CN115220085B - Method for detecting initial transverse position of tunneling ionized electrons - Google Patents
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Abstract
The invention relates to a method for detecting the initial transverse position of tunneling ionized electrons, which comprises the steps of ionizing molecules by using a laser field to obtain a first photoelectron momentum spectrum with a zero angle between the polarization direction of the laser field and the arrangement direction of the molecules and a second photoelectron momentum spectrum with a non-zero angle; and obtaining a transverse momentum offset of the central position of the photoelectron holographic interference zero-order maximum stripe relative to the central position of the photoelectron holographic interference zero-order maximum stripe under the zero arrangement angle when the arrangement angle of the molecules and the polarization direction of the laser field is a non-zero angle according to the first photoelectron momentum spectrum and the second photoelectron momentum spectrum, and obtaining the initial transverse position of the tunneling ionization electron wave packet according to the transverse momentum offset. The method and the device realize the acquisition of the initial transverse position of the tunneling ionization electronic wave packet, and have the advantages of simpler acquisition method, more accurate obtained result and stronger feasibility and universality.
Description
Technical Field
The invention relates to the technical field of attosecond science and intense field physics, in particular to a method for detecting an initial transverse position of tunneling ionization electrons.
Background
The ultra-fast ultra-strong laser field is used for detecting and controlling the electron dynamics process of the attosecond magnitude in atoms and molecules, and is one of hot spot problems in the field of intense field physics. In the strong laser field, the atomic molecules are ionized, ionized electrons do acceleration motion in the laser field, wherein part of electrons directly reach the detector, and the other part of electrons are reversely collided and scattered with parent ions, so that a series of strong field ultrafast phenomena are caused. The accurate detection of the dynamics of the ionized electron wave packet is the basis for understanding and applying these strong field ultrafast phenomena. In particular, the photoelectric separation position of atoms and molecules, that is, the initial ionization position of ionized electrons, has attracted extensive attention from expert students at home and abroad. The concept of electron trajectories is often used to explain the different physical processes of laser interactions with atoms and molecules. In this concept, tunneling ionization is the first step in many strong field ultrafast phenomena in the field of attosecond science, and the initial position of an electron affects the subsequent kinetics of the electron. Thus, the precise initial position of the electrons is critical for the accurate understanding of the intense field ultrafast process based on the concept of electron trajectories. The initial position of the electron is an important parameter in the analysis of the intense field physics research. When the theoretical calculation result is compared with the experimental result, an inaccurate electronic initial position may lead to erroneous conclusions.
In general, the initial longitudinal position (parallel to the polarization direction of the laser field) of the ionized electrons can be determined using formula I p Evaluation of E (t), wherein I p Is the ionization potential of an atom or molecule and E (t) is the transient laser field. Recently, using the attosecond technique, one measured a more accurate electronic initial longitudinal position. For the initial lateral position of the electron, this value is always zero in the atom tunneling ionization. For molecules, the initial lateral position of the electron is shown to be related to molecular orbitals and alignment. In the prior research work, an attempt is made to introduce an initial phase of an electronic wave packet into a theoretical model, and compare the calculated asymmetric holographic interference with the experimentally obtained holographic interference to obtain the initial phase of the electronic wave packet, thereby extracting the initial transverse position of the electronic wave packet therefrom. Recently, it has been proposed to analyze p y > 0 and p y Holographic interference phase difference in < 0 momentum region to obtain initial transverse position (p) y Is the photoelectron end momentum perpendicular to the laser polarization direction). However, the above detection method has a certain difficulty in practical application, such as complicated detection steps. The first method is based on the known molecular structure, wherein the influence of coulomb potential on an electron wave packet is not negligible, which is unfavorable for people to accurately acquire any initial transverse position of molecular tunneling ionization. In the second method, |p, as the laser wavelength decreases y Holographic interference at larger locations is not clear (|p) y I is the magnitude of the final momentum of the photoelectrons perpendicular to the laser polarization direction), which is detrimental to the extraction of the holographic interference phase and the acquisition of the initial lateral position of the electron from that phase. Thus, accurate detection of the electronic initial lateral position is an important part of the attosecond scientific field and the intense field physical field, for which many research efforts have expanded and proposed many detection methods. However, more compact, electronic initial lateral position detection methods with higher accuracy have been explored.
In 2011, huisman et al pointed out that under the action of ultra-fast intense laser, photoelectron holographic interference can be generated by coherent interference between direct and scattered electron wave packets generated by atom and molecule tunneling ionization. The photoelectron interference principle is very similar to that of holographic imaging in optics, a scattered electron wave packet is used as a signal wave, a direct electron wave packet is used as a reference wave, and the strong field photoelectron holographic interference has the potential of detecting atomic and molecular structure information and electron dynamics information. This is now confirmed by many theoretical and experimental studies. However, how to accurately acquire the initial lateral position of ionized electrons using the high field photoelectron holographic technique remains a challenging task.
Disclosure of Invention
Therefore, the technical problem to be solved by the invention is to overcome the defects in the prior art, and provide the method for detecting the initial transverse position of the tunneling ionization electron wave packet, which can achieve the acquisition of the initial transverse position of the tunneling ionization electron wave packet, and has the advantages of simpler acquisition method, more accurate obtained result and stronger feasibility and universality.
In order to solve the technical problems, the invention provides a method for detecting the initial transverse position of tunneling ionized electrons, which comprises the following steps:
ionizing molecules by using a laser field, enabling the polarization direction of the laser field to form a zero angle with the arrangement direction of the molecules, and obtaining a first photoelectron momentum spectrum when the molecules are ionized;
re-ionizing the molecules by using the laser field to enable the polarization direction of the laser field to form a non-zero angle with the arrangement direction of the molecules, and obtaining a second photoelectron momentum spectrum when the molecules are ionized;
according to the first photoelectron momentum spectrum and the second photoelectron momentum spectrum, obtaining a transverse momentum offset of the central position of the photoelectron holographic interference zero-order maximum stripe relative to the central position of the photoelectron holographic interference zero-order maximum stripe under the zero arrangement angle when the arrangement angle of the molecules and the polarization direction of the laser field is a non-zero angle;
And obtaining the initial transverse position of the tunneling ionization electron wave packet according to the transverse momentum offset.
Preferably, according to the first photoelectron momentum spectrum and the second photoelectron momentum spectrum, a lateral momentum offset of a central position of the photoelectron holographic interference zero-order maximum stripe when the arrangement angle of the molecules and the polarization direction of the laser field is a non-zero angle is obtained, and the lateral momentum offset is specifically:
obtaining first photoelectron holographic interference when the polarization direction of the laser field and the molecular arrangement direction form a zero angle according to the first photoelectron momentum spectrum, and obtaining second photoelectron holographic interference when the polarization direction of the laser field and the molecular arrangement direction form a non-zero angle according to the second photoelectron momentum spectrum;
finding a first photoelectron holographic interference zero-order maximum stripe center position with a zero angle between the polarization direction of the laser field and the arrangement direction of the molecules in the first photoelectron holographic interference, and finding a second photoelectron holographic interference zero-order maximum stripe center position with a non-zero angle between the polarization direction of the laser field and the arrangement direction of the molecules in the second photoelectron holographic interference;
And the central position of the second photoelectron holographic interference zero-order maximum stripe is differed from the central position of the first photoelectron holographic interference zero-order maximum stripe, so that the transverse momentum offset of the central position of the photoelectron holographic interference zero-order maximum stripe relative to the central position of the photoelectron holographic interference zero-order maximum stripe under the zero arrangement angle when the arrangement angle of the molecules and the polarization direction of the laser field is a non-zero angle is obtained.
Preferably, the first photoelectron holographic interference when the polarization direction of the laser field and the molecular arrangement direction form 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 form a non-zero angle is obtained according to the second photoelectron momentum spectrum, specifically:
uniform extraction of non-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 photoelectrons obtains a first photoelectron transverse momentum distribution, and the first photoelectron transverse momentum distribution is used as the first photoelectron holographic interference;
uniform extraction of non-linear momentum parallel to the polarization direction of the laser field within the target momentum range of the second photoelectron momentum spectrum 
And obtaining a second photoelectron transverse momentum distribution according to the photoelectron yield corresponding to photoelectrons, and taking the second photoelectron transverse momentum distribution as the second photoelectron holographic interference. />
Preferably, the first photoelectron momentum spectrum has a final momentum in a direction parallel to the polarization direction of the laser field and is uniformly extracted in a target momentum range of the first photoelectron momentum spectrum
The first photoelectron transverse momentum distribution is obtained by photoelectron corresponding photoelectron yield, which is specifically as follows:
setting a square momentum area in a target momentum range of the first photoelectron momentum spectrum, wherein the momentum length of the square momentum area in a direction perpendicular to the polarization direction of the laser field is δp y Momentum length delta p in parallel to polarization direction of laser field x The method comprises the steps of carrying out a first treatment on the surface of the Uniformly extracting the non-momentum parallel to the polarization direction of the laser field in the square momentum region
And having an end momentum perpendicular to the polarization direction of the laser>
Photo-electron yield corresponding to photoelectrons, extracting all the extracted photoelectrons with the final momentum in the square momentum region>
Average value of photoelectron yields corresponding to photoelectrons as having a final momentum +.>
Photo-electron yield corresponding to photoelectrons, extracting all the extracted photoelectrons with the final momentum in the square momentum region >
Average value of photoelectron yields corresponding to photoelectrons as having a final momentum +.>
Photoelectron yield corresponding to photoelectrons; each of the target momentum ranges having a final momentum +.>
As the first photoelectron lateral momentum distribution;
uniform extraction of non-linear momentum parallel to the polarization direction of the laser field within the target momentum range of the second photoelectron momentum spectrum
The photoelectron corresponding photoelectron yield to obtain a second photoelectron transverse momentum distribution, which is specifically as follows:
setting a square momentum area in a target momentum range of the second photoelectron momentum spectrum, wherein the momentum length of the square momentum area in a direction perpendicular to the polarization direction of the laser field is δp y Momentum length delta p in parallel to polarization direction of laser field x The method comprises the steps of carrying out a first treatment on the surface of the Uniformly extracting the non-momentum parallel to the polarization direction of the laser field in the square momentum region
And having an end momentum perpendicular to the polarization direction of the laser>
Photo-electron yield corresponding to photoelectrons, extracting all the extracted photoelectrons with the final momentum in the square momentum region>
Average value of photoelectron yields corresponding to photoelectrons as having a final momentum +. >
Photo-electron yield corresponding to photoelectrons, extracting all the extracted photoelectrons with the final momentum in the square momentum region>
Average value of photoelectron yields corresponding to photoelectrons as having a final momentum +.>
Photoelectron yield corresponding to photoelectrons; each of the target momentum ranges having a final momentum +.>
As said second photoelectron lateral momentum distribution.
Preferably, a first photoelectron holographic interference zero-order maximum stripe center position where 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 a second photoelectron holographic interference zero-order maximum stripe center position where 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 item of the first photoelectron holographic interference, acquiring the central position of each level of fringes of the first photoelectron holographic interference according to the first interference item, and acquiring the central position of the zero-level maximum fringes of the first photoelectron holographic interference according to the central position of each level of fringes of the first photoelectron holographic interference;
Extracting a second interference term of the second photoelectron holographic interference, obtaining the central position of each level of fringes of the second photoelectron holographic interference according to the second interference term, and obtaining the central position of the zero-level maximum fringes of the second photoelectron holographic interference according to the central position of each level of fringes of the second photoelectron holographic interference.
Preferably, the first interference term is cos (ΔΦ 1 ) Wherein ΔΦ 1 For the first interference phase, ΔΦ 1 The calculation method of (1) is as follows:
ΔΦ 1 ＝1/2[p y -k y (0)] 2 (t r -t 0 )+α；
the second interference term is cos (delta phi) 2 ) Wherein ΔΦ 2 For the second interference phase, ΔΦ 2 The calculation method of (1) is as follows:
ΔΦ 2 ＝1/2[p y -k y (θ)] 2 (t r -t 0 )+α；
wherein p is y Is the photoelectron final momentum perpendicular to the polarization direction of the laser field, t r To scatter the electron scattering time, t 0 For the ionization time of scattered electrons, α is the scattering amplitude phase of the molecule; k (k) y Is the regular momentum, k, of scattered electrons y (0) For the regular momentum of tunneling ionization scattered electrons when the polarization direction of the laser field and the molecular arrangement direction form a zero angle, θ is the included angle between the polarization direction of the laser field and the molecular arrangement direction, k y And (theta) is the regular momentum of tunneling ionized scattered electrons when the included angle between the polarization direction of the laser field and the molecular arrangement direction is theta.
Preferably, when extracting a first interference term of the first photoelectron holographic interference, polynomial fitting is performed on the photoelectron yield in the first photoelectron holographic interference by using an exponential function, the photoelectron yield in the first photoelectron holographic interference is divided by a polynomial obtained by fitting, and the obtained result is used as the first interference term;
And when a second interference term of the second photoelectron holographic interference is extracted, polynomial fitting is carried out on the photoelectron yield in the second photoelectron holographic interference by using an exponential function, the photoelectron yield in the second photoelectron holographic interference is divided by a polynomial obtained by fitting, and the obtained result is used as the second interference term.
Preferably, the central position of each first photoelectron holographic interference level stripe is obtained according to the first interference item, and the central position of the first photoelectron holographic interference zero-level maximum stripe is obtained according to the central position of each first photoelectron holographic interference level stripe, specifically:
establishing the central position of each stage of fringes of the first photoelectron holographic interference
Wherein ΔΦ 1 N pi, n=0, ±1, ±2, ±3..; when n=0, ΔΦ 1 When the value of the first photoelectron holographic interference zero-order maximum stripe is=0, the central position of the first photoelectron holographic interference zero-order maximum stripe is obtained>
The central position of each level of second photoelectron holographic interference fringes is obtained according to the second interference item, and the central position of the second photoelectron holographic interference zero-level maximum fringes is obtained according to the central position of each level of second photoelectron holographic interference fringes, specifically:
establishing the center position of the second photoelectron holographic interference zero-level maximum stripe 
Wherein ΔΦ 2 N pi, n=0, ±1, ±2, ±3..; when n=0, ΔΦ 2 Obtaining the central position of the second photoelectron holographic interference zero-order maximum stripe when the number of the second photoelectron holographic interference zero-order maximum stripes is =0>
Preferably, the lateral momentum offset Δp y ＝k y (θ)。
Preferably, the initial lateral position of the tunneling ionization electron wave packet is obtained according to the lateral momentum offset, specifically:
establishing an initial lateral position R of ionized electrons b And k is equal to y Relation of (θ): k (k) y (θ)＝±R b /(t r -t 0 ) Bind Δp y ＝k y (θ) to obtain the initial lateral position of the ionized electrons
Compared with the prior art, the technical scheme of the invention has the following advantages:
according to the invention, when the molecular arrangement angle is a non-zero angle, the initial transverse position of the tunneling ionization electron wave packet is obtained by analyzing the transverse momentum offset of the central position of the photoelectron holographic interference zero-order maximum stripe relative to the central position of the holographic interference zero-order maximum stripe under the zero arrangement angle in the direction perpendicular to the polarization direction of the laser field, the obtaining method is simpler, the obtained result is more accurate, and the feasibility and universality of the invention are stronger.
Drawings
In order that the invention may be more readily understood, a more particular description of the invention will be rendered by reference to specific embodiments thereof that are illustrated in the appended drawings, in which
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a schematic diagram of the formation of photoelectron holographic interference obtained when the polarization direction of the laser field and the arrangement direction of hydrogen molecules are 0 degrees and 45 degrees in the embodiment of the invention;
FIG. 3 is an image of holographic interference fringes extracted from the photoelectron momentum spectrum of FIG. 2 in an embodiment of the present invention;
FIG. 4 is a diagram of a detection process of an initial lateral position of tunneling ionized electrons in an embodiment of the present invention;
FIG. 5 is a photoelectron momentum spectrum of nitrogen molecular tunneling ionization in an embodiment of the present invention;
fig. 6 is a diagram of a detection process of an initial lateral position of a nitrogen molecular tunneling ionization electron in an embodiment of the present invention.
Detailed Description
The present invention will be further described with reference to the accompanying drawings and specific examples, which are not intended to be limiting, so that those skilled in the art will better understand the invention and practice it. The terms "first," "second," and the like, are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated.
Under the action of ultra-fast super-strong laser, molecules are ionized, ionized electrons do accelerated motion in a laser field, and part of electrons return and collide with the geometric center of parent ions for scattering. The scattered electron wave packet interferes with the direct electron wave packet that does not interact with the parent ion, and this interference structure contains information of the parent ion and the laser field, similar to the principle of holographic interference in optics, known as intense field photoelectron holographic interference.
As shown in the flowchart of fig. 1, a method for detecting the initial lateral position of tunneling ionized electrons is disclosed, which comprises the following steps:
s1: ionizing molecules by using a laser field, enabling the polarization direction of the laser field to form a zero angle with the arrangement direction of the molecules, and obtaining a first photoelectron momentum spectrum when the molecules are ionized; electrons are separated from the constraint of the parent nucleus through tunneling ionization during molecular ionization, and the photoelectron momentum spectrum can be measured by using a detector and is two-dimensional.
S2: and re-ionizing the molecules by using the laser field, so that the polarization direction of the laser field and the arrangement direction of the molecules 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, molecules can be arranged in a cold target recoil particle momentum imaging spectrometer (Cold Target Recoil-ion Momentum Spectroscopy, COLTRIMS) or a particle velocity imager (Velocity Map Imagery, VMI), and then a beam of laser pulse with a polarization direction forming a zero angle and a non-zero angle with the molecular arrangement direction is used for acting on the molecules, so that a first photoelectron momentum spectrum and a second photoelectron momentum spectrum are obtained.
S3: and obtaining the transverse momentum offset of the central position of the photoelectron holographic interference zero-order maximum stripe relative to the central position of the photoelectron holographic interference zero-order maximum stripe under the zero arrangement angle when the arrangement angle of the molecules and the polarization direction of the laser field is a non-zero angle according to the first photoelectron momentum spectrum and the second photoelectron momentum spectrum.
S3.1: and obtaining first photoelectron holographic interference when the polarization direction of the laser field and the molecular arrangement direction form a zero angle according to the first photoelectron momentum spectrum, and obtaining second photoelectron holographic interference when the polarization direction of the laser field and the molecular arrangement direction form a non-zero angle according to the second photoelectron momentum spectrum.
S3.1.1: uniform extraction of non-momentum parallel to the polarization direction of the laser field within the target momentum range of the first photoelectron momentum spectrum
The photoelectron corresponding photoelectron yield of the second photoelectron momentum spectrum is used for obtaining a first photoelectron transverse momentum distribution, and the final momentum in the polarization direction parallel to the laser field is uniformly extracted in the target momentum range of the second photoelectron momentum spectrum
The photoelectron yield corresponding to photoelectrons to obtain a second photoelectron transverse momentum distribution. The target momentum p in the present embodiment x In the range of 0.75 atomic units to 1.45 atomic units. And the value is taken in the target momentum range, so that clear holographic interference fringes can be obtained from the photoelectron momentum spectrum.
S3.1.1.1: setting a square momentum area in a target momentum range of the first photoelectron momentum spectrum, wherein the momentum length of the square momentum area in a direction perpendicular to the polarization direction of the laser field is δp y Momentum length delta p in parallel to polarization direction of laser field x The method comprises the steps of carrying out a first treatment on the surface of the Setting a square momentum area in a target momentum range of the second photoelectron momentum spectrum, wherein the momentum length of the square momentum area in a direction perpendicular to the polarization direction of the laser field is δp y Momentum length delta p in parallel to polarization direction of laser field x . δp in this embodiment y Value 0 atomic unit, δp x The value of 0.02 atomic unit can reduce the influence of an interference structure in the photoelectron momentum spectrum by setting a square momentum region, and clear photoelectron holographic interference is obtained.
S3.1.1.2: uniformly extracting the non-momentum parallel to the polarization direction of the laser field in the square momentum region
And having an end momentum perpendicular to the polarization direction of the laser>
Photo-electron yield corresponding to photoelectrons, extracting all the extracted photoelectrons with the final momentum in the square momentum region >
Average value of photoelectron yields corresponding to photoelectrons as having a final momentum
Photo-electron yield corresponding to photoelectrons, extracting all the extracted photoelectrons with the final momentum in the square momentum region>
Average value of photoelectron yields corresponding to photoelectrons as having a final momentum +.>
Photoelectron yield corresponding to photoelectrons;
uniformly extracting the non-momentum parallel to the polarization direction of the laser field in the square momentum region
And having an end momentum perpendicular to the polarization direction of the laser>
Photoelectron yield corresponding to photoelectrons, and the square momentum regionAll extracted have a final momentum +.>
Average value of photoelectron yields corresponding to photoelectrons as having a final momentum +.>
Photo-electron yield corresponding to photoelectrons, extracting all the extracted photoelectrons with the final momentum in the square momentum region>
Average value of photoelectron yields corresponding to photoelectrons as having a final momentum +.>
Photoelectron yield corresponding to photoelectrons of (c).
S3.1.1.3: each of the final momentums obtained by uniformly taking values in the target momentum range
Taking the photoelectron yield corresponding to photoelectrons as the first photoelectron transverse momentum distribution, and uniformly taking values in the target momentum range to obtain each photoelectron yield with the final momentum +. >
As said second photoelectron lateral momentum distribution.
S3.1.2: the first photoelectron lateral momentum distribution is used as the first photoelectron holographic interference, and the second photoelectron lateral momentum distribution is used as the second photoelectron holographic interference.
S3.2: finding the center position of a first photoelectron holographic interference zero-order maximum stripe, wherein 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 finding the center position of a second photoelectron holographic interference zero-order maximum stripe, wherein 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.
S3.2.1: extracting a first interference term of the first photoelectron holographic interference and extracting a second interference term of the second photoelectron holographic interference. The method comprises the following steps: performing polynomial fitting on the photoelectric yield in the first photoelectric holographic interference by using an exponential function, dividing the photoelectric yield in the first photoelectric holographic interference by a polynomial obtained by fitting, and taking the result obtained by dividing the polynomial as a first interference term; and when the second interference term of the second photoelectron holographic interference is extracted, polynomial fitting is carried out on the photoelectron yield in the second photoelectron holographic interference by using an exponential function, the photoelectron yield in the second photoelectron holographic interference is divided by a polynomial obtained by fitting, and the obtained result is taken as the second interference term. Fitting the photoelectron yield using an exponential function can eliminate the envelope function of the photoelectron momentum distribution.
The first interference term is cos (delta phi) 1 ) Wherein ΔΦ 1 For the first interference phase, ΔΦ 1 The calculation method of (1) is as follows:
ΔΦ 1 ＝1/2[p y -k y (0)] 2 (t r -t 0 )+α；
the second interference term is cos (delta phi) 2 ) Wherein ΔΦ 2 For the second interference phase, ΔΦ 2 The calculation method of (1) is as follows:
ΔΦ 2 ＝1/2[p y -k y (θ)] 2 (t r -t 0 )+α；
wherein p is y Is the photoelectron final momentum perpendicular to the polarization direction of the laser field, t r To scatter the electron scattering time, t 0 For the ionization time of scattered electrons, α is the scattering amplitude phase of the molecule; k (k) y Is the regular momentum, k, of scattered electrons y (0) For the regular momentum of tunneling ionization scattered electrons when the polarization direction of the laser field and the molecular arrangement direction form a zero angle, θ is the included angle between the polarization direction of the laser field and the molecular arrangement direction, k y (θ) is the tunneling ionization scattering electron when the angle between the polarization direction of the laser field and the direction of molecular alignment is θThe regular momentum. The first photoelectron holographic interference and the second photoelectron holographic interference meet an 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 Ionization amplitude for direct electron wave packet, I r Ionization amplitude of near forward scattering electron wave packet, ΔΦ is ΔΦ 1 Or DeltaPhi 2 The phase difference (interference phase) between the direct electron wave packet and the near-forward scattered electron wave packet is represented, and the magnitude of the different physical quantities is represented.
S3.2.2: acquiring the central position of each level of first photoelectron holographic interference fringes according to the first interference item, and acquiring the central position of the first photoelectron holographic interference zero-level maximum fringes according to the central position of each level of first photoelectron holographic interference fringes; and acquiring the central position of each level of second photoelectron holographic interference fringes according to the second interference term, and acquiring the central position of the second photoelectron holographic interference zero-level maximum fringes according to the central position of each level of second photoelectron holographic interference fringes. The method comprises the following steps:
for any momentum p parallel to the polarization direction of the laser field x Establishing the central position of each stage of fringes of the first photoelectron holographic interference
Wherein ΔΦ 1 N pi, n=0, ±1, ±2, ±3..; when n=0, ΔΦ 1 Obtaining the center position of the first photoelectron holographic interference zero-order maximum stripe when the number of the first photoelectron holographic interference zero-order maximum stripes is=0
For any momentum p parallel to the polarization direction of the laser field x Establishing the center position of the second photoelectron holographic interference zero-order maximum stripe
Wherein ΔΦ 2 N pi, n=0, ±1, ±2, ±3..; when n=0, ΔΦ 2 Obtained when=0The center position of the second photoelectron holographic interference zero-order maximum stripe
Zero-order maximum representation of holographic interference for arbitrary p x At p y In the momentum region around =0, the maximum of the holographic interference fringe.
S3.3: the central position of the second photoelectron holographic interference zero-order maximum stripe is differenced from the central position of the first photoelectron holographic interference zero-order maximum stripe, and the transverse momentum offset delta p of the central position of the photoelectron holographic interference zero-order maximum stripe relative to the central position of the photoelectron holographic interference zero-order maximum stripe under the zero arrangement angle when the arrangement angle of the polarization direction of the molecules and the laser field is a non-zero angle is obtained y ＝k y (θ)。
Lateral momentum offset
Where there is k y (0) =0, since for the first photoelectron holographic interference, experimental and theoretical research results show that the holographic interference zero-order maximum fringe center position
Always zero (as can also be seen from fig. 2 (e) and 5 (a)), there is k y (0) =0, thereby obtaining Δp y ＝k y (θ). The formula shows that the change of the actual holographic interference zero-order maximum stripe along with the molecular arrangement angle is consistent with the result of a quantum track method without considering scattering amplitude, and the results are k y (θ). Scattering time t of scattered electrons r And ionization time t 0 The real part does not change with the nuclear spacing and alignment angle of the molecules, and therefore Δp y Is a real number.
S4: and obtaining the initial transverse position of the tunneling ionization electron wave packet according to the transverse momentum offset.
Establishing an initial lateral position R of ionized electrons b And k is equal to y (θ)Is defined by the relation: k (k) y (θ)＝±R b /(t r -t 0 ) Bind Δp y ＝k y (θ) to obtain the initial lateral position of the ionized electrons
In order that the invention may be more readily understood, a detailed description of the invention will be rendered by reference to specific embodiments that are illustrated in the appended drawings.
The present invention will be described in further detail with reference to the accompanying drawings and examples.
Example one: the hydrogen molecular ions are ionized by using a trapezoid-enveloping multicycle linear polarized laser field, and the initial position of tunneling ionized electrons in the direction perpendicular to the polarization direction of the laser field is detected by using an photoelectroholographic interference technology. The laser field wavelength used was 1000nm and the intensity was 2.5X10 14 W/cm 2 。
As shown in FIG. 2, the principle diagram of the photoelectron holographic interference is obtained when the polarization direction of the laser field and the arrangement direction of hydrogen molecules are 0 degrees and 45 degrees in the embodiment. Wherein fig. 2 (a) shows the electric field of the laser pulse and the corresponding sagittal/laser frequency, the horizontal axis shows the ionization time of the electrons, and the vertical axis shows the electric field and sagittal/laser frequency of the electrons in the ionization instant laser pulse. The black solid line is the change of the electric field along with time, the black dotted line is the sagittal potential/laser frequency change along with time, the gray part represents the generation time of the electron wave packet forming photoelectron holographic interference, and the two arrows respectively represent the forward scattering electron wave packet and the direct electron wave packet; fig. 2 (b) is a schematic diagram of photoelectron holographic interference, electrons are ionized from one side of a molecule under the action of a laser field, an electron wave packet is generated, a part of the electron wave packet is accelerated under the action of the laser field, and the electron wave packet returns to the geometrical center of the parent ion and the molecule to collide and scatter, such as a scattered electron wave packet shown by a solid line with an arrow. The other part of the ionized electron wave packet directly reaches the detector without interaction with the parent nucleus, and forms a direct electron wave packet with an arrow dotted line. The two electron wave packets are coherent in photoelectron momentum spectrum to form photoelectron holographic interference; FIG. 2 (c) shows the polarization direction of the laser field and the molecular alignment Fig. 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; FIG. 2 (e) shows the holographic interference in the actual photoelectron momentum spectrum when the arrangement angles of the molecules are 0℃respectively, and FIG. 2 (f) shows the holographic interference in the actual photoelectron momentum spectrum when the arrangement angles of the molecules are 45℃respectively; the black dashed lines in fig. 2 (d) and 2 (f) represent the holographic interference zero-order maximum fringe center positions. As can be seen from fig. 2 (c) and fig. 2 (d), there is a fork-shaped interference structure in the photoelectron momentum distribution parallel to the polarization direction of the laser field, so that setting a square momentum region eliminates other interference structures in the photoelectron momentum spectrum, and a single photoelectron holographic interference structure can be obtained. Selecting a momentum range (0.7 to 1.5 atomic units) which is clear and stable in structure and is parallel to the polarization direction of laser from the images (e) and (f) in fig. 2, uniformly taking values, obtaining the corresponding momentum distribution perpendicular to the polarization direction of the laser field for each value, and recording the transverse offset delta p of the central position of the corresponding holographic interference zero-order maximum stripe when the molecular arrangement angle is 45 DEG relative to the central position of the holographic interference zero-order maximum stripe when the molecular arrangement angle is 0 DEG y 。
Shown in fig. 3 is a holographic interference fringe extracted from the photoelectron momentum spectrum shown in fig. 2. FIG. 3 (a) shows the holographic interference extracted from the photoelectromotive energy spectrum at an arbitrary momentum p x The photoelectron momentum distribution along the direction perpendicular to the polarization direction of the laser field, wherein the solid line and the dotted line respectively represent the results of the 45 DEG arrangement angle and the 0 DEG arrangement angle of molecules; FIG. 3 (b) is an interference term cos (ΔΦ) of the holographic structure extracted from the momentum spectrum shown in FIG. 3 (a); the abscissa of fig. 3 (a) and 3 (b) is the photoelectron end momentum in the direction perpendicular to the polarization direction of the laser field, and the ordinate is the photoelectron yield. At molecular arrangement angles of 45 deg. and 0 deg., momentum p parallel to the polarization direction of laser field x =1.4 and p x For example, the offset Δp is extracted with 1.0 atomic unit y . FIGS. 3 (a) and 3 (b) are the momentum p in the polarization direction of the laser field x =1.4 and p x Photoelectron momentum distribution curve perpendicular to the polarization direction of laser at 1.0 atomic unit. Fitting the photoelectron output by using an exponential function, eliminating the envelope of photoelectron momentum distribution,the holographic structural interference term cos (ΔΦ) is obtained as shown in fig. 3 (c) and 3 (d). From fig. 3 (c) and 3 (d), it can be seen that the interference term cos (ΔΦ) oscillates with the change in the photoelectron end momentum perpendicular to the laser polarization direction. Momentum p in a direction perpendicular to the polarization of the laser field y Near=0, the photoelectron final momentum in the direction perpendicular to the laser polarization direction corresponding to the cos (ΔΦ) oscillation maximum is the center position of the photoelectron holographic interference zero-order maximum stripe.
Fig. 4 shows the detection process of the initial lateral position of the tunneling ionized electrons in the present embodiment. FIG. 4 (a) is a graph showing the lateral momentum shift Δp of the center position of the zero-order maximum fringes of the photoelectron holographic interference at a molecular alignment angle of 45℃extracted from the interference term cos (. DELTA.phi.) shown in FIG. 3, relative to the center position of the zero-order maximum fringes of the holographic interference at an alignment angle of 0 ° y It can be seen that Δp y As the momentum in the polarization direction of the laser field changes; FIG. 4 (b) is a graph based on the formula Δp y ＝±R b /(t r -t 0 ) The initial transverse position R of the tunneling ionization electron is finally obtained b . Fig. 4 (c) shows the evolution of the electron wave function over time, wherein the abscissa is the evolution time and the ordinate is the electron position perpendicular to the polarization direction of the laser. Wherein the black dashed line represents the electron position perpendicular to the polarization direction of the laser field corresponding to the maximum value of the electron wave function. Δp y Is the laser field polarization direction momentum p x Is a function of (2). Prediction formula according to quantum trajectory model
By analysis of Δp y The initial lateral position of the hydrogen molecular ion tunneling ionization electron can be detected from the holographic interference offset, and the initial lateral position is 1.46 atomic units, as shown in fig. 4 (b). In quantum mechanics, the most probable density of electron wave packets in the direction perpendicular to the polarization of the laser field characterizes the lateral position of the tunneling ionized electrons. The initial lateral position of the tunneling ionized electrons 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 direction of the laser field, as shown in fig. 4 (c). The ordinate corresponding to the brightest color position in FIG. 4 (c) is The electron wave packet at the most probable density position perpendicular to the polarization direction of the laser field, marked with a black dashed line, has a size of 1.44 atomic units, which is substantially consistent with 1.46 atomic units obtained using the method of the present invention, confirming the accuracy and feasibility of the present invention.
Example two: the nitrogen molecules are ionized by using a trapezoid-enveloping multicycle linear polarized laser field, and the initial position of tunneling ionized electrons perpendicular to the polarization direction of the laser is detected by using an photoelectroholographic interference technology. The laser field wavelength used was 1000nm and the intensity was 2.5X10 14 W/cm 2 。
Fig. 5 shows the photoelectron momentum spectrum of another molecular (nitrogen molecule) tunneling ionization in the present embodiment, fig. 5 (a) shows the photoelectron momentum spectrum when the polarization direction of the laser field is 0 ° to the molecular arrangement direction, and fig. 5 (b) shows the photoelectron momentum spectrum when the polarization direction of the laser field is 0 ° to the molecular arrangement direction. The black dashed line in fig. 5 (b) represents the holographic interference zero-order maximum fringe center position.
Fig. 6 shows the detection result of the initial lateral position of another molecule (nitrogen molecule) tunneling ionized electrons in the present embodiment. FIG. 6 (a) shows the lateral offset Δp of the center position of the corresponding zero-order maximum fringe of holographic interference at an extracted molecular alignment angle of 45℃relative to the center position of the zero-order maximum fringe of holographic interference at a molecular alignment angle of 0 ° y . Prediction formula using quantum trajectory model
Offset Δp from photoelectron holographic interference y Obtain the initial transverse position R of nitrogen molecular tunneling ionization electron b As shown in FIG. 6 (b), the result was 1.6 atomic units. The black dashed line in fig. 6 (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 electron wave packets in the direction perpendicular to the polarization of the laser field characterizes the lateral position of the tunneling ionized electrons. The transverse position of the tunneling ionized electrons measured by the scheme of the invention is consistent with the most probable density position of the electron wave packet in the direction perpendicular to the polarization direction of the laser field. As shown in FIG. 6 (c), the brightest color of the pair of FIG. 6The vertical axis of the electron wave packet is the most probable density position perpendicular to the polarization direction of the laser field, and is marked by a black dotted line, and the size of the electron wave packet is 1.58 atomic units, which is basically consistent with 1.6 atomic units obtained by using the method of the invention, and the accuracy and feasibility of the invention are also verified.
According to the invention, when the molecular arrangement angle is a non-zero angle, the initial transverse position of the tunneling ionization electron wave packet is obtained by analyzing the transverse momentum offset of the central position of the photoelectron holographic interference zero-order maximum stripe relative to the central position of the holographic interference zero-order maximum stripe under the zero arrangement angle in the direction perpendicular to the polarization direction of the laser field. Compared with other tunneling ionization electron initial transverse position detection methods in ultrafast and strong field physics, the method for detecting the initial transverse position of the tunneling ionization electron is simpler, the obtained result is more accurate, the feasibility and universality of the method are stronger, and therefore the method is beneficial to deeper and more detailed research in the ultrafast and strong field physics field.
It will be appreciated by those skilled in the art that embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
It is apparent that the above examples are given by way of illustration only and are not limiting of the embodiments. Other variations and modifications of the present invention will be apparent to those of ordinary skill in the art in light of the foregoing description. It is not necessary here nor is it exhaustive of all embodiments. And obvious variations or modifications thereof are contemplated as falling within the scope of the present invention.
Claims (7)
1. A method of detecting an initial lateral position of tunneling ionized electrons, comprising the steps of:
ionizing molecules by using a laser field, enabling the polarization direction of the laser field to form a zero angle with the arrangement direction of the molecules, and obtaining a first photoelectron momentum spectrum when the molecules are ionized;
re-ionizing the molecules by using the laser field to enable the polarization direction of the laser field to form a non-zero angle with the arrangement direction of the molecules, and obtaining a second photoelectron momentum spectrum when the molecules are ionized;
according to the first photoelectron momentum spectrum and the second photoelectron momentum spectrum, obtaining a transverse momentum offset of the central position of the photoelectron holographic interference zero-order maximum stripe relative to the central position of the photoelectron holographic interference zero-order maximum stripe under the zero arrangement angle when the polarization directions of the molecules and the laser field are non-zero arrangement angles;
obtaining an initial transverse position of the tunneling ionization electron wave packet according to the transverse momentum offset;
according to the first photoelectron momentum spectrum and the second photoelectron momentum spectrum, obtaining a transverse momentum offset of the center position of the photoelectron holographic interference zero-order maximum stripe relative to the center position of the photoelectron holographic interference zero-order maximum stripe under the zero arrangement angle when the polarization directions of the molecules and the laser field are non-zero arrangement angles, specifically:
Obtaining first photoelectron holographic interference when the polarization direction of the laser field and the molecular arrangement direction form a zero angle according to the first photoelectron momentum spectrum, and obtaining second photoelectron holographic interference when the polarization direction of the laser field and the molecular arrangement direction form a non-zero angle according to the second photoelectron momentum spectrum;
finding a first photoelectron holographic interference zero-order maximum stripe center position with a zero angle between the polarization direction of the laser field and the arrangement direction of the molecules in the first photoelectron holographic interference, and finding a second photoelectron holographic interference zero-order maximum stripe center position with a non-zero angle between the polarization direction of the laser field and the arrangement direction of the molecules in the second photoelectron holographic interference;
the central position of the second photoelectron holographic interference zero-order maximum stripe is differed from the central position of the first photoelectron holographic interference zero-order maximum stripe, and the transverse momentum offset of the central position of the photoelectron holographic interference zero-order maximum stripe relative to the central position of the photoelectron holographic interference zero-order maximum stripe under the zero arrangement angle when the arrangement angle of the molecules and the polarization direction of the laser field is a non-zero angle is obtained;
According to the first photoelectron momentum spectrum, obtaining first photoelectron holographic interference 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, obtaining second photoelectron holographic interference when the polarization direction of the laser field and the molecular arrangement direction form a non-zero angle, specifically:
uniform extraction of non-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 photoelectrons obtains a first photoelectron transverse momentum distribution, and the first photoelectron transverse momentum distribution is used as the first photoelectron holographic interference;
uniform extraction of non-linear momentum parallel to the polarization direction of the laser field within the target momentum range of the second photoelectron momentum spectrum
Obtaining a second photoelectron transverse momentum distribution according to the photoelectron yield corresponding to photoelectrons, and taking the second photoelectron transverse momentum distribution as the second photoelectron holographic interference;
uniform extraction of non-momentum parallel to the polarization direction of the laser field within the target momentum range of the first photoelectron momentum spectrum
The first photoelectron transverse momentum distribution is obtained by photoelectron corresponding photoelectron yield, which is specifically as follows:
Setting a square momentum area in a target momentum range of the first photoelectron momentum spectrum, wherein the momentum length of the square momentum area in a direction perpendicular to the polarization direction of the laser field is δp y Momentum length delta p in parallel to polarization direction of laser field x The method comprises the steps of carrying out a first treatment on the surface of the Uniformly extracting the non-momentum parallel to the polarization direction of the laser field in the square momentum region
And having an end momentum perpendicular to the polarization direction of the laser>
Photo-electron yield corresponding to photoelectrons, extracting all the extracted photoelectrons with the final momentum in the square momentum region>
Average value of photoelectron yields corresponding to photoelectrons as having a final momentum +.>
Photo-electron yield corresponding to photoelectrons, extracting all the extracted photoelectrons with the final momentum in the square momentum region>
Average value of photoelectron yields corresponding to photoelectrons as having a final momentum +.>
Photoelectron yield corresponding to photoelectrons; each of the target momentum ranges having a final momentum +.>
As the first photoelectron lateral momentum distribution;
uniform extraction of non-linear momentum parallel to the polarization direction of the laser field within the target momentum range of the second photoelectron momentum spectrum 
The photoelectron corresponding photoelectron yield to obtain a second photoelectron transverse momentum distribution, which is specifically as follows:
setting a square momentum area in a target momentum range of the second photoelectron momentum spectrum, wherein the momentum length of the square momentum area in a direction perpendicular to the polarization direction of the laser field is δp y Momentum length delta p in parallel to polarization direction of laser field x The method comprises the steps of carrying out a first treatment on the surface of the Uniformly lifting in the square momentum areaTaking a final momentum parallel to the polarization direction of the laser field
And having an end momentum perpendicular to the polarization direction of the laser>
Photo-electron yield corresponding to photoelectrons, extracting all the extracted photoelectrons with the final momentum in the square momentum region>
Average value of photoelectron yields corresponding to photoelectrons as having a final momentum +.>
Photo-electron yield corresponding to photoelectrons, extracting all the extracted photoelectrons with the final momentum in the square momentum region>
Average value of photoelectron yields corresponding to photoelectrons as having a final momentum +.>
Photoelectron yield corresponding to photoelectrons; each of the target momentum ranges having a final momentum +.>
As said second photoelectron lateral momentum distribution.
2. The method of detecting an initial lateral position of a tunneling ionized electron of claim 1, wherein: finding a first photoelectron holographic interference zero-order maximum stripe center position with a zero angle between the polarization direction of the laser field and the arrangement direction of the molecules in the first photoelectron holographic interference, and finding a second photoelectron holographic interference zero-order maximum stripe center position with a non-zero angle between the polarization direction of the laser field and the arrangement direction of the molecules in the second photoelectron holographic interference, wherein the first photoelectron holographic interference zero-order maximum stripe center position is specifically:
Extracting a first interference item of the first photoelectron holographic interference, acquiring the central position of each level of fringes of the first photoelectron holographic interference according to the first interference item, and acquiring the central position of the zero-level maximum fringes of the first photoelectron holographic interference according to the central position of each level of fringes of the first photoelectron holographic interference;
extracting a second interference term of the second photoelectron holographic interference, obtaining the central position of each level of fringes of the second photoelectron holographic interference according to the second interference term, and obtaining the central position of the zero-level maximum fringes of the second photoelectron holographic interference according to the central position of each level of fringes of the second photoelectron holographic interference.
3. The method of detecting an initial lateral position of a tunneling ionized electron according to claim 2, wherein: the first interference term is cos (delta phi) 1 ) Wherein ΔΦ 1 For the first interference phase, ΔΦ 1 The calculation method of (1) is as follows:
ΔΦ 1 ＝1/2[p y -k y (0)] 2 (t r -t 0 )+α；
the second interference term is cos (delta phi) 2 ) Wherein ΔΦ 2 For the second interference phase, ΔΦ 2 The calculation method of (1) is as follows:
wherein p is y Is the photoelectron final momentum perpendicular to the polarization direction of the laser field, t r To scatter the electron scattering time, t 0 For the ionization time of scattered electrons, α is the scattering amplitude phase of the molecule; k (k) y Is the regular momentum, k, of scattered electrons y (0) To tunnel ionized scattered electrons when the polarization direction of the laser field is at zero angle to the molecular arrangement directionMomentum, θ is the angle between the polarization direction of the laser field and the molecular alignment direction, k y And (theta) is the regular momentum of tunneling ionized scattered electrons when the included angle between the polarization direction of the laser field and the molecular arrangement direction is theta.
4. The method of detecting an initial lateral position of a tunneling ionized electron according to claim 2, wherein: when a first interference term of the first photoelectron holographic interference is extracted, polynomial fitting is carried out on the photoelectron yield in the first photoelectron holographic interference by using an exponential function, the photoelectron yield in the first photoelectron holographic interference is divided by a polynomial obtained by fitting, and an obtained result is used as the first interference term;
and when a second interference term of the second photoelectron holographic interference is extracted, polynomial fitting is carried out on the photoelectron yield in the second photoelectron holographic interference by using an exponential function, the photoelectron yield in the second photoelectron holographic interference is divided by a polynomial obtained by fitting, and the obtained result is used as the second interference term.
5. The method of detecting an initial lateral position of a tunneling ionized electron according to claim 3, wherein: the central position of each first photoelectron holographic interference level fringe is obtained according to the first interference item, and the central position of the first photoelectron holographic interference zero-level maximum fringe is obtained according to the central position of each first photoelectron holographic interference level fringe, specifically:
Establishing the central position of each stage of fringes of the first photoelectron holographic interference
Wherein ΔΦ 1 N pi, n=0, ±1, ±2, ±3..; when n=0, ΔΦ 1 When the value of the first photoelectron holographic interference zero-order maximum stripe is=0, the central position of the first photoelectron holographic interference zero-order maximum stripe is obtained>
The central position of each level of second photoelectron holographic interference fringes is obtained according to the second interference item, and the central position of the second photoelectron holographic interference zero-level maximum fringes is obtained according to the central position of each level of second photoelectron holographic interference fringes, specifically:
establishing the center position of the second photoelectron holographic interference zero-level maximum stripe
Wherein ΔΦ 2 N pi, n=0, ±1, ±2, ±3..; when n=0, ΔΦ 2 Obtaining the central position of the second photoelectron holographic interference zero-order maximum stripe when the number of the second photoelectron holographic interference zero-order maximum stripes is =0>
6. The method of detecting an initial lateral position of a tunneling ionized electron of claim 5, wherein: the lateral momentum offset Δp y ＝k y (θ)。
7. The method of detecting an initial lateral position of a tunneling ionized electron of claim 6, wherein: the initial transverse position of the tunneling ionization electron wave packet is obtained according to the transverse momentum offset, specifically:
establishing an initial lateral position R of ionized electrons b And k is equal to y Relation of (θ): k (k) y (θ)＝±R b /(t r -t 0 ) Bind Δp y ＝k y (θ) to obtain the initial lateral position of the ionized electrons
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