# Nonlinear TeraHertz Transmission by Liquid Water at 1 THz
## 3 Results and Discussion
Here we suggest that a field-sensitive detector should be able to probe simultaneously both the changes in the extinction coefficient as well as in the index of refraction, possibly with better resolution. In order to prove this assumption, we performed additional open aperture z scan measurements on the empty and the water-filled diamond cell, and detected the transmitted THz peak field with EOS. Time resolved THz experiments or \"pump scans\" are routinely performed at the peak position of the THz field, and allow estimating the overall size of the signal and the dynamics [38]. Contrarily to intensity measurements with, e.g., a bolometer, the amplitude of the THz peak is affected not only by the change in absorption, but also by the change of the index of refraction of the sample, which can delay the pulse in time [38]. For this reason, by comparing the results of z scan measurements performed with bolometer and field-sensitive techniques, in the following we estimate the nonlinear absorption and the nonlinear refraction. In Figure 3a we show the full THz fields transmitted by the empty cell (black) and by the diamond cell filled with a 50 \(\upmu\)m thick water layer (blue). The peak THz field transmitted by the water-filled (empty) sample holder is marked with E\({}_{\text{wat}}\) (E\({}_{0}\)). In Figure 3b we show open aperture z scan measurements, where the balanced EOS detection measures the peak amplitude of the THz field (E) transmitted by the empty (E\({}_{0}\), black in Figure 3b) and water-filled cell (E\({}_{\text{wat}}\), blue in Figure 3b). In order to compare the electric field transmitted by the filled and empty cell, the field is in each case normalized to the value of the transmission at low THz power, E(z = 22 mm). As shown in Figure 3b and expected for nonlinear transmission, the detected THz peak field varies as a function of the position of the z stage. However, in these field-sensitive experiments the maximum signal is not found at z = 0. This originates from a small drift of the THz spot size imaged at the detection crystal, which was checked with the THz camera and is unchanged for empty and filled cell. This systematic error can be present only when detecting the field amplitude and not the area-integrated signal (e.g., bolometer, Figure 2). This can be removed by comparing the two z scan experiments. In order to quantify the nonlinear field transmission by the water layer (Equation (6)), we use the same approach outlined above for the intensity transmission (Figure 2d). The quantity:  
\[\mathrm{d_{E}(z)}=2\times\frac{\mathrm{E_{wat}(z)}}{\mathrm{E_{wat}(z=22\;mm)} }-\frac{\mathrm{E_{0}(z)}}{\mathrm{E_{0}(z=22\;mm)}} \tag{6}\]  
is shown in Figure 3c. The amplitude of \(\mathrm{d_{E}}\) at the THz focus can be estimated to \(1.018\pm 0.005\) with a Gaussian function (solid red line in Figure 3c). We chose a slightly different spacer for EOS z scans (50 \(\mathrm{\SIUnitSymbolMicro m}\), Figure 3) with respect to the intensity measurements (100 \(\mathrm{\SIUnitSymbolMicro m}\), Figure 2). As expected, for the  
Figure 3: (**a**) We used a 100 \(\mathrm{\SIUnitSymbolMicro m}\) ZrTe crystal to detect the THz field transmitted by the empty cell holder (black), and by the sample holder filled with a 50-micron thick layer of pure water (blue). The peak THz field transmitted by the empty (water-filled) cell is marked with \(\mathrm{E_{0}}\) (\(\mathrm{E_{wat}}\)). (**b**) Z scan measurements of the peak field transmission of the empty diamond cell (black), and of the liquid cell filled with a 50-micron thick water layer (blue). The error bars are indicated and correspond to the standard error of the mean calculated from 100 measurements. Solid circles and squares represent the experimental results. Solid lines are guides to the eye. (**c**) The nonlinear field transmission of the water layer is estimated to the difference of the field transmissions of filled and empty cells (\(\mathrm{d_{E}}\)). The red solid line is a Gaussian fit.