High-order harmonic signals generated in molecules are the consequence of coherent summation of complex laser-induced transition dipoles $d(\theta ,\omega )$ with each fixed-in-space molecule; here $\theta$ is the angle of the molecular axis with respect to the laser polarization axis and $\omega$ is the harmonic energy. In the so-called rotational coherent spectroscopy, it is proposed to extract the fixed-in-space $d(\theta ,\omega )$ in the molecular frame by measuring harmonics generated by a probing laser from the rotational molecular wave packets that have been prepared by a prior pump laser. By varying the time delay between the two lasers, methods have been utilized to extract the $\theta$ dependence of both the amplitude and phase of each individual harmonic, but the relative phase between harmonics cannot be retrieved. Here we report that this limitation can be removed. It requires the additional measurement of harmonic spectra versus the pump-probe angles at one fixed time delay. The two-dimensional input harmonic data (time-delay and pump-probe angle) are then used to retrieve the full complex transition dipole $d(\theta ,\omega )$ using a retrieval method based on machine learning algorithms. We demonstrate this method on ${\mathrm{N}}_2$ and ${\mathrm{CO}}_2$ molecules.

中文翻译：

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从具有排列分子的激光诱导高阶谐波信号中检索分子框架中与角度和能量有关的完全复杂跃迁偶极子

分子中产生的高阶谐波信号是复杂激光诱导的跃迁偶极子相干求和的结果 $d（\theta ，\omega ）$每个空间固定分子 这里$\theta$ 是分子轴相对于激光偏振轴的角度，并且 $\omega$是谐波能量。在所谓的旋转相干光谱学中，提出了提取空间固定的方法。$d（\theta ，\omega ）$通过测量探测激光器从旋转的分子波包中产生的谐波来探测分子框架中的旋转，该旋转的分子波包由现有的泵浦激光器制备。通过改变两个激光器之间的时间延迟，已经采用了一些方法来提取$\theta$每个谐波的幅度和相位都依赖，但是谐波之间的相对相位无法获取。在这里，我们报告可以消除此限制。它需要在一个固定的时间延迟内对谐波频谱与泵浦探针角度进行额外的测量。然后使用二维输入谐波数据（时间延迟和泵浦探针角）来检索完整的复变跃迁偶极子$d（\theta ，\omega ）$使用基于机器学习算法的检索方法。我们在${\mathrm{ñ}}_2$ 和 ${\mathrm{一氧化碳}}_2$ 分子。