Fig. 1. Three-process theory of terahertz (THz) radiation, with figures reproduced with permission from Ref. [24, 35-36, 39, 56]. (a) Three-process model of THz wave generation via femtosecond laser filamentation: (Ⅰ) four-wave mixing (4WM) and (Ⅱ) photocurrent (PC) oscillation dominate the first two processes^[24,35], respectively; (Ⅲ) the spatially confined transmission of THz waves is considered as the third process^[56]. (b) Best fittings of the experimental results are achieved with the three-process model^[36]. Black dots represent the experimental evolution of the time-domain THz peak-to-peak amplitudes in orthogonal directions with the rotation angle of the frequency-doubling crystal. Fitting lines correspond to the results obtained by using 4WM, PC, 4WM+PC and the three-process model (4WM+PC+1DND), respectively. (c) Far-field radiation profiles (Ⅰ) and the frequency dependence (Ⅱ) of THz waves from different filament lengths are obtained via the off-axis phase-matching model^[39]. (d) Diameter variation and frequency dependence of THz beams in the filament region (with strong spatial confinement) and far field^[56] are shown in (Ⅰ) as experimental results, and in (Ⅱ) as a schematic view

Fig. 2. Experimental detection skills of strong spatial confinement phenomena of THz waves, with figures reproduced with permission from Ref. [58-60]. (a) Three experimental methods for detecting the strong spatial confinement of THz waves^[58] are longitudinal translation of the blocker (Ⅰ), knife-edge (KE) measurement (Ⅱ), and two-dimensional scanning imaging (Ⅲ); (b) the temporal advance phenomenon of THz pulses (I)^[59] given by the longitudinal method, which further leads to the THz refractive index distribution as shown in (Ⅱ)^[60]; (c) a typical result given by the transverse KE detection method (Ⅰ) and the evolution of THz beam diameters with the filament propagation distance (Ⅱ)^[61], where the side view of the filament can be found in the upper left corner of (Ⅱ); (d) the two-dimensional scanning imaging result of THz distributions within the cross section of the filament^[58]

Fig. 3. Theoretical models for the spatial confinement effect of THz waves, with figures reproduced with permission from Ref. [56-57,61-62]. (a) Numerical model^[61]: (Ⅰ) the plasma density, refractive index at 0.4 THz and radial distribution of the simulated THz modal field; (Ⅱ) the cross sections of THz modes at 0.2, 0.4 and 0.6 THz. (b) Micro-cavity oscillation model^[57]: (Ⅰ) the ray-tracing diagram of THz wave oscillations in a simplified “air-plasma-air” cavity; (Ⅱ) the field distribution of the THz mode inside the cavity. (c) One-dimensional negative dielectric (1DND) waveguide model^[56,62]: (Ⅰ) the radial real part of the dielectric constant (black solid line) and refractive index distribution (blue dashed line) of the plasma filament^[56]; (Ⅱ)(Ⅲ) the schematic diagram of a metal nanowire as a negative dielectric constant optical waveguide^[62]; (Ⅳ) the radial distribution of the THz modal field given by the 1DND model, where “a” is defined as the radial distance at which Re[ε_r]=0^[56]

Fig. 4. Applications based on the strong spatial confinement of THz waves, with figures reproduced with permission from Ref. [56,61,65-68]. (a) Super-resolution THz imaging^[61]: (Ⅰ) the experimental setup; (Ⅱ) comparison between the optical and THz images; (Ⅲ) comparison of one-dimensional data. (b) Evolution of THz energy and electric field intensity along the filament (Ⅰ)^[56], the relationship between the maximum THz electric field and the distance from the BBO crystal to the focal point (BFD) (Ⅱ)^[56], and the enhancement of THz radiation with a dual-filament array (Ⅲ)^[65]. (c) By adjusting the pumping laser power and the transverse electrostatic bias of the filaments, the relative time delay of the orthogonal THz components can be modulated (Ⅰ), leading to the conversion of the output THz polarization states (Ⅱ)^[66-68]