| ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS |
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Role of trajectory symmetry in solid high-order harmonic generation |
| Shuang Wang(王爽)1, Yu Zhao(赵宇)1, Hui-Rong Wang(王慧荣)1, Yun-He Xing(邢云鹤)1, Xiao-Xin Huo(霍晓鑫)2, and Jun Zhang(张军)1,† |
1 Institute of Atomic and Molecular Physics, Jilin University, Changchun 130012, China;
2 School of Science, Shenyang Ligong University, Shenyang 110159, China |
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Abstract High-order harmonic generation (HHG) from a ZnO crystal has been investigated theoretically using a two-band model driven by a few-cycle laser pulse. We observe that harmonics in the cut-off region exhibit periodic frequency shifts with changes in the carrier envelope phase (CEP) of the laser field. When the CEP of the laser pulse is an integer multiple of $\pi$, the cut-off region is dominated by even-order harmonics rather than odd-order harmonics. To illustrate the physical mechanism behind the even-order harmonics, we track the trajectories of electrons and holes between two successive half-cycles by performing time-frequency analysis and applying the recollision model. The results show that the maximum electron displacement is symmetric between successive half-cycles for odd-order harmonics. In contrast, the half-cycle symmetry of the maximum displacement is broken in the case of even-order harmonics.
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Received: 30 August 2025
Revised: 30 August 2025
Accepted manuscript online: 09 September 2025
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PACS:
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42.65.Ky
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(Frequency conversion; harmonic generation, including higher-order harmonic generation)
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32.80.Rm
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(Multiphoton ionization and excitation to highly excited states)
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42.65.Re
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(Ultrafast processes; optical pulse generation and pulse compression)
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| Fund: This work was supported by the Natural Science Foundation of Jilin Province of China (Grant No. 20230101014JC) and the National Natural Science Foundation of China (Grant No. 12374265). |
Corresponding Authors:
Jun Zhang
E-mail: junzhang@jlu.edu.cn
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Cite this article:
Shuang Wang(王爽), Yu Zhao(赵宇), Hui-Rong Wang(王慧荣), Yun-He Xing(邢云鹤), Xiao-Xin Huo(霍晓鑫), and Jun Zhang(张军) Role of trajectory symmetry in solid high-order harmonic generation 2026 Chin. Phys. B 35 044204
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