## 3 Results and Discussion  
In the first set of experiments we study the CARS signal of O\({}_{2}\) molecules by filling the gas cell with air at different pressures. As the first step towards optimizing the beam alignment and time delays for pump/probe pulses, we collect the CARS spectrum showing rotational-vibrational structure of oxygen molecule (Figure 2), where several peaks can be clearly distinguished. The signal was collected for 2.2 s at atmospheric pressure at 1 kHz. The main peak of the spectrum (1555.6 cm\({}^{-1}\)) corresponds to the Q-branch (\(\Delta J\) = 0) vibrational transition from the vibrational ground level of the oxygen molecule. Smaller peaks on the left and on the right to the Q-branch transition represent O- (\(\Delta J\) = \(-\)2) and S- (\(\Delta J\) = +2) transitions correspondingly [37]. Thereafter, we use the maximum CCD count value from the region of Raman shift 1556 \(\pm\) 1 cm\({}^{-1}\), i.e., the intensity of the Q-branch vibrational line to examine the dependence of the CARS signal on gas concentration and pressure. Before calculating the maximum intensity, the zero-pressure background signal was subtracted from the data. We find using the maximum intensity to be more convenient and yet sufficiently precise for studying the dependence of the CARS signal on molecular concentration, when the absolute concentration of gas species is irrelevant. However, it is worth mentioning, that the fitting curves parameters for integrated intensity data points differ from the peak fittings by less than one standard deviation (4.6%). During these measurements laser power fluctuations at 1 kHz repetition rate were below 0.5% and the signal was integrated for 5.2 s. The long integration time aids in significantly reducing the signal intensity fluctuations, but forces us to use at least ND = 3.0 filter at ambient conditions in order to avoid saturation of the CCD. First, the cell is filled with a gas mixture of ambient air and pure nitrogen (Figure 3, solid circles). We assume the oxygen presence in air to be 21% and vary the partial pressures of air and nitrogen while keeping the total pressure in the cell constant. These measurements allow us to study the dependence of CARS signal on the concentration of O\({}_{2}\) with different amounts of background molecules (N\({}_{2}\)). In this case, the CARS signal scales as a square of the relative oxygen concentration. Next, we fill the cell with ambient air at various pressures, keeping the gas composition and ratio of oxygen molecules to background molecules constant. We control the total pressure inside the gas cell by a ball valve, and perform measurements for the range from 0.01 bar to 1.07 bar. The experimental data with a fit curve are shown in Figure 3 (hollow diamonds), where the signal is proportional to the square of the gas pressure. Hence, we conclude that in both cases of constant gas mixture at different pressures and varied gas compositions at constant pressure, the CARS signal is proportional to the square of the number of O\({}_{2}\) molecules. Figure 2: CARS spectrum of molecular oxygen in ambient air. Arrows mark the locations with maximum intensities, and corresponding wavenumbers and final quantum rotational numbers are given. In the next set of experiments, we replace the gas cell with a 1 mm round nozzle connected to a cylinder with N\({}_{2}\) gas and pointed in the direction perpendicular to the beams propagation. Hereafter, we obtain the CARS signal for O\({}_{2}\) molecules in ambient air in front of the nozzle in the vicinity of the focal plane of the beam (Figure 4), where zero of the X-axis corresponds to the nozzle surface and zero of the Y-axis to the center of the nozzle. After we set the gas pressure such that the gas flow from the nozzle remains constant (estimated at \(\approx\)4.5 m/s), we move the nozzle in a direction transverse to the axis of the beam propagation direction (Y and X axes in the figure).