Fig. 1. Schematic diagram of the tilted-pulse front in LiNbO₃ crystal^[20]

Fig. 2. Schematic diagram of air plasma terahertz source device (DAC: diamond anvil cell, a setup can generate hydrostatic pressure condition)

Fig. 3. Ultrabroad terahertz spectra obtained in our laboratory. (a) Time-domain spectrum; (b) frequency-domain spectrum after fast Fourier transform (FFT); (c) square of the frequency-domain amplitude; (d) phase spectrum after FFT

Fig. 4. Terahertz metasurface nanogap and time-domain spectroscopy^[40]. (a) Light-induced alternating current charges the nanogap, thereby enhancing the electric field as represented by the gradual colour contour; (b) a cross-section of the nearly free-standing nanogap sample structure before FIB (focus ion beam) processing and a scanning electron microscopy (SEM) image of the area indicated in the main panel; (c) terahertz time-domain spectroscopy of the sample is measured by electro-optic sampling, where an SEM image shows the geometry and dimensions of the nanogap (a 70 nm width nanogap perforated on gold film)

Fig. 5. Full-wave simulations of the electric field enhancement in the SRR and nonlinear THz transmission experiment^[41]. (a) Resonant field enhancement as a function of position; (b) simulated time-dependent THz field strength (red) in the horizontal gaps using experimental data (blue) as the input; (c) frequency-dependent in-gap field enhancement obtained from the ratio of Fourier amplitudes of the simulated in-gap and measured incident fields in Fig.(b); (d) field-dependent nonlinear transmission spectra of SRR on VO₂ at 324 K, for in-gap field strength ranging from 0.3 to 3.3 MV/cm; (e) full-wave simulations of SRR response for in-gap conductivities ranging from 30 to 400 (Ω·cm)^-1 (assuming real part conductivity σ₁ changes only in the gaps)

Fig. 6. Localized surface plasmon polariton enhancing field at the metallic tip apex^[45]

Fig. 7. THz-STM and its applications. (a) THz-STM in GBA Branch of Aerospace Information Research Institute, Chinese Academy of Sciences; (b)‒(c) measured autocorrelation signal and silicon surface image (the temporal resolution is about 350 fs and the spatial resolution is about 0.1 nm)

Fig. 8. Investigation of the THz-induced impact ionization in silicon^[51]. (a) Schematic diagram of the pump-probe setup used to investigate THz-induced IMI in silicon, where a CCD image of unit cell of the antenna array with bright probe spot (dashed circle) is shown in the inset; (b) calculated local electric field enhancement profile near the antenna tip; (c) carrier transitions in silicon band structure: interband transitions due to pump beam (1), L-to-X intervalley scattering (2), carrier multiplication through IMI (3), and phonon-assisted interband transition (4)

Fig. 9. Schematic of the electronic band structure of GaAs and related excitation mechanisms^[52]. ① The 800 nm pump pulse excites electrons and holes in the normally insulating GaAs sample, with the electrons being injected into the higher mobility central Γ valley in the conduction band. ② The electrons quickly thermalize within 1 ps to the bottom of the Γ-valley. ③‒④ A high-field THz probe pulse accelerates the photoexcited electrons to higher energies in the Γ-valley, which may result in intervalley scattering to the L-valley

Fig. 10. Coherent interlayer shear mode in WTe₂ measured using relativistic ultrafast electron diffraction^[61]. (a) Lattice structure of Td-WTe₂; (b) schematic of SLAC 3-MeV relativistic ultrafast electron diffraction setup ( intense terahertz pump pulses are used to induce interlayer shear strain in WTe₂); (c) measured electron diffraction pattern of WTe₂ at equilibrium. (d)‒(e) changes in Bragg peak intensity as a function of time delay between the terahertz pump pulses and the electron beam; (f) FFT amplitude of the coherent oscillation, indicating the 0.24 THz shear phonon mode along the b axis

Fig. 11. Coherent terahertz control of spin waves^[67]. (a) Faraday rotation (dots: experimental results; line: numerical simulation) induced by a single terahertz magnetic field pulse (red curve); (b) excitation by two pulses (red curve) with a mutual time delay of Δt=6 ps launches a coherent magnon oscillation and, subsequently, enhances its amplitude by a factor of almost 2 (shaded area); (c) excitation with Δt=6.5 ps switches the magnon on and off coherently

Fig. 12. THz light-driven coupling of lattice to spins^[73]. (a) Two-dimensional Fourier spectrum of the nonlinear amplitude; (b) a pictorial of the magnon-mediated excitation of the B_1g phonon by a THz magnetic field. The unperturbed antiferromagnetic state of the CoF₂ unit cell is shown at the bottom. A THz photon resonantly populates the coherent magnonic state at the frequency Ω_m, thus creating an intermediate state. Another THz photon at the frequency of Ω_ph-Ω_m interacts with this intermediate state and coherently excites the B_1g phonon

Fig. 13. Principle of spin control by a terahertz-induced anisotropy torque^[78]. (a) Spin and lattice structure of TmFeO₃ in the Γ24 phase; (b) spin reorientation phase transitions; (c) the crystal field splits the ground state 3H6 of the rare-earth Tm³⁺ ions into several energy levels with an energy spacing of ~1‒10 meV (upper panel: the corresponding orbital wavefunctions set the magnetic anisotropy for the iron spins in thermal equilibrium; lower panel: ultrafast transitions between these energy levels resonantly induced by terahertz pulses should exert an abrupt torque on the spins and act as an efficient trigger for coherent spin dynamics)

Fig. 14. Schematic of THz-STL measurement^[83] (the figure shows the tip and sample and the inset shows the luminescence principle: luminescence from a localized plasmon is induced by THz-field-driven inelastically tunneled electrons)

Fig. 15. Carrier-envelope phase-stable terahertz high-harmonic generation in bulk GaSe^[87]. (a) High-harmonic intensity spectrum (solid line and shaded area) emitted from a GaSe single crystal driven by the phase-locked terahertz pulse; (b) dependence of the intensity I13 of the 13th harmonic on the incident terahertz amplitude E_a (top scale) and the terahertz field strength E_int (bottom scale) obtained from E_a by accounting for reflection at the crystal surface; (c) the spectral interference between the frequency-doubled sixth harmonic and 12th harmonic confirms the stability of the high-harmonic radiation; (d) electronic band dispersion of GaSe between the G- and K-points

Fig. 16. Schematic and main results of the THz high-harmonic generation^[90]. (a) Schematic of the experiment; (b) terahertz induced high harmonics ( red line, amplitude spectrum of the incident pump THz wave at the fundamental frequency f=0.3 THz with peak field strength E_f=85 kV/cm, determined in the reference measurement. Blue line, the spectrum of the same THz wave transmitted through graphene on a substrate, with clearly visible generated harmonics of third, fifth and seventh order. The shaded area represents the detector cut-off); (c) pump wave (black line) and generated third, fifth and seventh THz harmonics for the case in Fig.(b); (d) thermodynamic model calculation, corresponding to the measurements in Figs.(b) and (c), using the experimental fundamental pump wave at frequency f=0.3 THz (black line) and the basic parameters of graphene in full thermal equilibrium at 300 K as input parameters

Fig. 17. High-harmonic emission from a topological insulator^[91]. (a) Experimental scheme, where the right sketches represent the high-order harmonic generation from the bulk (top) and the surface (bottom), respectively, and the light gray represents Dirac-like dispersion of the TSS and the dark gray represents parabolic bulk bands; (b) high-order harmonic spectra for five driving frequencies between 25 THz and 42 THz; (c) amplitude transmission, t_s, of a 6.5 μm thick Bi₂Te₃ crystal, obtained by THz time-domain spectroscopy, where the edge at about 37 THz corresponds to the bulk bandgap, and the coloured arrows mark the frequencies of the THz waveforms in Fig.(b); (d) intensity of 7th and 14th order harmonic as a function of THz electric field