# High-Harmonic and Terahertz Spectroscopy (HATS): Methods and Applications
### Rescattering Process and the Joint Measurement of HATS  
The (plasma) current model for THz generation is analogous to the other strong field phenomena by treating the electron dynamics as the radiation source. Temporal and spatial asymmetric current could contribute to the THz generation under strong dual-color field scheme. In the sparse gas circumstance, atoms or molecules are far away from each other, thus the emissions can be treated as the coherent summation over the individual emitters. Therefore, rescattering process of the tunneling electron from one atom or molecule could be understood via analyzing the far-field THz emissions, as well as the HHG. It is of great interest to know which part of the electron dynamics dominates the contribution of THz wave generation. Trying to reach the answer, we recall the low-energy structure (LES) of above-threshold ionization. In 2009, [PERSON] [13] and [PERSON] [14] observed the appearance of the anomalous spectral peaks of photoelectrons in the low energy region. These LES peaks can be reproduced by the TDSE calculations but not by the SFA model. [PERSON], who raised the SFA model, suggested the effect of the long-range Coulomb potential on the forward-resacattering of the tunneling electrons in interpreting the LES [41]. The following experiments and theoretical developments support his interpretation. By using the elliptically polarized laser to ionize electrons, which suppresses the rescattering process, LES is found to disappear [13; 42]. The semi-classical calculations based on quantum orbit theory also confirm the influence of atomic potential on the rescattered electrons for the LES [43; 44]. By comparing the forward-scattering from the Yukawa potential or the long-range Coulomb potential, the LES of photoelectrons is proven to be determined by the forward rescattering of electrons with the Coulomb long-range tail [45]. On the other hand, the three-dimensional classical-trajectory Monte Carlo (3D-CTMC) method and the 3D-TDSE results suggest that the low-energy photoelectrons, with the kinetic energy less than 1.2 \(U_{p}\), are responsible for the THz emissions from dual-color laser scheme [19; 20]. In [PERSON]'s plasma current model, only the current formed by the freed electrons is considered as the source for THz wave generation, and the Coulomb interaction is being neglected. However, according to the observations of LES, the long-range Coulomb interaction can dominantly influence the motion of the low-energy photoelectrons. Therefore, due to the effect of the Coulomb field and the forward-rescattered electrons, the optimal phase for THz yield should be different from the one as predicted by the plasma current model. Previous calculations suggest that, under the typical laser condition (800 nm, with the laser intensity around \(10^{14}\) W/cm\({}^{2}\)), the forward-rescattered photoelectrons with Coulomb attraction dominate the current for THz yields, resulting in the optimal phase for THz yield around 0.8\(\pi\)[19]. By carrying out the simultaneous detection of HATS from argon, we used the attosecond resolution of harmonic chirp to gauge the THz emissions, presenting the dual-color phase dependence of THz modulations and clarifying the importance of the forward-rescattered electrons in the THz generation process [17; 18]. These experimental results suggest the importance of Coulomb interaction on the rescattered electrons and update the understanding of the generation process of THz wave. The major advantage of HATS is that it allows a simultaneous observation of the two ends of the emitted spectra from atom or molecule under strong field interaction, which correlates the fast and slow electron motions via observing and manipulating the HATS. Measuring HATS is actually the observation of different rescattered electrons during the strong field process, since the \"hard\" recollision electrons emit high harmonics, while the escaping and forward rescattered electrons contribute to THz generation.