Full Three-dimensional Particle-In-Cell Simulation for Phase-matched Ion-based High-order Harmonic Generation in Water-window X-ray

Ying-Shan Chen, Hsu-Hsin Chu, Shih-Hung Chen, and Yao-Li Liu

Chinese Journal of Physics, 2026

Journal Paper High-Harmonic Generation Particle-in-Cell Simulation Electromagnetic

Abstract

We perform a full three-dimensional particle-in-cell (3D-PIC) simulation to investigate a phase-matching scheme of ion-based high-order harmonic generation (HHG). A high-intensity laser pulse (~10¹⁶ W/cm², 405-nm wavelength, 50-fs pulse duration) is employed to produce He ions as the interacting medium for extending the cutoff photon energy to the water-window X-ray spectral region. The simulation result shows that phase matching for the 179^th harmonic (2.26 nm) is achieved by compensating the positive dipole phase with negative plasma and geometric phase shifts through laser divergence control. The relative conversion efficiency can be higher than 91% of the value with the ideal phase-matching condition.

Numerical experiment of phase-matched ion-based high-order harmonic generation in the water-window x-ray spectral region via electromagnetic envelope equation

Yao-Li Liu, Ying-Shan Chen, Shih-Hung Chen, and Hsu-hsin Chu

Optics Express, 2024

Journal Paper High-Harmonic Generation Numerical Simulation Electromagnetic

Abstract

We present a phase-matching scheme for efficient high-order harmonic generation in the water-window x-ray spectral region using a 405-nm driving pulse. A high-intensity pulse (∼10¹⁶ W/cm²) is used to produce He¹⁺ ions as the target medium, increasing the cutoff photon energy to the water-window x-ray spectral region. By adjusting the driving pulse divergence, the positive dipole phase variation balances the negative plasma dispersion and geometrical phase shift, achieving phase matching. Using the electromagnetic envelope equation coupled with the Keldysh ionization model, numerical experiments identify the optimal conditions. Results show that the relative conversion efficiencies of the 95^th harmonic (4.26 nm) and the 169^th harmonic (2.4 nm) reach 66% and 79% of the perfect phase-matching conditions, respectively.

Numerical Simulation of Ion-Based Water-Window High-Harmonic Generation

Ying-Shan Chen, Yao-Li Liu, Shih-Hung Chen, and Hsu-hsin Chu

2024 Annual meeting of the Physical Society of Taiwan @ Taoyuan City, Taiwan

• Oral presentation.
• Finalist for Oral Presentation Award
National Conference High-Harmonic Generation Numerical Simulation Electromagnetic

Numerical Simulation of Ion-Based Water-Window Harmonic Generation in Laser-Irradiated Gases

Ying-Shan Chen, Yao-Li Liu, Shih-Hung Chen, and Hsu-hsin Chu

7th Asia-Pacific Conference on Plasma Physics (AAPPS-DPP2023) @ Nagoya, Japan

• Oral presentation.
International Conference High-Harmonic Generation Numerical Simulation Electromagnetic