CN105758840A - Method for realizing molecular orbit tomographic imaging by utilizing high harmonic amplitudes - Google Patents

Abstract

The invention discloses a method for realizing molecular orbit tomographic imaging by utilizing high harmonic amplitudes. The method comprises the following steps of: carrying out deconvolution on the high harmonic amplitudes of arrangement molecular assembly radiation detected by an experiment to obtain angular distribution of high harmonic radiation of a single molecular layer; and calculating equivalent reply dipole moments of molecules under a speed specification. An equivalent reply dipole phase and a molecular orbit are reconstructed by utilizing an iterative algorithm. The invention provides a brand new method of realizing the molecular orbit tomographic imaging by only utilizing high harmonic amplitude information, and the reconstruction of the molecular orbit is realized through phase information lacked by the reconstruction of the iterative algorithm. The method is simple and effective, and has wide applicability.

Description

A kind of method utilizing higher hamonic wave amplitude to realize molecular orbit tomography

Technical field

The present invention relates to technical field of ultrafast laser, be specifically related to a kind of method utilizing higher hamonic wave amplitude to realize molecular orbit tomography.

Background technology

Molecular orbit tomography (Tomographicimagingofmolecularorbitals) research based on arrangement molecule higher hamonic wave, due to the spatial resolution of its temporal resolution that can realize Ah's second-time and angstrom magnitude, cause the great interest of researcheres in recent years.Molecular orbit tomography refers to and utilizes High-order Harmonic Generation signal dependency to molecules align angle in laser field, extract molecule reply dipole moment information of highest occupied molecular orbital under different arrangement angles, and by the highest occupied molecular orbital of Fourier projection chromatography method reconstruct molecule.

When using existing molecular orbit chromatography imaging method to carry out molecular orbit imaging, it is necessary to the information of acquisition comprises the higher hamonic wave amplitude under each arrangement angles of molecule and phase place.Owing to the electric field of High-order Harmonic Generation can be expressed as two unrelated and relevant with molecular orbit product

E_HHG(ω,θ)∝W(ω,θ)d_v(ω,θ)

Wherein W (ω, θ) is unrelated with molecular orbit, represents the continuous electronic ripple bag amplitude replied, and for molecule or the atom of identical ionization energy, this is unrelated with the track of selected molecule or atom.By measuring the higher hamonic wave signal that there is the atom of close ionization energy under the same conditions, it is possible to obtain relational expression

$\frac{E_{HHG}^{mol}(\mathrm{\ω},\mathrm{\θ})}{E_{HHG}^{atom}\left(\mathrm{\ω}\right)}=\mathrm{\η}\left(\mathrm{\θ}\right)\frac{d_v^{mol}(\mathrm{\ω},\mathrm{\θ})}{d_v^{atom}\left(\mathrm{\ω}\right)}$

Wherein η (θ) is that molecular ionization rate is angular distribution, and the structure of referencing atom is relatively simple, and it is known for replying dipole moment.Target molecule reply dipole moment under velocity gauge can be successfully obtained by referencing atom

${d_v}^{mol}(\mathrm{\ω},\mathrm{\θ})=\frac{1}{\mathrm{\η}\left(\mathrm{\θ}\right)}\frac{A^{mol}(\mathrm{\ω},\mathrm{\θ})}{A^{atom}\left(\mathrm{\ω}\right)}\frac{e^{{\mathrm{i\φ}}^{mol}(\mathrm{\ω},\mathrm{\θ})}}{e^{{\mathrm{i\φ}}^{atom}\left(\mathrm{\ω}\right)}}{d_v}^{atom}\left(\mathrm{\ω}\right)$

The reply dipole moment of molecule is strongly relevant to molecular structure, replys dipole moment from molecule and can extract molecular orbit information and realize molecular orbit imaging.2004, when researcher realizes molecular orbit tomography first, only detect the amplitude of higher hamonic wave, and employed the higher hamonic wave phase place (J.Itatanietal., Nature432,867 (2004)) of Theoretical Calculation；On this basis, 2010, researcher has recorded higher hamonic wave phase place by RABITT technology, but simply recorded the association phase place between different harmonic order, association phase place under different molecular arrangement angles is made that the 17th subharmonic phase place under different molecular arrangement angles is the hypothesis (S.Haessleretal. of 0 entirely, Naturephysics6,200 (2010))；Further, in 2011, researcher utilizes Kaczmarz algorithm to extract the phase information of higher hamonic wave from the higher hamonic wave amplitude signal detected, the same association phase place simply obtained between different harmonic order, then the association phase place (C.Vozzietal. under different molecular arrangement angles is calculated again by scattering theory (QRS), Naturephysics7,822 (2011)).

Thing followed problem is, in existing molecular orbit chromatography imaging method, need to use the amplitude of higher hamonic wave and phase place due to indispensable, make in molecular orbit tomographic process, the acquisition of higher hamonic wave phase place to be had to use priori or certain it is assumed that thus constrain the application in practice of molecular orbit tomography and development.

Summary of the invention

Defect for existing molecular orbit chromatography imaging method, it is an object of the invention to provide a kind of and need to measure higher hamonic wave amplitude, by the method that iterative algorithm carries out molecular orbit tomography, it is intended to break through and completely experimentally cannot accurately obtain this bottleneck of higher hamonic wave phase place.

For achieving the above object, the invention provides a kind of and need to measure higher hamonic wave amplitude, by the method that iterative algorithm carries out molecular orbit tomography.The method is characterized in that, first, the higher hamonic wave amplitude of the arrangement molecule assemblage radiation that experiment is recorded, the angular distribution of the High-order Harmonic Generation of unimolecule aspect is obtained by deconvolution, and the referencing atom higher hamonic wave signal recorded under the same terms, calculate equivalence and reply dipole moment amplitude；Secondly, dipole moment amplitude is replied for equivalence, by error decrement algorithm (error-reductionalgorithm, and Mixed design-output algorithm (hydridInput-outputalgorithm ER), HIO), using Fourier transformation and inverse Fourier transform to iterate between thing territory and frequency domain computing, dipole moment phase information is replied in the equivalence progressively rebuilding loss.

Dipole moment amplitude | D | is replied in the physical quantity that data can directly obtain by experiment only equivalence, then passes through iterative algorithm and progressively rebuilds the equivalence reply dipole moment phase place of lossAnd thing territory object function f, wherein thing territory object function f molecular orbit wave function just.The detailed process of this iterative algorithm is as follows:

(1) the calculated equivalence of data by experiment is utilized to reply dipole moment amplitude | D | and random phaseObtain frequency domain

(2) rightCarry out inverse Fourier transform, obtain thing territory function f'=FFT^-1(D)；

(3) thing territory function f' is carried out the boundary condition constraint of thing territory, obtains thing territory object function f；

(4) again thing territory object function f is carried out Fourier transformation, obtain frequency domain

(5) utilize the calculated equivalence of data by experiment to reply dipole moment amplitude | D | to replaceIn | D'|, obtain

So far, whole iterative algorithm completely carries out once.Then repeating above step (2) to (5), until obtaining stable output result, the thing territory object function wherein exported is designated as f₁, namely first generation iteration completes.The thing territory object function f of various (limited) output obtained with first generation iteration again₁For ground state, dipole moment amplitude reply dipole moment Amplitude Comparison calculated with data by experiment are replied in calculating one by one, by thing territory object function f minimum for error₁Elect " well behaved basis because of " of first generation iteration as, be designated as f_gene。

When carrying out second filial generation iteration, useF in replacement step (4), then according to the order iteration of step (4) (5) (2) (3) (4), until obtaining stable output result, namely second filial generation iteration completes.

When carrying out third generation iteration, useReplace the f in the second filial generation₂, then according to the order iteration of second filial generation iteration, until obtaining stable output result, namely third generation iteration completes.Repeat this process, until it is stable and unique to export result when iterating to for the n-th generation, remember that when the n-th generation iteration terminates, the thing territory object function of output is f_n, it is final result.

Terminate whole iterative algorithm.

Compared with prior art, the inventive method has the advantages that prior art carries out molecular orbit imaging and must use higher hamonic wave amplitude and these two groups of parameters of phase place, and the inventive method only need to be measured higher hamonic wave amplitude and can realize molecular orbit imaging.Wherein, higher hamonic wave amplitude can accurately be measured in an experiment, and prior art must use certain approximate or hypothesis when obtaining phase information.The inventive method has only to detection higher hamonic wave amplitude, rebuilds the phase information of disappearance either directly through iterative algorithm, it is achieved MO reconstruct, it is not necessary to carries out any approximate and assumes.This is the brand-new molecular orbit chromatography imaging method that a kind of practicality is more extensive and precision is higher.

Accompanying drawing explanation

Fig. 1 be the present invention utilize only measure higher hamonic wave amplitude realize molecular orbit tomography flow chart；

Fig. 2 is the experimental provision measuring higher hamonic wave；

Fig. 3 is the CO that experiment records₂15th to 35 high order harmonic spectrum；

Fig. 4 is the CO that experimental data deconvolution is obtained₂The angular distribution of the High-order Harmonic Generation of unimolecule aspect；

Fig. 5 is the CO that the present invention carries out obtaining after four generation iteration under gene targeting₂The thing territory object function of MO stable output；

Fig. 6 is the CO that the present invention obtains₂The CO of molecular orbit and ab iitio₂CO under molecular orbit and Fourier's limit₂The section comparison diagram that molecular orbit intercepts；

Fig. 7 is that present invention iteration under gene targeting obtains C₂H₂The thing territory object function of MO stable output；

Fig. 8 is that present invention iteration under gene targeting obtains N₂The thing territory object function of MO stable output.

Detailed description of the invention

In order to make the purpose of the present invention, technical scheme and advantage clearly understand, below in conjunction with drawings and Examples, the present invention is further elaborated.Should be appreciated that specific embodiment described herein is only in order to explain the present invention, is not intended to limit the present invention.

As it is shown in figure 1, the invention provides a kind of method utilizing higher hamonic wave amplitude to realize molecular orbit tomography, comprise the following steps:

(1) the higher hamonic wave amplitude of the arrangement molecule assemblage radiation arrived by experimental detection, obtains the angular distribution of the High-order Harmonic Generation of unimolecule aspect by deconvolution；

(2) utilize the angular distribution of the High-order Harmonic Generation of unimolecule aspect and the higher hamonic wave amplitude testing the referencing atom recorded, calculate the reply dipole moment amplitude of molecule

$\left|{d_v}^{mol}(\mathrm{\ω},\mathrm{\θ})\right|=\frac{1}{\mathrm{\η}\left(\mathrm{\θ}\right)}\frac{A^{mol}(\mathrm{\ω},\mathrm{\θ})}{A^{atom}\left(\mathrm{\ω}\right)}{d_v}^{atom}\left(\mathrm{\ω}\right)$

Dipole moment amplitude is replied in definition equivalence simultaneously

$\left|D(\mathrm{\ω},\mathrm{\θ})\right|=\frac{\left|{d_v}^{mol}(\mathrm{\ω},\mathrm{\θ})\right|}{k_{\mathrm{\ω}}}$

Wherein k_ωRepresent the momentum of ω subharmonic；

(3) iteration concrete steps:

I () utilizes the equivalence that data by experiment obtain to reply dipole moment amplitude | D |, with the random phase that dipole moment is replied in input equivalenceNamelyOpen first time iteration；

(ii) rightCarry out inverse Fourier transform and obtain thing territory function f'；

(iii) thing territory function f' is carried out boundary constraint and obtain thing territory object function f；

(iv) thing territory object function f is carried out Fourier transformation to obtain

V () uses | D | to replace | D'|, obtainOpen second time iteration；

(vi) repeating above iterative step (ii) to (v), until obtaining stable output result, first generation iteration completes.

(4) calculate the various thing territories object function exported with step (3) respectively and (be designated as f₁) for the reply dipole moment amplitude of ground stateThe reply dipole moment amplitude obtained with data by experimentContrast, relative error function

$erfF=\underset{\mathrm{\ω}}{\Σ}\underset{\mathrm{\θ}}{\Σ}\left(\frac{\left|\right|d_v^{mol}(\mathrm{\ω},\mathrm{\θ})|-|d_v^{ite}(\mathrm{\ω},\mathrm{\θ})\left|\right|}{\left|d_v^{mol}(\mathrm{\ω},\mathrm{\θ})\right|}\right)$

By screening minimum error function, corresponding thing territory object function is elected as " well behaved basis because of "；

(5) by obtain well behaved basis because of time thing territory object function be designated as f_gene, use f_geneAnd f₁F in the square root replacement step (3 (iii)) of product, opens second filial generation iteration；

(6) repeating step (3) (4) (5), until output result is stable and unique, namely the thing territory object function f of output is the molecular orbit finally given.

Below in conjunction with accompanying drawing, with CO₂For target molecule, Kr is referencing atom, and as embodiment, the invention will be further described:

In an embodiment of the invention, target molecule is CO₂, referencing atom is Kr.Experimental provision as in figure 2 it is shown, a branch of centre wavelength 800nm, pulsewidth 35fs, repetition rate 1kHz femtosecond laser by beam splitter be divided into arrangement light and drive light.Gas is arranged in the polarization direction of arrangement light by arrangement light, drive light to be controlled with half-wave plate (not shown) by the delay line arranged in light light path respectively with angle theta relative to the time delay Δ t of arrangement light, after arrangement light and driving combiner, pass through convex lens focus.Experiment arranges light and the intensity respectively 0.4 × 10 driving light and gas to interact¹⁴W/cm²With 2.3 × 10¹⁴W/cm², gas passes into vacuum chamber by the snifting valve that diameter is 100 μm, and the higher hamonic wave of generation is shown on MCP display screen by after optical grating diffraction.

Fig. 3 is that to record arrangement angles be CO when 0 degree in experiment₂15th to 35 high order harmonic spectrum.

Fig. 4 is to CO₂The angular distribution of the harmonic radiation of the unimolecule aspect obtained after the 19th subharmonic amplitude deconvolution.Wherein, during deconvolution, molecule arrangement angles probability distribution solves rotational wave bag obtain by calculating the time-dependent Schrodinger equation of molecule rotation, Fourier's cosine series that the angular distribution coefficient of the harmonic radiation of unimolecule aspect is undetermined are launched, and employ the first six of Fourier's cosine series expansion in embodiments of the present invention.Then pass through and test the higher hamonic wave arrangement angles radiation recorded, and driving light is that two constraintss solve Fourier's cosine series expansion term coefficient with the High-order Harmonic Generation under arrangement light different delayed time.

Fig. 5 is the present invention under " well behaved basis because of " guiding, carry out four generation iteration after stablize and uniquely thing territory object function, i.e. CO₂Molecular orbit.

Fig. 6 is the CO that the inventive method obtains₂The real CO that molecular orbit and ab iitio obtain₂CO under molecular orbit and Fourier's limit₂Molecular orbit, the section intercepting them carries out quantitative contrast.By Quantitative Comparison it can be seen that the present invention reconstruct CO₂Molecular orbit is qualitative or quantitatively reflects CO all accurately₂The actual trajcctorics of molecule.

Use the present invention " a kind of method utilizing higher hamonic wave amplitude to realize molecular orbit tomography ", also successfully respectively with C₂H₂(Fig. 7) and N₂(Fig. 8) molecular orbit tomography is achieved for embodiment.Wherein, CO₂、C₂H₂And N₂Molecule highest occupied molecular orbital respectively π_g、π_uAnd σ_gMolecular orbit three kinds different.

Those skilled in the art will readily understand; the foregoing is only presently preferred embodiments of the present invention; not in order to limit the present invention, all any amendment, equivalent replacement and improvement etc. made within the spirit and principles in the present invention, should be included within protection scope of the present invention.

Claims (7)

1.A kind of method utilizing higher hamonic wave amplitude to realize molecular orbit tomography, it is characterised in that described method comprises the steps:

The higher hamonic wave amplitude that S1, the arrangement molecule assemblage arrived by experimental detection radiate, obtains the angular distribution of the High-order Harmonic Generation of unimolecule aspect by deconvolution, calculates molecule equivalence under velocity gauge and replys dipole moment amplitude；

S2, by described equivalence reply dipole moment amplitude, by first generation iterative algorithm rebuild molecular orbit；

S3, the various molecular orbits obtained by described first generation iterative algorithm respectively, as ground state, calculate it and reply dipole moment amplitude, and compared with recording result with experiment, choose error function reckling for " well behaved basis because of ", are designated as f_gene；

S4, under the guiding of described " well behaved basis because of ", gradually carry out the second filial generation, the third generation ... iterative computation, until output is stable and unique result.

2. asClaimUtilize, described in 1, the method that higher hamonic wave amplitude realizes molecular orbit tomography, it is characterized in that, the higher hamonic wave of the arrangement molecule assemblage radiation in described step S1, being interacted by the gas molecule of femtosecond laser with arrangement to produce, gas molecule is the one in diatomic or polyatomic molecule gas.

3. asClaimUtilize, described in 1 or 2, the method that higher hamonic wave amplitude realizes molecular orbit tomography, it is characterized in that, the angular distribution of the High-order Harmonic Generation of the unimolecule aspect in described step S1, it is that usage factor Fourier's cosine series undetermined are launched and molecules align angle probability distribution, is obtained by deconvolution；Wherein, described molecules align angle probability distribution be by solve describe interaction between laser and metal Schrodinger equation obtain.

4. asClaimUtilizing, described in 1 or 2, the method that higher hamonic wave amplitude realizes molecular orbit tomography, it is characterised in that the first generation iteration in described step S2, its step includes:

The random phase of dipole moment amplitude | D | and input is replied in the calculated equivalence of S1, by experiment dataObtain frequency domain

S2, rightCarry out inverse Fourier transform, obtain thing territory function f'=FFT^-1(D)；

S3, thing territory function f' is carried out the constraint of thing territory boundary condition, obtain thing territory object function f；

S4, again thing territory function target f is carried out Fourier transformation, obtain frequency domain

S5, use equivalence are replied dipole moment amplitude | D | and are replacedIn | D'|, obtainAnd circulate repetition step S2, S3, S4, S5 until exporting stabilization result.

5. asClaimUtilize, described in 1 or 2, the method that higher hamonic wave amplitude realizes molecular orbit tomography, it is characterised in that " well behaved basis because of " in described step S3, is by calculating error functionChoose the thing territory object function that the first generation iteration corresponding to error function minima exports.

6. asClaimUtilize, described in 1 or 2, the method that higher hamonic wave amplitude realizes molecular orbit tomography, it is characterized in that, second filial generation iteration in described step S4, is the iteration carried out under " well behaved basis because of " guiding, and third generation iteration and higher algebraically iteration method therefor are identical with second filial generation iteration.

7. asClaimDescribed in 6?Utilize the method that higher hamonic wave amplitude realizes molecular orbit tomography, it is characterised in that described " well behaved basis because of " guiding, refer to when carrying out the n-th generation iteration, useReplace f_n-1The iteration carried out, wherein n is be more than or equal to 2.