spectroscopy measured the EF of THz pulse near the resonators, and then they analyzed the spectral response of the resonators.In the strong near-field effect in the nanogaps, the considerable enhancement of the molecular sensitivity gain was achieved with the spectral features of the molecular response, resulting in the successive discrimination of isomeric molecules such as α-lactose and maltose monohydrates.The structural features such as nanogaps and the radius of coaxial ring-shaped resonators can be tuned for controlling the resonance frequency, enabling the multispectral resonant response in a single wafer platform for measuring the THz spectral response in different sites with distinct target molecules.In addition, Heo et al. developed the near-field THz conductance measurement for characterization of the proteins (Figure 6f ). [94]y using frequency-dependent optical conductance measurements with the THz near-field spectroscopy, they observed the conductance change of the biosamples in a physiological buffer solution with varying molar concentrations of monomer, oligomer, and fibrillar forms of the amyloid beta (Aβ) protein, to demonstrate the identification of the progressive Alzheimer's disease Figure 6.The THz near-field nanosensing for carriers and molecules.a) The ultrafast THz-STM of pentacene molecular orbital in a state-selective tunneling.Reproduced with permission. [88]Copyright 2016, Springer Nature.b) The coherence measurements of a single H 2 molecule in the cavity of the tip and the Cu 2 N island by using ultrafast THz-STM.Reproduced with permission. [89]Copyright 2022, AAAS.c) The measurement of the mobile carrier in a single transistor with high carrier concentrations by using the THz s-SNOM integrated with the Michelson interferometry.Reproduced with permission. [92]opyright 2008, American Chemical Society.d) The detection of the carrier dynamics in an InAs nanowire by using the near-field THz photocurrent measurements, reveals the distinct contribution of the bolometric and PTE currents.Reproduced with permission. [93]Copyright 2020, Springer Nature.e) The subwavelength THz resonance imaging of biomolecular materials such as lactose and maltose in coaxial ring resonators with a nanogap.Reproduced with permission. [91]Copyright 2022, American Chemical Society.f ) The identification of the protein states by using the near-field THz conductance measurement.The different protein states such as monomer, oligomer, and fibril states were categorized in the measurements based on the DQ values.Reproduced with permission. [94]Copyright 2020, American Chemical Society.
with the oligomerization and fibrillization of the Aβ protein.In the low-frequency limit in THz spectrum, the conductance was high as the dominant monomer state, meanwhile, it was low and insulating for oligomer and fibril states, respectively.By modeling optical conductance of the protein states in the Drude-Smith model, the structural localization parameters were extracted.The evolution of the fibrillization states in given molar concentration was parameterized as the dementia quotient (DQ) values to identify the fibrillization state of Aβ protein.DQ values were set to 0 and 1 for the monomer state and fibril states, respectively, and the intermediate values of DQ indicated the intermixed localization with oligomer states.In this demonstration, it was revealed that the near-field THz conductance measurement is feasible to perform the label-free diagnosis of Alzheimer's disease with the well-defined parameters, allowing early detection of the disease.These demonstrations allow us to step forward the development of THz molecular detections for practical use.

THz Near-Field Nanosensors for 2D Materials
[99][100][101] Alonso-Gonzalez et al. demonstrated the THz nanoimaging of acoustic graphene plasmon by measuring the THz photocurrent in a graphene/insulator/metal geometry with a split-gate architecture forming spatial sectioning of carrier densities (Figure 7a). [97]The tip, which was shined by incident THz light, generated the scattered THz light with a high in-plane momentum, resulting in the propagating acoustic graphene plasmons.They measured the thermoelectric photocurrent via the graphene with varying the tip position and the carrier densities.In their experiment, it was revealed that the graphene plasmon shows a linear dispersion with %70 times reduced wavelength compared to that of the incident THz plane wave, indicating the acoustic graphene plasmon with the strong field confinement.Moreover, Lundeberg et al. demonstrated the full quantum description of the massless Dirac electron gas with the nonlocal quantum effects in graphene by using tip-enhanced near-field imaging and the measurement of the photocurrents. [98]Figure 7b shows the tip-enhanced THz near-field nanoscopy, demonstrating the tuning quantum nonlocal effects in graphene plasmonics.The nonlocal quantum effects including single-particle velocity matching, interactionenhanced Fermi velocity, and interaction-reduced compressibility in the graphene electron liquid were revealed in the interactions of enhanced EF at the tip with the incident THz light and the graphene plasmons.
The pump-probe experiment integrated with the near-field THz nanoscopy has been developed to investigate the excitons in 2D transition metal dichalcogenide (TMD) materials such The near-field THz imaging of the acoustic graphene plasmon in the graphene/insulator/metal structures.Reproduced with permission. [97]Copyright 2017, Springer Nature.b) The demonstration of the quantum nonlocal effects in graphene plasmon by using the near-field THZ imaging with photocurrent measurements.Reproduced with permission. [98]Copyright 2017, AAAS.c) The pump-probe measurement integrated with the near-field THz nanoscopy, investigating the interlayer tunneling transport in van der Waals heterobilayers of WSe 2 and WS 2 .Reproduced with permission. [99]Copyright 2021, Springer Nature.d) The demonstration of the phonon-polariton with the hyperbolic dispersion in a biaxial van der Waals crystal.The FELs generating bright THz light were employed to resolve the THz phonon-polariton in a narrow spectral range.Reproduced with permission. [90]Copyright 2021, Wiley-VCH.
as WSe 2 and WS 2 .Plankl et al. developed the subcycle temporalresolution contact-free pump-probe experiment integrated with the near-field THz nanoscopy, measuring the transient local polarizability of electron-hole pairs in the TMD heterobilayers with the evanescent THz fields generated by the scattering at the tip (Figure 7c). [99]They demonstrated the femtosecond videography of the interlayer tunneling transport in van der Waals heterobilayers composed of WSe 2 and WS 2 and found the change of the localization and annihilation of interlayer excitons in nanometer scales.In addition, by using the same method, Siday et al. demonstrated the measurement of the nonequilibrium dynamics of the high-density exciton phases in monolayer and bilayer WSe 2 by using the pump-probe experiment with the near-field THz nanoscopy. [101]They observed the dynamics of excitons in bilayer WSe 2 with Mott transition and revealed the interplay of electronic correlations and interlayer coupling, resulting in the density-dependent transition of the exciton gas phase into an electron-hole plasma phase.
Furthermore, for the investigation of van der Waals materials, enhancing signal-to-noise ratio of the THz signal from the scattering tip is crucial to measure the THz optical response.One possible way to increase the signal-to-noise ratio is employing the high-power THz light source such as lasers.Oliveira et al. employed a FEL generating a tunable THz wave with the narrow spectral bandwidth (Figure 7d). [90]They investigated the biaxial van der Waals crystal, α-MoO 3 showing hyperbolic dispersion in the fine spectral resolution at transverse-optical and longitudinaloptical phonon frequencies.The THz polaritons were excited by the bright THz light source from the FEL which is illuminated to the tip.They measured the THz optical response of α-MoO 3 by performing s-SNOM.The results revealed that the low-loss photon polaritons generated by THz light coupled to the lattice vibrations can be excited with the in-plane hyperbolic dispersion and the strong field confinement in van der Waals materials.The near-field THz nanoimaging can be a robust platform to understand the dynamics of quasi-particles such as plasmons, phonons, and excitons in van der Waals 2D materials, enabling new nanosensor platforms controlling light beyond the diffraction limit into a deep subwavelength regime.

Conclusion
We have reviewed the expanding field of THz nanosensing by providing insights into the physical principles, theoretical models, and practical applications of THz nanoresonators and near-field nanosensors.Interestingly, when the electric field is funneled inside THz nanoresonators, its magnitude can be significantly enhanced while the MF remains largely unchanged compared to the incident wave.This means that the ratio E 2 =S is another factor that can increase the absorption cross-section of single molecules.Furthermore, we discussed two approaches for improving the quality factor (Q ) and FOM in resonators.One proposed method involves using asymmetric double SRRs connected by a microstrip line, resulting in a resonance with significantly reduced radiative losses and an enhanced Q-factor.A second approach utilizes Fano resonances in metamaterial structures with asymmetrically fabricated gaps in the outer rectangles of nested SRRs to create high Q-factors.
These THz nanoresonators offer promising opportunities for sensing applications, particularly due to recent advancements in fabricating large-area nanoresonator array.The presence of a strongly localized and enhanced electric field near the metal nanogap enables the detection of minute quantities of molecules.This intense near-field light-matter interaction near the nanogap leads to significant changes in the far-field spectrum, including frequency shifts and alterations in transmission/reflection. Lastly, by combining these THz nanosensors with near-field imaging techniques, researchers may be able to analyze complex nanoscale systems, including 2D materials, in a way that will revolutionize our understanding of quantum dynamics in molecules, mobile carriers in semiconductors, quantum nonlocal effects, and excitons and polaritons in THz frequencies.By combining THz nanosensors with trapping techniques, [21,22] these THz nanosensors have a great potential impact on the advancement of fingerprinting explosives, viruses, proteins, and lipid bilayers at ultralow density.

Figure 1 .
Figure 1.a) Schematic for sensing a substance with dielectric constant ε and thickness d using THz wave and the expected spectral peak shift and decrease of the transmitted THz wave by the refractive index δn and the absorption coefficient δα of ε. b) Single rectangular slot antenna punctured in a thin perfect electric conductor (PEC) layer (upper) and the transmittance normalized by the aperture area as a function of wavelength for different aspect ratios between a x and a y .Two different shapes of the aperture (square and circle) are compared with respect to their transmittances in the inset.Reproduced with permission.[28]Copyright 2005, American Physical Society.https://doi.org/10.1103/PhysRevLett.95.103901.c) (top) Single rectangular slot antenna on a dielectric substrate with thickness t.Reproduced with permission.[30]Copyright 2009, Optical Society of America.(Bottom) The calculated electric field (EF) enhancement at the center of the output aperture as a function of frequency for different values of t.Reproduced with permission.[34]Copyright 2010, AIP Publishing.d) 1D array of THz nanoresonators with period d on a Si substrate (upper) and the calculated transmitted amplitude of THz wave, normalized by aperture area and plotted as a function of frequency, for different values of d and the number of nanoresonators in a fixed sample area (bottom).Reproduced with permission.[67]Copyright 2011, American Physical Society.https://doi.org/10.1103/PhysRevLett.106.013902.e) A unit cell of ultrabroadband THz nanoresonators mimicking log-periodic antennas (upper) and the calculated normalized-to-area amplitudes of the transmitted THz wave as a function of frequency for two different values of d x (bottom).Reproduced with permission.[33]Copyright 2010, AIP Publishing.

Figure 2 .
Figure 2. a) SRR unit cell with definitions of geometries (top left).The corresponding TL RLC-circuit model (top right).Measured (thick solid gray curves) and theoretical values using the full TL-RLC model (thick dashed black curves) compared to individual LC (thin black dashed curves), dipole resonances (thin black dotted curves), and the model without the coupling (thin solid gray) (bottom).Reproduced with permission.[69]Copyright 2008, AIP Publishing.b) SRR with single nanogap unit cell.Calculated transmission spectra for 5 and 10 nm gap SRRs are compared to that of a square ring array with no gap.Reproduced with permission.[38]Copyright 2018, American Chemical Society.c) Reconfigurable SRR depending on applied bias V (left).The cantilever height h determined by the radius R of the curvature and the angle θ (top middle) is controlled by the driving volage V (bottom left).The LC resonance frequencies of SRR as a function of h are compared between experiment (exp) and theory (sim) for three different locations of the gap in SRRs.Reproduced with permission.[70]Copyright 2014, Springer Nature.d) Calculated current distributions for the dipole resonance of independent SRR at f 1 and JSRR at f 2 and new resonance appearing only in JSRR at f 3 (left).Transmission amplitude (left vertical axis) and Q-factor (right vertical axis) as a function of the length of microstrip line d x (bottom right).Reproduced with permission.[71]Copyright 2014, American Physical Society.https:// doi.org/10.1103/PhysRevLett.112.183903.e) Schematics of the THz unit cell at oblique angle (top left) and top views with geometries (bottom left).The refractive index sensitivity of the THz sensor at three different resonance frequencies f 1 , f 2 , and f 3 (right).Reproduced with permission.[72]Copyright 2020, IOP Publishing.f ) 3D schematic illustration of three different shapes of vertical SRR (VSRR) unit cells (left) depending on gap positions.Refractive index sensing with a constant thickness of analyte (right).Reproduced with permission.[73]Copyright 2017, Optical Society of America.

Figure 3 .
Figure3.a) Illustration of enhanced absorption of molecules inside a THz nanoslot antenna (left) and THz transmittance spectra of two kinds of nanoslot antennas with four different amounts of RDX molecules of which absorption resonance is around 0.9 THz (center).The antenna lengths are 90 and 150 μm corresponding to the resonance frequencies are %0.9 and %0.5 THz, respectively.Effective absorption coefficient (left axis) and cross-section (right axis) of RDX molecules extracted from the experimental results of the reduced transmission, as a function of slot width (w) (right).The fitted line (dashed line) shows a 1/w dependence.Reproduced with permission.[3]Copyright 2013, American Chemical Society.b) A schematic (left, top) and scanning electron microscope (SEM) images (left, middle, and bottom) of gap region of terahertz dipole nanoantenna covered with a cadmium selenide (CdSe) quantum dot (QD) monolayer.The QD has a phonon resonance around 5.6 THz.Terahertz transmission spectra of dipole antenna arrays covered with a CdSe monolayer for four different structures.Reproduced with permission.[76]Copyright 2015, American Chemical Society.c) A photograph (center) and THz transmittance image (right) of two kinds of sugar molecules (D-glucose (left, bottom) and fructose (right, top)) dropped down onto an array of nanoslot antennas.The antenna resonance is matched with the absorption resonance of fructose, which leads to a larger transmission reduction for fructose.Reproduced with permission.[36]Copyright 2015, Springer Nature.

Figure 4 .
Figure 4. a) Schematic image for THz nanoresonator-based virus sensing using SRR (left).Resonance frequency shift, Δf versus surface density of viruses with respect to various size of nanogap from 0.2 to 3 μm (center).Gap width-dependent sensitivity showing 1/w dependence (right).Reproduced with permission.[1]Copyright 2017, Optical Society of America.b) Schematic image of annual-nanogap-loop-shaped metasurface covered by insulating layer, Al 2 O 3 , where the thickness of cover layer is comparable with the size of nanogap (left).Frequency-dependent transmitted amplitude of the annual-nanogap-loop nanoresonator with nanogap size of 2, 5, and 10 nm, where THz transmittance is sensitively affected by relative scale between enhancement region and thickness of covering insulating layer (right).Reproduced with permission.[42]Copyright 2015, American Chemical Society.c) Schematic and SEM image for THz nanoresonators with nm-sized gap (left, top).Frequency-dependent transmitted amplitude of two-types of nanogap for detecting viruses: unetched and etched nanogap result in accuracy difference for locating target molecules on desired position (left, bottom).Resonance frequency shift, Δf versus surface density of viruses with unetched (red circles) and etched (blue circles) nanogap (right), where improved resonance frequency shift for etched case is obtained due to complete overlapping of THz wave and viruses.Reproduced with permission.[19]Copyright 2023, De Gruyter.

Figure 5 .
Figure5.The near-field THz microscopy.a) The s-SNOM in the mid-IR wavelength.Reproduced with permission.[48]Copyright 2002, Springer Nature.b) The s-SNOM in THz frequency regime for characterization of the optical properties of the graphene shows near-perfect THz light reflection with high in-plane momentum.Reproduced with permission.[45]Copyright 2018, American Chemical Society.c) The ultrafast THz pulse-integrated STM with the spatial resolution of 2 nm and the temporal resolution of <500 fs.Reproduced with permission.[49]Copyright 2013, Springer Nature.d) The self-mixing intermode-beatnote spectroscopy composed of the THz QCL FCs and the s-SNOM.Reproduced with permission.[50]Copyright 2022, Wiley-VCH GmbH.e) The THz near-field vectorial imaging of subwavelength apertures.The full-vectorial electric fields near the subwavelength apertures were extracted and reconstructed to visualize the evanescent fields.Reproduced with permission.[51]Copyright 2009, Optical Society of America.

Figure 7 .
Figure7.The THz near-field nanosensing for van der Waals materials.a) The near-field THz imaging of the acoustic graphene plasmon in the graphene/insulator/metal structures.Reproduced with permission.[97]Copyright 2017, Springer Nature.b) The demonstration of the quantum nonlocal effects in graphene plasmon by using the near-field THZ imaging with photocurrent measurements.Reproduced with permission.[98]Copyright 2017, AAAS.c) The pump-probe measurement integrated with the near-field THz nanoscopy, investigating the interlayer tunneling transport in van der Waals heterobilayers of WSe 2 and WS 2 .Reproduced with permission.[99]Copyright 2021, Springer Nature.d) The demonstration of the phonon-polariton with the hyperbolic dispersion in a biaxial van der Waals crystal.The FELs generating bright THz light were employed to resolve the THz phonon-polariton in a narrow spectral range.Reproduced with permission.[90]Copyright 2021, Wiley-VCH.