Optimal generation of soft x-ray high harmonics through free adjustment of laser parameters: A comparison of three commonly used atoms

Tabletop soft x-ray (SXR) high harmonics, produced through the interaction of ultrashort mid-infrared lasers with rare gas atoms, offer significant potential for diverse scientific applications. However, optimizing their generation efficiency remains challenging. In this work, we establish optimal conditions for generating SXR high harmonics by systematically selecting rare gas atoms and gas pressures, assuming that laser parameters can be fully adjusted. First, we accurately reproduce the high-order harmonic generation (HHG) results from Fan et al.'s experiments [Optica 9, 399–407 (2022)] using a macroscopic propagation theory. To explain the observed ranking order of harmonic conversion efficiency (CE) among the three most common atoms under different driving wavelengths–helium (He), neon (Ne), and argon (Ar)–and their corresponding gas pressures, we develop a combined one-dimensional propagation model and a non-adiabatic phase-matching model. This ranking arises from the interplay of coherence length, absorption length, gas pressure, and single-atom response intensity. Additionally, we modify the constraint conditions and extend the cutoff energy while comparing the HHG results of the three atoms under different driving wavelengths. The ranking order remains consistent: He exhibits the highest CE at the highest gas pressure, followed by Ne at an intermediate gas pressure, and Ar shows the lowest harmonic CE at the lowest gas pressure. Our findings provide experimentalists with a robust theoretical framework for selecting optimal atomic species and gas pressures to maximize SXR HHG yield across various laser configurations.