Numerical Simulation of Phase-Matched High Harmonics Generation through Laser Plasma Interaction

Ying-Shan Chen^1*, Yao-Li Liu², Shih-Hung Chen¹, Hsu-Hsin Chu¹

¹Department of Physics, National Central Unerversity, Taoyuan, Taiwan
²Institute of Space and Plasma Sciences, National Cheng Kung University, Tainan, Taiwan

* Presenter:Ying-Shan Chen, email:cindy1999881114@gmail.com

High harmonic generation (HHG) which is emerged by laser-irradiated atomic or molecular gases is an important method to generate short-wavelength electromagnetic waves in laser-plasma interactions. The focused laser pulse ionizes gas targets, and the escaped electrons are undergoing acceleration and recombination processes to induce photon emission [1]. However, there are two problems to be solved while using this approach. The first one is the low conversion efficiency caused by the relative phase between the driving laser field and the harmonic field. The relative phase is dertermined by the neutral gas dispersion, the plasma dispersion, the geometrical phase shift (Gouy phase shift), and intensity-dependent HHG intrinsic dipole phase variation. The other problem is the small cutoff frequency predicted to be E_{cutoff} = I_p + 3.18U_p = hf_{cutoff}, where I_p is the ionization potential of the atom and U_p is the ponderomotive energy. Therefore, we can increase the driving laser pulse intensity to raise U_p and use ion which has higher I_p than atom as our HHG source in order to extend the cutoff energy to a shorter wavelength region.
In the study, we use Lax-Wendroff method to solve the numerical solution of Poisson’s equation, relativistic electron equation of motion, and the electromagnetic wave equation [2]. Use the first two equations to get the equilibrium plasma density, view it as a source term of wave equation, and then get the solution of the wave equation for describing laser pulse propagation. It is more efficient to obtain the distribution of laser intensity and particles density using the simplified model as compared to using 3D PIC simulations. The parameter of the driving laser (focal position x_f, energy E, waist size at focal position w) and Helium gas density N_{gas} can be varied in the simulation. We aim to find the phase-matching conditions for the two ends of water-window X-ray regime, i.e. λ=2.4 nm and λ=4 nm generated by He^{2+}, which are widely used on both industry and scientific research.

[1] Roling, S. & Zacharias, Helmut. (2010). Coherence of XUV Laser Sources. 10.5772/13289.
[2]Gibbon, Paul. (2005). Short Pulse Laser Interactions with Matter: An Introduction. 10.1142/P116.

Keywords: High harmonic generation, laser-plasma interaction, highly ionized plasma, phase matching condition, numerical simulation