# High-Harmonic and Terahertz Spectroscopy (HATS): Methods and Applications
###### Abstract  
Electrons driven from atom or molecule by intense dual-color laser fields can coherently radiate high harmonics from extreme ultraviolet to soft X-ray, as well as an intense terahertz (THz) wave from millimeter to sub-millimeter wavelength. The joint measurement of high-harmonic and terahertz spectroscopy (HATS) was established and further developed as a unique tool for monitoring electron dynamics of argon from picoseconds to attoseconds and for studying the molecular structures of nitrogen. More insights on the rescattering process could be gained by correlating the fast and slow electron motions via observing and manipulating the HATS from atoms and molecules. We also propose the potential investigations of HATS of polar molecules, and solid and liquid sources. ultrafast intense laser; atoms and molecules; high harmonic generation; terahertz wave; electron dynamics +
Footnote †: journal: Applied Physics Letters  
_Applied Physics Letters_  
On the other side of the spectroscopy from strong field interaction, extremely nonlinear down-conversion of the laser frequency could take place via the terahertz (THz) wave generation, which has a millimeter and sub-millimeter wavelength [16]. Interestingly, the great discrepancy between HHG and THz output seems to be mainly determined by the ionization time of the emitter electrons, calling for a unified \"non-perturbative\" strong field viewpoint in understanding the classical \"perturbative\" region of laser and matter interaction. Slow electrons for THz output should be modeled differently from the ones for the plateau or cut-off of high harmonics even though they are driven by the same laser fields, because the slow electron motion could be strongly distorted by the Coulomb potential. This Coulomb field effect has been identified by tracing the phases of THz wave with the help of high harmonics [17; 18], and by analyzing the underlying dynamics via classical [19] and quantum calculations [20]. Therefore, the simultaneous detection of the high-harmonic and THz spectroscopy (HATS) gives us an opportunity to illustrate more aspects of the ultrafast dynamics of electrons with different ionization times, especially for the electrons contributing to the low-energy THz wave generation. Furthermore, the joint measurement in HATS allows the in situ simultaneous manipulations on the two ends of emissions, which could be realized by varying the accumulated phase during the electron propagation (e.g., using dual-color laser fields [17]) or varying the potential curve (e.g., varying the molecular alignment [21]). The first experimental demonstration of HATS from gaseous argon was reported in 2012 [17]. With the help of a weak second-harmonic, the symmetry of the consecutive half cycles of the fundamental laser fields is broken to produce significant intensities of the even-order high harmonics [22] and THz wave [16], whose yields depend on the relative phase between the two colors. Note that the in situ simultaneous manipulation is carried out on all electrons in the laser fields, thus it helps to build a phase-locked connection between different scales of electronic movements with various kinetic energies and collision processes. Meanwhile, the simultaneous generations and manipulations of HATS can also serve as a more convenient choice in carrying out the time-resolved THz pump/X-ray probe measurements via a table-top femtosecond laser, in comparison to the expensive and huge electron bunch setup or free electron laser light source [23; 24; 25]. Here, we review the state-of-the-art HATS technology. Firstly, we give a general introduction to the physical concept of this method. Next, we discuss two examples of HATS detection from argon. In the first example, we demonstrate the simultaneous detection of HATS from argon to study the THz generation with attosecond time resolution, thanks to the intrinsic chirp of the electron wave packet and the corresponding HHG.