CN115220085B - Method for detecting initial transverse position of tunneling ionized electrons - Google Patents

Abstract

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

Method for detecting the initial lateral position of tunneling ionized electrons

Technical Field

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.

Background Art

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.

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.

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.

Summary of the invention

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.

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:

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;

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;

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;

The initial transverse position of the tunneling ionized electron wave packet is obtained according to the transverse momentum offset.

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:

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;

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;

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.

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:

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;

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.

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:

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;

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:

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.

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:

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;

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.

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:

ΔΦ ₁ =1/2[p _y -k _y (0)] ² (t _r -t ₀ )+α;

The second interference term is cos(ΔΦ ₂ ), where ΔΦ ₂ is the second interference phase, and the calculation method of ΔΦ ₂ is:

ΔΦ ₂ =1/2[p _y -k _y (θ)] ² (t _r -t ₀ )+α;

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.

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;

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.

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:

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:

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:

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:

Preferably, the lateral momentum offset Δp _y = _ky (θ).

Preferably, the initial lateral position of the tunneling ionized electron wave packet is obtained according to the lateral momentum offset, specifically:

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

The above technical solution of the present invention has the following advantages compared with the prior art:

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.

BRIEF DESCRIPTION OF THE DRAWINGS

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

Fig. 1 is a flow chart of the present invention;

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;

FIG3 is an image of holographic interference fringes extracted from the photoelectron momentum spectrum of FIG2 in an embodiment of the present invention;

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;

FIG5 is a photoelectron momentum spectrum of nitrogen molecule tunneling ionization in an embodiment of the present invention;

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.

DETAILED DESCRIPTION

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.

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.

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: 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: 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.

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: 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: 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.

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p_x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: 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.

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;

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.

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: 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: 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: 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.

The first interference term is cos(ΔΦ ₁ ), where ΔΦ ₁ is the first interference phase, and the calculation method of ΔΦ ₁ is:

ΔΦ ₁ =1/2[p _y -k _y (0)] ² (t _r -t ₀ )+α;

The second interference term is cos(ΔΦ ₂ ), where ΔΦ ₂ is the second interference phase, and the calculation method of ΔΦ ₂ is:

ΔΦ ₂ =1/2[p _y -k _y (θ)] ² (t _r -t ₀ )+α;

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: 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:

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:

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:

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: 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.

Lateral Momentum Offset

始终为零(也可以从图2(e)和图5(a)中看出)，所以有k_y(0)＝0，进而可得Δp_y＝k_y(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k_y(θ)。散射电子的散射时间t_r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Δp_y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: Obtaining the initial transverse position of the tunneling ionized electron wave packet according to the transverse momentum offset.

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

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.

The present invention is further described in detail below with reference to the accompanying drawings and embodiments.

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 .

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 _° .

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.

通过分析Δp_y，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.

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 .

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.

从光电子全息干涉偏移量Δp_y中获得氮气分子隧穿电离电子初始横向位置R_b，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.

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.

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.

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.

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.

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.

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.

Claims (7)

1. A method for detecting the initial lateral position of a tunneling ionized electron, comprising the following steps: 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; 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; 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 polarization direction of the molecule and the laser field is at a non-zero arrangement angle relative to the center position of the zero-order maximum fringe of the photoelectron holographic interference at a zero arrangement angle is obtained; Obtaining an initial transverse position of a tunneling ionized electron wave packet according to the transverse momentum offset; 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 polarization direction of the molecule and the laser field is at a non-zero arrangement angle relative to the center position of the zero-order maximum fringe of the photoelectron holographic interference at a zero arrangement angle is obtained, specifically: 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; 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; 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 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; 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: 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; 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; 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 of the first photoelectron transverse momentum distribution is obtained, specifically: 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; 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: 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. 2. The method for detecting the initial lateral position of the tunneling ionized electron according to claim 1 is characterized in that: in the first photoelectron holographic interference, the center position of the first photoelectron holographic interference zero-order maximum fringe where the polarization direction of the laser field and the arrangement direction of the molecules are zero angles is found, and in the second photoelectron holographic interference, the center position of the second photoelectron holographic interference zero-order maximum fringe where the polarization direction of the laser field and the arrangement direction of the molecules are non-zero angles is found, specifically: 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; 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. 3. The method for detecting the initial lateral position of the tunneling ionized electron according to claim 2, characterized in that: the first interference term is cos(ΔΦ ₁ ), wherein ΔΦ ₁ is the first interference phase, and the calculation method of ΔΦ ₁ is: ΔΦ ₁ =1/2[p _y -k _y (0)] ² (t _r -t ₀ )+α; The second interference term is cos(ΔΦ ₂ ), where ΔΦ ₂ is the second interference phase, and the calculation method of ΔΦ ₂ is:

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. 4. The method for detecting the initial lateral position of the tunneling ionized electron according to claim 2, characterized in that: 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; 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. 5. The method for detecting the initial lateral position of the tunneling ionized electron according to claim 3 is characterized in that: 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: 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:

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: 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:

6 . The method for detecting the initial transverse position of a tunneling ionized electron according to claim 5 , wherein the transverse momentum offset Δp _y = _ky (θ). 7. The method for detecting the initial transverse position of the tunneling ionized electron according to claim 6, characterized in that: the initial transverse position of the tunneling ionized electron wave packet is obtained according to the transverse momentum offset, specifically: 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

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