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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 - PowerPoint PPT Presentation
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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