采用Lewenstein路径积分模型和准经典“三步”模型,计算了不同脉宽的超短脉冲高次谐波波谱。通过比较模型截止频率随载波包络相位的变化关系的差异,对辐射过程中的量子效应进行了研究。结果显示,随脉宽的减小,以上两种模型计算结果出现的偏离增加,谐波辐射中的量子效应愈加明显。当脉宽减小至0.5T (T为光学周期)时,准经典“三步”模型已不能用以解释Lewenstein模型的计算结果。

We study the quantum effects on the high-order harmonic generation of ultra-short laser pulse represented by the disagreement, which are calculated by the Lewenstein model and the "three-step" model, of the relationship between the cutoff frequencies of the high-order harmonic generation spectrum and the carrier-envelope phases for ultra-short laser pulses with different pulse durations. The results show that with the ultra-short pulse widths decreasing, the quantum effects appears to be more serious. When the pulse width decreases to 0.5T (T is the optical cycle), the "three-step" model has been unable to give reasonable explanation for the Lewenstein model.