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    Optimization of ultraintense laser focus utilizing far-field patterns of second-order harmonics from laser-foil interaction

    Shirui Xu1, Zhuo Pan1, Yulan Liang1, Tianqi Xu1, Qingfan Wu1, Tan Song1, Yujia Zhang1, Haoran Chen1, Qihang Han1 et al.

    Chenghao Hua1, Zhangyi Wu1, Ke Chen1, Jundong Shen1, Ziyang Peng1, Xuan Liu1, Zihao Zhang1, Shiyou Chen1, Yanying Zhao1, Ying Gao1,*, Jiarui Zhao1, Zi-Yu Chen5, Xueqing Yan1,2,3,4, and Wenjun Ma1,2,3,4,†

    • 1State Key Laboratory of Nuclear Physics and Technology, School of Physics, Peking University, Beijing 100871, China
    • 2Beijing Laser Acceleration Innovation Center, Huairou, Beijing 101400, China
    • 3Institute of Guangdong Laser Plasma Technology, Baiyun, Guangzhou 510540, China
    • 4Collaborative Innovation Center of Extreme Optics, Shanxi University, Shanxi 030006, China
    • 5Key Laboratory of High Energy Density Physics and Technology (MoE), College of Physics, Sichuan University, Chengdu 610064, China

    • *Contact author: ying_gao@pku.edu.cn
    • †Contact author: wenjun.ma@pku.edu.cn

    Phys. Rev. Applied 25, 024068 – Published 23 February, 2026

    DOI: https://doi.org/10.1103/y64k-ghtc

    Abstract

    In ultraintense laser experiments, optimizing on-target high-power focal spots to maximize peak intensity is critical for achieving optimal outcomes such as maximized accelerated ion energy. This requires minimizing laser aberrations, which remains challenging due to the lack of in situ, real-time, on-target focal diagnostics at ultrahigh intensity. In this study, we systematically investigated the far-field patterns of a second-order harmonic (2ωL) emitted from thin foil interaction with typical astigmatic laser. Aberrated laser wave fronts and nonuniform intensity profiles jointly shape the accelerated electron sheets together, thereby imprinting astigmatism information in their 2ωL emission far-field patterns. Based on this, we propose an easy-to-implement scheme that utilizes real-time 2ωL far-field-pattern feedback to guide astigmatism compensation via off-axis parabolic mirror (OAP) tuning. Optimized focal spots following this scheme yields higher proton cutoff energy, increased proton number, and more symmetrical beam profiles in laser-driven ion-acceleration experiments.

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