CN105758840B - A method of molecular orbit tomography is realized using higher hamonic wave amplitude - Google Patents
A method of molecular orbit tomography is realized using higher hamonic wave amplitude Download PDFInfo
- Publication number
- CN105758840B CN105758840B CN201610115677.9A CN201610115677A CN105758840B CN 105758840 B CN105758840 B CN 105758840B CN 201610115677 A CN201610115677 A CN 201610115677A CN 105758840 B CN105758840 B CN 105758840B
- Authority
- CN
- China
- Prior art keywords
- hamonic wave
- higher hamonic
- molecular orbit
- generation
- amplitude
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Expired - Fee Related
Links
Classifications
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
- G01N21/62—Systems in which the material investigated is excited whereby it emits light or causes a change in wavelength of the incident light
- G01N21/71—Systems in which the material investigated is excited whereby it emits light or causes a change in wavelength of the incident light thermally excited
Abstract
The invention discloses a kind of methods for realizing molecular orbit tomography using higher hamonic wave amplitude.To the higher hamonic wave amplitude for the arrangement molecule assemblage radiation that experimental detection arrives, the angular distribution of the High-order Harmonic Generation of unimolecule level is obtained by deconvolution, calculates equivalent reply dipole moment amplitude of the molecule under velocity gauge.Equivalent reply dipole moment phase and molecular orbit are rebuild using iterative algorithm.Only needing to detect higher hamonic wave amplitude information the invention proposes one kind can be realized the completely new approach of molecular orbit tomography, the phase information of missing is rebuild by iterative algorithm, realize the reconstruct of molecular orbit, this is a kind of simple and effective, and has the method for broad applicability.
Description
Technical field
The present invention relates to technical field of ultrafast laser, and in particular to a kind of to realize molecular orbit layer using higher hamonic wave amplitude
The method for analysing imaging.
Background technique
Molecular orbit tomography (Tomographic imaging of based on arrangement molecule higher hamonic wave
Molecular orbitals) research, since temporal resolution and the space point of angstrom magnitude of Ah's second-time may be implemented in it
Resolution causes the great interest of researchers in recent years.Molecular orbit tomography, which refers to, utilizes High-order Harmonic Generation signal
To the dependence at molecules align angle in laser field, the reply dipole moment of molecule highest occupied molecular orbital under different arrangement angles is extracted
Information, and pass through the highest occupied molecular orbital of Fourier projection chromatography method reconstruct molecule.
When carrying out molecular orbit imaging using existing molecular orbit chromatography imaging method, the information for needing to obtain includes point
Higher hamonic wave amplitude and phase under each arrangement angles of son.Since the electric field of High-order Harmonic Generation can be expressed as and molecular orbit
Unrelated and related two products
EHHG(ω,θ)∝W(ω,θ)dv(ω,θ)
Wherein W (ω, θ) is unrelated with molecular orbit, the continuous electronic wave packet amplitude replied is indicated, for identical ionization energy
Molecule or atom, this is unrelated with the track of selected molecule or atom.There is the atom of close ionization energy by measuring
Higher hamonic wave signal under the same conditions, available relational expression
Wherein η (θ) is the distribution of molecular ionization rate angle, and the structure of referencing atom is relatively simple, and it is known for replying dipole moment.
Reply dipole moment of the target molecule under velocity gauge can be successfully obtained by referencing atom
The reply dipole moment of molecule is strongly related to molecular structure, replys i.e. extractable molecular orbit in dipole moment from molecule
Information simultaneously realizes that molecular orbit is imaged.2004, when researcher realizes molecular orbit tomography for the first time, high order is only detected
The amplitude of harmonic wave, and used higher hamonic wave phase (J.Itatani et al., the Nature 432,867 of theoretical calculation
(2004))；On this basis, 2010, researcher measured higher hamonic wave phase by RABITT technology, however only measures
Association phase between different harmonic orders, for the association phase under different molecular arrangement angles is made that the 17th subharmonic exists
Phase is all 0 hypothesis (S.Haessler et al., Nature physics 6,200 under different molecular arrangement angles
(2010))；Further, in 2011, researcher is using Kaczmarz algorithm from the higher hamonic wave amplitude signal detected
The phase information of higher hamonic wave has been extracted, it is same only to have obtained the association phase between different harmonic orders, then borrow again
Scattering theory (QRS) is helped to calculate (C.Vozzi et al., the Nature physics of the association phase under different molecular arrangement angles
7,822 (2011)).
Accompanying problem is that in existing molecular orbit chromatography imaging method, due to needing to use indispensablely
To the amplitude and phase of higher hamonic wave, so that having in molecular orbit tomographic process to the acquisition of higher hamonic wave phase
Use priori knowledge or certain it is assumed that constrain the application and development of molecular orbit tomography in practice.
Summary of the invention
For the defect of existing molecular orbit chromatography imaging method, height need to be only measured the purpose of the present invention is to provide a kind of
Subharmonic amplitude, the method that molecular orbit tomography is carried out by iterative algorithm, it is intended to which breaking through can not be completely experimentally quasi-
The bottleneck that really obtaining higher hamonic wave phase.
To achieve the above object, higher hamonic wave amplitude only need to be measured the present invention provides a kind of, is carried out by iterative algorithm
The method of molecular orbit tomography.The method is characterized in that firstly, the height of the arrangement molecule assemblage radiation measured to experiment
Subharmonic amplitude, by deconvolution obtain the High-order Harmonic Generation of unimolecule level angular distribution and the same terms under survey
The referencing atom higher hamonic wave signal obtained, calculates equivalent reply dipole moment amplitude；Secondly, shaking for equivalent reply dipole moment
Width passes through error decrement algorithm (error-reduction algorithm, ER) and Mixed design-output algorithm (hydrid
Input-output algorithm, HIO), with Fourier transformation and inverse Fourier transform between object domain and frequency domain repeatedly
Interative computation gradually rebuilds the equivalent reply dipole moment phase information of loss.
There was only equivalent reply dipole moment amplitude by the physical quantity that experimental data can directly obtain | D |, then by repeatedly
The equivalent reply dipole moment phase of loss is gradually rebuild for algorithmAnd object domain objective function f, wherein object domain objective function f is being just
It is molecular orbit wave function.Detailed process is as follows for the iterative algorithm:
(1) the equivalent reply dipole moment amplitude being calculated by experimental data is utilized | D | and random phaseObtain frequency
Domain
(2) rightInverse Fourier transform is carried out, object domain function f'=FFT is obtained-1(D)；
(3) boundary condition constraint in object domain is carried out to object domain function f', obtains object domain objective function f；
(4) Fourier transformation is carried out to object domain objective function f again, obtains frequency domain
(5) the equivalent reply dipole moment amplitude being calculated by experimental data is utilized | D | to replace
In | D'| is obtained
So far, entire iterative algorithm has completely carried out primary.Then above step (2) are repeated and arrive (5), until being stablized
Output as a result, the object domain objective function wherein exported is denoted as f1, i.e. first generation iteration completion.It is obtained again with first generation iteration
The object domain objective function f of various (limited) outputs1For ground state, calculate one by one reply dipole moment amplitude and with pass through experimental data
The reply dipole moment Amplitude Comparison being calculated, by the smallest object domain objective function f of error1It is selected as the " benign of first generation iteration
Gene " is denoted as fgene。
When carrying out second generation iteration, useF in replacement step (4), then according to step (4)
(5) the sequence iteration of (2) (3) (4), until obtaining stable output as a result, i.e. second generation iteration is completed.
When carrying out third generation iteration, useReplace the f in the second generation2, then change according to the second generation
The sequence iteration in generation, until obtaining stable output as a result, i.e. third generation iteration is completed.This process is repeated, until iteration
Output result is stable and unique when to the n-th generation, and the object domain objective function exported at the end of remembering the n-th generation iteration is fn, as finally
As a result.
Terminate entire iterative algorithm.
Compared with prior art, the method for the present invention has the advantages that prior art progress molecular orbit imaging must
Higher hamonic wave amplitude and phase this two groups of parameters must be used, and the method for the present invention need to only measure higher hamonic wave amplitude and can be realized point
Sub-track imaging.Wherein, higher hamonic wave amplitude can be measured accurately in an experiment, and the prior art must when obtaining phase information
Certain approximation or hypothesis must be used.The method of the present invention only needs to detect higher hamonic wave amplitude, is directly rebuild by iterative algorithm
The phase information of missing realizes the reconstruct of molecular orbit, does not need to carry out any approximate and assume.This be a kind of practicability more
The extensive and higher completely new molecular orbit chromatography imaging method of precision.
Detailed description of the invention
Fig. 1 is the flow chart that the present invention realizes molecular orbit tomography using only measurement higher hamonic wave amplitude；
Fig. 2 is the experimental provision for measuring higher hamonic wave；
Fig. 3 is the CO that experiment measures215th to 35 high order harmonic spectrum；
Fig. 4 is the CO obtained to experimental data deconvolution2The angular distribution of the High-order Harmonic Generation of unimolecule level；
Fig. 5 is that the present invention carries out the CO obtained after four generation iteration under gene targeting2The stable output of molecular orbit
Object domain objective function；
Fig. 6 is the CO that the present invention obtains2The CO of molecular orbit and ab iitio2Under molecular orbit and Fourier's limit
CO2The slice comparison diagram of molecular orbit interception；
Fig. 7 is that present invention iteration under gene targeting obtains C2H2The object domain objective function for stablizing output of molecular orbit；
Fig. 8 is that present invention iteration under gene targeting obtains N2The object domain objective function for stablizing output of molecular orbit.
Specific embodiment
In order to make the objectives, technical solutions, and advantages of the present invention clearer, with reference to the accompanying drawings and embodiments, right
The present invention is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, and
It is not used in the restriction present invention.
As shown in Figure 1, the present invention provides a kind of method for realizing molecular orbit tomography using higher hamonic wave amplitude,
The following steps are included:
(1) the higher hamonic wave amplitude for the arrangement molecule assemblage radiation for arriving experimental detection, obtains unimolecule by deconvolution
The angular distribution of the High-order Harmonic Generation of level；
(2) high order of the referencing atom measured using the angular distribution of the High-order Harmonic Generation of unimolecule level and experiment is humorous
Wave-amplitude calculates the reply dipole moment amplitude of molecule
Defining equivalent reply dipole moment amplitude simultaneously is
Wherein kωIndicate the momentum of ω subharmonic；
(3) iteration specific steps:
(i) the equivalent reply dipole moment amplitude obtained by experimental data is utilized | D |, with the equivalent reply dipole moment of input
Random phaseI.e.Open first time iteration；
(ii) rightIt carries out inverse Fourier transform and obtains object domain function f'；
(iii) boundary constraint is carried out to object domain function f' and obtains object domain objective function f；
(iv) Fourier transformation is carried out to object domain objective function f to obtain
(v) use | D | replacement | D'| is obtainedOpen second of iteration；
(vi) it repeats the above iterative step (ii) and arrives (v), until obtaining stable output as a result, first generation iteration is completed.
(4) it calculates separately and f (is denoted as with the various object domains objective function of step (3) output1) be ground state reply dipole moment
AmplitudeWith the reply dipole moment amplitude obtained by experimental dataComparison, relative error function
By screening the smallest error function, corresponding object domain objective function is selected as " well behaved basis because "；
(5) by obtain well behaved basis because when object domain objective function be denoted as fgene, use fgeneAnd f1The square root of product replaces step
Suddenly the f in (3 (iii)) opens second generation iteration；
(6) step (3) (4) (5) are repeated, until output result is stable and unique, the object domain objective function f of output is most
The molecular orbit obtained eventually.
Below in conjunction with attached drawing, with CO2For target molecule, Kr is referencing atom, makees the present invention into one as embodiment
Step explanation:
In an embodiment of the invention, target molecule CO2, referencing atom Kr.Experimental provision is as shown in Fig. 2, one
Beam center wavelength 800nm, pulsewidth 35fs, repetition rate 1kHz femtosecond laser by beam splitter be divided into arrangement light and driving light.
Arrangement light by gas be arranged in arrangement light polarization direction, driving light relative to arrangement light delay Δ t with angle theta respectively by arranging
Delay line and half-wave plate (not shown) in column light optical path control, and are focused after arrangement light and driving combiner by convex lens.It is real
Testing middle arrangement light and driving light and the intensity of gas interaction is respectively 0.4 × 1014W/cm2With 2.3 × 1014W/cm2, gas
It is passed through vacuum chamber by the snifting valve that diameter is 100 μm, the higher hamonic wave of generation is by being shown in MCP display screen after optical grating diffraction
On.
Fig. 3 is to test the CO measured when arrangement angles are 0 degree215th to 35 high order harmonic spectrum.
Fig. 4 is to CO2Angular point of the harmonic radiation of the unimolecule level obtained after 19th subharmonic amplitude deconvolution
Cloth.Wherein, the time-dependent Schrodinger equation solution rotational wave that molecule arrangement angles probability distribution passes through calculating molecule rotation when deconvolution
Packet obtains, the angular distribution coefficient of the harmonic radiation of unimolecule level Fourier's cosine series expansion undetermined, in the present invention
The first six for having used Fourier's cosine series to be unfolded in embodiment.Then the higher hamonic wave arrangement angles spoke measured by experiment
It penetrates, and driving light and the High-order Harmonic Generation arranged under light different delayed time are that two constraint conditions solve Fourier's cosine series
Term coefficient is unfolded.
Fig. 5, which is the present invention, stablized after four generation iteration and unique object domain target " well behaved basis because " guiding is lower
Function, i.e. CO2Molecular orbit.
Fig. 6 is the CO that the method for the present invention obtains2The true CO that molecular orbit and ab iitio obtain2Molecular orbit and
CO under Fourier's limit2Molecular orbit, the slice for intercepting them carry out quantitative contrast.By quantitative comparison it is found that the present invention
The CO of reconstruct2No matter qualitative molecular orbit is or quantitatively all accurately reflects CO2The actual trajcctorics of molecule.
Using the present invention " a method of utilize higher hamonic wave amplitude realize molecular orbit tomography ", also successfully divide
Not with C2H2(Fig. 7) and N2(Fig. 8) is that embodiment realizes molecular orbit tomography.Wherein, CO2、C2H2And N2Molecule most
It is respectively π that height, which occupies track,g、πuAnd σgThree kinds of different molecular orbits.
As it will be easily appreciated by one skilled in the art that the foregoing is merely illustrative of the preferred embodiments of the present invention, not to
The limitation present invention, any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should all include
Within protection scope of the present invention.
Claims (7)
1. a kind of method for realizing molecular orbit tomography using higher hamonic wave amplitude, which is characterized in that the method includes
Following steps:
S1, the higher hamonic wave amplitude for radiating the arrangement molecule assemblage that experimental detection arrives, obtain unimolecule level by deconvolution
High-order Harmonic Generation angular distribution, calculate equivalent reply dipole moment amplitude of the molecule under velocity gauge；
S2, by the equivalent reply dipole moment amplitude, pass through first generation iterative algorithm and rebuild molecular orbit；
S3, the various molecular orbits for respectively obtaining the first generation iterative algorithm calculate it and reply dipole moment vibration as ground state
Width, and compared with experiment measures result, choosing error function reckling is well behaved basis because being denoted as fgene；
S4, the well behaved basis because guiding under, gradually carry out the second generation, the third generation ... iterative calculation, until output stablize
And unique result.
2. the method for realizing molecular orbit tomography using higher hamonic wave amplitude as described in claim 1, which is characterized in that
The higher hamonic wave of arrangement molecule assemblage radiation in the step S1, is interacted by femtosecond laser and the gas molecule of arrangement
It generates, gas molecule is one of diatomic or polyatomic molecule gas.
3. the method for realizing molecular orbit tomography using higher hamonic wave amplitude as claimed in claim 1 or 2, feature exist
In the angular distribution of the High-order Harmonic Generation of the unimolecule level in the step S1 is more than usage factor Fourier undetermined
String series expansion and molecules align angle probability distribution, are obtained by deconvolution；Wherein, molecules align angle probability distribution is logical
The Schrodinger equation for crossing solution description interaction between laser and metal obtains.
4. the method for realizing molecular orbit tomography using higher hamonic wave amplitude as claimed in claim 1 or 2, feature exist
In, first generation iteration in the step S2, step includes:
S1, the equivalent reply dipole moment amplitude being calculated by experimental data | D | and the random phase of inputObtain frequency domain
's
It is S2, rightInverse Fourier transform is carried out, object domain function f'=FFT is obtained-1(D)；
S3, boundary condition constraint in object domain is carried out to object domain function f', obtain object domain objective function f；
S4, Fourier transformation is carried out to object domain function target f again, obtains frequency domain
S5, with equivalent reply dipole moment amplitude | D | replacementIn | D'| is obtainedAnd
Circulating repetition step S2, S3, S4, S5 is until output stabilization result.
5. the method for realizing molecular orbit tomography using higher hamonic wave amplitude as claimed in claim 1 or 2, feature exist
In the well behaved basis in the step S3 is because being by calculating error functionIt chooses
The object domain objective function of the output of first generation iteration corresponding to error function minimum value,For step S3 calculating
Obtained reply dipole moment amplitude,The reply dipole moment amplitude being calculated for the step S1.
6. the method for realizing molecular orbit tomography using higher hamonic wave amplitude as claimed in claim 1 or 2, feature exist
It is the iteration in " well behaved basis because " lower progress of guiding in, second generation iteration in the step S4, third generation iteration and higher
Algebra iteration method therefor is identical as second generation iteration.
7. the method for realizing molecular orbit tomography using higher hamonic wave amplitude as claimed in claim 6, which is characterized in that
The benign gene targeting refers to when carrying out the n-th generation iteration, usesReplace fn-1The iteration of progress,
Wherein n is more than or equal to 2.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201610115677.9A CN105758840B (en) | 2016-03-01 | 2016-03-01 | A method of molecular orbit tomography is realized using higher hamonic wave amplitude |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201610115677.9A CN105758840B (en) | 2016-03-01 | 2016-03-01 | A method of molecular orbit tomography is realized using higher hamonic wave amplitude |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN105758840A CN105758840A (en) | 2016-07-13 |
| CN105758840B true CN105758840B (en) | 2019-01-29 |
Family
ID=56332215
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201610115677.9A Expired - Fee Related CN105758840B (en) | 2016-03-01 | 2016-03-01 | A method of molecular orbit tomography is realized using higher hamonic wave amplitude |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN105758840B (en) |
Families Citing this family (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109060732B (en) * | 2018-07-19 | 2020-06-02 | 华中科技大学 | Method for detecting molecular rotation wave packet |
Citations (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103399203A (en) * | 2013-08-09 | 2013-11-20 | 重庆大学 | High-precision harmonic parameter estimation method based on composite iterative algorithm |
-
2016
- 2016-03-01 CN CN201610115677.9A patent/CN105758840B/en not_active Expired - Fee Related
Patent Citations (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103399203A (en) * | 2013-08-09 | 2013-11-20 | 重庆大学 | High-precision harmonic parameter estimation method based on composite iterative algorithm |
Non-Patent Citations (6)
| Title |
|---|
| Attosecond imaging of molecular electronic wavepackets;S. Haessler et al.;《Nature physics》;20100331;第6卷;第200-206页 |
| Generalized molecular orbital tomography;C. Vozzi et al.;《Nature physics》;20111031;第7卷;第822-826页 |
| High harmonic generation and molecular orbital tomography in multielectron systems;Zengxiu Zhao et al.;《The journal of chemical physics》;20070320;第126卷(第11期);第114306-1至114306-13页 |
| Tomographic imaging of molecular orbital;J. Itatani et al.;《Nature》;20041216;第432卷;第867-871页 |
| 不同取向角下CO2分子波长依赖的垂直谐波效率;李雁鹏等;《物理学报》;20151231;第64卷(第18期);第183102-1至183102-8页 |
| 利用高次谐波实现分子的轨道成像：两中心干涉效应;陈彦军、刘杰;《物理》;20081231;第37卷(第10期);第697-700页 |
Also Published As
| Publication number | Publication date |
|---|---|
| CN105758840A (en) | 2016-07-13 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Jensen et al. | Probing reionization with LOFAR using 21-cm redshift space distortions | |
| Farris et al. | Binary black hole mergers in gaseous disks: Simulations in general relativity | |
| Mizuno et al. | Comparison of the ion-to-electron temperature ratio prescription: GRMHD simulations with electron thermodynamics | |
| Seo et al. | The foreground wedge and 21-cm BAO surveys | |
| Picheyev et al. | Ground state polarized photofragments study by using resonance and off-resonance probe beam techniques | |
| Ghara et al. | 21 cm signal from cosmic dawn–II. Imprints of the light-cone effects | |
| Loginov et al. | Spectroscopy on Rydberg states of sodium atoms on the surface of helium nanodroplets | |
| Harding et al. | Using ion imaging to measure velocity distributions in surface scattering experiments | |
| Kim et al. | Ultrafast X-ray diffraction in liquid, solution and gas: present status and future prospects | |
| Shao et al. | Imaging coherent electronic motion in atoms by ultrafast electron diffraction | |
| Zawada et al. | Light-cone anisotropy in the 21 cm signal from the epoch of reionization | |
| Galán et al. | The soft-photon approximation in infrared-laser-assisted atomic ionization by extreme-ultraviolet attosecond-pulse trains | |
| Li et al. | Transition from SAMO to Rydberg state ionization in C60 in femtosecond laser fields | |
| Kimpson et al. | Pulsar timing in extreme mass ratio binaries: a general relativistic approach | |
| Borsa et al. | The GAPS Programme at TNG-XXXI. The WASP-33 system revisited with HARPS-N | |
| Kuznetsov et al. | Spatially resolved energetic electron properties for the 21 May 2004 flare from radio observations and 3D simulations | |
| Sato et al. | First-principles simulations for attosecond photoelectron spectroscopy based on time-dependent density functional theory | |
| Mauger et al. | High-harmonic spectroscopy of transient two-center interference calculated with time-dependent density-functional theory | |
| Liu et al. | Offset angles of photocurrents generated in few-cycle circularly polarized laser fields | |
| Gregory et al. | Towards molecular frame photoelectron angular distributions in polyatomic molecules from lab frame coherent rotational wavepacket evolution | |
| Diveki et al. | Molecular orbital tomography from multi-channel harmonic emission in N2 | |
| Mehner et al. | Spectroscopic and photometric oscillatory envelope variability during the S Doradus outburst of the luminous blue variable R71 | |
| Kheifets | Wigner time delay in atomic photoionization | |
| Domínguez-Fernández et al. | Morphology of radio relics–II. Properties of polarized emission | |
| Song et al. | Inelastic scattering of CO with He: Polarization dependent differential state-to-state cross sections |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| C06 | Publication | ||
| PB01 | Publication | ||
| C10 | Entry into substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant | ||
| CF01 | Termination of patent right due to non-payment of annual fee |
Granted publication date: 20190129 Termination date: 20200301 |
|
| CF01 | Termination of patent right due to non-payment of annual fee |