CN102507021A - Method for measuring attosecond X-ray impulse strength and chirp time distribution and application thereof - Google Patents

Abstract

The invention discloses a method for measuring attosecond X-ray impulse strength and chirp time distribution and application thereof. According to parametric calculation formulas, relative laser phase of each measured photoelectron can be determined by the photoelectron spectrums acquired from measurement of two different laser strengths, and shape and specific time structures of impulse, including impulse strength and chirp time distribution, are reconstructed by the spectrum analysis technology of the transformation equations of the photoelectron spectrums. Without a great quantity of time-resolved measurement of the photoelectron spectrum or tedious iterative computation or test data fitting process, the method can assist in reconstructing time-domain characteristics of the attosecond X-ray impulse from the two photoelectron spectrums acquired by measuring. Measurement results of the method, serving as reference data, can be used for researching, analyzing, evaluating and optimizing technical parameters and property indexes of the attosecond X-ray impulse light source, and can be used for researching and analyzing relative information varies along with time during the process of superfast reaction dynamics.

Description

The measuring method and the application of the Ah second X-ray pulse intensity and the time distribution of warbling

Technical field

The invention belongs to ultrafast optics, be specifically related to a kind of method and application thereof of measuring the Ah second X-ray pulse intensity and the time distribution of warbling simultaneously.

Background technology

Produce or use Ah second (10 no matter be ^-18Second) the X-ray, all need study the time response with the measuring light pulse, i.e. the function that distributes in time of intensity and frequency (warbling).Owing to lack the nonlinear optical effect and corresponding medium of available measurement Ah second X-ray, can't directly measure these parameters with instrument at present.But, the X-ray with like the gas atom matter interaction, can produce photoelectron by photoelectric effect.If these photoelectrons are simultaneously by the laser electric field effect, its final states momentum will have certain distribution.The structure of this distribution and atom or molecule is relevant with the time response and the laser parameter of X-ray, can calculate through separating schrodinger equation in theory.Experimentally, through measuring photoelectronic momentum or energy distribution,, can obtain temporal information and the valence bond or the MO dynamic evolution-information of Ah second X-ray pulse itself as become the photoelectron spectroscopy of 0 ° or 180 ° with the laser linear polarization direction.Photoelectron spectroscopy has comprised these temporal informations, but it and the time response of pulse or the relation between the molecular orbit characteristic are not intuitively.This is that photoelectron spectroscopy has complicacy because photoelectric effect is a typical quantum process, has comprised the quantum interference result between the photoelectricity Wavelet Packet that different moment produce.Utilize existing Ah second's spectrum phase interference direct electric field reconstruction method SPIDER (spectral phase interferometry for direct electric field reconstruction) technology; Need carry out beam split to Ah second X-ray monopulse, make it to become two that be equal to and have a monopulse sequence of certain hour difference.Excite the time response of obtaining Ah second X-ray monopulse with the interference image between the photoelectron of a branch of gas atom generation through measuring and analyze these two monopulses.The technical requirement of this measuring method is very high, need carry out beam split, focusing and high resolving power electron spectroscopy measurement to monopulse.The Ah second FROG technology that use is got up by the frequency discrimination grating FROG in traditional energy photons field (frequency-resolved optical gating) principle development; Experimentally need be in the time in dozens of minutes, measurement tens to hundreds of is individual to have the photoelectron time-resolved spectrum of the X-ray pulse energizing gas atom generation of different time delays, the temporal information that could rebuild these ultrashort pulses to hundreds of thousands time iterative computation several thousand times with respect to laser pulse.This not only experimental work amount is big, the time is long, calculation of complex and tediously long, and isoparametric stable, fluctuation of the burst length shake, laser carrier-envelope phase CEP (carrier-envelope phase) and the laser pulse intensity that occur during the control survey and drift are proposed the very requirement of strictness.

Summary of the invention

In order to promote the metrological development of Ah second; Need a kind of while accurately to measure the intensity of Ah second X-ray pulse and the method for frequency (promptly warbling) time distribution; Adopt a kind of analyticity method of confirming method and photoelectron spectroscopy integral transformation equation directly, fast based on the relevant laser phase of photoelectron for this reason; Utilize the auxiliary X-ray gas ionization technology of laser, the intensity of accurately measuring Ah second X-ray pulse simultaneously distributed with the time of warbling.

One object of the present invention is to propose the measuring method of a kind of Ah second X-ray pulse intensity and the time distribution of warbling.

The measuring method that Ah second X-ray pulse intensity of the present invention and the time of warbling distribute may further comprise the steps being parallel to laser linear polarization direction θ=0 ° of photoelectron spectroscopy that measures:

1) Ah second X-ray pulse and linearly polarized laser pulse carry out cross correlation on time and space, and assemble;

2) Ah second X-ray pulse and laser pulse through hydrogen or inert gas, excite hydrogen atom or inert atom to produce photoelectron after assembling;

3) Ah second X-ray and the laser pulse photoelectronic energy W (t) that excites jointly, produce constantly at t, fly out on ° direction of θ=0 satisfies following formula:

$W\left(t\right)=W_0+2U_p{F}^2\left(t\right){\sin }^2({\mathrm{\ω}}_{L}t+\mathrm{\Φ})$

$+\sqrt{8U_p{W}_0}F\left(t\right)\sin ({\mathrm{\ω}}_{L}t+\mathrm{\Φ})---\left(1\right)$

Wherein, W ₀=ω _X-I _pBe photoelectronic kinetic energy just, and ω _XAnd I _pBe respectively the ionization energy of X-ray pulse photon energy and gas atom or molecule,

Be photoelectronic matter kinetic energy; I is a laser intensity for laser peak power density, ω _LBe the laser angular frequency, Φ is laser pulse carrier wave-envelope phase, and F (t) is 1 gaussian-shape laser electric field envelope function for amplitude;

4) at two kinds of different laser intensity low-intensity I _LWith high strength I _HDown, be parallel to the photoelectron of laser linear polarization direction θ=0 ° of outgoing, obtain respectively at low-intensity I with flight time TOF spectrometer or other photoelectron spectrograph measurements _LWith high strength I _HUnder normalized photoelectron spectroscopy n _L(W) and n _H(W), by Ah second X-ray pulse and laser pulse excite jointly, produce constantly, fly out on ° direction of θ=0 at t photoelectronic, at laser intensity I _LAnd I _HDown, energy is respectively W ^LAnd W ^HSatisfy following integral equation:

$\underset{t_s}{\overset{t}{\&Integral;}}f\left(t_1\right){\mathrm{<figure-callout\; id="1"\; label="dt"\; filenames="HDA0000126402850000021.png"\; state="\{\{state\}\}">dt</figure-callout>}}_1=\mathrm{\&mu;}\underset{W_{\min }^L}{\overset{W^L}{\&Integral;}}n\left(W_1\right){\mathrm{dW}}_1---\left(2\right)$

$\underset{t_s}{\overset{t}{\&Integral;}}f\left(t_2\right){\mathrm{<figure-callout\; id="2"\; label="dt"\; filenames="HDA0000126402850000011.png"\; state="\{\{state\}\}">dt</figure-callout>}}_2=\mathrm{\&mu;}\underset{W_{\min }^H}{\overset{W^H}{\&Integral;}}n\left(W_2\right){\mathrm{dW}}_2---\left(3\right)$

Wherein f (t) representes that the intensity time of Ah second X-ray pulse to be measured distributes t and W ^LAnd W ^HBe respectively photoelectron and produce constantly and its energy position on power spectrum t _sAnd

With

Difference indicating impulse start time and photoelectron spectroscopy n _L(W) and n _H(W) low energy end position, μ are that constant is set to 1;

5) derive from formula (2), formula (3) and formula (1), two kinds of different laser intensity I _LAnd I _H, corresponding matter kinetic energy is respectively

With

Down, the normalized photoelectron spectroscopy that measures has identical energy product score value place, the energy position W on the corresponding different power spectrums ^LAnd W ^H, and the time parameter t that calculates f (t) with the equation batch total and the frequencies omega (t) of this Ah second X-ray pulse constantly:

$\left\{\begin{array}{c}F\left(t\right)\sin ({\mathrm{\&omega;}}_{L}t+\mathrm{\&Phi;})=\frac{\sqrt{W^H}-\sqrt{W^L}}{\sqrt{2U_p^H}-\sqrt{2U_p^L}}\\ \mathrm{\&omega;}\left(t\right)=[\sqrt{W^H}-\sqrt{2U_p^H}\frac{\sqrt{W^H}-\sqrt{W^L}}{\sqrt{2U_p^H-\sqrt{2U_p^L}}}]+I_p\end{array}\right.---\left(4\right)$

For a time width less than being positioned near the Ah second X-ray pulse of t=0 constantly on half laser cycle, time, factor F (t) ≈ 1 in the formula (4), formula (4) is the computing formula that time of warbling of photoelectron laser phase and Ah second X-ray pulse distributes;

6) intensity of Ah second X-ray pulse in time distribution function f (t) use computes:

$f\left(t\right)=\mathrm{\&mu;}\frac{\mathrm{dW}\left(t\right)}{\mathrm{dt}}n\left(W\right)---\left(5\right)$

Wherein, n (W) is laser intensity I _LOr I _HThe normalized photoelectron spectroscopy n that measures down _L(W) or n _H(W), derivative term dW (t)/dt is with formula (1) and corresponding laser intensity I _LOr I _HCalculate, coefficient μ value is 1, and the f (t) that calculates is distributed, and handles through amplitude normalization, has just obtained Ah second X-ray pulse waveform.

The measuring method that Ah second X-ray pulse intensity of the present invention and the time of warbling distribute may further comprise the steps being antiparallel to laser linear polarization direction θ=180 ° of photoelectron spectroscopies that measure:

1) Ah second X-ray pulse and linearly polarized laser pulse carry out cross correlation on time and space, and assemble;

2) Ah second X-ray pulse and laser pulse through hydrogen or inert gas, excite hydrogen atom or inert atom to produce photoelectron after assembling;

3) Ah second X-ray and the laser pulse photoelectronic energy W (t) that excites jointly, produce constantly at t, fly out on ° direction of θ=180 satisfies following formula:

$W\left(t\right)=W_0+2U_p{F}^2\left(t\right){\sin }^2({\mathrm{\&omega;}}_{L}t+\mathrm{\&Phi;})$

$-\sqrt{8U_p{W}_0}F\left(t\right)\sin ({\mathrm{\&omega;}}_{L}t+\mathrm{\&Phi;})---\left(6\right)$

Wherein, W ₀=ω _X-I _pBe photoelectronic kinetic energy just, and ω _XAnd I _pBe respectively the ionization energy of X-ray pulse photon energy (warbling) and gas atom or molecule,

Be photoelectronic matter kinetic energy; I is a laser intensity for laser peak power density, ω _LBe the laser angular frequency, Φ is laser pulse carrier wave-envelope phase, and F (t) is 1 gaussian-shape laser electric field envelope function for amplitude;

4) at two kinds of different laser intensity low-intensity I _LWith high strength I _HDown, be antiparallel to the photoelectron of laser linear polarization direction θ=180 ° of outgoing, obtain respectively at low-intensity I with flight time TOF spectrometer or other photoelectron spectrograph measurements _LWith high strength I _HUnder normalized photoelectron spectroscopy n _L(W) and n _H(W), by Ah second X-ray pulse and laser pulse excite jointly, produce constantly, fly out on ° direction of θ=180 at t photoelectronic, two kinds of different laser intensity I _LAnd I _HDown, energy is respectively W ^LAnd W ^HSatisfy following integral equation:

$\underset{t_s}{\overset{t}{\&Integral;}}f\left(t_1\right){\mathrm{<figure-callout\; id="1"\; label="dt"\; filenames="HDA0000126402850000021.png"\; state="\{\{state\}\}">dt</figure-callout>}}_1=\mathrm{\&mu;}\underset{W_{\min }^L}{\overset{W^L}{\&Integral;}}n\left(W_1\right){\mathrm{dW}}_1---\left(7\right)$

$\underset{t_s}{\overset{t}{\&Integral;}}f\left(t_2\right){\mathrm{<figure-callout\; id="2"\; label="dt"\; filenames="HDA0000126402850000011.png"\; state="\{\{state\}\}">dt</figure-callout>}}_2=\mathrm{\&mu;}\underset{W_{\min }^H}{\overset{W^H}{\&Integral;}}n\left(W_2\right){\mathrm{dW}}_2---\left(8\right)$

Wherein f (t) the expression Ah second X-ray pulse time to be measured distributes t and W ^LAnd W ^HBe respectively photoelectron and produce constantly and its energy position on power spectrum t _sAnd

With

Difference indicating impulse start time and photoelectron spectroscopy n _L(W) and n _H(W) low energy end position, μ are that constant is set to 1;

5) can derive from formula (7), formula (8) and formula (6), two kinds of different laser intensity I _LAnd I _H, corresponding matter kinetic energy is respectively

With

Down, the normalized photoelectron spectroscopy that measures has identical energy product score value place, and corresponding different can spectral position W ^LAnd W ^H, and the time parameter t that calculates f (t) with the equation batch total and the frequencies omega (t) of this Ah second X-ray pulse constantly:

$\left\{\begin{array}{c}F\left(t\right)\sin ({\mathrm{\&omega;}}_{L}t+\mathrm{\&Phi;})=-\frac{\sqrt{W^H}-\sqrt{W^L}}{\sqrt{2U_p^H}-\sqrt{2U_p^L}}\\ \mathrm{\&omega;}\left(t\right)=[\sqrt{W^H}-\sqrt{2U_p^H}\frac{\sqrt{W^H}-\sqrt{W^L}}{\sqrt{2U_p^H-\sqrt{2U_p^L}}}]+I_p\end{array}\right.---\left(9\right)$

For a time width less than being positioned near the Ah second X-ray pulse of t=0 constantly on half laser cycle, time, factor F (t) ≈ 1 in the formula (9), formula (9) is the computing formula that time of warbling of photoelectron laser phase and Ah second X-ray pulse distributes;

6) intensity of Ah second X-ray pulse in time distribution function f (t) use computes:

$f\left(t\right)=-\mathrm{\&mu;}\frac{\mathrm{dW}\left(t\right)}{\mathrm{dt}}n\left(W\right)---\left(10\right)$

Wherein, n (W) is laser intensity I _LOr I _HThe normalized photoelectron spectroscopy n that measures down _L(W) or n _H(W), derivative term dW (t)/dt is with formula (6) and corresponding laser intensity I _LOr I _HCalculate, coefficient μ value is 1, and the f (t) that calculates is distributed, and handles through amplitude normalization, has just obtained Ah second X-ray pulse waveform.

Another object of the present invention is that the measuring method that proposes the Ah second X-ray pulse intensity and the time of warbling distribute is used to study, analyze, evaluate and optimize the technical parameter of Ah second X-ray pulse light source and the purposes of performance index; And the purposes that is used for studying, analyzing the time dependent relevant information of supper-fast reaction kinetics process.Measurement result of the present invention can be used as chirped pulse generation, transmission equally, monopulse is selected and the important references information of detection.Time dependent relevant information in the supper-fast reaction kinetics process can be studied, analyzed to the Ah second X-ray of measuring as exciting and direct impulse.

Advantage of the present invention:

Method of the present invention is utilized the photoelectronic relevant laser phase that parameterized computing formula confirms that each measures or the time parameter of X-ray density distribution; Utilize the spectral technology of separating of energy of photoelectron integral spectrum and analyticity, measure the intensity time distribution of Ah second X-ray pulse and the time distribution of warbling simultaneously.Method of the present invention does not need the time discrimination measurement of a large amount of photoelectron spectroscopies; Iterative computation and experimental data fit procedure that also need be not tediously long to photoelectron spectrum; The photoelectron spectroscopy that can measure under two different laser intensities directly reconstructs the time domain specification of Ah second X-ray pulse, comprises intensity and the distribution of warbling in time.According to the result who measures, can assess the correlation parameter index of Ah second X-ray pulse light source.

Description of drawings

Fig. 1 is generation of the present invention and the synoptic diagram of measuring the experimental provision of Ah second X-ray pulse;

Fig. 2 (a) is measuring method of the present invention and τ _XThe curve map that the distribution in time of warbling of=300 Ah seconds' Ah second X-ray pulse is compared (b) is measuring method of the present invention and τ _XThe curve map that the intensity of=300 Ah seconds' Ah second X-ray pulse distributes in time and compares.

Embodiment

Below in conjunction with accompanying drawing,, further set forth the present invention through specific embodiment.

Fig. 1 is the synoptic diagram that produces and measure the experimental provision of Ah second X-ray pulse.Strong and short laser is that the laser pulse of 7fs focuses on back and neon atom 2 effect generation higher hamonic waves through Ag mirror 1 like time width.Before laser beam, separate the Ah second X-ray pulse that obtains higher-energy with zirconium optical filtering 3 on the line direction.The center of light beam is Ah second X-ray pulse, is surrounded by laser pulse on every side.Light beam carries out cross correlation (cross-correlation) through obtaining the linearly polarized laser beam of desirable strength behind the diaphragm 4 with Ah second X-ray pulse on time and space.Relative delay between Ah second X-ray pulse and the laser pulse (or optical path difference) is accurately regulated by two coaxial optical convergence catoptrons 5.Ah second X-ray pulse convergence reflex mirror is arranged on the piezoelectrics PZT (piezoelectric transducer), and the length of PZT can be stretched by Control of Voltage, thereby can accurately control the relative delay between X-ray pulse and the laser pulse.X-ray pulse and laser pulse through hydrogen or inert gas, excite hydrogen atom or inert atom to produce photoelectron through the convergence reflex mirror reflection.The photoelectron that is parallel to laser linear polarization direction (θ=0 °) outgoing is surveyed by flight time TOF (time-of-flight) spectrometer 6, thereby obtains the photoelectronic energy W (t) that excited jointly, produce constantly at t, flown out on ° direction of θ=0 by X-ray and laser pulse

The photoelectronic energy W (t) that Ah second X-ray and laser pulse excite jointly, produce constantly at t, fly out on ° direction of θ=0 satisfies following formula:

$W\left(t\right)=W_0+2U_p{F}^2\left(t\right){\sin }^2({\mathrm{\&omega;}}_{L}t+\mathrm{\&Phi;})$

$+\sqrt{8U_p{W}_0}F\left(t\right)\sin ({\mathrm{\&omega;}}_{L}t+\mathrm{\&Phi;})---\left(11\right)$

Wherein, W ₀=ω _X-I _pBe photoelectronic kinetic energy just, and ω _XAnd I _pBe respectively the ionization energy of X-ray pulse photon energy (warbling) and gas atom or molecule,

Be photoelectronic matter kinetic energy; I is a laser intensity for laser peak power density, ω _LBe the laser angular frequency, Φ is laser pulse carrier wave-envelope phase, and F (t) is 1 gaussian-shape laser electric field envelope function for amplitude.

At two kinds of different laser intensity: low-intensity I _LWith high strength I _HDown, be parallel to the photoelectron of laser linear polarization direction θ=0 ° of outgoing, obtain two normalized photoelectron spectroscopies (the interior photoelectron number of unit energy is with the distribution of energy of photoelectron) n with flight time TOF spectrometer or other photoelectron spectrograph measurements _L(W) and n _H(W).By Ah second X-ray pulse and laser pulse excite jointly, produce constantly, fly out on ° direction of θ=0 at t photoelectronic, under different laser intensity, energy is respectively W ^LAnd W ^HSatisfy following integral equation:

$\underset{t_s}{\overset{t}{\&Integral;}}f\left(t_1\right){\mathrm{<figure-callout\; id="1"\; label="dt"\; filenames="HDA0000126402850000021.png"\; state="\{\{state\}\}">dt</figure-callout>}}_1=\mathrm{\&mu;}\underset{W_{\min }^L}{\overset{W^L}{\&Integral;}}n\left(W_1\right){\mathrm{dW}}_1---\left(12\right)$

$\underset{t_s}{\overset{t}{\&Integral;}}f\left(t_2\right){\mathrm{<figure-callout\; id="2"\; label="dt"\; filenames="HDA0000126402850000011.png"\; state="\{\{state\}\}">dt</figure-callout>}}_2=\mathrm{\&mu;}\underset{W_{\min }^H}{\overset{W^H}{\&Integral;}}n\left(W_2\right){\mathrm{dW}}_2---\left(13\right)$

Wherein f (t) the expression Ah second X-ray pulse time to be measured distributes t and W ^LAnd W ^HBe respectively photoelectron and produce constantly and its energy position on power spectrum t _sAnd

With

Difference indicating impulse start time and photoelectron spectroscopy n _L(W) and n _H(W) low energy end position, μ are constant.For amplitude normalization f (t) and area normalization n _L(W) and n _H(W), μ can be set to 1 simply.

With different laser intensity but other identical laser pulse parameters, because formula (12) is identical with formula (13) left side numerical value, so formula (12) is identical with formula (13) the right numerical value for identical Ah second X-ray pulse.Can derive from formula (12), formula (13) and formula (11), two kinds of different laser intensity I _LAnd I _H, corresponding matter kinetic energy is respectively With

Down, the normalized photoelectron spectroscopy that measures has identical energy product score value place, and corresponding different can spectral position W ^LAnd W ^H, and can calculate the time parameter t of f (t) and the frequencies omega (t) of this Ah second X-ray pulse constantly with the equation batch total:

$\left\{\begin{array}{c}F\left(t\right)\sin ({\mathrm{\&omega;}}_{L}t+\mathrm{\&Phi;})=\frac{\sqrt{W^H}-\sqrt{W^L}}{\sqrt{2U_p^H}-\sqrt{2U_p^L}}\\ \mathrm{\&omega;}\left(t\right)=[\sqrt{W^H}-\sqrt{2U_p^H}\frac{\sqrt{W^H}-\sqrt{W^L}}{\sqrt{2U_p^H-\sqrt{2U_p^L}}}]+I_p\end{array}\right..---\left(14\right)$

For a time width less than being positioned near the X-ray pulse of t=0 constantly, laser electric field vector potential or sin (ω here on half laser cycle, time _LT+ Φ) function monotone variation, because electrical field envelope F (t) variation is relatively slow, factor F (t) ≈ 1 in the formula (14).Formula (14) is instantaneous frequency (warbling) computing formula of photoelectron laser phase and Ah second X-ray pulse.

The intensity of Ah second X-ray pulse distribution function f (t) is in time used computes:

$f\left(t\right)=\mathrm{\&mu;}\frac{\mathrm{dW}\left(t\right)}{\mathrm{dt}}n\left(W\right)---\left(15\right)$

Wherein, n (W) is laser intensity I _LOr I _HThe normalization photoelectron spectroscopy n that measures down _L(W) or n _H(W).Derivative term dW (t)/dt is with formula (11) and corresponding laser intensity I _LOr I _HCalculate, coefficient μ value is 1.F (t) to calculating distributes, and handles through amplitude normalization, has just obtained Ah second X-ray pulse waveform.From the ω (t) that formula (4) calculates, be warbling of Ah second X-ray pulse and distribute in time.

For the measurement of antiparallel and laser linear polarization direction θ=180 °, as long as negative sign, formula (14) first formulas the right add negative sign, formula (15) the right adds negative sign with adding before the 3rd on formula (11) the right, other processing procedures are same as described above.

Fig. 2 (a) and (b): measuring method of the present invention and τ _XThe curve map that warble and the intensity of=300 Ah seconds' Ah second X-ray distributes in time and compares.Solid line is represented warbling of Ah second X-ray pulse among Fig. 2 (a), i.e. Ah second X-ray photons frequency distribution function in time: ω _i(t)=283.7+20t (eV).With the Ah second X-ray gaussian-shape strength distribution curve f shown in the solid line among it and Fig. 2 (b) ₀(t) substitution contains time quantum mechanics schrodinger equation, at two kinds of laser intensity (I _L=4 * 10 ¹³W/cm ², I _H=12 * 10 ¹³W/cm ², optical maser wavelength 750nm, pulse width τ _L=7 femtoseconds, carrier wave-envelope phase Φ=0 °) under, through numerical computation method, calculate the photoelectron spectroscopy of hydrogen atom on ° direction of θ=0, obtain n respectively _L(W) and n _H(W).Dotted line is the Ah second X-ray pulse that obtains with the method for the present invention distribution curve in time of warbling among Fig. 2 (a); It and initial input distribution (solid line) meet very goodly; Both maximum deviations are Δ ω=1.34eV; Average (Mean) deviation delta ω=0.18eV, root mean square (RMS) deviation delta ω=0.22eV.Be Ah second X-ray gaussian-shape strength distribution curve f shown in the solid line among Fig. 2 (b) ₀(t), pulse width (halfwidth) τ _X=300 Ah seconds, the center is at t=0.Dotted line is from numerical evaluation spectrum n _L(W) and n _H(W) rebuild the gaussian-shape Ah second X-ray density distribution curve f (t) that obtains.F (t) and initial distribution f ₀(t) compare, f (t) is very near f ₀(t), maximum time deviation be Δ t=12.8 Ah second (away from t=0), average (Mean) time deviation Δ t=0.63 Ah second, root mean square (RMS) time deviation Δ t=1.66 Ah second.These frequencies of being brought by method itself are compared with experimental error with time error, can ignore, and therefore chirped pulse can accurately measured and locate to measuring method of the present invention.

Compare and can find out with the digital experiment result from above measuring method of the present invention, impulsive measurement has provided the information such as the distribution of warbling, intensity distributions shape, pulse center position (regularly) and burst length width of Ah second X-ray pulse dry straightly.Pulse information through said process is rebuild can be used as time location and laser intensity that reference data removes to readjust chirped pulse, in the hope of obtaining better experimental data and measurement result more accurately.These measurement results can be used as chirped pulse generation, transmission equally, monopulse is selected and the important references information of detection.Also can be used as reference data, be used to study, analyze, assess, optimize the technical parameter and the performance index of Ah second X-ray pulse light source.Time dependent relevant information in the supper-fast reaction kinetics process can be studied, analyzed to the Ah second X-ray of measuring as exciting and direct impulse.Improve the stability of laser parameter and measuring condition, with quality that significantly improves measurement data and impulsive measurement result's precision.

Above-described embodiment is used to limit the present invention, and any those skilled in the art is not breaking away from the spirit and scope of the present invention, can make various conversion and modification, so protection scope of the present invention is looked the claim scope and defined.

Claims (6)

1. Ah second X-ray pulse intensity and the measuring method that the time of warbling distributes is characterized in that, may further comprise the steps being parallel to laser linear polarization direction θ=0 ° of photoelectron spectroscopy that measures:

1) Ah second X-ray pulse and linearly polarized laser pulse carry out cross correlation on time and space, and assemble;

2) Ah second X-ray pulse and laser pulse through hydrogen or inert gas, excite hydrogen atom or inert atom to produce photoelectron after assembling;

3) Ah second X-ray and the laser pulse photoelectronic energy W (t) that excites jointly, produce constantly at t, fly out on ° direction of θ=0 satisfies following formula:

$W\left(t\right)=W_0+2U_p{F}^2\left(t\right){\sin }^2({\mathrm{\&omega;}}_{L}t+\mathrm{\&Phi;})$

$+\sqrt{8U_p{W}_0}F\left(t\right)\sin ({\mathrm{\&omega;}}_{L}t+\mathrm{\&Phi;})---\left(1\right)$

Wherein, W ₀=ω _X-I _pBe photoelectronic kinetic energy just, and ω _XAnd I _pBe respectively the ionization energy of X-ray pulse photon energy and gas atom or molecule,

Be photoelectronic matter kinetic energy; I is a laser intensity for laser peak power density, ω _LBe the laser angular frequency, Φ is laser pulse carrier wave-envelope phase, and F (t) is 1 gaussian-shape laser electric field envelope function for amplitude;

4) at two kinds of different laser intensity low-intensity I _LWith high strength I _HDown, be parallel to the photoelectron of laser linear polarization direction θ=0 ° of outgoing, obtain respectively at low-intensity I with detector measurement _LWith high strength I _HUnder normalized photoelectron spectroscopy n _L(W) and n _H(W), by Ah second X-ray pulse and laser pulse excite jointly, produce constantly, fly out on ° direction of θ=0 at t photoelectronic, at laser intensity I _LAnd I _HDown, energy is respectively W ^LAnd W ^HSatisfy following integral equation:

$\underset{t_s}{\overset{t}{\&Integral;}}f\left(t_1\right){\mathrm{dt}}_1=\mathrm{\&mu;}\underset{W_{\min }^L}{\overset{W^L}{\&Integral;}}n\left(W_1\right){\mathrm{dW}}_1---\left(2\right)$

$\underset{t_s}{\overset{t}{\&Integral;}}f\left(t_2\right){\mathrm{dt}}_2=\mathrm{\&mu;}\underset{W_{\min }^H}{\overset{W^H}{\&Integral;}}n\left(W_2\right){\mathrm{dW}}_2---\left(3\right)$

Wherein f (t) representes that the intensity time of Ah second X-ray pulse to be measured distributes t and W ^LAnd W ^HBe respectively photoelectron and produce constantly and its energy position on power spectrum t _sAnd With

Difference indicating impulse start time and photoelectron spectroscopy n _L(W) and n _H(W) low energy end position, μ are that constant is set to 1;

5) derive from formula (2), formula (3) and formula (1), two kinds of different laser intensity I _LAnd I _H, corresponding matter kinetic energy is respectively

With

Down, the normalized photoelectron spectroscopy that measures has identical energy product score value place, the energy position W on the corresponding different power spectrums ^LAnd W ^H, and the time parameter t that calculates f (t) with the equation batch total and the frequencies omega (t) of this Ah second X-ray pulse constantly:

$\left\{\begin{array}{c}F\left(t\right)\sin ({\mathrm{\&omega;}}_{L}t+\mathrm{\&Phi;})=\frac{\sqrt{W^H}-\sqrt{W^L}}{\sqrt{2U_p^H}-\sqrt{2U_p^L}}\\ \mathrm{\&omega;}\left(t\right)=[\sqrt{W^H}-\sqrt{2U_p^H}\frac{\sqrt{W^H}-\sqrt{W^L}}{\sqrt{2U_p^H-\sqrt{2U_p^L}}}]+I_p\end{array}\right.---\left(4\right)$

For a time width less than being positioned near the Ah second X-ray pulse of t=0 constantly on half laser cycle, time, factor F (t) ≈ 1 in the formula (4), formula (4) is the computing formula that time of warbling of photoelectron laser phase and Ah second X-ray pulse distributes;

6) intensity of Ah second X-ray pulse in time distribution function f (t) use computes:

$f\left(t\right)=\mathrm{\&mu;}\frac{\mathrm{dW}\left(t\right)}{\mathrm{dt}}n\left(W\right)---\left(5\right)$

Wherein, n (W) is laser intensity I _LOr I _HThe normalized photoelectron spectroscopy n that measures down _L(W) or n _H(W), derivative term dW (t)/dt is with formula (1) and corresponding laser intensity I _LOr I _HCalculate, coefficient μ value is 1, and the f (t) that calculates is distributed, and handles through amplitude normalization, has just obtained Ah second X-ray pulse waveform.

2. Ah second X-ray pulse intensity and the measuring method that the time of warbling distributes is characterized in that, may further comprise the steps being antiparallel to laser linear polarization direction θ=180 ° of photoelectron spectroscopies that measure:

1) Ah second X-ray pulse and linearly polarized laser pulse carry out cross correlation on time and space, and assemble;

2) Ah second X-ray pulse and laser pulse through hydrogen or inert gas, excite hydrogen atom or inert atom to produce photoelectron after assembling;

3) Ah second X-ray and the laser pulse photoelectronic energy W (t) that excites jointly, produce constantly at t, fly out on ° direction of θ=180 satisfies following formula:

$W\left(t\right)=W_0+2U_p{F}^2\left(t\right){\sin }^2({\mathrm{\&omega;}}_{L}t+\mathrm{\&Phi;})$

$-\sqrt{8U_p{W}_0}F\left(t\right)\sin ({\mathrm{\&omega;}}_{L}t+\mathrm{\&Phi;})---\left(6\right)$

Wherein, W ₀=ω _X-I _pBe photoelectronic kinetic energy just, and ω _XAnd I _pBe respectively the ionization energy of X-ray pulse photon energy (warbling) and gas atom or molecule,

Be photoelectronic matter kinetic energy; I is a laser intensity for laser peak power density, ω _LBe the laser angular frequency, Φ is laser pulse carrier wave-envelope phase, and F (t) is 1 gaussian-shape laser electric field envelope function for amplitude;

4) at two kinds of different laser intensity low-intensity I _LWith high strength I _HDown, be antiparallel to the photoelectron of laser linear polarization direction θ=180 ° of outgoing, obtain respectively at low-intensity I with detector measurement _LWith high strength I _HUnder normalized photoelectron spectroscopy n _L(W) and n _H(W), by Ah second X-ray pulse and laser pulse excite jointly, produce constantly, fly out on ° direction of θ=180 at t photoelectronic, two kinds of different laser intensity I _LAnd I _HDown, energy is respectively W ^LAnd W ^HSatisfy following integral equation:

$\underset{t_s}{\overset{t}{\&Integral;}}f\left(t_1\right){\mathrm{dt}}_1=\mathrm{\&mu;}\underset{W_{\min }^L}{\overset{W^L}{\&Integral;}}n\left(W_1\right){\mathrm{dW}}_1---\left(7\right)$

$\underset{t_s}{\overset{t}{\&Integral;}}f\left(t_2\right){\mathrm{dt}}_2=\mathrm{\&mu;}\underset{W_{\min }^H}{\overset{W^H}{\&Integral;}}n\left(W_2\right){\mathrm{dW}}_2---\left(8\right)$

Wherein f (t) the expression Ah second X-ray pulse time to be measured distributes t and W ^LAnd W ^HBe respectively photoelectron and produce constantly and its energy position on power spectrum t _sAnd

With Difference indicating impulse start time and photoelectron spectroscopy n _L(W) and n _H(W) low energy end position, μ are that constant is set to 1;

5) can derive from formula (7), formula (8) and formula (6), two kinds of different laser intensity I _LAnd I _H, corresponding matter kinetic energy is respectively

With

Down, the normalized photoelectron spectroscopy that measures has identical energy product score value place, and corresponding different can spectral position W ^LAnd W ^H, and the time parameter t that calculates f (t) with the equation batch total and the frequencies omega (t) of this Ah second X-ray pulse constantly:

$\left\{\begin{array}{c}F\left(t\right)\sin ({\mathrm{\&omega;}}_{L}t+\mathrm{\&Phi;})=-\frac{\sqrt{W^H}-\sqrt{W^L}}{\sqrt{2U_p^H}-\sqrt{2U_p^L}}\\ \mathrm{\&omega;}\left(t\right)=[\sqrt{W^H}-\sqrt{2U_p^H}\frac{\sqrt{W^H}-\sqrt{W^L}}{\sqrt{2U_p^H-\sqrt{2U_p^L}}}]+I_p\end{array}\right.---\left(9\right)$

For a time width less than being positioned near the Ah second X-ray pulse of t=0 constantly on half laser cycle, time, factor F (t) ≈ 1 in the formula (9), formula (9) is the computing formula that time of warbling of photoelectron laser phase and Ah second X-ray pulse distributes;

6) intensity of Ah second X-ray pulse in time distribution function f (t) use computes:

$f\left(t\right)=-\mathrm{\&mu;}\frac{\mathrm{dW}\left(t\right)}{\mathrm{dt}}n\left(W\right)---\left(10\right)$

Wherein, n (W) is laser intensity I _LOr I _HThe normalized photoelectron spectroscopy n that measures down _L(W) or n _H(W), derivative term dW (t)/dt is with formula (6) and corresponding laser intensity I _LOr I _HCalculate, coefficient μ value is 1, and the f (t) that calculates is distributed, and handles through amplitude normalization, has just obtained Ah second X-ray pulse waveform.

3. according to claim 1 or claim 2 measuring method; It is characterized in that; Relative delay in step 1) between Ah second X-ray pulse and the laser pulse or optical path difference; Accurately regulated by two coaxial optical convergence catoptrons, Ah second X-ray pulse convergence reflex mirror is arranged on the piezoelectrics PZT.

4. according to claim 1 or claim 2 measuring method is characterized in that, is flight time TOF spectrometer or other photoelectron spectrographs at detector described in the step 4).

5. the measuring method that distributes is used to study, analyze, assess, optimize the technical parameter of Ah second X-ray pulse light source and the purposes of performance index claim 1 or 2 Ah second X-ray pulse and the time of warbling.

6. the measuring method of claim 1 or 2 the Ah second X-ray pulse and the time distribution of warbling is used for studying, analyzing the purposes of the time dependent relevant information of supper-fast reaction kinetics process.

Images