Role of trajectory symmetry in solid high-order harmonic generation

doi:10.1088/1674-1056/ae04da

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.

Keywords: high-order harmonic generation recollision model trajectory analyses

Received: 30 August 2025
Revised: 30 August 2025
Accepted manuscript online: 09 September 2025

PACS:	42.65.Ky	(Frequency conversion; harmonic generation, including higher-order harmonic generation)
	32.80.Rm	(Multiphoton ionization and excitation to highly excited states)
	42.65.Re	(Ultrafast processes; optical pulse generation and pulse compression)

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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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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Role of trajectory symmetry in solid high-order harmonic generation

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