Through high-order harmonic generation driven by intense ultrashort vortex infrared or midinfrared lasers, a nonzero orbital angular momentum can be imprinted onto extreme ultraviolet (XUV) or soft-x-ray (SXR) light pulses. Here we simulate the generation of vortex XUV harmonics in the gas medium as well as their propagation in vacuum till reaching the far field. We find that the intensity and phase of generated high harmonics are very sensitive to the position of gas jet with respect to the laser focus. The topological charge of the $q\mathrm{th}$ harmonic is found to be $q$ times that of the driving Laguerre-Gaussian beam. Each harmonic in the far field appears as a single ring in the transverse plane with an invariant diameter which is scalable with the fundamental topological charge only when the gas jet is placed after the laser focus. The underlying phase-matching mechanism is analyzed by examining the spatial map of the coherence length and by calculating the evolution of harmonic emission in the medium. We anticipate this work to stimulate interest in generating intense vortex XUV or SXR attosecond pulses for probing dynamics of molecules where special molecular features are difficult to be detected with linear or circular XUV or SXR pulses.

中文翻译：

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非零轨道角动量拉盖尔-高斯光束在高次谐波产生中的相位匹配分析

通过强烈的超短涡旋红外或中红外激光驱动的高次谐波产生，可以将非零轨道角动量压印到极紫外（XUV）或软X射线（SXR）光脉冲上。在这里，我们模拟了气体介质中涡旋XUV谐波的产生以及它们在真空中的传播直至到达远场。我们发现，所产生的高次谐波的强度和相位对于气体射流相对于激光聚焦的位置非常敏感。的拓扑电荷$q日$ 发现谐波为 $q$是拉盖尔-高斯光束的倍数。远场中的每个谐波在横向平面上都显示为单个环，直径不变，仅当将气体射流置于激光聚焦之后时，它才能随基本拓扑电荷扩展。通过检查相干长度的空间图并通过计算介质中谐波发射的演化来分析潜在的相位匹配机制。我们预计这项工作会激发人们产生强烈的涡旋XUV或SXR阿秒脉冲的兴趣，以探测分子的动力学，这些分子很难用线性或圆形XUV或SXR脉冲检测到特殊的分子特征。