Generally, high-order harmonic generation (HHG) from atoms and molecules can be explained by the “ionization-acceleration-recombination” model and the classical results are agreement with the quantum results. In this paper, we report a multiple-acceleration process in the “[Formula: see text]” waveform structure. It is found that due to the nonzero initial velocity in the multiple-acceleration process, the emitted photon energies from the quantum results are larger than those from the classical results. Moreover, with the optimization of this “[Formula: see text]” waveform structure, much more energy can be obtained for the accelerated electron, thus leading to the improvement of the HHG. Further, with the introduction of a half-cycle pulse, the effects of the two “[Formula: see text]” structures in the “[Formula: see text]” structure on the HHG are discussed. It shows that the latter “[Formula: see text]” structure plays the more important role in HHG modulation. Finally, through the Fourier transformation of the spectral continuum, a number of sub-40 as pulses with intensity enhancements of 1 order and 2 orders of magnitudes can be obtained, respectively.

中文翻译：

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“W”波形结构中的多重加速，用于改善高次谐波

一般来说，原子和分子的高次谐波产生（HHG）可以用“电离-加速-复合”模型来解释，经典结果与量子结果一致。在本文中，我们报告了“[公式：见文本]”波形结构中的多重加速过程​​。研究发现，由于多次加速过程中的初始速度非零，量子结果的发射光子能量大于经典结果的光子能量。此外，通过对这种“[公式：见正文]”波形结构的优化，加速电子可以获得更多的能量，从而改善HHG。此外，随着半周期脉冲的引入，“[公式：见正文]”中的两个“[公式：见正文]”结构的效果：见文本]”结构上的 HHG 进行了讨论。这表明后一种“[公式：见正文]”结构在 HHG 调制中起着更重要的作用。最后，通过光谱连续谱的傅里叶变换，可以得到多个亚40个脉冲，强度分别增强1个数量级和2个数量级。