7th Asia-Pacific Conference on Plasma Physics, 12-17 Nov, 2023 at Port Messe Nagoya

Numerical Simulation of Ion-Based Water-Window Harmonic Generation in
Laser-Irradiated Gases
Ying-Shan Chen1, Yao-Li Liu2, Shih-Hung Chen1, Hsu-Hsin Chu1
1
Department of physics, National Central University, Taoyuan City, Taiwan
2
Institute of Space and Plasma Sciences, National Cheng Kung University, Tainan City, Taiwan
e-mail (speaker): cindy1999881114@gmail.com
High-harmonic generation (HHG) induced in laserirradiated atomic or molecular gases is an important
method to generate water-window soft X-ray. The focusedlaser pulse ionizes the gas medium, and the released
electrons undergo the acceleration and recombination
processes to emit short-wavelength photons [1]. The
figure of merits to characterize the performance of HHG
are the cutoff photon energy and the conversion efficiency.
The cutoff photon energy of HHG !! can be derived
that !! = #" + 3.17)" , where #" is the ionization
potential, and )" is the ponderomotive energy. In order
to increase Ec, e.g. water-window X-ray range, ion species
is a better HHG emitters. Ion has higher ionization
potential than atom, cause the higher cutoff energy. Inaddition, with higher #" , the ions can only be ionizedunder a higher laser intensity, which increase )" . Basedon the above conditions, we choose He as our neutral gas
target, and generate the high harmonic by He and He#$ .
The conversion efficiency of HHG is mainly
determined by the phase-matching condition of thegeneration process. It is determined by four mechanisms,i.e., neutral gas dispersion, plasma dispersion, geometricalphase shift (Gouy phase shift), and intensity-dependent
dipole phase variation. Moreover, using a shorter
wavelength driving laser can also enhance the conversion
efficiency, since the single-atom response scales with~-%& between interactions of different laser wavelengths
with the same atom [2]. However, in the highly-ionizedplasma regime, which represents high density HHG
source, plasma dispersion is hardly to be balanced.
Therefore, the phase-matching condition is difficult to beachieved, such that generation of high efficiency HHG atshort wavelength becomes a big challenge.
In this paper, we perform a numerical simulation of theion-based HHG. We found that phase-matching condition
can be achieved for water-window x-ray emission driven
by 405-nm femtosecond pulses. We first apply the 3+1dimensional hybrid advective-diffusion electromagnetic(EM) envelope equation with cylindrical symmetry,
together with Keldysh’s optical-field ionization model, toresolve the propagation of the driving pulse in a He gas
target. The moving-window algorithm is adapted whilesolving the equation, as shown in Figure 1. Then we canhave the ion/electron density distributions and calculate
the phase-matching condition and the HHG yield.
The driving pulse specification is optimized to 16.5-mJ
energy, 405-nm wavelength, and 30-fs duration. It is
focused to a waist radius of 30 μm at z = 0. The Helium
gas is located between z = 7 mm and z = 10 mm, witha uniform density distribution 1.8 × 10#' cm%( . The
resulted laser intensity, gas density, and electron density

in z-r space are shown in Figure 2. The phase-matchingcondition is achieved for the 93rd-order harmonic (4.35nm) on the propagation axis (r = 0), as shown in Figure 3.
The 4.35-nm output yield generated through the processesof He → He#$ → He and He#$ → He)$ → He#$ , aswell as the total HHG yield, are accumulated
constructively within the entire interacting region.
References[1] Roling, S. & Zacharias, Helmut. (2010). Coherenceof XUV Laser Sources. 10.5772/13289.
[2] M. Frolov, N. Manakov, and A. Starace, Phys. Rev.
Lett. 100, 173001 (2008).
[3] Gibbon, Paul. (2005). Short Pulse Laser Interactions
with Matter: An Introduction. 10.1142/P116.

Figure 1. Schematic illustration of the numericalalgorithm. 67 is the normalization density and 8 is thenormalization wave vector amplitude.

Figure 2. Simulation results show spatial profiles of laser
intensity, helium gas density and electron density in z-r
space.

Figure 3. Phase matching condition and HHG yield varies
along the propagation axis (9 = 0).