## 2 Materials and Methods
### Experimental Setups
#### 2.2.2 Quasi-Optical THz Beam Delivery Setups  
As depicted in Figure 1, the two types of quasi-optical beam delivery setups were used to bring THz radiation to the gasoline samples and, next, onto the detector. In the _4f_ setup (Figure 1a), the measuring cuvette was positioned in the Fourier plane of the optical system at a midway distance between the transmitter and receiver. The relationship between the Tx transmitter-emitted beam waist, \(\omega_{trans}\), which is next collimated and focused down to the focused beam waist size, \(\omega_{focus}\), can be deduced from the Gaussian beam theory, which is explained in detail in Appendix A. In short, away from its source, the THz beam appears to diverge from the central point of the Tx transmitter, with the half-divergence angle, \(\theta_{trans}\), being proportional to the wavelength of the radiation, \(\lambda\), and inversely proportional to \(\omega_{trans}\). For the Tx transmitter, \(\omega_{trans}\) can be approximated by the radius of the photoconductive antenna lens, which defines the final output aperture of the emitted THz pulse. A simple proportionality relation links \(\omega_{trans}\) and \(\omega_{focus}\) with the focal lengths of the collimating and focusing mirrors in the _4f_-type beam delivery setup. The formal derivation of this relation, which is expressed by Equation (A8), is given in Appendix A.  
Figure 1: Schematic representation of the measurement setups: (**a**) _4f_ setup consisting of four 90\({}^{\circ}\) off-axis parabolic mirrors, which were used to measure THz pulse TOFs through the gasoline admixtures samples in quartz cuvettes of 1.00, 2.00, and 5.00 mm lengths in a focused beam configuration without a time-reference pulse; (**b**) _2f_ setup consisting of two 90\({}^{\circ}\) off-axis parabolic mirrors used for the measurements in a 10.00 mm-long TPX cuvette with a time-reference pulse. Note that the diameter of the THz beam is somewhat larger than the size of the cuvette and passes freely through the inert gas, serving as a reference for the measured TOF. The indicated focal lengths are not to scale. Actually, \(\omega_{focus}\) is independent of the wavelength or frequency of the radiation. This is a favorable situation from the point of view of TDS measurements, assuring comparable sizes of the irradiation spots focused on the sample. A tradeoff, in this case, is the frequency-dependent Rayleigh length, \(Z_{R}\), which defines the distance along which the beam propagating through the cuvette can be considered parallel to the optical axis. When \(Z_{R}\) is substantially shorter than the cuvette length, the paraxial beam approximation is no longer valid. The propagation paths of the spectral components of THz become not equal, becoming an additional source of errors contributing to measuring the TOF of the pulse. To minimize these errors, thin samples or short cuvettes with \(l\ll Z_{R}\) should preferably be together with the 4\(f\) systems. However, shorter cuvettes mean shorter optical paths and faster TOFs through a cuvette and, in consequence, lower precision of the pulse time-of-flight determination. The Rayleigh lengths can be estimated by means of Equation (A9) from Appendix A. In the 4\(f\) setup from Figure 2a, large-aperture parabolic mirrors with 50.8 mm (2-inches) diameters and focal lengths \(f_{trans}\) = 76.2 mm (3-inches) and \(f_{focus}\) = 50.8 mm were used. Since the emitted beam waist \(\omega_{trans}\) can be approximated by the radius of the Tx transmitter lens, which in our case was \(\omega_{trans}\) = 2.5 mm, we can estimate 3 mm \(\leq Z_{R}\leq\) 175 mm. These boundary values are representative of the spectral bandwidth of the THz pulse (Figure 2b). The longest \(Z_{R}\) = 175 mm is related to the highest frequency component of the THz pulse, \(\sim\)6.0 THz, and the shortest wavelength, \(\lambda\sim\) 0.05 mm. It is nearly fivefold longer than the \(l\) = 5.00 mm, the longest quartz cuvette which was used in our measurements.