CN101660948A - Chirp picosecond pulse frequency spectrum interference measurement method - Google Patents

Abstract

A chirp picosecond pulse frequency spectrum interference measurement method comprises the following steps: firstly, a second-order autocorrelator and a spectrometer are used for measuring the pulse width T of the reference femtosecond pulse light₁Sum bandwidth Δ ω₀(ii) a Establishing a measuring light path; carefully adjusting the delayer, and when the interference pattern on the grating spectrometer is completely symmetrical; recording interference patterns of the chirped picosecond pulse light to be detected and the reference femtosecond pulse light by using the grating spectrometer to obtain an experimental curve; and calculating the pulse width and the chirp coefficient alpha of the chirped picosecond pulse light to be detected. The method has the characteristics of simple measurement implementation and high measurement precision.

Description

Method for measuring chirped picosecond pulses by frequency spectrum interference

Technical field

The present invention relates to picopulse (be called for short ps pulse), particularly a kind of method for measuring chirped picosecond pulses by frequency spectrum interference is used to measure the pulsewidth and the chirp coefficient of the chirped laser pulse of ps level.

Technical background

Pumping detecting method is to use measuring method very widely when the research femtosecond laser drives ultrafast physical process, in the method, sometimes need the direct impulse broadening of femtosecond is become the chirped pulse of picosecond, utilize the time resolution function of chirped pulse to carry out time-resolved single-shot measurement [referring to document [1] Xiao-Yu Peng, Oswald Willi, Min Chen, and Alexander Pukhov, " Optimal chirpedprobe pulse length for terahertz pulse measurement ", Opt.Expr.16 (16), 12342,2008 and document [2] J.-P.Geindre, P.Audebert, S.Rebibo, and J.-C.Gauthier, " Single-shot spectralinterferometry with chirped pulses ", Opt.Lett.26 (20), 2001].In the method, need accurately know the pulsewidth and the chirp coefficient of the ps pulse of warbling.In principle, pulsewidth and chirp coefficient can be learnt according to the calculation of parameter of stretcher (grating pair or prism to), yet to experimentize to the pulse of this broadening to measure and but have some difficulties: on the one hand, the second order autocorrelation function analyzer of the most frequently used measurement pulsewidth can't be measured the ps pulse, as the most frequently used instrument streak camera of pulsewidth of measuring picopulse cost an arm and a leg and in ultrafast research, use less, because of rather than each ultrafast laboratory outfit is all arranged.On the other hand, use and also can be used on three rank autocorrelation function analyzers and FROG or the SPIDER principle measuring this chirped picosecond pulses, but need original device is redesigned, and measuring process is loaded down with trivial details.

Summary of the invention

The objective of the invention is to overcome above-mentioned the deficiencies in the prior art, propose a kind of pulsewidth of the chirped laser pulse that is used to measure the ps level and the method for measuring chirped picosecond pulses by frequency spectrum interference of chirp coefficient, this method has simple and the high characteristics of measuring accuracy implemented of measuring.

Technical solution of the present invention is as follows:

A kind of method for measuring chirped picosecond pulses by frequency spectrum interference, characteristics are to comprise the following steps:

1. earlier measure pulsewidth T with reference to femtosecond pulse light with second order autocorrelation function analyzer and spectrometer ₁And bandwidth delta omega ₀

2. set up to measure light path: chirped picosecond pulses light to be measured enters through catoptron and closes the bundle sheet, with reference to femtosecond pulse light through going into the grating spectrometer described closing on the bundle sheet behind the chronotron with chirped picosecond pulses combiner to be measured is laggard;

3. the described chronotron of careful adjusting, on described grating spectrograph, begin to occur tangible interference fringe, continue the described chronotron of fine setting, when the interference pattern on the described grating spectrograph is symmetrical fully, be chirped picosecond pulses light to be measured and overlap fully with reference to femtosecond pulse light, this moment chirped picosecond pulses light to be measured and with reference to time delay τ=0 of femtosecond pulse light;

4. write down chirped picosecond pulses light to be measured and, promptly obtain empirical curve with described grating spectrometer with reference to femtosecond pulse interference of light pattern;

5. calculate the pulsewidth and the chirp coefficient of chirped picosecond pulses light to be measured, utilize following formula, by changing T ₂Value this interference pattern is fitted, draw a plurality of simulation curves:

$I\left(\mathrm{\&omega;}\right)={\mathrm{\&pi;<figure-callout\; id="1"\; label="T"\; filenames="A2009101959100008H1.png"\; state="\{\{state\}\}">T</figure-callout>}}_1^2\exp (-\frac{1}{2}{\mathrm{<figure-callout\; id="1"\; label="T"\; filenames="A2009101959100008H1.png"\; state="\{\{state\}\}">T</figure-callout>}}_1^2{(\mathrm{\&omega;}-{\mathrm{\&omega;}}_0)}^2)+\frac{{\mathrm{\&pi;<figure-callout\; id="2"\; label="T"\; filenames="A2009101959100008H1.png"\; state="\{\{state\}\}">T</figure-callout>}}_2^2}{\sqrt{1+{\mathrm{<figure-callout\; id="2"\; label="a"\; filenames="A2009101959100008H1.png"\; state="\{\{state\}\}">a</figure-callout>}}^2}}\exp (-\frac{1}{2}\frac{{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="A2009101959100008H1.png"\; state="\{\{state\}\}">T</figure-callout>}}_2^2{(\mathrm{\&omega;}-{\mathrm{\&omega;}}_0)}^2}{(1+a^2)})$

$+\frac{{2\mathrm{\&pi;T}}_1{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="A2009101959100008H1.png"\; state="\{\{state\}\}">T</figure-callout>}}_2}{\sqrt[4]{1+{\mathrm{<figure-callout\; id="2"\; label="a"\; filenames="A2009101959100008H1.png"\; state="\{\{state\}\}">a</figure-callout>}}^2}}\exp (-\frac{{(\mathrm{\&omega;}-{\mathrm{\&omega;}}_0)}^2{\mathrm{<figure-callout\; id="1"\; label="T"\; filenames="A2009101959100008H1.png"\; state="\{\{state\}\}">T</figure-callout>}}_1^2}{4}-\frac{{(\mathrm{\&omega;}-{\mathrm{\&omega;}}_0)}^2{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="A2009101959100008H1.png"\; state="\{\{state\}\}">T</figure-callout>}}_2^2}{4(1+a^2)})\cos ((\mathrm{\&omega;}-{\mathrm{\&omega;}}_0)\mathrm{\&tau;}+\frac{{(\mathrm{\&omega;}-{\mathrm{\&omega;}}_0)}^2{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="A2009101959100008H1.png"\; state="\{\{state\}\}">T</figure-callout>}}_2^{2}a}{4(1+a^2)}-\frac{{(\mathrm{\&omega;}-{\mathrm{\&omega;}}_0)}^2{\mathrm{<figure-callout\; id="1"\; label="T"\; filenames="A2009101959100008H1.png"\; state="\{\{state\}\}">T</figure-callout>}}_1^2}{4}-\frac{\mathrm{\&pi;}}{2})$

Wherein: $a=\frac{1}{2}\mathrm{\&alpha;}{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="A2009101959100008H1.png"\; state="\{\{state\}\}">T</figure-callout>}}_2^2,$ Δ ω ₀=ω-ω ₀, T ₁Be pulsewidth with reference to femtosecond pulse light, T ₂Be the pulsewidth of chirped picosecond pulses light to be measured, select and the coincide T of best simulation curve of empirical curve ₂, be the pulsewidth of chirped picosecond pulses light to be measured;

6. calculate according to following formula, obtain the chirp coefficient α of chirped picosecond pulses light to be measured:

α≈Δω ₀/T ₂

In the formula:, Δ ω ₀For surveying the frequency span of chirped picosecond pulses light.

Advantage of the present invention:

1, measures enforcement simply.Do not need additionally to purchase or build other equipment for measuring chirped picosecond pulses, a grating spectrometer that need all possess with general ultrafast laboratory, second order autocorrelation function analyzer etc. can be finished measurement.

2, measuring accuracy height.Measuring accuracy is determined by the frequency range of femtosecond pulse mainly, and general condition can reach 20fs and reach more high resolving power.

Description of drawings

Fig. 1 is measurement mechanism figure of the present invention

Fig. 2 is that chirped pulse to be measured and reference pulse relative time delay are 0 o'clock interference pattern.

Fig. 3 is the pulsewidth Inversion Calculation synoptic diagram of chirped pulse

Embodiment

The invention will be further described below in conjunction with embodiment and accompanying drawing, but should not limit protection scope of the present invention with this.

See also Fig. 1 earlier, Fig. 1 is measurement mechanism figure of the present invention.Broadened chirped picosecond pulses light 1 to be measured and behind the delayer 3 of over-compensation light path, closing bundle sheet 4 and close Shu Ranhou and enter grating spectrograph 5 and measure its interference patterns with crossing one with reference to femtosecond pulse light 2.The principle of the inventive method is as follows:

The light field of the reference femtosecond pulse light 2 of Gaussian distribution can be expressed as:

$E_1\left(t\right)=\exp \left({-t}^2{T}_1^{-2}\right)---\left(1\right)$

Wherein: T ₁Be pulse width.Chirped picosecond pulses light 1 behind the broadening is expressed as:

$E_2\left(t\right)=\exp (-(1+\mathrm{ia})t^2{T}_2^{-2})---\left(2\right)$

Wherein, $2a=\mathrm{\&alpha;}{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="A2009101959100008H1.png"\; state="\{\{state\}\}">T</figure-callout>}}_2^2,$ α linear chrip coefficient is approximately equal to the ratio of pulse bandwidth and burst length width, promptly

α≈Δω ₀/T ₂ (3)

Time delay with reference to femtosecond pulse light 2 and chirped picosecond pulses light 1 is expressed as τ, and two-beam interference pattern at frequency domain on grating spectrograph 5 is

$I\left(\mathrm{\&omega;}\right)={|{\tilde{E}}_1\left(\mathrm{\&omega;}\right)+{\tilde{E}}_2\left(\mathrm{\&omega;}\right)|}^2---\left(4\right)$

Wherein:

Be respectively E ₁(t) and E ₂(t) Fourier transform:

${\tilde{E}}_1\left(\mathrm{\&omega;}\right)=\sqrt{\mathrm{\&pi;}}{\mathrm{<figure-callout\; id="1"\; label="T"\; filenames="A2009101959100008H1.png"\; state="\{\{state\}\}">T</figure-callout>}}_1\exp ({\mathrm{i\&phi;}}_1\left(\mathrm{\&omega;}\right)-\frac{{(\mathrm{\&omega;}-{\mathrm{\&omega;}}_0)}^2{\mathrm{<figure-callout\; id="1"\; label="T"\; filenames="A2009101959100008H1.png"\; state="\{\{state\}\}">T</figure-callout>}}_1^2}{4})---\left(5\right)$

${\tilde{E}}_2\left(\mathrm{\&omega;}\right)=\frac{\sqrt{\mathrm{\&pi;}}{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="A2009101959100008H1.png"\; state="\{\{state\}\}">T</figure-callout>}}_2}{\sqrt[4]{1+a^2}}\exp ({\mathrm{i\&phi;}}_2\left(\mathrm{\&omega;}\right)-\frac{{(\mathrm{\&omega;}-{\mathrm{\&omega;}}_0)}^2{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="A2009101959100008H1.png"\; state="\{\{state\}\}">T</figure-callout>}}_2^2}{4(1+a^2)})---\left(6\right)$

Wherein: ${\mathrm{\&phi;}}_2\left(\mathrm{\&omega;}\right)=-\frac{1}{2}\arctan \left(a\right)+\frac{1}{4}\frac{{\mathrm{aT}}_2^2{(\mathrm{\&omega;}-{\mathrm{\&omega;}}_0)}^2}{(1+a^2)},$ φ ₁(ω)=φ ₂(ω) | _A=0Substitution formula (4) can obtain

$I\left(\mathrm{\&omega;}\right)={|\tilde{E}\left(\mathrm{\&omega;}\right)+{\tilde{E}}_2\left(\mathrm{\&omega;}\right)|}^2$

$={\left|{\tilde{E}}_1\left(\mathrm{\&omega;}\right)\right|}^2+{\left|{\tilde{E}}_2\left(\mathrm{\&omega;}\right)\right|}^2+2\mathrm{Re}{\mathrm{<figure-callout\; id="2"\; label="E"\; filenames="A2009101959100008H1.png"\; state="\{\{state\}\}">E</figure-callout>}}_2^{*}\left(\mathrm{\&omega;}\right)E_1\left(\mathrm{\&omega;}\right)$

$={\mathrm{\&pi;<figure-callout\; id="1"\; label="T"\; filenames="A2009101959100008H1.png"\; state="\{\{state\}\}">T</figure-callout>}}_1^2\exp (-\frac{1}{2}{\mathrm{<figure-callout\; id="1"\; label="T"\; filenames="A2009101959100008H1.png"\; state="\{\{state\}\}">T</figure-callout>}}_1^2{(\mathrm{\&omega;}-{\mathrm{\&omega;}}_0)}^2)+\frac{{\mathrm{\&pi;<figure-callout\; id="2"\; label="T"\; filenames="A2009101959100008H1.png"\; state="\{\{state\}\}">T</figure-callout>}}_2^2}{\sqrt{1+a^2}}\exp (-\frac{1}{2}\frac{{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="A2009101959100008H1.png"\; state="\{\{state\}\}">T</figure-callout>}}_2^2{(\mathrm{\&omega;}-{\mathrm{\&omega;}}_0)}^2}{(1+a^2)})$

$+\frac{{2\mathrm{\&pi;T}}_1{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="A2009101959100008H1.png"\; state="\{\{state\}\}">T</figure-callout>}}_2}{\sqrt[4]{1+a^2}}\exp (-\frac{{(\mathrm{\&omega;}-{\mathrm{\&omega;}}_0)}^2{\mathrm{<figure-callout\; id="1"\; label="T"\; filenames="A2009101959100008H1.png"\; state="\{\{state\}\}">T</figure-callout>}}_1^2}{4}-\frac{{(\mathrm{\&omega;}-{\mathrm{\&omega;}}_0)}^2{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="A2009101959100008H1.png"\; state="\{\{state\}\}">T</figure-callout>}}_2^2}{4(1+a^2)})\cos ((\mathrm{\&omega;}-{\mathrm{\&omega;}}_0)\mathrm{\&tau;}+\frac{{(\mathrm{\&omega;}-{\mathrm{\&omega;}}_0)}^2{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="A2009101959100008H1.png"\; state="\{\{state\}\}">T</figure-callout>}}_2^{2}a}{4(1+a^2)}-\frac{{(\mathrm{\&omega;}-{\mathrm{\&omega;}}_0)}^2{\mathrm{<figure-callout\; id="1"\; label="T"\; filenames="A2009101959100008H1.png"\; state="\{\{state\}\}">T</figure-callout>}}_1^2}{4}-\frac{\mathrm{\&pi;}}{2})---\left(7\right)$

Wherein: parameter a can be according to formula (3) bandwidth delta omega and pulsewidth T to be measured ₂Represent:

$a=\frac{1}{2}\mathrm{\&alpha;}{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="A2009101959100008H1.png"\; state="\{\{state\}\}">T</figure-callout>}}_2^2=\frac{1}{2}{\left(\frac{\mathrm{\&Delta;\&omega;}}{T_2}\right)}^2{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="A2009101959100008H1.png"\; state="\{\{state\}\}">T</figure-callout>}}_2^2=\frac{1}{2}{\mathrm{\&Delta;\&omega;}}^2{T}_2---\left(8\right)$

Earlier measure width T with reference to femtosecond pulse light 2 with second order autocorrelation function analyzer and spectrometer ₁And bandwidth delta omega ₀, the frequency span Δ ω of the chirped picosecond pulses light 1 behind the broadening ₀Substantially constant, i.e. Δ ω ₀≈ Δ ω, according to formula (7) and formula (8), when the relative delay of two-beam τ one regularly, on the spectrometer interference pattern of gained only with the width T of chirped pulse ₂Relevant.Therefore, need only the interference pattern that records two pulsed lights by grating spectrometer, promptly can obtain the pulsewidth of chirped picosecond pulses light 1 by Inversion Calculation.Then by formula (3) and then can obtain the chirp coefficient of pulse.

Because the grating spectrograph spectral resolution of using is far above the spectrum width of our used pulse laser, so the temporal resolution of this measuring method is mainly by the spectrum width Δ ω of reference light ₀Decision, temporal resolution Δ t ≈ 2 π/Δ ω ₀Therefore, the frequency spectrum of surveying light is wide more, and the temporal resolution of detection is high more.For example, if survey the gloss titanium precious stone laser, centre wavelength 800nm, if spectrum width (halfwidth) is 45nm, the temporal resolution of Ce Lianging can reach 20fs so.

The pulsewidth of our reference femtosecond pulse light 2 that embodiment adopted is 40fs, centre wavelength 800nm, and recording spectrum width with spectrometer is 45nm.In experiment through a pair of grating pair, with this femtosecond pulse light broadening chirped pulse optical that is picosecond as chirped picosecond pulses light 1 to be measured.Now to measure the pulsewidth and the chirp coefficient of the chirped picosecond pulses light 1 to be measured after broadened.Measuring process is as follows:

1. earlier measure pulsewidth T with reference to femtosecond pulse light 2 with second order autocorrelation function analyzer and spectrometer ₁Be 40fs, and bandwidth delta omega ₀Be 45nm;

2. set up to measure light path: chirped picosecond pulses light 1 to be measured enters through catoptron 6 and closes bundle sheet 4, closes Shu Houjin with chirped picosecond pulses light 1 to be measured on the sheet 4 and goes into grating spectrometer 5 through closing chronotron 3 after to restraint with reference to femtosecond pulse light 2;

3. utilize the frequency spectrum interference pattern of grating spectrometer 5 observation two-beams, the described chronotron 3 of careful adjusting, on described grating spectrograph 5, begin to occur tangible interference fringe, continue the described chronotron 3 of fine setting, when the interference pattern on the described grating spectrograph 5 is symmetrical fully, as shown in Figure 2, chirped picosecond pulses light 1 to be measured and overlap fully with reference to femtosecond pulse light 2, this moment chirped picosecond pulses light 1 to be measured and with reference to time delay τ=0 of femtosecond pulse light 2;

4. with described grating spectrometer 5 record chirped picosecond pulses light 1 to be measured with reference to the interference pattern of femtosecond pulse light 2, promptly obtain empirical curve, as the curve d among Fig. 3 _o

5. calculate the pulsewidth and the chirp coefficient of chirped picosecond pulses light to be measured, utilize following formula, by changing T ₂Value this interference pattern is fitted, draw a plurality of simulation curves:

$I\left(\mathrm{\&omega;}\right)={\mathrm{\&pi;<figure-callout\; id="1"\; label="T"\; filenames="A2009101959100008H1.png"\; state="\{\{state\}\}">T</figure-callout>}}_1^2\exp (-\frac{1}{2}{\mathrm{<figure-callout\; id="1"\; label="T"\; filenames="A2009101959100008H1.png"\; state="\{\{state\}\}">T</figure-callout>}}_1^2{(\mathrm{\&omega;}-{\mathrm{\&omega;}}_0)}^2)+\frac{{\mathrm{\&pi;<figure-callout\; id="2"\; label="T"\; filenames="A2009101959100008H1.png"\; state="\{\{state\}\}">T</figure-callout>}}_2^2}{\sqrt{1+a^2}}\exp (-\frac{1}{2}\frac{{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="A2009101959100008H1.png"\; state="\{\{state\}\}">T</figure-callout>}}_2^2{(\mathrm{\&omega;}-{\mathrm{\&omega;}}_0)}^2}{(1+a^2)})$

$+\frac{{2\mathrm{\&pi;T}}_1{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="A2009101959100008H1.png"\; state="\{\{state\}\}">T</figure-callout>}}_2}{\sqrt[4]{1+a^2}}\exp (-\frac{{(\mathrm{\&omega;}-{\mathrm{\&omega;}}_0)}^2{\mathrm{<figure-callout\; id="1"\; label="T"\; filenames="A2009101959100008H1.png"\; state="\{\{state\}\}">T</figure-callout>}}_1^2}{4}-\frac{{(\mathrm{\&omega;}-{\mathrm{\&omega;}}_0)}^2{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="A2009101959100008H1.png"\; state="\{\{state\}\}">T</figure-callout>}}_2^2}{4(1+a^2)})\cos ((\mathrm{\&omega;}-{\mathrm{\&omega;}}_0)\mathrm{\&tau;}+\frac{{(\mathrm{\&omega;}-{\mathrm{\&omega;}}_0)}^2{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="A2009101959100008H1.png"\; state="\{\{state\}\}">T</figure-callout>}}_2^{2}a}{4(1+a^2)}-\frac{{(\mathrm{\&omega;}-{\mathrm{\&omega;}}_0)}^2{\mathrm{<figure-callout\; id="1"\; label="T"\; filenames="A2009101959100008H1.png"\; state="\{\{state\}\}">T</figure-callout>}}_1^2}{4}-\frac{\mathrm{\&pi;}}{2})$

Wherein: $a=\frac{1}{2}\mathrm{\&alpha;}{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="A2009101959100008H1.png"\; state="\{\{state\}\}">T</figure-callout>}}_2^2,$ Δ ω ₀=ω-ω ₀, T ₁Be pulsewidth with reference to femtosecond pulse light 2, T ₂Be the pulsewidth of chirped picosecond pulses light 1 to be measured, select and the coincide T of best simulation curve of empirical curve ₂, be the pulsewidth of chirped picosecond pulses light 1 to be measured, shown in a, b, three curves of c among Fig. 3, work as T ₂When getting 4.2ps, simulation curve and empirical curve coincide best, so the pulsewidth of this chirped pulse is 4.2ps _o

6. calculate according to following formula, obtain the chirp coefficient α of chirped picosecond pulses light 1 to be measured:

α≈Δω ₀/T ₂

In the formula:, Δ ω ₀For surveying the frequency span of chirped picosecond pulses light 1.

Calculate the chirp coefficient a=473 of this pulse.

Claims (1)

1, a kind of method for measuring chirped picosecond pulses by frequency spectrum interference is characterised in that to comprise the following steps:

1. earlier measure pulsewidth T with reference to femtosecond pulse light (2) with second order autocorrelation function analyzer and spectrometer ₁And bandwidth delta omega ₀

2. set up to measure light path: chirped picosecond pulses light to be measured (1) enters through catoptron (6) and closes bundle sheet (4), is closing that bundle sheet (4) is gone up and chirped picosecond pulses light to be measured (1) closes Shu Houjin and goes into grating spectrometer (5) with reference to femtosecond pulse light (2) through chronotron (3) after;

3. the careful described chronotron (3) of regulating, on described grating spectrograph (5), begin to occur tangible interference fringe, continue fine setting described chronotron (3), when the interference pattern on the described grating spectrograph (5) is symmetrical fully, chirped picosecond pulses light then to be measured (1) and overlap fully with reference to femtosecond pulse light (2), promptly the time postpones τ=0;

4. use described grating spectrometer (5) record chirped picosecond pulses light to be measured (1) and, promptly obtain empirical curve with reference to the interference pattern of femtosecond pulse light (2);

5. calculate the pulsewidth and the chirp coefficient of chirped picosecond pulses light to be measured, utilize following formula, by changing T ₂Value this interference pattern is fitted, draw a plurality of simulation curves:

$I\left(\mathrm{\&omega;}\right)=\mathrm{\&pi;}{T_1}^2\exp (-\frac{1}{2}{T_1}^2{(\mathrm{\&omega;}-{\mathrm{\&omega;}}_0)}^2)+\frac{\mathrm{\&pi;}{T_2}^2}{\sqrt{1+a^2}}\exp (-\frac{1}{2}\frac{{T_2}^2{(\mathrm{\&omega;}-{\mathrm{\&omega;}}_0)}^2}{(1+a^2)})$

$+\frac{2\mathrm{\&pi;}{T}_1{T}_2}{\sqrt[4]{1+a^2}}\exp (-\frac{{(\mathrm{\&omega;}-{\mathrm{\&omega;}}_0)}^2{T_1}^2}{4}-\frac{{(\mathrm{\&omega;}-{\mathrm{\&omega;}}_0)}^2{T_2}^2}{4(1+a^2)})\cos ((\mathrm{\&omega;}-{\mathrm{\&omega;}}_0)\mathrm{\&tau;}+\frac{{(\mathrm{\&omega;}-{\mathrm{\&omega;}}_0)}^2{T_2}^{2}a}{4(1+a^2)}-\frac{{(\mathrm{\&omega;}-{\mathrm{\&omega;}}_0)}^2{T_1}^2}{4}-\frac{\mathrm{\&pi;}}{2})$

Wherein: $a=\frac{1}{2}\mathrm{\&alpha;}{T_2}^2,$ Δ ω ₀=ω-ω ₀, T ₁Be pulsewidth with reference to femtosecond pulse light (2), T ₂Be the pulsewidth of chirped picosecond pulses light to be measured (1), select and the coincide T of best simulation curve of empirical curve ₂, be the pulsewidth of chirped picosecond pulses light to be measured (1);

6. calculate according to following formula, obtain the chirp coefficient α of chirped picosecond pulses light to be measured (1):

α≈Δω ₀/T ₂

In the formula:, Δ ω ₀For surveying the frequency span of chirped picosecond pulses light (1).

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