Particle-in-Cell Simulation of Phase-Matched High Harmonics Generation in Highly-Ionized Plasma

Ying-Shan Chen^1*, Yao-Li Liu¹, Shih-Hung Chen¹

¹Physics, National Central University, Zhongli, Taoyuan City, Taiwan

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

Gas-based high-order harmonic generation (HHG) driven by ultra-short intense laser pulses has been proven a reliable coherent light source from extreme-ultraviolet (EUV) to x-ray. HHG is generated through the processes of ionization, acceleration, and then recombination of bound electrons in neutral atoms, leading to a cut-off photon energy of E_cutoff = I_p+3.17U_p, where I_p is the ionization potential of the bound electron and U_p is the ponderomotive potential of the driving laser field. The overall conversion efficiency is critically determined by the relative phase between the driving laser field and the harmonic field, which is affected by various dispersive effects including neutral gas dispersion, plasma dispersion, geometrical phase shift, and intrinsic dipole phase variation. Phase matching in the weak ionization regime is done by balancing the neutral gas dispersion and the plasma dispersion. To push HHG toward shorter wavelength with higher efficiency, high-Z ions are promising interacting media because high-Z ions have higher ionization potentials leading to shorter harmonic wavelengths. However, existing phase-matching methods cannot compensate for the large plasma dispersion in the strong ionization regime.
We proposed a new idea to achieve the dispersion balance between the intrinsic dipole phase variation and the plasma dispersion for the implementation of the phase-matched ion-based HHG. The scheme is verified by 2D particle-in-cell simulation (PIC) for the HHG order 203^th and 337^th corresponding to the two ends of water-window X-ray, i.e. 4 nm and 2.4 nm, respectively. In the simulations, an intense laser pulse (810 nm, 50 fs) is focused before the helium gas target with a spot size 5 um to purposely facilitate a large intensity gradient. Moreover, the intensity should be high enough to guarantee the generation of He^(2+) during the interacting process. Consequently, the resulting intrinsic dipole phase variation compensates the plasma dispersion elaborately to achieve the phase-matching of ion-based HHG. The simulation results will be validated by our experiments.

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Keywords: High harmonic generation, Phase matching, Laser plasma interaction