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    Localized orbital perspective on orientation-dependent high-harmonic generation in MgO

    Tong Wu1,*, Zitan Zuo1,*, Xiang Li1, Shengzhe Pan1,†, Shicheng Jiang1,‡, Ruifeng Lu2, and Jian Wu1,3,4

    • *These authors contributed equally to this work.
    • †Contact author: szpan@lps.ecnu.edu.cn
    • ‡Contact author: scjiang@lps.ecnu.edu.cn

    Phys. Rev. B 114, 045122 – Published 21 July, 2026

    DOI: https://doi.org/10.1103/zvhj-cp16

    Abstract

    In this work, we experimentally observe orientation-dependent high-harmonic spectra in rocksalt crystal MgO driven by a linearly polarized 790 nm laser, featuring distinct peaks at 0∘, 45∘, and 90∘ that correspond to orientation angles between the laser polarization and [100] crystal axis of MgO. A localized orbital framework is developed to understand these spectral features from an atomic orbital perspective. Decomposition using atomiclike Wannier orbitals shows that low-order harmonics are primarily dominated by couplings among Mg−s, O−s, and O−p orbitals. Conversely, the response at higher orders is governed by Mg−p and Mg−d orbitals, with their relative contributions varying systematically with harmonic order and laser intensity. In the minimal model where only O−p–Mg−s couplings are retained, the O−px–Mg−s and O−py–Mg−s channels produce yield maxima at 0∘ and 90∘, respectively, and each generates symmetric features near 45∘. Their constructive superposition at 45∘ results in a local maximum of the total yield at this angle. This work establishes a localized orbital picture of high-harmonic generation in crystals, bridging atomic orbital interactions and macroscopic polarization dynamics in periodic systems.

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