# Few-Cycle, \(\mu\)J-Class, Deep-UV Source from Gas Media
## 4 Conclusions  
In conclusion, we have demonstrated, by experiment and simulation, that DUV production via third-order harmonics is critically dependent on the gas cell position with respect to the laser focus. The careful optimization of DUV by considering nonlinear features has allowed us to achieve \(\sim\)1 uJ class DUV pulses in the 3.6-5.7 eV range (at  
Figure 6: Simulated nonlinear DUV generation dynamics in Ar. The left column (**a**–**d**) and the right column (**e**–**h**) panels are the results for the two different cell positions: \(\mathrm{z}_{0}=-14\) mm and +14 mm, respectively. (**a**,**e**) shows the \(z\)-dependent on-axis (\(r=0\)) electron densities after the laser has passed. (**b**,**f**) are the two-dimensional (\(r\) and \(z\)) electron density profiles. The spectra of propagating fundamental (**c**,**g**) and the third-order harmonic (**d**,**h**) were taken from the on-axis (\(r=0\)). In (**c**,**g**), the mean photon energies of the fundamental laser are indicated by the dashed lines to visualize the blue-shift.  
the \(-20\) dB intensity level), which supports a transform-limited sub-2.5-fs pulse, from Ar gas at a sub-atmosphere (0.8 bar) pressure. From an engineering point of view, the achievement of 1 \(\upmu\)J class DUV using sub-atmospheric pressure is significant, especially for experiments that require a high-vacuum level. The pulse duration can be estimated in a perturbative regime of a moderate intensity condition, as in our case, by using an analytic solution \(P_{3}\propto\chi^{(3)}E^{3}\). It was evaluated to be 2.6 fs. Refs. [15,16] have reported the pulse measurement, giving approximately consistent results to the analytic evaluations. Furthermore, it was reported that, when the laser intensity becomes non-perturbative, the plasma effects make the pulse duration even shorter [4]. From these considerations, we judge that the DUV source has a pulse duration of 2.6 fs or so.  
It was revealed that, despite the symmetric intensity distribution of the laser beam near the laser focus, the DUV generation efficiency and the amount of blue-shifts are adjusted by the cell location, either before or after laser focus. This tendency was explained by the results of numerical simulation. Careful simultaneous optimizations of the gas type, gas pressure, laser intensity, and the location of the cell can lead to highly efficient UV generation by striking a balance between the third-order response of gas materials and highly nonlinear processes.  
Conceptualization, T.K., J.-H.M. and D.-E.K.; Data curation, T.K. and J.-H.M.; Formal analysis, T.K. and J.-H.M.; Funding acquisition, J.-H.M. and D.-E.K.; Investigation, T.K., J.H. and Y.L.; Methodology, T.K., J.-H.M., J.H. and Y.L.; Project administration, J.-H.M. and D.-E.K.; Resources, J.H. and Y.L.; Software, T.K. and J.-H.M.; Supervision, D.-E.K.; Validation, T.K. and J.-H.M.; Visualization, T.K. and J.-H.M.; Writing--original draft, T.K., J.-H.M. and D.-E.K.; Writing--review and editing, T.K., J.-H.M. and D.-E.K. All authors have read and agreed to the published version of the manuscript.  
This work was supported by Max Planck POSTECH/KOREA Research Initiative Program (No. 2016K1A4A4A01922028) through the National Research Foundation of Korea (NRF) funded by Ministry of Science, ICT and Future Planning and in part by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT)[Grant No. 2020R1C1C1012953].  
Not applicable.  
The data presented in this study are available on request from the corresponding author. The data are not publicly available due to ethical restrictions.  
The authors declare no conflict of interest.  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l} HHG & High-order harmonic generation \\ THG & Third-order harmonic generation \\ NIR & Near infrared \\ Dscan & Dispersion scan \\ SEWA & Slowly evolving wave approximation \\ \end{tabular}