Role of trajectory symmetry in solid high-order harmonic generation

doi:10.1088/1674-1056/ae04da

中国物理B ›› 2026, Vol. 35 ›› Issue (4): 44204-044204.doi: 10.1088/1674-1056/ae04da

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

收稿日期:2025-08-30 修回日期:2025-08-30 接受日期:2025-09-09 发布日期:2026-04-01
通讯作者: Jun Zhang E-mail:junzhang@jlu.edu.cn
基金资助:
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).

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

Received:2025-08-30 Revised:2025-08-30 Accepted:2025-09-09 Published:2026-04-01
Contact: Jun Zhang E-mail:junzhang@jlu.edu.cn
Supported by:
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).

摘要/Abstract

摘要： 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.

关键词: high-order harmonic generation, recollision model, trajectory analyses

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.

Key words: high-order harmonic generation, recollision model, trajectory analyses

中图分类号: (Frequency conversion; harmonic generation, including higher-order harmonic generation)

42.65.Ky

32.80.Rm (Multiphoton ionization and excitation to highly excited states) 42.65.Re (Ultrafast processes; optical pulse generation and pulse compression)

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[J]. 中国物理B, 2026, 35(4): 44204-044204.

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Role of trajectory symmetry in solid high-order harmonic generation

Role of trajectory symmetry in solid high-order harmonic generation

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