## 3 Results
### Investigations of THz Pulse Time of Flights in Gasoline Solutions with Isopropanol  
Figure 8 shows the uncorrected, raw data waveforms of THz pulses obtained after propagation in gasoline mixtures containing isopropanol alcohol. The registrations were taken in quartz cuvettes of all three lengths. The cuvettes were located in the Fourier plane of the 4\(f\) quasi-optical beam delivery setup. The pulses indicated by the red arrow served as a \"zero-delay\" time reference for the later applied pulse position correction procedure (Section 3.1). They had to be acquired in separate registrations directly before time-of-flight measurements because the size of the focused THz beam in the 4\(f\) system is incomparable with the transverse dimensions of the cuvette. Despite different methods of registration, the reference waveforms were used in the time correction procedure that was the same for the 4\(f\) and 2\(f\) systems. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Substance** & **TOF \(n\)** & **Reference \(n\)** \\ \hline Isopropanol & \(n_{iso}\) = 1.50687 \(\pm\) 0.00081 & \(n\) = 1.50 1 \\ Gasoline & \(n_{gas}\) = 1.4308 \(\pm\) 0.0016 & \(n\) = 1.415 – 1.441 2–4 \\ \hline \hline \end{tabular} \({}^{\dagger}\) [PERSON] et al. [37], average 0.2–1.4 THz. 2 [PERSON] et al. [11], average 0.1–1.1 THz. 3 [PERSON] et al. [38], unspecified octane number, average 0.2–2 THz. 4 [PERSON] et al. [39], @1 THz, 93-octane gasoline.  
\end{table} 
Table 2: Comparison between the measured and reference refractive indices of pure isopropanol and pure gasoline. The source of the references is indicated below the table. The waveforms indicated by green, red and blue lines correspond to \(l\) = 1.00, 2.00 and 5.00 mm cuvettes, respectively. The actual isopropanol concentrations related to each of the series are summarized in Table 3. It is necessary to understand that the chosen range of isopropanol concentration in gasoline had to be carefully adjusted to the lengths of the cuvettes because transmission of THz radiation could be very limited over long propagation paths in the cuvettes. The blue arrows in the figure indicate the THz pulses after their interaction with gasoline samples and the dashed blue arrows-the pulses multiplied by the cuvettes after internal reflections. The measured TOFs were compared with predictions of Equation (11). The results of the comparison are depicted in Figure 9. In the first graph (Figure 9a), the measured TOF differences, \(\Delta t\), were plotted against the mass fractions of isopropanol, \(\phi_{1}\), from Table 1. The \"zero-delay\" time difference, \(\Delta t\) = 0, corresponds to the positions of pure gasoline pulses belonging to each of the series from Figure 8.  
A common characteristic that is apparent in Figure 9a is that, independent of cuvette lengths, the measured \(\Delta t\) increases approximately linearly with the isopropanol concentration. Moreover, for the fixed absolute value \(\phi_{1}\), \(\Delta t\) is proportional to the length of the cuvette, \(l\), and is manifested by increasing slopes of the measured points. Additionally, the time separation between them along the ordinate is visibly better when the optical lengths are longer, meaning that longer cuvettes are much better suited for sensitive measurements of trace concentrations of admixture in the solution. Even if the broadest span of the investigated mass fractions of isopropanol was from 0 to 750,000 ppm, i.e., 0 to 75%wt., such a large range of concentrations could only be covered in the shortest 1.00 mm cuvette because in other cases, the limited transmission of THz radiation precluded the registrations of the pulse waveforms with sufficient accuracy. Figure 8: Waveforms of the THz pulses registered with \(l\) = 1.00, 2.00 and 5.00 mm quartz cuvettes and gasoline isopropanol admixture samples. The curves represent raw, uncorrected data as measured with the THz-TDS spectrometer and 4\(f\) quasi-optical beam delivery system.