Laser-assisted photoionization for attosecond pulse measurements

Z. X. Zhao

KSU AMO seminar 9-29-2004

Outline

• Motivation• Review on ultrashort pulse

measurements• Theory of laser assisted photoionization• Spectra of circularly polarized laser

assisted XUV photoionization of argon• Pulse retrieving • Summary

Motivation

• Attosecond pulse generated by Zenghu’s group using polarization gating

• Measure it?

• In this work:– Using circularly

polarized laser pulses– laser-assisted

photoionization of Argon

– Study the procedures of measuring attosecond pulses

Left circularly polarized IR Right circularly polarized IR

Polarization gating

Gas target

as pulse IR

Gas

Spectra

?

as pulses?

Review on ultrashort pulse measurement

• Autocorrelation– The pulse is split into two parts and then overlapped temporally in a

nonlinear medium. – Limitation on wavelength.– X-ray pulses generated too weak.

• Cross-correlation– Laser-modified photoionization spectrum provides the nonlinearity

linking the x-ray to the laser pulse – The atomic gas serves as the nonlinear medium.– For long XUV pulses (>T0):– For sub-laser-cycle pulses (this talk)

Attosecond streak camera: cross-correlation

Time-resolved spectra

X-ray

Laser

Initiate atomic process

Linear or circular

Cross-correlation Probe atomic dynamics

Quantum mechanical model

Strong field approximation: neglect Coulomb field

Assuming no depletion of ground state, no structure

0 exp(iIp t) d3 pb(p , t)

p

Stationary phase equation: ts: Saddle point

Assume :XUV: ionization

Laser: modify energy

px IW 0

Linear polarized laser assisted photoionization

12

[p

A (t)]2 W0

Linear polarization:

p

p 0

A (t)

x

y

A Asin(t)

e x

Electron energy at observation angle :

classical model:

Linear polarized laser assisted photoionization

Laser-freemomentum distribution

A(t) (drift velocity)

XUV pulse

t0

t1

Circularly polarized laser assisted photoionization

p

p 0

A (t)

x

y

' Circular polarization:

A A[cos

e x sin

e y ] 2

A[sinte x cost

e y ]/ 2

W p W0 U p cos2( ) c 4W0U p cos( )

(Replace by ’ in that of linear case and noted that the definition of is different from PRL88,173903)

Circularly polarized laser assisted photoionization

t0

t1

t-1

Laser-free

A(t) (drift velocity)

XUV pulse

HOW to characterize attosecond pulses from

Laser-free photoionization of Argon

0

2 drrPPR ps

0

2 drrPPR pd

)32

31(6|| 222

RRd

]2

1cos31[4

2

tot

dd

Starting from 3P ground state, reduced dipole moment to s and d cont.:

Total cross section proportional to

Angular distribution:

Asymmetry parameter can be calculated from R- and R+

Single active electron model of Ar:

reerV rr /)6.114.51()( 682.3

Laser-free photoionization:Cross section and asymmetry parameter

XUV:1012W/cm2,0.1-2fs, 35 ev (21HG)

Ix()

Transform-limited vs chirped pulses

)exp()( 2

2

ttE)exp()( 2

2

E

1

)1(exp()( 2

2

iE

)exp(|~)(| 2

2

ttE

21

Transform-limited:

Chirped:

Do laser assisted photoionization to get pulse information

Laser:5x1013W/cm2,5fs, 1.65 eV (750 nm,2.5fs)XUV:1012W/cm2,0.1-2fs, 35 ev (21HG)

No chirp– dependence on the phase angle of circularly polarized laser

no laser

0.1 fs for xuv

xuv along x axis

Dependence on the Chirp

Procedures of pulse retrieving2

0 |)(| pb

00

0 0

)()(

)( dEepdpb

tE tiItiE p

22 |)(| |)(| Exppbpb

1) Laser-free PI spectra as input:

2) Free guess of the phases: )exp(|)(|)(000 pipbpb

3) Construct XUV pulse:

4) Calculate laser-assisted spectra:

5) Compared with measured one:

6) Find best fit of the phases:

1. genetic algorithm2. 5 parameter fitting

Straightforward Genetic Algorithm

Niii ,1 ,)()( Discretize the phases: Genetic algorithm: 15 bits, 200 parameters, 200 population, 200 generation

1fs, chirp 10 as an example

5-parameter GA

N

i

iia

1

10 )()( Taylor expansion of the phase:

Transform limited (no chirp) XUV pulses

• Energy width decreases as pulse duration increases

• The angular distribution of final momentum– For given energy– broader as XUV pulse duration

increases• For XUV duration approaching

laser cycle:– image expands in all direction– Sidebands begin to emerge

0.2 fs

0.5 fs

2 fs

no laser

Double-pulse XUV light

(a) no laser (b),(c),(d) laser phase with 0, /4 and /2

mapping

Chirp-dependence

Stationary phase equation (no chirp):

ts: Saddle point

12

p A l (ts) 2

ddt ts

Ip W0 t

Linearly chirped XUV pulse (, chirp parameter):

Energy center of gravity at given angles: spiral curve

E

Summary

• Calculated spectra• Retrieved electric field of attosecond pulse• Retrieving method can be further improved