# Nonlinear TeraHertz Transmission by Liquid Water at 1 THz
## 3 Results and Discussion  
In Figure 2c we show open aperture z scan measurements, where the bolometer detects the THz intensity (I) transmitted by the empty (I\({}_{0}\), black in Figure 2c) and water-filled cell (I\({}_{\mathrm{watt}}\), blue in Figure 2c). In order to compare the different transmission values of filled and empty cell, the intensity is in each case normalized to the corresponding value of the transmission at low peak power, I(z = 22 mm). The absolute value of the transmission by the filled cell is different than the transmission by the empty cell, because liquid water strongly absorbs THz radiation [33]. Thus, we plot the relative transmission values in Figure 2c: \(\frac{\mathrm{I_{0}}(z)}{\mathrm{I_{0}}(z\mathrm{=}22\ \mathrm{mm})}\) for the empty cell, and \(\frac{\mathrm{I_{watt}}(z)}{\mathrm{I_{watt}}(z\mathrm{=}22\ \mathrm{mm})}\) for the water-filled static sample holder. The transmission at z = 22 mm is the furthest point from the focus given the range of the mechanical stage, the peak power is reduced to the lowest possible value of ca. 10 MW/cm\({}^{2}\), and the  
Figure 1: (**a**) Sketch of the experimental setup. The terahertz source is TeraFERMI at the FERMI free-electron laser at the Elettra synchrotron. The beam path of the THz radiation is shown in green and routed with two off-axis parabolic mirror (OAPM). The sample holder is moved through the THz focus with a computer-controlled stage. The nonlinear transmission (red) reaches a maximum at the THz focal position (z = 0). When the static cell is empty, the nonlinear response can originate from the diamond windows (black). When the liquid holder is filled with water (blue), the nonlinear response can also originate from the liquid layer. Away from the focus, the transmission approaches the linear value (z > 20 mm). Two detecting apparatuses are alternatively used to measure the field (electro-optical sampling, EOS) or its intensity (silicon bolometer). (**b**) THz beam properties measured with a camera placed at the sample position. The green squares indicate the full-width at half maximum (FWHM) of the THz spot size measured as a function of the position of the z stage. The solid green line is a guide to the eye. The THz spot is ca. 1.1 mm at the focus z = 0. In this position, the peak power is maximum and amounts to P = 100% = 61.4 MW/cm\({}^{2}\). Moving away from the focus, P decreases for increasing THz spot area. transmission approaches the linear regime. Given the restricted beam time available, we were not able to acquire more data while keeping the same signal-to-noise. For this reason, the z scan measurements in, e.g., Figure 2c display a limited number of discrete points. As shown in Figure 2c, and expected for nonlinear transmission, the detected THz intensity varies as a function of the position of the z stage and is maximum around the focal point (z = 0). If the nonlinear response would be restricted to the diamond windows, we expect for the empty cell the nonlinear response of the two windows. In case of the water-filled cell, the THz intensity at the second diamond window is decreased by ca. 90% [33], therefore, the THz nonlinear response by the second diamond window can be neglected only when the liquid cell is filled. If water would not contribute to the nonlinearity, then the nonlinear response by the filled cell should be approximately half of the nonlinear response of the empty cell (one vs. two windows). However, by inspecting Figure 2c we note that the transmission of the water-filled cell increases by ca. 4% ( \(\frac{\text{I}_{\text{water}}(z=0)}{\text{I}_{\text{water}}(z=22\text{ mm})}\sim 1.04\)), while the transmission by the empty sample holder increases by \(\sim\)5% ( \(\frac{\text{I}_{0}(z=0)}{\text{I}_{0}(z=22\text{ mm})}\sim 1.05\)). This suggests that both the front diamond window as well as liquid water display nonlinear transmission when the cell is filled.