# Nonlinear TeraHertz Transmission by Liquid Water at 1 THz
## 1 Introduction  
Liquid water strongly absorbs terahertz (THz) radiation [1; 2; 3; 4; 5; 6; 7; 8; 9]. Intermolecular interactions determine the unique properties of water [10; 11] and can assist biochemical reactions [12; 13]. In the low frequency range water displays an overlap of different intermolecular hydrogen bond and Debye-like modes [4; 5]. Recent ab initio calculations described infrared (IR) and Raman spectra [14] and separated the intramolecular and intermolecular modes [15]. In order to disentangle the distinct modes, nonlinear techniques are required. This is especially challenging in the THz range due to lack of brilliant sources [4]. To this aim, a variety of nonlinear laser techniques have been used [16; 17; 18; 19; 20; 21; 22; 23; 24].  
The [PERSON] group developed a 2D spectroscopic tool that combines two pulses in the visible (Raman excitation) with a THz beam [16; 17] and suggested that the intermolecular translational band of water could be characterized by a quasi-inhomogeneous broadening with a correlation time of 370 fs [18]. THz-optical Kerr (TOK) spectroscopy combines an intense THz pump pulse with a weaker optical beam that probes the THz-induced birefringence. In this way, [PERSON] et al. [19] estimated that the nonlinear molecular alignment of a water dipole can be described with the parameter \(\mathrm{B}_{\mathrm{m}}^{(2)}=-2.5\times 10^{-14}\frac{\mathrm{cm}}{\mathrm{V}^{2}}\), which is on the same order of magnitude of the electronic effect detected by optical-optical Kerr [20; 21] experiments (see, e.g., Table 1 in [19]). With TOK, [PERSON] et al. [22; 25] recently found indication of a \(\sim\)0.5 ps long dynamical coupling between rotational and translational intermolecular water modes at low-frequency.  
Given the sequence of optical and THz fields, all these nonlinear techniques are sensitive only to modes that are strongly active both in Raman as well as in the far infrared. Thus, a complementary approach is to perform nonlinear experiments employing exclusively THz fields. We previously performed THz-THz Kerr experiments at 12.3 THz with the librational mode of water and found thatthe THz-induced birefringence is about three orders of magnitude larger than in TOK experiments [24]. [PERSON] et al. [23] reported the nonlinear transmission of almost single-cycle pulses centered at 0.75 THz by a liquid water jet. They performed typical z scan measurements [26], whereby the sample is moved through the beam focus and the intensity transmission is measured with a power detector, both with an open as well as with a partially closed aperture [27; 28]. This experimental approach is restricted to the large sample volume required to run a recirculating liquid jet, which to our knowledge needs at least hundreds of milliliters of liquid sample [29]. However, this prevents applications to expensive solutes that are not available in large quantities. In addition, it is preferable to use field-sensitive rather than intensity detectors because of their superior dynamic range [29; 30; 31].  
In order to overcome these two bottlenecks, here we report nonlinear transmission measurements of \(\sim\)1 THz pulses by small volumes of liquid enclosed in a static cell with diamond windows. By comparing field- and intensity-resolved z scan experiments, we were able to correctly quantify the nonlinear response of bulk water even in the presence of a large nonlinear signal caused by the empty sample holder.