CN106768337B - A kind of phase reconstruction method in two-dimensional Fourier transform electronic spectrum - Google Patents
A kind of phase reconstruction method in two-dimensional Fourier transform electronic spectrum Download PDFInfo
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Abstract
The present invention provides a kind of phase reconstruction method of two-dimensional Fourier transform electronic spectrum, and the inverting that this method includes at least spectral interference is calculated, to warbled interference spectrum D (ωt, τ) and inverse Fourier transform is carried out, the direct current in time domain with item is exchanged is filtered out, exchange item is then gained into frequency domain by discrete Fourier transform, S can be retrieved0(ωt) and f (ωt), pass through S0(ωt) and f (ωt) amplitude of local oscillations pulse and the amplitude and phase of photon-echo signal can be calculated.The present invention is by probing into the analysis in phase error source, it was found that the phase error of Two-dimensional electron spectrum determines that error has certain be associated with the zero-lag of coherence time and detection time, the relevant linear dependence with phase on emission shaft with tranmitting frequency is effectively eliminated, and then reconstructs real two-dimensional absorption spectrum.
Description
Technical field
The present invention relates to the phase correction field of spectrometer, more particularly in a kind of two-dimensional Fourier transform electronic spectrum
Phase reconstruction method.
Background technology
As a kind of effective detection means in Ultrafast spectrum, Two-dimensional electron spectrum (Two-Dimensional
Electronic Spectroscopy, 2DES) successfully it is used for detecting a system such as electronics and vibration coupling in complication system
The ultra-fast dynamics information of row basic process.But there are still three big technological challenges in the specific implementation of Two-dimensional electron spectrum：It is first
First, since excitation wavelength is from ultraviolet to near-infrared, the phase stability for realizing sub-wavelength range is extremely difficult, but current
For this problem, can be designed to deal with by the fine device of some complexity, it is main to include passive steady phase and actively steady phase；Its
Secondary, on detection direction, the scattering derived from sample can introduce experiment to Two-dimensional electron spectrum with the superposition between detectable signal and miss
Difference, scattering interference can be inhibited by modulating the method for phase-lock technique or phase loop measurement；Finally, in sub-wavelength precision
The phase information of interior accurate determining Two-dimensional electron spectrum is a greatly challenge, because the uncertainty of phase can lead to two dimension
The real and imaginary parts aliasing of spectrum causes two-dimensional absorption blending algorithm to deform, and therefore, corrects phase ambiguity for heterodyne detection two dimension
It is most important that correct complete Two-dimensional electron spectrum is reconstructed in electronic spectrum experiment.
For the phase fuzzy problem in above-mentioned Two-dimensional electron spectrum, up to now, may be used as there are mainly two types of method
Solve the problems, such as the phase reconstruction of Two-dimensional electron spectrum, i.e. projection slice theorem (projection-slice theorem) and preset
Global phase (presetting global phase).
Presently the most widely used phase reconstruction method is projection slice theorem, is exactly to pass through two-dimentional light in simple terms
Modal data is along ωτIntegral projection is carried out on axis to ωtAxis reappears spectrally resolved transient absorption spectra.In Phase Processing process
In, ωtOne-dimensional spectrum on axis needs to be multiplied by a correction phase factor item It is that a phase is normal
Amount, Δ tLORepresent the time interval t between signal pulse and local oscillations pulse (Local Oscillator, LO)LOZero prolong
Slow time error.Recent research indicate that only to ωtAxis direction carries out phase correction to restore the phase of two-dimension spectrum be inadequate
, it there is a need to ωτAxis applies an additional limitation, i.e., along ωτAxis carries out phase correction.It is missed in view of the time on τ axis
Difference, the phase correction factor can be written asHowever, this method is gone back in actual experiment
There are certain deficiencies.First, during the phase correction, needing simultaneously to optimize above three variable can just obtain
Correct pump probe spectrum, and the optimization program is along with numerous and diverse iterative fitting；Secondly, in pumping-spy as supplement
It is not that easy can realize to survey in experiment and repeat out identical experiment condition.Moreover, compared to heterodyne detection two dimension
Electronic spectrum, pumping-detection experimental signal have relatively low signal-to-noise ratio, just because of this, one are weighed with relatively low standard
A signal with high s/n ratio is clearly unreasonable.
In order to avoid phase distortion, another effective method is that the precise phase of completely determining pulse train is closed
System, and the correct global phase of preset excitation pulse before data acquisition.Experimentally, observational record four is come by using CCD
The interference fringe of beam light overlapping region.It is eliminated by the space interference striped between matching pulse 1 and 2, pulse 3 and LO pulses
Phase offset in the sub- period.Similarly, scattering light by measurement can also reach same in the spectral interference striped of focal point
The purpose of sample.But problem is, the method that such phase determines not is to be carried out in the nonlinear interaction area of sample,
The region, the transmission effects in sample may cause the phase error of very little.
Invention content
In view of the foregoing deficiencies of prior art, the purpose of the present invention is to provide a kind of two-dimensional Fourier transform electronics
Phase reconstruction method in spectrum effectively eliminates the relevant linear dependence with phase on emission shaft with frequency, and then reconstructs
Go out real two-dimensional absorption spectrum, restore true physical essence.
In order to achieve the above objects and other related objects, the present invention is provided in a kind of two-dimensional Fourier transform electronic spectrum
Phase reconstruction method, includes the following steps：1) the Two-dimensional electron spectrum of standard is built using the method for numerical simulation：Use three
The laser of beam having time difference excites sample, and photon is built by the numerical value for calculating receptance function and three exciting field convolution
Echo-signal：
Wherein, t1、t2、t3It is the time of first, second and third beam exciting light respectively, Rn (t1, t2, t3) it is the response of three rank of time domain
Function, E1(t-t3-t2-t1)、E2(t-t3-t2)、E3(t-t3) it is to distinguish before t moment system space somewhere is by t moment respectively
In t-t3-t2-t1, t-t3-t2, three electric fields of three laser pulses at t-t3 moment；
2) it introduces local concussion pulse and generates interference with the photon-echo signal, carry out heterodyne detection, construct spectrum
Interference strength：
Wherein, eiωtPhase factor is expressed as, LO is expressed as local concussion, ELO(t) it is expressed as the local oscillations electricity of t moment
, Esig(t) it is expressed as the photon-echo signal electric field of t moment；
3) inverting that spectral interference is carried out using self-reference spectral interference inversion algorithm is calculated, to restore in Two-dimensional electron spectrum
Complex value photon-echo electric field：
3a) the heterodyne detection spectrum D (ω to be detected by spectrometert, τ) and it shakes as photon-echo signal with local
The result of interference between pulse is swung, i.e.,
Wherein, S0(ωt)=| ELO(ωt)|2+|Esig(ωt)|2, (4)
Wherein, ωtIt is expressed as tranmitting frequency, ELO(ωt) the local electric field that shakes is expressed as with ωtVariation function,With ELO(ωt) in complex conjugate relationship, Esig(ωt) it is expressed as variation function of the photon-echo signal electric field with ω t；With Esig(ωt) in complex conjugate relationship, τ is coherence time, S0(ωt) it is the local amplitude and photon for shaking electric field
The quadratic sum of the amplitude of echo-signal, f (ωt) it is locally to shake electric field with ωtComplex conjugate and the photon-echo of variation function believe
Number electric field is with ωtChange the product of function；
3b) to warbled interference spectrum D (ωt, τ) carry out inverse Fourier transform, by the direct current in time domain with exchange
Item filters out, and exchange item then is gained frequency domain by discrete Fourier transform, can retrieve S0(ωt) and f (ωt),
Its formula is respectively：
S0(ωt)=| ELO(ωt)|2+|Esig(ωt)|2, (6)
3c) calculate the amplitude of local oscillations pulse, the amplitude and phase of photon-echo signal：
The magnitude determinations formula of local oscillations pulse is：
The magnitude determinations formula of photon-echo signal is：
The formula of the phase of photon-echo signal is：
Wherein, f (ωt) and S0(ωt) obtained by formula (6), (7),It is the input of local oscillations pulse
Phase, arg f (ωt) it is f (ωt) argument value.
In one embodiment of the present invention, before inverse Fourier transform is done, the step 3b) it further includes to frequency domain
Data carry out zero padding operating procedure, are suitable for adjusting the timing error Δ t between photon-echo signal and local oscillations pulseLO。
In one embodiment of the present invention, the zero padding operation is the zero padding behind the high-frequency data of frequency domain.
In one embodiment of the present invention, in step 3), the direct current in time-domain signal is filtered out with item is exchanged
Afterwards, exchange item is moved into time zero, it is desirable that shift length is equal to heterodyne detection time tLOAbsolute time.
In one embodiment of the present invention, the input phase of the local oscillations electric fieldPass through pulse characterization side
Method measures.
In one embodiment of the present invention, the pulse characterizing method is frequency resolved optical gating (FROG) or straight
Connect the spectrum phase interference method (SPIDER) of electric field reconstruct.
In one embodiment of the present invention, the accuracy of the wavelength, scope control of the spectrometer is in≤0.1nm.
In one embodiment of the present invention, state two-dimensional Fourier transform electronic spectrum phase reconstruction method further include with
Lower step：Choose the tranmitting frequency ω of two-dimensional phase spectrumtAs look-in frequency value, detect under the look-in frequency value not
During with time error delta τ, the spectrum phase of the two-dimensional phase spectrum with look-in frequency value dependence, using ωτ×Δτ
The linear fit that is carried out to the spectrum phase of linear phase, obtain and linearly become between the spectrum phase and look-in frequency value
The slope of change is equal to Δ τ.
In one embodiment of the present invention, the phase reconstruction method of the two-dimensional Fourier transform electronic spectrum further includes
Following steps：For all tranmitting frequency ωtΔ τ is acquired, Δ τ average values is then sought, produces with ωtLinear change and tiltedly
Rate is the line spectrum of Δ τ average values；The line spectrum will be subtracted in two-dimensional phase spectrum, to reconstruct correct two-dimensional phase
Position spectrum.
As described above, the phase reconstruction method in the two-dimensional Fourier transform electronic spectrum of the present invention, has beneficial below
Effect：
The data obtained obtained by numerical simulation, that is, is used under the premise according to actual tests situation in the present invention
The heterodyne detection spectrum D (ω that are detected of three beams of laser, local concussion pulse and spectrometert, τ) and it is numerical simulation institute
.The Two-dimensional electron spectrum of standard is built using the method for numerical simulation, thus can not only exclude experiment bring include
Error including phase instability and excitation scattering etc., and the knot that other methods can be obtained as a kind of benchmark theory
Fruit carries out cross validation.Using self-reference spectral interference inversion algorithm, by accurately adjusting tLO, and spectrum phase is monitored simultaneously
Flatness can significantly eliminate spectrum phase slope.
By probing into the analysis in phase error source, the phase error of Two-dimensional electron spectrum and coherence time and spy are found
The zero-lag for surveying the time determines that error has certain association, to this corresponding phase correction scheme of proposition, effectively eliminates
Phase, that is, by using the mode of Data Post, is removed along ω with the linear dependence of frequency on relevant and emission shafttAxis and
ωτThe line spectrum phase slope of axis, and then reconstruct real two-dimensional absorption spectrum.Pass through two after phase correction as a result,
Spectrum is tieed up, it can be found that more lost experimental phenomenas, restore true physical message essence.This method relies solely on
Simple data fitting and the phase correction method of processing, compare with conventional Phase Processing method, have and be easy to real
It applies, without complementarity experiment and the advantages of numerous and diverse iterative fitting.In combination with existing phase correction in Two-dimensional electron spectrum
Method, this algorithm also can be as the cross validation means of phase correction.
Description of the drawings
Fig. 1 is shown as pulse sequence diagram during heterodyne detection in Two-dimensional electron spectrum.
Fig. 2 is shown as in tLOInterference pattern during=400fs between signal pulse and LO pulses.
Fig. 3 is shown as that in the time domain, amplitude and phase diagram after item 400fs, 402fs are moved to time zero will be exchanged.
The calibration error that Fig. 4 is shown as spectrometer be wavelength be 800nm, wavelength error~0.5nm and accurate calibration spectrum
Figure is compared in instrument interference.
Fig. 5 is shown as the phase diagram that the not calibrated spectrometer with proper calibration of wavelength restores.
Heterodyne detection spectral interference figure when the zero-lag that Fig. 6 is shown as τ axis accurately determines.
Fig. 7 is shown as the pure absorption spectrum of two dimension reconstructed from Fig. 6.
Fig. 8 is shown as heterodyne detection spectral interference figure during timing error Δ τ=1fs.
Fig. 9 is shown as the pure abosrption spectrogram of two dimension reconstructed from Fig. 8.
Figure 10 is shown as ωtDuring=2.59rad/fs, spectrum phase is with ωτVariation diagram.
Figure 11 is shown as the phase component figure of two-dimension spectrum during Δ τ=0fs in corresponding diagram 10.
Figure 12 is shown as reference spectra phase diagram during Δ τ=0fs.
Figure 13 is shown as the phase component figure of two-dimension spectrum during Δ τ=1fs in corresponding diagram 12.
Figure 14 is shown as correcting the phase error in Figure 13 caused by timing error, is proportional to Δ τ's by removal
The two-dimensional phase bitmap that phase linearity variation obtains later.
Figure 15 is shown as the pure absorption spectrogram of two dimension after phase correction.
Figure 16 is shown as the pump probe datagram based on projection slice theorem.
Specific embodiment
Illustrate embodiments of the present invention below by way of specific specific example, those skilled in the art can be by this specification
Disclosed content understands other advantages and effect of the present invention easily.The present invention can also pass through in addition different specific realities
The mode of applying is embodied or practiced, the various details in this specification can also be based on different viewpoints with application, without departing from
Various modifications or alterations are carried out under the spirit of the present invention.It should be noted that in the absence of conflict, following embodiment and implementation
Feature in example can be combined with each other.
It should be noted that the diagram provided in following embodiment only illustrates the basic structure of the present invention in a schematic way
Think, component count, shape and size when only display is with related component in the present invention rather than according to actual implementation in schema then
It draws, kenel, quantity and the ratio of each component can be a kind of random change during actual implementation, and its assembly layout kenel
It is likely more complexity.
The present invention provides a kind of phase reconstruction methods in two-dimensional Fourier transform electronic spectrum, include the following steps：
1) the Two-dimensional electron spectrum of standard is built using the method for numerical simulation：Sample is carried out using the laser of three beams having time difference
Excitation builds photon-echo signal by the numerical value for calculating receptance function and three exciting field convolution：
Wherein, t1、t2、t3It is the time of first, second and third beam exciting light respectively, Rn (t1, t2, t3) it is the response of three rank of time domain
Function, E1(t-t3-t2-t1)、E2(t-t3-t2)、E3(t-t3) it is to distinguish before t moment system space somewhere is by t moment respectively
In t-t3-t2-t1, t-t3-t2, three electric fields of three laser pulses at t-t3 moment；The data obtained is in the present invention
Under the premise according to actual tests situation obtained by numerical simulation.
2) it introduces local concussion pulse and generates interference with the photon-echo signal, carry out heterodyne detection, construct spectrum
Interference strength：
Wherein, eiωtPhase factor is expressed as, LO is expressed as local concussion, ELO(t) it is expressed as the local oscillations electricity of t moment
, Esig(t) it is expressed as the photon-echo signal electric field of t moment；
3) inverting that spectral interference is carried out using self-reference spectral interference inversion algorithm is calculated, to restore in Two-dimensional electron spectrum
Complex value photon-echo electric field：
3a) the heterodyne detection spectrum D (ω to be detected by spectrometert, τ) and it shakes as photon-echo signal with local
The result of interference between pulse is swung, i.e.,
Wherein, S0(ωt)=| ELO(ωt)|2+|Esig(ωt)|2, (4)
Wherein, ωtIt is expressed as tranmitting frequency, ELO(ωt) the local electric field that shakes is expressed as with ωtVariation function,With ELO(ωt) in complex conjugate relationship, Esig(ωt) photon-echo signal electric field is expressed as with ωtVariation function；With Esig(ωt) in complex conjugate relationship, τ is coherence time, S0(ωt) it is the local amplitude and photon for shaking electric field
The quadratic sum of the amplitude of echo-signal, f (ωt) it is locally to shake electric field with ωtComplex conjugate and the photon-echo of variation function believe
Number electric field is with ωtChange the product of function；
3b) to warbled interference spectrum D (ωt, τ) carry out inverse Fourier transform, by the direct current in time domain with exchange
Item filters out, and exchange item then is gained frequency domain by discrete Fourier transform, can retrieve S0(ωt) and f (ωt),
Its formula is respectively：
S0(ωt)=| ELO(ωt)|2+|Esig(ωt)|2, (6)
3c) calculate the amplitude of local oscillations pulse, the amplitude and phase of photon-echo signal：
The magnitude determinations formula of local oscillations pulse is：
The magnitude determinations formula of photon-echo signal is：
The formula of the phase of photon-echo signal is：
Wherein, f (ωt) and S0(ωt) obtained by formula (6), (7),It is the input of local oscillations pulse
Phase, arg f (ωt) it is f (ωt) argument value.Pass through frequency resolved optical gating (FROG), direct electric field
Spectrum phase interference method (SPIDER) isopulse characterizing method of reconstruct measures,As it is known that argf (ωt) phase
Error is substantially exactlyCaused phase error.So for f (ω are influencedt) some factors pairIt is entangled
Just.
Two-dimensional Fourier transform electronic spectrum is detected based on third-order non-linear polarity effect, has used three beams
The laser of having time difference excites sample, this three-beam carries out object effect and produces a flashlight Esig(t), and
The signal pulse generated needs to obtain Two-dimensional electron spectrum with LO pulses progress heterodyne detection again.The reason of introducing LO has
Two：First, experimentally, three rank signal very littles, the ambient noise of infrared detector is bigger, directly signal pulse is sent into and is examined
Surveying device may be such that signal pulse is submerged in noise, folded to be concerned with signal pulse with 100 times bigger than signal or more of LO pulses
The influence of noise can be effectively reduced by adding；Second is that because LO pulses can help to detect the phase of signal pulse, so as to make mathematics Fu
In leaf transformation obtain tranmitting frequency ωτIt is possibly realized.
Phase distortion problem in two-dimensional Fourier transform electronic spectrum is derived mainly from two aspects, and one is that spectrum is done
Experimental error caused by interferometer, the other is the timing error of coherence time τ causes.
(1) spectrointerferometer error and phase correction
Referring to Fig. 1, pulse sequence diagram when Fig. 1 is shown as heterodyne detection in Two-dimensional electron spectrum.Spectrointerferometer is deposited
Deficiency be to generate along tranmitting frequency ωtThe main reason for phase error on direction.In spectral interference, determine that heterodyne is visited
Survey time tLOWhen timing error and spectrometer in wavelength calibration error can cause with ωtThe phase error of variation.
For spectral interference, the time delay between photon-echo signal and LO pulses need to be determined accurately in sub-wavelength precision
Range, because of the timing error Δ t of very littleLOA slope be may result in as Δ tLOWith ωtThe line spectrum phase of variation.So
And to realize such high-precision time delay, what this point was always difficult to realize in actual experiment.But, in the present invention
Spectral interference inversion algorithm in, can be by fine-tuning tLOAbove-mentioned phase slope is removed, it is true multiple so as to reconstruct
It is worth electric field signal.
In traditional inversion algorithm, usually by the direct inverse Fourier transform of spectral interference figure as shown in Figure 2 to time domain, choosing
Heterodyne ingredient therein is taken, is fourier transformed into frequency domain again later.
In the present invention, before inverse Fourier transform is done, zero padding operation has been carried out first to the data of frequency domain, preferably
Ground, the zero padding behind the high frequency of frequency domain.In this way, a large amount of frequency domain sample point can improve the resolution ratio in time domain, spectrometer is made up
The limited deficiency of pixel.So as to which after inverse Fourier transform, heterodyne exchange item can be well with time interval in the time domain
tLODC terms separate.In the present invention, the DC terms of time-domain signal are filtered out with item is exchanged by window function,
Exchange item is moved into time zero later, it is desirable that shift length is exactly equal to tLO.Then, DC terms are led to the item that exchanges after movement
It crosses discrete Fourier transform and returns frequency domain, thus to obtain S0(ωt) and f (ωt), S0(ωt) and f (ωt) calculation formula be respectively：
S0(ωt)=| ELO(ωt)|2+|Esig(ωt)|2,
DC terms return frequency domain with the item that exchanges after movement by discrete Fourier transform, can also obtain photon-echo signal
Amplitude | Esig(ωt) | and phase
The calculation formula of the amplitude of photon-echo signal is：
The calculation formula of the phase of photon-echo signal is：
Referring to Fig. 3, Fig. 3 is shown as stand-by period T=70fs and heterodyne detection time tLO=400fs and Δ tLO=
The amplitude and phase spectrum reconstructed during 402fs.During this reconstruct, tLOShift length can pass through real time monitoringFlatness is effectively adjusted, to ensure to remove t completelyLOCaused linear phase variation.Here, the shifting of item is exchanged
Bit length need to be exactly equal to tLO, because adjusting tLOWhen very little error will introduce with ωtThe line spectrum phase of variation.
In spectral interference inversion algorithm,Flatness cannot be by simply solvingIt obtains, because of sample
The third-order non-linear response of product is also resulted in dependent on ωtLine spectrum phase.In addition, the input phase of LO pulses
Must be measured by pulse characterizing method and fromIt subtracts, is ensured with thisCome solely from the non-linear sound of sample
It should.To sum up, using self-reference spectral interference inversion algorithm, by accurately adjusting tLO, and the flatness of spectrum phase is monitored simultaneously,
Spectrum phase slope can significantly be eliminated.
In addition, the wavelength calibration error of the spectrometer in experiment is also resulted in along ωtThe phase error of axis variation.It please join
Read Fig. 4, the calibration error that Fig. 4 is shown as spectrometer be wavelength be 800nm, wavelength error~0.5nm and accurate calibration spectrum instrument
Figure is compared in interference, the spectrum phase figure that line 42 be the calibration error of spectrometer in the figure when being 0.5nm (at 800nm), comparison light
The situation (shown in Fig. 4 lines 41) that spectrometer is precisely calibrated, there are one constant translations for the former spectrum phase.Referring to Fig. 5, line 51
It is the phase that the spectrometer of wavelength proper calibration restores, line 52 is the phase that the not calibrated spectrometer of wavelength restores, and is had certain
Phase difference.In consideration of it, in actual experiment, spectrometer should carry out carefully aligned, wavelength essence with the atomic emissions line of lamp
Exactness scope control is in≤0.1nm.
(2) coherence time zero-lag error and phase correction
For another situation in phase error source, the timing error of coherence time is inevitably introduced along ωτ
The phase factor of axis, and the pure absorption spectrum of serious distortion two dimension.
In an experiment, excitation pulse 1 and 2 scans to obtain complex phase position (rephasing) signal and non-complex phase position respectively
(non-rephasing) signal, the two signals are stitched together at τ=0, obtain the pure absorption spectra of two dimension.However, τ=0
It is difficult to it is accurately determined in sub-wavelength precision.Here, coherence time accurately determines the error of (τ=0) and coherence time there are 1fs
Using the heterodyne detection spectral interference figure of numerical value structure respectively such as Fig. 6 and Fig. 8 when (τ=1fs).During τ=0, interference fringe is very
Smoothly, without phase hit.During τ=1fs, interference fringe is very smooth at cross spider τ=0, without phase jitter.Due to two
Interference fringe in the case of kind is closely similar, causes to be difficult to offer a clear explanation.However, although the interference pattern of two kinds of situations is much like,
But the profile of the pure absorption spectrum of two dimension is different, as shown in figures 7 and 9.In fig.9, due to the pure absorption light of the presence of Δ τ two dimension
The profile of spectrum is deformed by strong distortions.Real experiment is simulated it is worth noting that, interference pattern during Δ τ=1fs is for we
Condition value structure.Main process is exactly to first pass through fixed pulse 2 in -70fs, and scanning pulse 1 is from -140fs to -71fs, so
In -71fs, two parts spectrum is finally stitched together fixed pulse 1 by scanning pulse 2 again from -70fs to -140fs afterwards.The first step
Scanning process, for fixed pulse 2 at -70fs, scanning pulse 1 is to generate Two-dimensional electron spectrum from -140fs to -70fs
Rephasing parts；Second step, fixed pulse 1, scanning pulse 2 are to obtain non-rephasing parts；By two parts
It is stitched together to obtain complete Two-dimensional electron spectrum.
Figure 11 is shown as the phase component figure of the corresponding two-dimension spectrums of Fig. 7, and white line (black arrow instruction) represents ωt=
Spectrum phase during 2.59 rad/fs, Figure 13 are shown as the phase component figure of the corresponding two-dimension spectrums of Fig. 9, white line (black arrow
Instruction) represent ωtSpectrum phase during=2.59rad/fs.Compare the two phase component figures, you can find the relevant of very little
Time timing error, which may result in phase spectrum and benchmark, very big deviation, causes the pure absorption spectra distortion distortion of two dimension.
Lead to the situation of phase error for more than coherence time timing error, the present invention chooses wherein tranmitting frequency ωt
As specific look-in frequency value.Spectrum phase under detection comparison detection frequency values during different time error is with look-in frequency value
Dependence, as in Figure 10 101,102,103 it is shown in solid.ω is used againτThe line spectrum of × Δ τ to spectrum phase into
Capable linear fit, as shown in the dotted line in Figure 10.Generally, spectrum phase and ωtBetween have good linear relationship, and
The slope of linear change is Δ τ.Based on above analysis, can by subtracted from the phase spectrum of having time error this with
ωtThe line spectrum of linear change reconstructs correct phase spectrum.It is Δ τ=1fs to please refer to Fig.1 a line in 2, Figure 12
When, remove the phase spectrum after phase slope, reference phase spectrum when another line is Δ τ=0fs, two lines are almost ideal
Coincide, illustrate the phase spectrum reproducing reference phase spectral results well after correcting.The program is applied to two-dimentional light
Each ω in spectrumt, then along ωtThe phase fuzzy problem in direction can be obtained by solution.
In actual experiment, the absolute zero-lag point of coherence time is difficult accurate determines.The present invention passes through to spectrum phase
Δ τ can be determined by carrying out linear fit, then to all ωtValue, which is fitted, acquires Δ τ, then seeks Δ τ average values, you can
Substantially estimate Δ τ value sizes practical in experiment.As an example, by each look-in frequency value ω in Figure 13t, produce with
ω t linear changes and the line spectrum that slope is Δ τ average values, subtract line spectrum phase, as a result from two-dimensional phase spectrum
Such as Figure 14, it can be finally inversed by the phase component figure of the standard two-dimensional spectrum of the accurate calibration in Figure 11 well, and from phase
In two-dimensional absorption spectrum (as shown in figure 15) after correction, spectral characteristic is also restored expected from discovery, this is confirmed well
The feasibility of phase correction algorithm of the present invention.The present invention proposes a kind of phase correction side that can offset two-dimensional absorption spectrum shape distortion
Method, this method only relies on simply data fitting and processing routine, so as to avoid additionally carrying out pumping-detection measurement and throwing
Iterative fitting algorithm in shadow Slice Theorem.
This method and projection slice theorem are confirmed.By two after the two-dimensional absorption spectrum of distortion and phase correction
Dimension absorption spectrum and the two-dimensional absorption spectrum of standard are compared with the method that pump probe projects, as shown in figure 16.In the figure
Line 163 represents that two-dimensional absorption spectrum is projected in pumping-detection during Δ τ=1fs, and line 161 represents two after phase correction in Fig. 4
The pumping-detection projection of absorption spectrum is tieed up, line 162 represents the pumping-detection projection of the two-dimensional absorption spectrum of standard, can from figure
Go out, the two-dimensional absorption spectrum of two-dimensional absorption spectrum and standard after phase correction coincide fine.Therefore, look-in frequency ωtSide
Upward phase twist can be by removing the spectrum phase ω of linear changeτ× Δ τ is effectively corrected.
In conclusion the present invention has found that the phase of Two-dimensional electron spectrum is missed by probing into the analysis in phase error source
Difference and the zero-lag of coherence time and detection time determine error have it is certain be associated with, corresponding phase correction side is proposed to this
Case effectively eliminates the relevant linear dependence with phase on emission shaft with frequency, and then reconstructs real two-dimensional absorption light
Spectrum；By the two-dimensional absorption spectrum after phase correction, it can be found that more lost experimental phenomenas, restore true physics
Essence.So the present invention effectively overcomes various shortcoming of the prior art and has high industrial utilization.
The above-described embodiments merely illustrate the principles and effects of the present invention, and is not intended to limit the present invention.It is any ripe
The personage for knowing this technology all can carry out modifications and changes under the spirit and scope without prejudice to the present invention to above-described embodiment.Cause
This, those of ordinary skill in the art is complete without departing from disclosed spirit and institute under technological thought such as
Into all equivalent modifications or change, should by the present invention claim be covered.
Claims (9)
- A kind of 1. phase reconstruction method of two-dimensional Fourier transform electronic spectrum, which is characterized in that include the following steps：1) the Two-dimensional electron spectrum of standard is built using the method for numerical simulation：Using the laser of three beams having time difference to sample It is excited, photon-echo signal is built by the numerical value for calculating receptance function and three exciting field convolution：Wherein, t1、t2、t3It is the time of first, second and third beam exciting light respectively, Rn (t1, t2, t3) it is three rank receptance function of time domain, E1(t-t3-t2-t1)、E2(t-t3-t2)、E3(t-t3) it is to be respectively at before t moment system space somewhere is by t moment respectively Three electric fields of three laser pulses at t-t3-t2-t1, t-t3-t2, t-t3 moment；2) it introduces local concussion pulse and generates interference with the photon-echo signal, carry out heterodyne detection, construct spectral interference Intensity：Wherein, eiωtPhase factor is expressed as, LO is expressed as local concussion, ELO(t) the local oscillations electric field of t moment is expressed as, Esig(t) it is expressed as the photon-echo signal electric field of t moment；3) inverting that spectral interference is carried out using self-reference spectral interference inversion algorithm is calculated, to restore answering in Two-dimensional electron spectrum It is worth photon-echo electric field：3a) the heterodyne detection spectrum D (ω to be detected by spectrometert, τ) and as photon-echo signal and local oscillations arteries and veins Result of interference between punching, i.e.,Wherein, S0(ωt)=| ELO(ωt)|2+|Esig(ωt)|2, (4)Wherein, ωtIt is expressed as tranmitting frequency, ELO(ωt) the local electric field that shakes is expressed as with ωtVariation function,With ELO(ωt) in complex conjugate relationship, Esig(ωt) photon-echo signal electric field is expressed as with ωtVariation function；With Esig(ωt) in complex conjugate relationship, τ is coherence time, S0(ωt) it is the local concussion amplitude of pulse and shaking for photon-echo signal The quadratic sum of width, f (ωt) it is locally to shake electric field with ωtVariation function complex conjugate and photon-echo signal electric field with ωt Change the product of function；3b) inverse Fourier is carried out to carrying out the frequency modulation(PFM) interference spectrum D (ω t, τ) obtained by heterodyne detection by using spectrometer Transformation, the direct current in time domain is filtered out with item is exchanged, and exchange item then is gained frequency domain by discrete Fourier transform, can To retrieve S0(ωt) and f (ωt), formula is respectively：S0(ωt)=| ELO(ωt)|2+|Esig(ωt)|2, (6)3c) calculate the amplitude of local oscillations pulse, the amplitude and phase of photon-echo signal：The magnitude determinations formula of local oscillations pulse is：The magnitude determinations formula of photon-echo signal is：The formula of the phase of photon-echo signal is：Wherein, f (ωt) and S0(ωt) obtained by formula (6), (7),It is the input phase of local oscillations pulse, arg f(ωt) it is f (ωt) argument value.
- 2. the phase reconstruction method of two-dimensional Fourier transform electronic spectrum according to claim 1, it is characterised in that：It is doing Before inverse Fourier transform, the step 3b) it further includes zero padding operating procedure is carried out to the data of frequency domain, it is suitable for adjusting photon Timing error Δ t between echo-signal and local oscillations pulseLO。
- 3. the phase reconstruction method of two-dimensional Fourier transform electronic spectrum according to claim 2, it is characterised in that：It is described Zero padding operation is the zero padding behind the high-frequency data of frequency domain.
- 4. the phase reconstruction method of two-dimensional Fourier transform electronic spectrum according to claim 1, it is characterised in that：In step It is rapid 3) in, by the direct current in time-domain signal with exchange after item filters out, exchange item is moved into time zero, it is desirable that shift length Equal to heterodyne detection time tLOAbsolute time.
- 5. the phase reconstruction method of two-dimensional Fourier transform electronic spectrum according to claim 1, it is characterised in that：It is described The input phase of local oscillations pulseIt is measured by pulse characterizing method.
- 6. the phase reconstruction method of two-dimensional Fourier transform electronic spectrum according to claim 5, which is characterized in that described The spectrum phase interference method that pulse characterizing method is reconstructed for frequency resolved optical gating or direct electric field.
- 7. the phase reconstruction method of two-dimensional Fourier transform electronic spectrum according to claim 1, it is characterised in that：It is described The accuracy of the wavelength, scope control of spectrometer is in≤0.1nm.
- 8. the phase reconstruction method of two-dimensional Fourier transform electronic spectrum according to claim 1, it is characterised in that：It is described The phase reconstruction method of two-dimensional Fourier transform electronic spectrum is further comprising the steps of：Choose the tranmitting frequency of two-dimensional phase spectrum ωtAs look-in frequency value, when detecting different time error delta τ under the look-in frequency value, the two-dimensional phase spectrum Spectrum phase with look-in frequency value dependence, using ωτThe line that the linear phase of × Δ τ carries out the spectrum phase Property fitting, obtain linear change between the spectrum phase and look-in frequency value slope be equal to Δ τ.
- 9. the phase reconstruction method of two-dimensional Fourier transform electronic spectrum according to claim 8, it is characterised in that：It is described The phase reconstruction method of two-dimensional Fourier transform electronic spectrum is further comprising the steps of：For all tranmitting frequency ωtΔ τ is acquired, Δ τ average values is then sought, produces with ωtLinear change and slope are Δ The line spectrum of τ average values；The line spectrum will be subtracted in two-dimensional phase spectrum, to reconstruct correct two-dimensional phase spectrum.
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| CN101523773A (en) * | 2006-09-22 | 2009-09-02 | 卢森特技术有限公司 | Reconstruction and restoration of an optical signal field |
| CN101598798A (en) * | 2008-12-31 | 2009-12-09 | 中国资源卫星应用中心 | A kind of system and method to rebuilding spectrum of high spectrum intervention data |
| CN104272072A (en) * | 2012-02-20 | 2015-01-07 | 国立大学法人大阪大学 | Waveform reconstruction device, waveform reconstruction system, and waveform reconstruction method |
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| US6061555A (en) * | 1998-10-21 | 2000-05-09 | Parkervision, Inc. | Method and system for ensuring reception of a communications signal |
| CN101523773A (en) * | 2006-09-22 | 2009-09-02 | 卢森特技术有限公司 | Reconstruction and restoration of an optical signal field |
| CN101598798A (en) * | 2008-12-31 | 2009-12-09 | 中国资源卫星应用中心 | A kind of system and method to rebuilding spectrum of high spectrum intervention data |
| CN104272072A (en) * | 2012-02-20 | 2015-01-07 | 国立大学法人大阪大学 | Waveform reconstruction device, waveform reconstruction system, and waveform reconstruction method |
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