# Few-Cycle, \(\mu\)J-Class, Deep-UV Source from Gas Media
## 3 Results and Discussion
When the gas cell is placed in front of the laser focus, the DUV yield is slightly smaller than when the gas cell is placed behind the focus regardless of the gas type. Furthermore, the DUV spectra are noticeably different depending on the cell position. To examine the variations in the generated DUV spectra more closely, we take cross sections (or spectra) at several gas cell positions (dashed lines in Figure 3c,d). In Figure 5a, a notable difference in the DUV spectrum depending on the gas cell location is observed. The DUV spectrum taken from the gas cell condition at z\({}_{0}\) = +14 mm exhibits a spectral blue-shift compared to the spectrum from the condition at z\({}_{0}\) = -14 mm. The same tendency is observed from the Ne result (Figure 5c). To understand these experimental observations, we have simulated the propagation of an ultrashort optical pulse in a gas medium by numerically solving the nonlinear envelope equation under the slowly evolving wave approximation (SEWA) [28]. In the simulation, nonlinear effects, such as nonlinear absorption, plasma dispersion, and the third-order susceptibility of the medium are included. While a focused laser beam has a symmetric intensity distribution with respect to the laser focus, nonlinear laser-matter interaction mechanisms can be asymmetric between the gas cell positions, being placed before and after the laser focus. In HHG, it has been studied already that there are plentiful cell-position-dependent mechanisms [20; 21; 22]. In the present THG results, the asymmetric  
Figure 4: Atomic neutral densities and THG yields. (**a**,**b**) show the variation of neutral-atomic densities and laser intensity for different cell positions. (**c**,**d**) are estimated THG yields, indicating that the maximum DUV yield is expected when the cell is placed off the laser focus in the case of Ar. For Ne (**a**), 25% of the neutral atoms are expected to be ionized when the cell is positioned at the laser focus. For Ar (**b**), the neutral atoms are totally depleted near the focus. blue-shifting tendency was reproduced by simulation, which is shown in Figure 5b,d. The simulated spectral shape deviates from the experimental observations, due to the reduced detection efficiency of the near vacuum-UV components (above 5.7 eV), compared to the DUV components. Figure 6 shows more details of the simulation result for the Ar target, when the cell is located at \(z_{0}=\pm 14\) mm. Figure 6a-d shows the results for \(z_{0}=-14\) mm, i.e., when the gas cell is placed 14 mm before the laser focus. The simulation results for \(z_{0}=+14\) mm are displayed in Figure 6e-h. For both \(z_{0}=\pm 14\) mm, the laser is strong enough to ionize the atoms at the leading edge (z \(-\)\(z_{0}\approx-5\) mm) of the initial gas profile (dashed lines in Figure 6a,e) as can be seen in Figure 6a,b or Figure 6e,f. In Figure 5, the experimental and numerical results show that the blue-shift is less significant when the cell is located at \(z_{0}=-14\) mm compared to when \(z_{0}=+14\) mm. This is because the laser beam interacts with the leading edge of the gas profile before the laser is tightly focused. The generated electron density is an order of magnitude smaller than in the case of \(z_{0}=+14\) mm, as shown in Figure 6a,b. In Figure 6c,d, the on-axis spectral intensities of the NIR (c) and DUV (d) lights are shown. Although the laser beam becomes naturally stronger by the focusing geometry, the relatively low-density plasma makes the beam diverge so that the on-axis NIR intensity is reduced over the first half of the propagation; the beam then becomes stronger again in the next half of the propagation. The mean photon energy of the NIR light is blue-shifted and then returns to its initial spectral shape, because low-frequency light diverges further in the plasma. On the other hand, when the gas cell is at \(z_{0}=+14\) mm, the atoms are irradiated with a diverging laser beam. The approximately 10 times higher 0.07 bar of the atoms can be ionized at the leading edge of the gas profile.