CN115220085B - Method for detecting initial transverse position of tunneling ionized electrons - Google Patents
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Abstract
本发明涉及一种探测隧穿电离电子初始横向位置的方法,包括使用激光场电离分子,获得激光场偏振方向与分子的排列方向呈零角度的第一光电子动量谱和呈非零角度的第二光电子动量谱;根据第一光电子动量谱和第二光电子动量谱得到分子与激光场偏振方向排列角度为非零角度时的光电子全息干涉零级极大条纹中心位置相对于零排列角度下光电子全息干涉零级极大条纹中心位置的横向动量偏移量,根据所述横向动量偏移量得到隧穿电离电子波包的初始横向位置。本发明实现了隧穿电离电子波包的初始横向位置的获取,获取方法更简单、获得的结果更精确,可行性和普适性更强。
The invention relates to a method for detecting the initial lateral position of tunneling ionized electrons, which includes using a laser field to ionize molecules, and obtaining a first photoelectron momentum spectrum with a zero angle between the polarization direction of the laser field and the alignment direction of the molecules and a second photoelectron momentum spectrum with a non-zero angle. Photoelectron momentum spectrum; According to the first photoelectron momentum spectrum and the second photoelectron momentum spectrum, the photoelectron holographic interference when the polarization direction of the molecules and the laser field is at a non-zero angle is obtained. The transverse momentum offset of the central position of the zero-order maximum fringe, and the initial transverse position of the tunneling ionized electron wave packet is obtained according to the transverse momentum offset. The invention realizes the acquisition of the initial lateral position of the tunneling ionized electron wave packet, the acquisition method is simpler, the obtained result is more accurate, and the feasibility and universality are stronger.
Description
技术领域Technical Field
本发明涉及阿秒科学与强场物理技术领域,尤其是指一种探测隧穿电离电子初始横向位置的方法。The invention relates to the technical fields of attosecond science and strong field physics, and in particular to a method for detecting the initial lateral position of tunneling ionized electrons.
背景技术Background Art
利用超快超强激光场探测和控制原子及分子中阿秒量级的电子动力学过程是强场物理领域的热点课题之一。在强激光场中,原子分子会发生电离,电离电子在激光场中做加速运动,其中部分电子直接到达探测器,另一部分电子则反向与母离子碰撞散射,引发一系列强场超快现象。精确探测电离电子波包的动力学过程是理解和应用这些强场超快现象的基础。特别地,原子及分子的光电离位置,即电离电子的初始电离位置引起了国内外专家学者的广泛关注。电子轨迹的概念常被用于解释激光与原子和分子相互作用的不同物理过程。在这一概念中,隧穿电离是阿秒科学领域许多强场超快现象的第一步,电子初始位置会影响电子的后续动力学过程。因此,精确的电子初始位置对于基于电子轨迹概念的强场超快过程的准确理解十分关键。电子初始位置是强场物理研究分析中的重要参量。当理论计算结果与实验结果作比较时,不准确的电子初始位置,会导致得出错误的结论。Using ultrafast and ultra-intense laser fields to detect and control the electron dynamics of atoms and molecules at the attosecond level is one of the hot topics in the field of strong field physics. In a strong laser field, atoms and molecules will be ionized, and the ionized electrons will accelerate in the laser field. Some of the electrons will directly reach the detector, while the other part will collide and scatter with the parent ion in the opposite direction, triggering a series of strong field ultrafast phenomena. Accurately detecting the dynamics of the ionized electron wave packet is the basis for understanding and applying these strong field ultrafast phenomena. In particular, the photoionization position of atoms and molecules, that is, the initial ionization position of the ionized electron, has attracted widespread attention from experts and scholars at home and abroad. The concept of electron trajectory is often used to explain the different physical processes of the interaction between lasers and atoms and molecules. In this concept, tunneling ionization is the first step of many strong field ultrafast phenomena in the field of attosecond science, and the initial position of the electron will affect the subsequent dynamic process of the electron. Therefore, the accurate initial position of the electron is critical for the accurate understanding of the strong field ultrafast process based on the concept of electron trajectory. The initial position of the electron is an important parameter in the research and analysis of strong field physics. When the theoretical calculation results are compared with the experimental results, inaccurate initial position of the electron will lead to wrong conclusions.
通常,电离电子的初始纵向位置(平行于激光场的偏振方向)可以用公式Ip/E(t)评估,其中Ip是原子或分子的电离势,E(t)是瞬时激光场。最近,利用阿秒钟技术,人们测得了更精确的电子初始纵向位置。对于电子的初始横向位置,在原子隧穿电离中该值始终为零。对于分子,电子的初始横向位置被证明与分子轨道和排列有关。在已有的研究工作中,人们尝试在理论模型中引入一个电子波包初始相位,通过将计算得到的不对称的全息干涉与实验得到的全息干涉比较,获取电子波包的初始相位,进而从中提取电子波包的初始横向位置。最近,人们提出通过分析py>0和py<0动量区域内的全息干涉相位差获取电子波包初始横向位置(py是垂直于激光偏振方向的光电子末动量)。但是,上述探测方法在实际应用中存在一定困难,如探测步骤繁琐。第一个方法是建立在已知分子结构的基础上,其中库伦势对电子波包的影响不可忽略,这不利于人们精确获取任意分子隧穿电离初始横向位置。在第二个方法中,随着激光波长的减小,|py|较大处的全息干涉并不清晰(|py|是垂直于激光偏振方向上的光电子末动量的大小),这不利于全息干涉相位的提取,以及从该相位中获取电子初始横向位置。因此,精确探测电子初始横向位置是阿秒科学领域和强场物理领域重要的一部分,许多研究工作都对这一部分展开了讨论,并提出了许多探测方法。但是,更简洁,具有更高精确度的电子初始横向位置探测方法一直在被探索。Usually, the initial longitudinal position of the ionized electron (parallel to the polarization direction of the laser field) can be evaluated by the formula Ip /E(t), where Ip is the ionization potential of the atom or molecule and E(t) is the instantaneous laser field. Recently, using attosecond technology, people have measured more accurate initial longitudinal positions of electrons. For the initial transverse position of electrons, this value is always zero in atomic tunneling ionization. For molecules, the initial transverse position of electrons has been shown to be related to molecular orbitals and arrangements. In existing research work, people have tried to introduce an initial phase of an electron wave packet into the theoretical model, and obtain the initial phase of the electron wave packet by comparing the calculated asymmetric holographic interference with the experimentally obtained holographic interference, and then extract the initial transverse position of the electron wave packet from it. Recently, people have proposed to obtain the initial transverse position of the electron wave packet by analyzing the holographic interference phase difference in the momentum region of py >0 and py <0 ( py is the final momentum of the photoelectron perpendicular to the laser polarization direction). However, the above detection method has certain difficulties in practical applications, such as cumbersome detection steps. The first method is based on the known molecular structure, in which the influence of the Coulomb potential on the electron wave packet cannot be ignored, which is not conducive to accurately obtaining the initial lateral position of any molecular tunneling ionization. In the second method, as the laser wavelength decreases, the holographic interference at the larger |p y | is not clear (|p y | is the magnitude of the final momentum of the photoelectron perpendicular to the laser polarization direction), which is not conducive to the extraction of the holographic interference phase and the acquisition of the electron's initial lateral position from the phase. Therefore, accurate detection of the electron's initial lateral position is an important part of the field of attosecond science and strong field physics. Many research works have discussed this part and proposed many detection methods. However, a simpler and more accurate method for detecting the electron's initial lateral position has been explored.
2011年,Huisman等人在《Science》上指出,在超快强激光作用下,原子和分子隧穿电离产生的直接和散射电子波包之间会相干产生光电子全息干涉。这种光电子干涉原理与光学里全息成像十分类似,散射电子波包作为信号波,直接电子波包作为参考波,而强场光电子全息干涉具有探测原子、分子结构信息和探测电子动力学信息的潜力。这一点目前已被很多理论和实验研究证实。然而,如何利用强场光电子全息技术精确获取电离电子的初始横向位置依然是一项具有挑战性的任务。In 2011, Huisman et al. pointed out in Science that under the action of ultrafast intense lasers, direct and scattered electron wave packets generated by atomic and molecular tunneling ionization will coherently produce photoelectron holographic interference. The principle of this photoelectron interference is very similar to holographic imaging in optics, with scattered electron wave packets as signal waves and direct electron wave packets as reference waves. Strong-field photoelectron holographic interference has the potential to detect atomic and molecular structural information and electron dynamics information. This has been confirmed by many theoretical and experimental studies. However, how to use strong-field photoelectron holography to accurately obtain the initial lateral position of ionized electrons is still a challenging task.
发明内容Summary of the invention
为此,本发明所要解决的技术问题在于克服现有技术中的不足,提供一种探测隧穿电离电子初始横向位置的方法,可以实现隧穿电离电子波包的初始横向位置的获取,获取方法更简单、获得的结果更精确,可行性和普适性更强。To this end, the technical problem to be solved by the present invention is to overcome the deficiencies in the prior art and provide a method for detecting the initial lateral position of tunneling ionized electrons, which can achieve the acquisition of the initial lateral position of the tunneling ionized electron wave packet. The acquisition method is simpler, the results obtained are more accurate, and the feasibility and universality are stronger.
为解决上述技术问题,本发明提供了一种探测隧穿电离电子初始横向位置的方法,包括以下步骤:In order to solve the above technical problems, the present invention provides a method for detecting the initial lateral position of tunneling ionized electrons, comprising the following steps:
使用激光场电离分子,使所述激光场偏振方向与所述分子的排列方向呈零角度,获取所述分子电离时的第一光电子动量谱;Ionizing molecules using a laser field so that the polarization direction of the laser field and the arrangement direction of the molecules form a zero angle, and obtaining a first photoelectron momentum spectrum when the molecules are ionized;
使用所述激光场再次电离所述分子,使所述激光场偏振方向与所述分子排列方向呈非零角度,获取所述分子电离时的第二光电子动量谱;ionizing the molecule again using the laser field so that the polarization direction of the laser field and the molecular arrangement direction form a non-zero angle, and obtaining a second photoelectron momentum spectrum when the molecule is ionized;
根据所述第一光电子动量谱和所述第二光电子动量谱,得到所述分子与所述激光场偏振方向排列角度为非零角度时的光电子全息干涉零级极大条纹中心位置相对于零排列角度下光电子全息干涉零级极大条纹中心位置的横向动量偏移量;According to the first photoelectron momentum spectrum and the second photoelectron momentum spectrum, a lateral momentum offset of the center position of the zero-order maximum fringe of the photoelectron holographic interference when the arrangement angle between the molecule and the polarization direction of the laser field is non-zero relative to the center position of the zero-order maximum fringe of the photoelectron holographic interference at zero arrangement angle is obtained;
根据所述横向动量偏移量得到隧穿电离电子波包的初始横向位置。The initial transverse position of the tunneling ionized electron wave packet is obtained according to the transverse momentum offset.
作为优选的,根据所述第一光电子动量谱和所述第二光电子动量谱,得到所述分子与所述激光场偏振方向排列角度为非零角度时的光电子全息干涉零级极大条纹中心位置相对于零排列角度下光电子全息干涉零级极大条纹中心位置的横向动量偏移量,具体为:Preferably, according to the first photoelectron momentum spectrum and the second photoelectron momentum spectrum, the lateral momentum offset of the center position of the zero-order maximum fringe of the photoelectron holographic interference when the arrangement angle between the molecule and the polarization direction of the laser field is non-zero relative to the center position of the zero-order maximum fringe of the photoelectron holographic interference at zero arrangement angle is obtained, specifically:
根据所述第一光电子动量谱得到所述激光场偏振方向与所述分子排列方向呈零角度时的第一光电子全息干涉,根据所述第二光电子动量谱得到所述激光场偏振方向与所述分子排列方向呈非零角度时的第二光电子全息干涉;According to the first photoelectron momentum spectrum, a first photoelectron holographic interference is obtained when the polarization direction of the laser field and the molecular arrangement direction form a zero angle, and according to the second photoelectron momentum spectrum, a second photoelectron holographic interference is obtained when the polarization direction of the laser field and the molecular arrangement direction form a non-zero angle;
在所述第一光电子全息干涉中找到所述激光场偏振方向与所述分子的排列方向呈零角度的第一光电子全息干涉零级极大条纹中心位置,在所述第二光电子全息干涉中找到所述激光场偏振方向与所述分子的排列方向呈非零角度的第二光电子全息干涉零级极大条纹中心位置;Find the center position of the first photoelectron holographic interference zero-order maximum fringe in which the polarization direction of the laser field and the arrangement direction of the molecules form a zero angle in the first photoelectron holographic interference, and find the center position of the second photoelectron holographic interference zero-order maximum fringe in which the polarization direction of the laser field and the arrangement direction of the molecules form a non-zero angle in the second photoelectron holographic interference;
将所述第二光电子全息干涉零级极大条纹中心位置与所述第一光电子全息干涉零级极大条纹中心位置做差,得到所述分子与所述激光场偏振方向排列角度为非零角度时的光电子全息干涉零级极大条纹中心位置相对于零排列角度下光电子全息干涉零级极大条纹中心位置的横向动量偏移量。The center position of the zero-order maximum fringe of the second photoelectron holographic interference is subtracted from the center position of the zero-order maximum fringe of the first photoelectron holographic interference to obtain the lateral momentum offset of the center position of the zero-order maximum fringe of the photoelectron holographic interference when the arrangement angle between the molecule and the polarization direction of the laser field is non-zero relative to the center position of the zero-order maximum fringe of the photoelectron holographic interference at zero arrangement angle.
作为优选的,根据所述第一光电子动量谱得到所述激光场偏振方向与所述分子排列方向呈零角度时的第一光电子全息干涉,所述根据所述第二光电子动量谱得到所述激光场偏振方向与所述分子排列方向呈非零角度时的第二光电子全息干涉,具体为:Preferably, the first photoelectron holographic interference when the polarization direction of the laser field and the molecular arrangement direction are at a zero angle is obtained according to the first photoelectron momentum spectrum, and the second photoelectron holographic interference when the polarization direction of the laser field and the molecular arrangement direction are at a non-zero angle is obtained according to the second photoelectron momentum spectrum, specifically:
在所述第一光电子动量谱的目标动量范围内均匀提取平行于激光场偏振方向上具有末动量的光电子对应的光电子产量得到第一光电子横向动量分布,将所述第一光电子横向动量分布作为所述第一光电子全息干涉;Uniformly extract the final momentum of the photoelectrons parallel to the polarization direction of the laser field within the target momentum range of the first photoelectron momentum spectrum. The photoelectron yield corresponding to the photoelectron is used to obtain a first photoelectron transverse momentum distribution, and the first photoelectron transverse momentum distribution is used as the first photoelectron holographic interference;
在所述第二光电子动量谱的所述目标动量范围内均匀提取平行于激光场偏振方向上具有末动量的光电子对应的光电子产量得到第二光电子横向动量分布,将所述第二光电子横向动量分布作为所述第二光电子全息干涉。Uniformly extract the final momentum parallel to the polarization direction of the laser field within the target momentum range of the second photoelectron momentum spectrum. The photoelectron yield corresponding to the photoelectron is used to obtain a second photoelectron transverse momentum distribution, and the second photoelectron transverse momentum distribution is used as the second photoelectron holographic interference.
作为优选的,在所述第一光电子动量谱的目标动量范围内均匀提取平行于激光场偏振方向上具有末动量的光电子对应的光电子产量得到第一光电子横向动量分布,具体为:Preferably, within the target momentum range of the first photoelectron momentum spectrum, the photoelectrons having the final momentum parallel to the polarization direction of the laser field are uniformly extracted. The photoelectron yield corresponding to the photoelectron of the first photoelectron transverse momentum distribution is obtained, specifically:
在所述第一光电子动量谱的目标动量范围内设置方形动量区域,所述方形动量区域在垂直于激光场偏振方向上的动量长度为δpy、在平行于激光场偏振方向上动量长度为δpx;在所述方形动量区域内均匀提取平行于激光场偏振方向的具有末动量和垂直于激光偏振方向的具有末动量的光电子对应的光电子产量,将所述方形动量区域内提取到的所有具有末动量的光电子对应的光电子产量的平均值作为具有末动量的光电子对应的光电子产量,将所述方形动量区域内提取到的所有具有末动量的光电子对应的光电子产量的平均值作为具有末动量的光电子对应的光电子产量;将所述目标动量范围内均匀取值得到的每一具有末动量的光电子对应的光电子产量作为所述第一光电子横向动量分布;A square momentum region is set within the target momentum range of the first photoelectron momentum spectrum, wherein the momentum length of the square momentum region in the direction perpendicular to the polarization direction of the laser field is δpy and the momentum length in the direction parallel to the polarization direction of the laser field is δpx ; and the photoelectrons with final momentum parallel to the polarization direction of the laser field are uniformly extracted from the square momentum region. and a wave with terminal momentum perpendicular to the laser polarization direction The photoelectron yield corresponding to the photoelectron is the total photoelectron with final momentum extracted from the square momentum region. The average value of the photoelectron yield corresponding to the photoelectron with final momentum The photoelectron yield corresponding to the photoelectron is the total photoelectron with final momentum extracted from the square momentum region. The average value of the photoelectron yield corresponding to the photoelectron with final momentum The photoelectron yield corresponding to the photoelectron of the target momentum range is uniformly obtained for each photoelectron with the final momentum The photoelectron yield corresponding to the photoelectron is used as the transverse momentum distribution of the first photoelectron;
在所述第二光电子动量谱的所述目标动量范围内均匀提取平行于激光场偏振方向上具有末动量的光电子对应的光电子产量得到第二光电子横向动量分布,具体为:Uniformly extract the final momentum parallel to the polarization direction of the laser field within the target momentum range of the second photoelectron momentum spectrum. The photoelectron yield corresponding to the photoelectron of the second photoelectron transverse momentum distribution is obtained, specifically:
在所述第二光电子动量谱的目标动量范围内设置方形动量区域,所述方形动量区域在垂直于激光场偏振方向上的动量长度为δpy、在平行于激光场偏振方向上动量长度为δpx;在所述方形动量区域内均匀提取平行于激光场偏振方向的具有末动量和垂直于激光偏振方向的具有末动量的光电子对应的光电子产量,将所述方形动量区域内提取到的所有具有末动量的光电子对应的光电子产量的平均值作为具有末动量的光电子对应的光电子产量,将所述方形动量区域内提取到的所有具有末动量的光电子对应的光电子产量的平均值作为具有末动量的光电子对应的光电子产量;将所述目标动量范围内均匀取值得到的每一具有末动量的光电子对应的光电子产量作为所述第二光电子横向动量分布。A square momentum region is set within the target momentum range of the second photoelectron momentum spectrum, wherein the momentum length of the square momentum region in the direction perpendicular to the polarization direction of the laser field is δpy and the momentum length in the direction parallel to the polarization direction of the laser field is δpx ; and the photoelectrons with final momentum parallel to the polarization direction of the laser field are uniformly extracted from the square momentum region. and a wave with terminal momentum perpendicular to the laser polarization direction The photoelectron yield corresponding to the photoelectron is the total photoelectron with final momentum extracted from the square momentum region. The average value of the photoelectron yield corresponding to the photoelectron with final momentum The photoelectron yield corresponding to the photoelectron is the total photoelectron with final momentum extracted from the square momentum region. The average value of the photoelectron yield corresponding to the photoelectron with final momentum The photoelectron yield corresponding to the photoelectron of the target momentum range is uniformly obtained for each photoelectron with the final momentum The photoelectron yield corresponding to the photoelectron is used as the transverse momentum distribution of the second photoelectron.
作为优选的,在所述第一光电子全息干涉中找到所述激光场偏振方向与所述分子的排列方向呈零角度的第一光电子全息干涉零级极大条纹中心位置,在所述第二光电子全息干涉中找到所述激光场偏振方向与所述分子的排列方向呈非零角度的第二光电子全息干涉零级极大条纹中心位置,具体为:Preferably, the center position of the first photoelectron holographic interference zero-order maximum fringe in which the polarization direction of the laser field and the arrangement direction of the molecules form a zero angle is found in the first photoelectron holographic interference, and the center position of the second photoelectron holographic interference zero-order maximum fringe in which the polarization direction of the laser field and the arrangement direction of the molecules form a non-zero angle is found in the second photoelectron holographic interference, specifically:
提取所述第一光电子全息干涉的第一干涉项,根据所述第一干涉项获取第一光电子全息干涉各级条纹的中心位置,根据所述第一光电子全息干涉各级条纹的中心位置得到所述第一光电子全息干涉零级极大条纹中心位置;Extracting a first interference term of the first photoelectron holographic interference, obtaining the center position of each level of fringes of the first photoelectron holographic interference according to the first interference term, and obtaining the center position of the zero-order maximum fringes of the first photoelectron holographic interference according to the center position of each level of fringes of the first photoelectron holographic interference;
提取所述第二光电子全息干涉的第二干涉项,根据所述第二干涉项获取第二光电子全息干涉各级条纹的中心位置,根据所述第二光电子全息干涉各级条纹的中心位置得到所述第二光电子全息干涉零级极大条纹中心位置。The second interference term of the second photoelectron holographic interference is extracted, and the center position of each level of fringes of the second photoelectron holographic interference is obtained according to the second interference term. The center position of the zero-order maximum fringes of the second photoelectron holographic interference is obtained according to the center position of each level of fringes of the second photoelectron holographic interference.
作为优选的,所述第一干涉项为cos(ΔΦ1),其中ΔΦ1为第一干涉相位,ΔΦ1的计算方法为:Preferably, the first interference term is cos(ΔΦ 1 ), where ΔΦ 1 is the first interference phase, and the calculation method of ΔΦ 1 is:
ΔΦ1=1/2[py-ky(0)]2(tr-t0)+α;ΔΦ 1 =1/2[p y -k y (0)] 2 (t r -t 0 )+α;
所述第二干涉项为cos(ΔΦ2),其中ΔΦ2为第二干涉相位,ΔΦ2的计算方法为:The second interference term is cos(ΔΦ 2 ), where ΔΦ 2 is the second interference phase, and the calculation method of ΔΦ 2 is:
ΔΦ2=1/2[py-ky(θ)]2(tr-t0)+α;ΔΦ 2 =1/2[p y -k y (θ)] 2 (t r -t 0 )+α;
其中,py为垂直于激光场偏振方向的光电子末动量,tr为散射电子的散射时间,t0为散射电子的电离时间,α为分子的散射振幅相位;ky是散射电子的正则动量,ky(0)为当激光场偏振方向与分子排列方向呈零角度时隧穿电离散射电子的正则动量,θ为激光场偏振方向与分子排列方向之间的夹角,ky(θ)为当激光场偏振方向与分子排列方向之间的夹角为θ时隧穿电离散射电子的正则动量。Wherein, p y is the final momentum of the photoelectron perpendicular to the polarization direction of the laser field, t r is the scattering time of the scattered electron, t 0 is the ionization time of the scattered electron, and α is the scattering amplitude phase of the molecule; ky is the canonical momentum of the scattered electron, ky (0) is the canonical momentum of the tunneling ionized scattered electron when the polarization direction of the laser field and the molecular arrangement direction are at zero angle, θ is the angle between the polarization direction of the laser field and the molecular arrangement direction, and ky (θ) is the canonical momentum of the tunneling ionized scattered electron when the angle between the polarization direction of the laser field and the molecular arrangement direction is θ.
作为优选的,提取所述第一光电子全息干涉的第一干涉项时,使用指数函数对所述第一光电子全息干涉中的光电子产量进行多项式拟合,将所述第一光电子全息干涉中的光电子产量除以拟合得到的多项式,将得到的结果作为第一干涉项;Preferably, when extracting the first interference term of the first photoelectron holographic interferometry, a polynomial fitting is performed on the photoelectron yield in the first photoelectron holographic interferometry using an exponential function, the photoelectron yield in the first photoelectron holographic interferometry is divided by the fitted polynomial, and the result is used as the first interference term;
提取所述第二光电子全息干涉的第二干涉项时,使用指数函数对所述第二光电子全息干涉中的光电子产量进行多项式拟合,将所述第二光电子全息干涉中的光电子产量除以拟合得到的多项式,将得到的结果作为第二干涉项。When extracting the second interference term of the second photoelectron holographic interference, an exponential function is used to perform polynomial fitting on the photoelectron yield in the second photoelectron holographic interference, and the photoelectron yield in the second photoelectron holographic interference is divided by the fitted polynomial, and the result is used as the second interference term.
作为优选的,根据所述第一干涉项获取第一光电子全息干涉各级条纹的中心位置,根据所述第一光电子全息干涉各级条纹的中心位置得到所述第一光电子全息干涉零级极大条纹中心位置,具体为:Preferably, the center position of each level of fringes of the first photoelectron holographic interference is obtained according to the first interference term, and the center position of the zero-order maximum fringes of the first photoelectron holographic interference is obtained according to the center position of each level of fringes of the first photoelectron holographic interference, specifically:
建立所述第一光电子全息干涉各级条纹的中心位置其中,ΔΦ1=nπ,n=0,±1,±2,±3...;当n=0、ΔΦ1=0时得到所述第一光电子全息干涉零级极大条纹中心位置 Establish the center position of each level of the first photoelectron holographic interference fringes Wherein, ΔΦ 1 =nπ, n=0, ±1, ±2, ±3...; when n=0 and ΔΦ 1 =0, the center position of the zero-order maximum fringe of the first photoelectron holographic interference is obtained:
根据所述第二干涉项获取第二光电子全息干涉各级条纹的中心位置,根据所述第二光电子全息干涉各级条纹的中心位置得到所述第二光电子全息干涉零级极大条纹中心位置,具体为:The center position of each level of fringes of the second photoelectron holographic interference is obtained according to the second interference term, and the center position of the zero-order maximum fringes of the second photoelectron holographic interference is obtained according to the center position of each level of fringes of the second photoelectron holographic interference, specifically:
建立所述第二光电子全息干涉零级极大条纹中心位置其中,ΔΦ2=nπ,n=0,±1,±2,±3...;当n=0、ΔΦ2=0时得到所述第二光电子全息干涉零级极大条纹中心位置 Establish the center position of the zero-order maximum fringe of the second photoelectron holographic interference Wherein, ΔΦ 2 =nπ, n=0, ±1, ±2, ±3...; when n=0, ΔΦ 2 =0, the center position of the zero-order maximum fringe of the second photoelectron holographic interference is obtained:
作为优选的,所述横向动量偏移量Δpy=ky(θ)。Preferably, the lateral momentum offset Δp y = ky (θ).
作为优选的,根据所述横向动量偏移量得到隧穿电离电子波包的初始横向位置,具体为:Preferably, the initial lateral position of the tunneling ionized electron wave packet is obtained according to the lateral momentum offset, specifically:
建立电离电子的初始横向位置Rb与ky(θ)的关系式:ky(θ)=±Rb/(tr-t0),结合Δpy=ky(θ),得到电离电子的初始横向位置 The relationship between the initial lateral position R b of the ionized electron and ky (θ) is established: ky (θ) = ±R b /(t r -t 0 ), combined with Δpy = ky (θ), the initial lateral position of the ionized electron is obtained
本发明的上述技术方案相比现有技术具有以下优点:The above technical solution of the present invention has the following advantages compared with the prior art:
本发明通过分析在分子排列角度为非零角度时,光电子全息干涉零级极大条纹中心位置相对于零排列角下全息干涉零级极大条纹中心位置沿垂直于激光场偏振方向上的横向动量偏移量,实现了隧穿电离电子波包的初始横向位置的获取,获取方法更简单、获得的结果更精确,本发明的可行性和普适性更强。The present invention achieves the acquisition of the initial lateral position of the tunneling ionized electron wave packet by analyzing the lateral momentum offset of the center position of the zero-order maximum fringe of the photoelectron holographic interference relative to the center position of the zero-order maximum fringe of the holographic interference at zero arrangement angle along the direction perpendicular to the polarization direction of the laser field when the molecular arrangement angle is non-zero. The acquisition method is simpler and the obtained result is more accurate. The feasibility and universality of the present invention are stronger.
附图说明BRIEF DESCRIPTION OF THE DRAWINGS
为了使本发明的内容更容易被清楚的理解,下面根据本发明的具体实施例并结合附图,对本发明作进一步详细的说明,其中In order to make the content of the present invention more clearly understood, the present invention is further described in detail below according to specific embodiments of the present invention in conjunction with the accompanying drawings, wherein
图1是本发明的流程图;Fig. 1 is a flow chart of the present invention;
图2是本发明实施例中激光场偏振方向与氢分子离子排列方向呈0°和45°时,得到的光电子全息干涉形成原理图;FIG2 is a schematic diagram showing the principle of photoelectron holographic interference formation when the polarization direction of the laser field and the arrangement direction of the hydrogen molecule ions are at 0° and 45° in an embodiment of the present invention;
图3是本发明实施例中从图2的光电子动量谱中提取的全息干涉条纹的图像;FIG3 is an image of holographic interference fringes extracted from the photoelectron momentum spectrum of FIG2 in an embodiment of the present invention;
图4是本发明实施例中隧穿电离电子初始横向位置的探测过程图;FIG4 is a diagram of the detection process of the initial lateral position of the tunneling ionized electrons in an embodiment of the present invention;
图5是本发明实施例中氮气分子隧穿电离的光电子动量谱;FIG5 is a photoelectron momentum spectrum of nitrogen molecule tunneling ionization in an embodiment of the present invention;
图6是本发明实施例中氮气分子隧穿电离电子初始横向位置的探测过程图。FIG. 6 is a diagram showing the detection process of the initial lateral position of the electrons ionized by the tunneling of nitrogen molecules in an embodiment of the present invention.
具体实施方式DETAILED DESCRIPTION
下面结合附图和具体实施例对本发明作进一步说明,以使本领域的技术人员可以更好地理解本发明并能予以实施,但所举实施例不作为对本发明的限定。术语“第一”、“第二”仅用于描述目的,而不能理解为指示或暗示相对重要性或者隐含指明所指示的技术特征的数量。The present invention is further described below in conjunction with the accompanying drawings and specific embodiments so that those skilled in the art can better understand the present invention and implement it, but the embodiments are not intended to limit the present invention. The terms "first" and "second" are used only for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features.
在超快超强激光作用下,分子会发生电离,电离电子在激光场中做加速运动,部分电子会返回并与母离子的几何中心发生碰撞散射。该散射电子波包与未与母离子相互作用的直接电子波包相互干涉,这种干涉结构包含母离子和激光场的信息,与光学上的全息干涉原理类似,被称为强场光电子全息干涉。Under the action of ultrafast and ultra-intense lasers, molecules will be ionized, and the ionized electrons will accelerate in the laser field. Some of the electrons will return and collide and scatter with the geometric center of the parent ion. The scattered electron wave packet interferes with the direct electron wave packet that has not interacted with the parent ion. This interference structure contains information about the parent ion and the laser field, which is similar to the principle of holographic interference in optics and is called strong-field photoelectron holographic interference.
如图1流程图所示公开了一种探测隧穿电离电子初始横向位置的方法,包括以下步骤:As shown in the flow chart of FIG1 , a method for detecting the initial lateral position of a tunneling ionized electron is disclosed, comprising the following steps:
S1:使用激光场电离分子,使所述激光场偏振方向与所述分子的排列方向呈零角度,获取所述分子电离时的第一光电子动量谱;分子电离时电子通过隧穿电离而脱离母核的束缚,利用探测器可以测量得到光电子动量谱,光电子动量谱为二维光电子动量谱。S1: Use a laser field to ionize molecules, so that the polarization direction of the laser field is at zero angle to the arrangement direction of the molecules, and obtain the first photoelectron momentum spectrum when the molecules are ionized; when the molecules are ionized, the electrons are freed from the constraints of the parent nucleus through tunneling ionization, and the photoelectron momentum spectrum can be measured using a detector. The photoelectron momentum spectrum is a two-dimensional photoelectron momentum spectrum.
S2:使用所述激光场再次电离所述分子,使所述激光场偏振方向与所述分子排列方向呈非零角度,获取所述分子电离时的第二光电子动量谱。S2: using the laser field to ionize the molecules again, so that the polarization direction of the laser field and the molecular arrangement direction form a non-zero angle, and obtaining a second photoelectron momentum spectrum when the molecules are ionized.
激光场可以为近红外激光场或中红外激光场,也可以在冷靶反冲粒子动量成像谱仪(Cold Target Recoil-ion Momentum Spectroscopy,COLTRIMS)或粒子速度影像仪(Velocity Map Imagery,VMI)中排列分子,然后用一束偏振方向与分子排列方向成零角度和非零角度的激光脉冲作用于该分子,获取第一光电子动量谱和第二光电子动量谱。The laser field can be a near-infrared laser field or a mid-infrared laser field, or the molecules can be arranged in a cold target recoil-ion momentum spectroscopy (COLTRIMS) or a velocity map imagery (VMI), and then a laser pulse with a polarization direction that forms a zero angle and a non-zero angle with the molecular arrangement direction is applied to the molecule to obtain a first photoelectron momentum spectrum and a second photoelectron momentum spectrum.
S3:根据所述第一光电子动量谱和所述第二光电子动量谱,得到所述分子与所述激光场偏振方向排列角度为非零角度时的光电子全息干涉零级极大条纹中心位置相对于零排列角度下光电子全息干涉零级极大条纹中心位置的横向动量偏移量。S3: According to the first photoelectron momentum spectrum and the second photoelectron momentum spectrum, the lateral momentum offset of the center position of the zero-order maximum fringe of the photoelectron holographic interference when the arrangement angle between the molecule and the polarization direction of the laser field is non-zero relative to the center position of the zero-order maximum fringe of the photoelectron holographic interference at zero arrangement angle is obtained.
S3.1:根据所述第一光电子动量谱得到所述激光场偏振方向与所述分子排列方向呈零角度时的第一光电子全息干涉,根据所述第二光电子动量谱得到所述激光场偏振方向与所述分子排列方向呈非零角度时的第二光电子全息干涉。S3.1: According to the first photoelectron momentum spectrum, a first photoelectron holographic interference is obtained when the polarization direction of the laser field and the molecular arrangement direction form a zero angle, and according to the second photoelectron momentum spectrum, a second photoelectron holographic interference is obtained when the polarization direction of the laser field and the molecular arrangement direction form a non-zero angle.
S3.1.1:在所述第一光电子动量谱的目标动量范围内均匀提取平行于激光场偏振方向上具有末动量的光电子对应的光电子产量得到第一光电子横向动量分布,在所述第二光电子动量谱的所述目标动量范围内均匀提取平行于激光场偏振方向上具有末动量的光电子对应的光电子产量得到第二光电子横向动量分布。本实施例中所述目标动量px范围为0.75原子单位~1.45原子单位。在该目标动量范围取值,能够从光电子动量谱中获取清晰的全息干涉条纹。S3.1.1: Uniformly extract the final momentum parallel to the polarization direction of the laser field within the target momentum range of the first photoelectron momentum spectrum. The photoelectron yield corresponding to the photoelectrons of the first photoelectron transverse momentum distribution is obtained, and the photoelectrons having the final momentum parallel to the polarization direction of the laser field are uniformly extracted within the target momentum range of the second photoelectron momentum spectrum. The photoelectron yield corresponding to the photoelectrons of the second photoelectron transverse momentum distribution is obtained. In this embodiment, the target momentum p x ranges from 0.75 atomic units to 1.45 atomic units. In this target momentum range, clear holographic interference fringes can be obtained from the photoelectron momentum spectrum.
S3.1.1.1:在所述第一光电子动量谱的目标动量范围内设置方形动量区域,所述方形动量区域在垂直于激光场偏振方向上的动量长度为δpy、在平行于激光场偏振方向上动量长度为δpx;在所述第二光电子动量谱的目标动量范围内设置方形动量区域,所述方形动量区域在垂直于激光场偏振方向上的动量长度为δpy、在平行于激光场偏振方向上动量长度为δpx。本实施例中δpy取值0原子单位、δpx取值0.02原子单位,通过设置方形动量区域,可以降低光电子动量谱中的干涉结构影响,得到清晰的光电子全息干涉。S3.1.1.1: A square momentum region is set within the target momentum range of the first photoelectron momentum spectrum, wherein the momentum length of the square momentum region in the direction perpendicular to the polarization direction of the laser field is δp y and the momentum length in the direction parallel to the polarization direction of the laser field is δp x ; A square momentum region is set within the target momentum range of the second photoelectron momentum spectrum, wherein the momentum length of the square momentum region in the direction perpendicular to the polarization direction of the laser field is δp y and the momentum length in the direction parallel to the polarization direction of the laser field is δp x . In this embodiment, δp y takes a value of 0 atomic unit and δp x takes a value of 0.02 atomic unit. By setting the square momentum region, the interference structure effect in the photoelectron momentum spectrum can be reduced, and a clear photoelectron holographic interference can be obtained.
S3.1.1.2:在所述方形动量区域内均匀提取平行于激光场偏振方向的具有末动量和垂直于激光偏振方向的具有末动量的光电子对应的光电子产量,将所述方形动量区域内提取到的所有具有末动量的光电子对应的光电子产量的平均值作为具有末动量的光电子对应的光电子产量,将所述方形动量区域内提取到的所有具有末动量的光电子对应的光电子产量的平均值作为具有末动量的光电子对应的光电子产量;S3.1.1.2: Uniformly extract the final momentum parallel to the polarization direction of the laser field in the square momentum region. and a wave with terminal momentum perpendicular to the laser polarization direction The photoelectron yield corresponding to the photoelectron is the total photoelectron with final momentum extracted from the square momentum region. The average value of the photoelectron yield corresponding to the photoelectron with final momentum The photoelectron yield corresponding to the photoelectron is the total photoelectron with final momentum extracted from the square momentum region. The average value of the photoelectron yield corresponding to the photoelectron with final momentum The photoelectron yield corresponding to the photoelectrons;
在所述方形动量区域内均匀提取平行于激光场偏振方向的具有末动量和垂直于激光偏振方向的具有末动量的光电子对应的光电子产量,将所述方形动量区域内提取到的所有具有末动量的光电子对应的光电子产量的平均值作为具有末动量的光电子对应的光电子产量,将所述方形动量区域内提取到的所有具有末动量的光电子对应的光电子产量的平均值作为具有末动量的光电子对应的光电子产量。The final momentum parallel to the polarization direction of the laser field is uniformly extracted in the square momentum region. and a wave with terminal momentum perpendicular to the laser polarization direction The photoelectron yield corresponding to the photoelectron is the total photoelectron with final momentum extracted from the square momentum region. The average value of the photoelectron yield corresponding to the photoelectron with final momentum The photoelectron yield corresponding to the photoelectron is the total photoelectron with final momentum extracted from the square momentum region. The average value of the photoelectron yield corresponding to the photoelectron with final momentum The photoelectron yield corresponding to the photoelectron.
S3.1.1.3:将所述目标动量范围内均匀取值得到的每一具有末动量的光电子对应的光电子产量作为所述第一光电子横向动量分布,将所述目标动量范围内均匀取值得到的每一具有末动量的光电子对应的光电子产量作为所述第二光电子横向动量分布。S3.1.1.3: Take each value obtained by uniformly taking values within the target momentum range and obtain the final momentum The photoelectron yield corresponding to the photoelectron of is taken as the first photoelectron transverse momentum distribution, and each photoelectron having a final momentum uniformly obtained within the target momentum range is The photoelectron yield corresponding to the photoelectron is used as the transverse momentum distribution of the second photoelectron.
S3.1.2:将所述第一光电子横向动量分布作为所述第一光电子全息干涉,将所述第二光电子横向动量分布作为所述第二光电子全息干涉。S3.1.2: Taking the first photoelectron transverse momentum distribution as the first photoelectron holographic interferometry, and taking the second photoelectron transverse momentum distribution as the second photoelectron holographic interferometry.
S3.2:在所述第一光电子全息干涉中找到所述激光场偏振方向与所述分子的排列方向呈零角度的第一光电子全息干涉零级极大条纹中心位置,在所述第二光电子全息干涉中找到所述激光场偏振方向与所述分子的排列方向呈非零角度的第二光电子全息干涉零级极大条纹中心位置。S3.2: In the first photoelectron holographic interference, find the center position of the zero-order maximum fringe of the first photoelectron holographic interference, where the polarization direction of the laser field is at a zero angle with the arrangement direction of the molecules; in the second photoelectron holographic interference, find the center position of the zero-order maximum fringe of the second photoelectron holographic interference, where the polarization direction of the laser field is at a non-zero angle with the arrangement direction of the molecules.
S3.2.1:提取所述第一光电子全息干涉的第一干涉项,提取所述第二光电子全息干涉的第二干涉项。具体为:使用指数函数对所述第一光电子全息干涉中的光电子产量进行多项式拟合,将第一光电子全息干涉中的光电子产量除以拟合得到的多项式,将其得到的结果作为第一干涉项;所述提取所述第二光电子全息干涉的第二干涉项时,使用指数函数对所述第二光电子全息干涉中的光电子产量进行多项式拟合,将第二光电子全息干涉中的光电子产量除以拟合得到的多项式,将其得到的结果作为第二干涉项。使用指数函数对光电子产量进行拟合,可以消除光电子动量分布的包络函数。S3.2.1: Extract the first interference term of the first photoelectron holographic interference, and extract the second interference term of the second photoelectron holographic interference. Specifically: use an exponential function to perform polynomial fitting on the photoelectron yield in the first photoelectron holographic interference, divide the photoelectron yield in the first photoelectron holographic interference by the fitted polynomial, and use the result as the first interference term; when extracting the second interference term of the second photoelectron holographic interference, use an exponential function to perform polynomial fitting on the photoelectron yield in the second photoelectron holographic interference, divide the photoelectron yield in the second photoelectron holographic interference by the fitted polynomial, and use the result as the second interference term. Fitting the photoelectron yield with an exponential function can eliminate the envelope function of the photoelectron momentum distribution.
所述第一干涉项为cos(ΔΦ1),其中ΔΦ1为第一干涉相位,ΔΦ1的计算方法为:The first interference term is cos(ΔΦ 1 ), where ΔΦ 1 is the first interference phase, and the calculation method of ΔΦ 1 is:
ΔΦ1=1/2[py-ky(0)]2(tr-t0)+α;ΔΦ 1 =1/2[p y -k y (0)] 2 (t r -t 0 )+α;
所述第二干涉项为cos(ΔΦ2),其中ΔΦ2为第二干涉相位,ΔΦ2的计算方法为:The second interference term is cos(ΔΦ 2 ), where ΔΦ 2 is the second interference phase, and the calculation method of ΔΦ 2 is:
ΔΦ2=1/2[py-ky(θ)]2(tr-t0)+α;ΔΦ 2 =1/2[p y -k y (θ)] 2 (t r -t 0 )+α;
其中,py为垂直于激光场偏振方向的光电子末动量,tr为散射电子的散射时间,t0为散射电子的电离时间,α为分子的散射振幅相位;ky是散射电子的正则动量,ky(0)为当激光场偏振方向与分子排列方向呈零角度时隧穿电离散射电子的正则动量,θ为激光场偏振方向与分子排列方向之间的夹角,ky(θ)为当激光场偏振方向与分子排列方向之间的夹角为θ时隧穿电离散射电子的正则动量。第一光电子全息干涉和第二光电子全息干涉满足干涉叠加公式:|I|2=|Id|2+|Ir|2+2|Id||Ir|cos(ΔΦ),其中,I表示干涉结构的电离振幅,Id为直接电子波包的电离振幅,Ir为近前向散射电子波包的电离振幅,ΔΦ为ΔΦ1或ΔΦ2,表示直接电子波包和近前向散射电子波包之间的相位差(干涉相位),||表示不同物理量的大小。Wherein, p y is the final momentum of the photoelectron perpendicular to the polarization direction of the laser field, t r is the scattering time of the scattered electron, t 0 is the ionization time of the scattered electron, and α is the scattering amplitude phase of the molecule; ky is the canonical momentum of the scattered electron, ky (0) is the canonical momentum of the tunneling ionized scattered electron when the polarization direction of the laser field and the molecular arrangement direction are at zero angle, θ is the angle between the polarization direction of the laser field and the molecular arrangement direction, and ky (θ) is the canonical momentum of the tunneling ionized scattered electron when the angle between the polarization direction of the laser field and the molecular arrangement direction is θ. The first photoelectron holographic interference and the second photoelectron holographic interference satisfy the interference superposition formula: |I| 2 =|I d | 2 +|I r | 2 +2|I d ||I r |cos(ΔΦ), where I represents the ionization amplitude of the interference structure, I d is the ionization amplitude of the direct electron wave packet, I r is the ionization amplitude of the near forward scattered electron wave packet, ΔΦ is ΔΦ 1 or ΔΦ 2 , representing the phase difference (interference phase) between the direct electron wave packet and the near forward scattered electron wave packet, and || represents the size of different physical quantities.
S3.2.2:根据所述第一干涉项获取第一光电子全息干涉各级条纹的中心位置,根据所述第一光电子全息干涉各级条纹的中心位置得到所述第一光电子全息干涉零级极大条纹中心位置;根据所述第二干涉项获取第二光电子全息干涉各级条纹的中心位置,根据所述第二光电子全息干涉各级条纹的中心位置得到所述第二光电子全息干涉零级极大条纹中心位置。具体为:S3.2.2: Obtain the center position of each level of fringes of the first photoelectron holographic interference according to the first interference term, and obtain the center position of the zero-order maximum fringes of the first photoelectron holographic interference according to the center position of each level of fringes of the first photoelectron holographic interference; obtain the center position of each level of fringes of the second photoelectron holographic interference according to the second interference term, and obtain the center position of the zero-order maximum fringes of the second photoelectron holographic interference according to the center position of each level of fringes of the second photoelectron holographic interference. Specifically:
对于任意平行于激光场偏振方向的动量px,建立所述第一光电子全息干涉各级条纹的中心位置其中,ΔΦ1=nπ,n=0,±1,±2,±3...;当n=0、ΔΦ1=0时得到所述第一光电子全息干涉零级极大条纹中心位置 For any momentum p x parallel to the polarization direction of the laser field, the center position of each level of the first photoelectron holographic interference fringes is established. Wherein, ΔΦ 1 =nπ, n=0, ±1, ±2, ±3...; when n=0 and ΔΦ 1 =0, the center position of the zero-order maximum fringe of the first photoelectron holographic interference is obtained:
对于任意平行于激光场偏振方向的动量px,建立所述第二光电子全息干涉零级极大条纹中心位置其中,ΔΦ2=nπ,n=0,±1,±2,±3...;当n=0、ΔΦ2=0时得到所述第二光电子全息干涉零级极大条纹中心位置 For any momentum p x parallel to the polarization direction of the laser field, the center position of the zero-order maximum fringe of the second photoelectron holographic interference is established. Wherein, ΔΦ 2 =nπ, n=0, ±1, ±2, ±3...; when n=0, ΔΦ 2 =0, the center position of the zero-order maximum fringe of the second photoelectron holographic interference is obtained:
全息干涉的零级极大表示对任意px,在py=0附近的动量区域内,全息干涉条纹的极大值处。The zeroth-order maximum of holographic interference represents the maximum value of the holographic interference fringes in the momentum region near p y =0 for any p x .
S3.3:将所述第二光电子全息干涉零级极大条纹中心位置与所述第一光电子全息干涉零级极大条纹中心位置做差,得到所述分子与所述激光场偏振方向排列角度为非零角度时的光电子全息干涉零级极大条纹中心位置相对于零排列角度下光电子全息干涉零级极大条纹中心位置的横向动量偏移量Δpy=ky(θ)。S3.3: Subtract the center position of the zero-order maximum fringe of the second photoelectron holographic interference from the center position of the zero-order maximum fringe of the first photoelectron holographic interference to obtain the lateral momentum offset Δp y =ky (θ) of the center position of the zero-order maximum fringe of the photoelectron holographic interference when the arrangement angle between the molecule and the polarization direction of the laser field is non- zero relative to the center position of the zero-order maximum fringe of the photoelectron holographic interference at zero arrangement angle.
横向动量偏移量 Lateral Momentum Offset
这里有ky(0)=0,因为对于第一光电子全息干涉,实验和理论的研究结果均表明,全息干涉零级极大条纹中心位置始终为零(也可以从图2(e)和图5(a)中看出),所以有ky(0)=0,进而可得Δpy=ky(θ)。该公式表明,实际的全息干涉零级极大条纹随分子排列角的变化与不考虑散射振幅的量子轨迹方法结果一致,均为ky(θ)。散射电子的散射时间tr和电离时间t0实部不随分子的核间距和排列角度变化,因此Δpy是一个实数。Here, k y (0) = 0, because for the first photoelectron holographic interference, both experimental and theoretical research results show that the center position of the zero-order maximum fringe of the holographic interference is It is always zero (as can be seen from Figure 2(e) and Figure 5(a)), so ky (0)=0, and then Δpy = ky (θ). This formula shows that the actual change of the zero-order maximum fringe of holographic interference with the molecular arrangement angle is consistent with the result of the quantum trajectory method without considering the scattering amplitude, both of which are ky (θ). The real part of the scattering time tr and ionization time t0 of the scattered electron does not change with the internuclear distance and arrangement angle of the molecule, so Δpy is a real number.
S4:根据所述横向动量偏移量得到隧穿电离电子波包的初始横向位置。S4: Obtaining the initial transverse position of the tunneling ionized electron wave packet according to the transverse momentum offset.
建立电离电子的初始横向位置Rb与ky(θ)的关系式:ky(θ)=±Rb/(tr-t0),结合Δpy=ky(θ),得到电离电子的初始横向位置 The relationship between the initial lateral position R b of the ionized electron and ky (θ) is established: ky (θ) = ±R b /(t r -t 0 ), combined with Δpy = ky (θ), the initial lateral position of the ionized electron is obtained
为使本发明更加明显易懂,下面结合实例和附图对本发明的具体实施方式做详细的说明。In order to make the present invention more obvious and easy to understand, the specific implementation methods of the present invention are described in detail below with reference to examples and drawings.
以下结合附图及实施例对本发明进行进一步详细说明。The present invention is further described in detail below with reference to the accompanying drawings and embodiments.
实例一:用梯形包络的多周期线性偏振激光场电离氢分子离子,用光电子全息干涉技术探测垂直于激光场偏振方向上的隧穿电离电子初始位置。使用的激光场波长为1000nm,强度为2.5×1014W/cm2。Example 1: Ionize hydrogen molecular ions with a multi-period linearly polarized laser field with a trapezoidal envelope, and use photoelectron holographic interference technology to detect the initial position of the tunneling ionized electrons perpendicular to the polarization direction of the laser field. The laser field used has a wavelength of 1000nm and an intensity of 2.5×10 14 W/cm 2 .
如图2所示是本实施例中激光场偏振方向与氢分子离子排列方向呈0°和45°时,得到的光电子全息干涉形成原理图。其中图2(a)为激光脉冲电场和相应的矢势/激光频率,横坐标为电子的电离时间,纵坐标为电子在电离瞬时激光脉冲的电场和矢势/激光频率大小。黑色实线为电场随时间的变化,黑色虚线为矢势/激光频率随时间的变化,灰色部分表示形成光电子全息干涉的电子波包的产生时间,两个箭头分别代表了前向散射电子波包与直接电子波包;图2(b)是光电子全息干涉形成示意图,在激光场作用下电子从分子一侧电离,产生电子波包,该电子波包一部分在激光场的作用下加速,并返回母离子与分子的几何中心发生碰撞散射,如带箭头的实线所示的散射电子波包。另一部分电离电子波包不与母核相互作用直接到达探测器,形成带箭头虚线所示的直接电子波包。这两部分电子波包在光电子动量谱中相干,形成光电子全息干涉;图2(c)为激光场偏振方向与分子排列方向呈0°时的光电子全息干涉示意图,图2(d)为激光场偏振方向与分子排列方向呈45°时的光电子全息干涉示意图;图2(e)为分子的排列角度分别为0°时实际光电子动量谱中的全息干涉,图2(f)为分子的排列角度分别为45°时实际光电子动量谱中的全息干涉;图2(d)和图2(f)中黑色虚线表示全息干涉零级极大条纹中心位置。从图2(c)和图2(d)可以看出,在平行于激光场偏振方向上的光电子动量分布中存在叉状干涉结构,因此设置方形动量区域消除光电子动量谱中的其他干涉结构,即可得到单一的光电子全息干涉结构。从图2(e)和2(f)中选择结构清晰、稳定的平行于激光偏振方向的动量范围(0.7到1.5原子单位)内均匀取值,对每一个取值获取其对应的垂直于激光场偏振方向上的动量分布,记录分子排列角为45°时对应的全息干涉零级极大条纹中心位置相对于分子排列角为0°时全息干涉零级极大条纹中心位置的横向偏移量Δpy。As shown in FIG2 , the principle diagram of photoelectron holographic interference formation is obtained when the polarization direction of the laser field and the arrangement direction of the hydrogen molecule ions are 0° and 45° in this embodiment. FIG2 (a) shows the electric field of the laser pulse and the corresponding vector potential/laser frequency, the horizontal axis is the ionization time of the electron, and the vertical axis is the electric field and vector potential/laser frequency of the laser pulse at the moment of ionization. The black solid line shows the change of the electric field over time, the black dotted line shows the change of the vector potential/laser frequency over time, the gray part shows the generation time of the electron wave packet that forms the photoelectron holographic interference, and the two arrows represent the forward scattered electron wave packet and the direct electron wave packet respectively; FIG2 (b) is a schematic diagram of the formation of photoelectron holographic interference. Under the action of the laser field, the electron is ionized from one side of the molecule to generate an electron wave packet. A part of the electron wave packet is accelerated under the action of the laser field and returns to the parent ion to collide and scatter with the geometric center of the molecule, such as the scattered electron wave packet shown by the solid line with an arrow. Another part of the ionized electron wave packet does not interact with the parent nucleus and directly reaches the detector, forming a direct electron wave packet shown by the dotted line with an arrow. The two parts of the electron wave packets are coherent in the photoelectron momentum spectrum, forming photoelectron holographic interference; Figure 2(c) is a schematic diagram of photoelectron holographic interference when the polarization direction of the laser field is 0° to the molecular arrangement direction, and Figure 2(d) is a schematic diagram of photoelectron holographic interference when the polarization direction of the laser field is 45° to the molecular arrangement direction; Figure 2(e) is the holographic interference in the actual photoelectron momentum spectrum when the molecular arrangement angles are 0°, and Figure 2(f) is the holographic interference in the actual photoelectron momentum spectrum when the molecular arrangement angles are 45°; the black dotted lines in Figures 2(d) and 2(f) indicate the center position of the zero-order maximum fringes of the holographic interference. It can be seen from Figures 2(c) and 2(d) that there is a fork-shaped interference structure in the photoelectron momentum distribution parallel to the polarization direction of the laser field. Therefore, a square momentum region is set to eliminate other interference structures in the photoelectron momentum spectrum, and a single photoelectron holographic interference structure can be obtained. From Figures 2(e) and 2(f), select uniform values within the momentum range (0.7 to 1.5 atomic units) with clear and stable structures parallel to the laser polarization direction, obtain the corresponding momentum distribution perpendicular to the laser field polarization direction for each value, and record the lateral offset Δp y of the center position of the zero-order maximum fringe of the holographic interference when the molecular arrangement angle is 45° relative to the center position of the zero-order maximum fringe of the holographic interference when the molecular arrangement angle is 0 ° .
如图3所示是从图2所示的光电子动量谱中提取的全息干涉条纹。图3(a)为从光电动量谱中提取的全息干涉在某一任意动量px处沿垂直于激光场偏振方向的光电子动量分布,图中实线和虚线分别表示分子45°排列角和0°排列角的结果;图3(b)为从图3(a)所示的动量谱中提取的全息结构的干涉项cos(ΔΦ);图3(a)和图3(b)的横坐标为垂直于激光场偏振方向上的光电子末动量,纵坐标为光电子产量。以分子排列角为45°和0°时,平行于激光场偏振方向上动量px=1.4和px=1.0原子单位为例提取偏移量Δpy。图3(a)和3(b)为激光场偏振方向上动量px=1.4和px=1.0原子单位处垂直于激光偏振方向的光电子动量分布曲线。使用指数函数对光电子产量拟合,消除光电子动量分布的包络,得到全息结构干涉项cos(ΔΦ),如图3(c)和3(d)所示。从图3(c)和3(d)可以看到干涉项cos(ΔΦ)随垂直于激光偏振方向上光电子末动量变化而振荡。在垂直于激光场偏振方向上动量py=0附近,cos(ΔΦ)振荡最大值对应的垂直于激光偏振方向上的光电子末动量即为光电子全息干涉零级极大条纹中心位置。As shown in FIG3, holographic interference fringes are extracted from the photoelectron momentum spectrum shown in FIG2. FIG3(a) shows the distribution of photoelectron momentum perpendicular to the laser field polarization direction at an arbitrary momentum px extracted from the photoelectron momentum spectrum. The solid line and the dotted line in the figure represent the results of the molecular arrangement angle of 45° and 0°, respectively; FIG3(b) shows the interference term cos(ΔΦ) of the holographic structure extracted from the momentum spectrum shown in FIG3(a); the abscissa of FIG3(a) and FIG3(b) is the photoelectron final momentum perpendicular to the laser field polarization direction, and the ordinate is the photoelectron yield. Taking the molecular arrangement angles of 45° and 0°, the momentum px = 1.4 and px = 1.0 atomic units parallel to the laser field polarization direction as examples, the offset Δp y is extracted. FIG3(a) and FIG3(b) show the distribution curves of photoelectron momentum perpendicular to the laser polarization direction at the momentum px = 1.4 and px = 1.0 atomic units in the laser field polarization direction. The photoelectron yield is fitted using an exponential function, the envelope of the photoelectron momentum distribution is eliminated, and the holographic structure interference term cos(ΔΦ) is obtained, as shown in Figures 3(c) and 3(d). From Figures 3(c) and 3(d), it can be seen that the interference term cos(ΔΦ) oscillates with the change of the photoelectron final momentum in the direction perpendicular to the laser polarization. Near the momentum p y = 0 perpendicular to the laser field polarization direction, the photoelectron final momentum in the direction perpendicular to the laser polarization corresponding to the maximum value of the cos(ΔΦ) oscillation is the center position of the zero-order maximum fringe of the photoelectron holographic interference.
如图4所示是本实施例周隧穿电离电子初始横向位置的探测过程。图4(a)为从图3所示的干涉项cos(ΔΦ)中提取的在分子排列角度为45°时,光电子全息干涉零级极大条纹中心位置相对于排列角度为0°时全息干涉零级极大条纹中心位置的横向动量偏移量Δpy,可以看出Δpy随激光场偏振方向上动量变化而变化;图4(b)为基于公式Δpy=±Rb/(tr-t0)最终得到的隧穿电离电子初始横向位置Rb。图4(c)为电子波函数随时间的演化,其中横坐标为演化时间,纵坐标为垂直于激光偏振方向上的电子位置。其中黑色虚线表示电子波函数最大值对应的垂直于激光场偏振方向上的电子位置。Δpy的幅值是激光场偏振方向动量px的函数。根据量子轨迹模型预测公式通过分析Δpy,即可从全息干涉偏移量中探测得到氢分子离子隧穿电离电子的初始横向位置,得到初始横向位置结果为1.46原子单位,如图4(b)所示。在量子力学中,电子波包在垂直于激光场偏振方向上的最概然密度表征隧穿电离电子的横向位置。使用本发明方法测得的隧穿电离电子的初始横向位置与电子波包在垂直于激光场偏振方向上的最概然密度位置一致,如图4(c)所示。图4(c)中颜色最亮的位置对应的纵坐标为电子波包在垂直于激光场偏振方向上的最概然密度位置,用黑色虚线标注,其大小为1.44原子单位,与使用本发明方法得到的1.46原子单位基本一致,证实了本发明的精确性与可行性。As shown in Figure 4, the detection process of the initial lateral position of the tunneling ionized electron in this embodiment. Figure 4(a) is the lateral momentum offset Δp y of the center position of the zero-order maximum fringe of the photoelectron holographic interference relative to the center position of the zero-order maximum fringe of the holographic interference when the molecular arrangement angle is 0°, which is extracted from the interference term cos(ΔΦ ) shown in Figure 3. It can be seen that Δp y changes with the momentum change in the polarization direction of the laser field; Figure 4(b) is the initial lateral position R b of the tunneling ionized electron finally obtained based on the formula Δp y = ±R b /(t r -t 0 ). Figure 4(c) is the evolution of the electron wave function with time, where the horizontal axis is the evolution time and the vertical axis is the electron position perpendicular to the laser polarization direction. The black dotted line represents the electron position perpendicular to the laser field polarization direction corresponding to the maximum value of the electron wave function. The amplitude of Δp y is a function of the momentum p x in the polarization direction of the laser field. According to the quantum trajectory model prediction formula By analyzing Δp y , the initial lateral position of the tunneling ionized electron of the hydrogen molecule ion can be detected from the holographic interference offset, and the initial lateral position result is 1.46 atomic units, as shown in Figure 4(b). In quantum mechanics, the most probable density of the electron wave packet in the direction perpendicular to the polarization of the laser field characterizes the lateral position of the tunneling ionized electron. The initial lateral position of the tunneling ionized electron measured using the method of the present invention is consistent with the most probable density position of the electron wave packet in the direction perpendicular to the polarization of the laser field, as shown in Figure 4(c). The vertical coordinate corresponding to the brightest color position in Figure 4(c) is the most probable density position of the electron wave packet in the direction perpendicular to the polarization of the laser field, marked with a black dotted line, and its size is 1.44 atomic units, which is basically consistent with the 1.46 atomic units obtained using the method of the present invention, confirming the accuracy and feasibility of the present invention.
实例二:用梯形包络的多周期线性偏振激光场电离氮气分子,用光电子全息干涉技术探测垂直于激光偏振方向上隧穿电离电子的初始位置。使用的激光场波长为1000nm,强度为2.5×1014W/cm2。Example 2: Ionize nitrogen molecules using a multi-period linearly polarized laser field with a trapezoidal envelope, and use photoelectron holographic interferometry to detect the initial position of the tunneling ionized electrons perpendicular to the laser polarization direction. The laser field used has a wavelength of 1000nm and an intensity of 2.5×10 14 W/cm 2 .
如图5所示是本实施例中另一种分子(氮气分子)隧穿电离的光电子动量谱,图5(a)为激光场偏振方向与分子排列方向呈0°时的光电子动量谱,图5(b)为激光场偏振方向与分子排列方向呈0°时的光电子动量谱。图5(b)中黑色虚线表示全息干涉零级极大条纹中心位置。As shown in FIG5 , it is the photoelectron momentum spectrum of another molecule (nitrogen molecule) tunneling ionization in this embodiment, FIG5(a) is the photoelectron momentum spectrum when the polarization direction of the laser field is 0° with the molecular arrangement direction, and FIG5(b) is the photoelectron momentum spectrum when the polarization direction of the laser field is 0° with the molecular arrangement direction. The black dotted line in FIG5(b) indicates the center position of the zero-order maximum fringe of the holographic interference.
如图6所示是本实施例中另一种分子(氮气分子)隧穿电离电子初始横向位置的探测结果。图6(a)所示是提取分子排列角为45°时对应的全息干涉零级极大条纹中心位置相对于分子排列角为0°时全息干涉零级极大条纹中心位置的横向偏量Δpy。利用量子轨迹模型预测公式从光电子全息干涉偏移量Δpy中获得氮气分子隧穿电离电子初始横向位置Rb,如图6(b)所示,获得的结果为1.6原子单位。图6(c)中黑色虚线表示电子波函数最大值对应的垂直于激光场偏振方向上的电子位置。在量子力学中,电子波包在垂直于激光场偏振方向上的最概然密度表征隧穿电离电子的横向位置。本发明方案测得的隧穿电离电子的横向位置与电子波包在垂直于激光场偏振方向上的最概然密度位置一致。如图6(c)所示,图6中颜色最亮的地方对应的纵坐标表示电子波包在垂直于激光场偏振方向上的最概然密度位置,用黑色虚线标注,其大小为1.58原子单位,与使用本发明方法得到的1.6原子单位基本一致,也证实了本发明的精确性与可行性。As shown in FIG6 , the detection result of the initial lateral position of the tunneling ionized electron of another molecule (nitrogen molecule) in this embodiment is shown. FIG6 (a) shows the lateral deviation Δp y of the center position of the zero-order maximum fringe of the holographic interference corresponding to the molecular arrangement angle of 45° relative to the center position of the zero-order maximum fringe of the holographic interference when the molecular arrangement angle is 0 ° . Using the quantum trajectory model prediction formula The initial transverse position R b of the tunneling ionized electron of the nitrogen molecule is obtained from the photoelectron holographic interference offset Δp y , as shown in FIG6(b), and the result obtained is 1.6 atomic units. The black dotted line in FIG6(c) represents the electron position perpendicular to the polarization direction of the laser field corresponding to the maximum value of the electron wave function. In quantum mechanics, the most probable density of the electron wave packet perpendicular to the polarization direction of the laser field characterizes the transverse position of the tunneling ionized electron. The transverse position of the tunneling ionized electron measured by the scheme of the present invention is consistent with the most probable density position of the electron wave packet perpendicular to the polarization direction of the laser field. As shown in FIG6(c), the ordinate corresponding to the brightest color in FIG6 represents the most probable density position of the electron wave packet perpendicular to the polarization direction of the laser field, marked with a black dotted line, and its size is 1.58 atomic units, which is basically consistent with the 1.6 atomic units obtained using the method of the present invention, and also confirms the accuracy and feasibility of the present invention.
本发明通过分析在分子排列角度为非零角度时,光电子全息干涉零级极大条纹中心位置相对于零排列角下全息干涉零级极大条纹中心位置沿垂直于激光场偏振方向上的横向动量偏移量,实现了隧穿电离电子波包的初始横向位置的获取。相比于超快、强场物理中其他隧穿电离电子初始横向位置探测方法,获取方法更简单、获得的结果更精确,本发明的可行性和普适性更强,从而有利于超快、强场物理领域更深入、更细节的研究。The present invention achieves the acquisition of the initial transverse position of the tunneling ionized electron wave packet by analyzing the transverse momentum offset of the center position of the zero-order maximum fringe of the photoelectron holographic interference relative to the center position of the zero-order maximum fringe of the holographic interference at zero arrangement angle in the direction perpendicular to the polarization direction of the laser field when the molecular arrangement angle is non-zero. Compared with other methods for detecting the initial transverse position of tunneling ionized electrons in ultrafast and strong field physics, the acquisition method is simpler and the results obtained are more accurate. The feasibility and universality of the present invention are stronger, which is conducive to deeper and more detailed research in the field of ultrafast and strong field physics.
本领域内的技术人员应明白,本申请的实施例可提供为方法、系统、或计算机程序产品。因此,本申请可采用完全硬件实施例、完全软件实施例、或结合软件和硬件方面的实施例的形式。而且,本申请可采用在一个或多个其中包含有计算机可用程序代码的计算机可用存储介质(包括但不限于磁盘存储器、CD-ROM、光学存储器等)上实施的计算机程序产品的形式。Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application may adopt the form of a computer program product implemented in one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that contain computer-usable program code.
本申请是参照根据本申请实施例的方法、设备(系统)、和计算机程序产品的流程图和/或方框图来描述的。应理解可由计算机程序指令实现流程图和/或方框图中的每一流程和/或方框、以及流程图和/或方框图中的流程和/或方框的结合。可提供这些计算机程序指令到通用计算机、专用计算机、嵌入式处理机或其他可编程数据处理设备的处理器以产生一个机器,使得通过计算机或其他可编程数据处理设备的处理器执行的指令产生用于实现在流程图一个流程或多个流程和/或方框图一个方框或多个方框中指定的功能的装置。The present application is described with reference to the flowchart and/or block diagram of the method, device (system) and computer program product according to the embodiment of the present application. It should be understood that each process and/or box in the flowchart and/or block diagram, and the combination of the process and/or box in the flowchart and/or block diagram can be realized by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device produce a device for realizing the function specified in one process or multiple processes in the flowchart and/or one box or multiple boxes in the block diagram.
这些计算机程序指令也可存储在能引导计算机或其他可编程数据处理设备以特定方式工作的计算机可读存储器中,使得存储在该计算机可读存储器中的指令产生包括指令装置的制造品,该指令装置实现在流程图一个流程或多个流程和/或方框图一个方框或多个方框中指定的功能。These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer-readable memory produce a manufactured product including an instruction device that implements the functions specified in one or more processes in the flowchart and/or one or more boxes in the block diagram.
这些计算机程序指令也可装载到计算机或其他可编程数据处理设备上,使得在计算机或其他可编程设备上执行一系列操作步骤以产生计算机实现的处理,从而在计算机或其他可编程设备上执行的指令提供用于实现在流程图一个流程或多个流程和/或方框图一个方框或多个方框中指定的功能的步骤。These computer program instructions may also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, whereby the instructions executed on the computer or other programmable device provide steps for implementing the functions specified in one or more processes in the flowchart and/or one or more boxes in the block diagram.
显然,上述实施例仅仅是为清楚地说明所作的举例,并非对实施方式的限定。对于所属领域的普通技术人员来说,在上述说明的基础上还可以做出其它不同形式变化或变动。这里无需也无法对所有的实施方式予以穷举。而由此所引申出的显而易见的变化或变动仍处于本发明创造的保护范围之中。Obviously, the above embodiments are merely examples for clear explanation and are not intended to limit the implementation methods. For those skilled in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to list all the implementation methods here. The obvious changes or modifications derived from these are still within the protection scope of the invention.
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CN108663702B (en) * | 2018-03-01 | 2020-07-10 | 中国科学院上海应用物理研究所 | X-ray coherence measurement device and measurement method |
US10658148B2 (en) * | 2018-04-30 | 2020-05-19 | Arizona Board Of Regents Of Behalf Of The University Of Arizona | Attomicroscopy: attosecond electron imaging and microscopy |
US11539181B2 (en) * | 2019-10-18 | 2022-12-27 | Wayne State University | System and method for determining absolute carrier-envelope phase of ultrashort laser pulses |
CN114061484B (en) * | 2021-11-12 | 2023-08-11 | 苏州科技大学 | Broadband light interference microscopic morphology measuring device and method |
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