1. Laser-assisted photoionization for attosecond pulse measurements
Z. X. Zhao
Thanks Zenghu, CD and XM.
KSU AMO seminar

2. Review on ultrashort pulse measurements
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
By the way, measuring fs using as is simple.

3. 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?
Attosecond pulses have been generated by a couple of groups. Zenghu’s group is one of them. They use polarization gating to produce attosecond pulses. The idea can be illustrated by this cartoon. We have two circularly polarized laser pulses with certain time delay, one is left polarized and the other one is right polarized. If we overlap them temporally, at the time that the instantaneous intensities of the two pulses are comparable, the combined electric field will be linearly polarized, the time duration of the linear part can be controlled by the time delay. If we focus them into gas target, harmonics will be emitted through the rescattering or recombination processes. If the linear part is shorter than one optical cycle, the emitted light will have broad and continuum spectrum which implies it is an attosecond pulse, here we assume only the linear part gives harmonic generation.
Once the attosecond pulse is generated, the first thing you want to do is to measure it to make sure its duration is really in attosecond region.
It has been suggested by Canadian and Austrian group that attosecond pulses can be measured through laser assisted photoionizaton so called attosecond streak camera. In fact, attosecond pulses have been measured by Austria group using linearly polarized light assisted photoioniztion.
Then, why are we doing this work?
First, since the generation of attoseocnd pulses starts with circularly polarized light, we are going to measure it using CPLAPI.
Second, Detail study on laser-assisted photoionization of Argon to provide general ideas of the spectra for the experimentalist.
Third, …

4. 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)
Traditional method of measuring pulse duration relies on the principle of autocorrelation. So far the XUV/x-ray pulses generated by high harmonics are too weak to induce measurable nonlinearities of atomic media.
Created in modified 8/20/04
In order to measure a short pulse in time, we have to use a shorter one. What if we can not find a shorter one, we can use the pulse to measure itself, that is autocorrelation.
However, autocorrelation is actually a fairly difficult measurement to make. It requires splitting the pulse into two replicas and then focusing and recombining them (overlapping them in space and time) in a second-harmonic-generation (SHG) crystal.
So FROG and SPIDER are developed, In their simplest form, FORG and SPIDER can be considered as autocorrelation setup, but all these methods can not be applied to attosecond pulse measurement directly
First it is the limitation on wavelength, difficult to find nonlinear medium working at soft X-ray region
Second, so far the xuv pulses are still too weak to produced measurable nonlinear effect.
Thus the concept of attosecond streak camera is developed.
By the way, measuring fs using as is simple.
This involves carefully aligning three sensitive degrees of freedom (two spatial and one temporal). It is also necessary to maintain this alignment while scanning the delay. Worse, the phase-matching-bandwidth condition mandates a thin SHG crystal, yielding a very weak signal and poor measurement sensitivity. This latter problem compounds alignment difficulties. As a result, an autocorrelator is a time-consuming and high-maintenance undertaking; it requires significant table space; and commercial devices cost ~ $20,000 or more.
Using a longer pulse to do cross-correlation measurement. In time we can only get resolution upto a quarter of laser cycle.
Which is based on laser-assisted photoionization. Attosecond pulses are cross correlated with Ti-Sapphire laser pulse, the atomic gas serves as the nonlinear medium.
There are two scenario one is for long pulses with duration larger than laser optical cycle and for sublaser-cycle pulse, we are going to focus on latter.
If we do time-delay measurement, we can get resolution upto a quarter of laser cycle.
By mapping the duration to spectra, (argon, I=6.3x10^14W/cm^2) can be upto 100 as.

5. Attosecond streak camera: cross-correlation
X-ray
Laser
Initiate atomic process
Linear or circular 
A general idea of building the cross-correlation can be demonstrated by a pump-probe scheme. Atomic process is initiated by the x-ray, then the evolution of the system is assisted by laser pulse. Laser field can be either linearly or circularly polarized. By changing the time delay between two pulses and measure the observables, one may get the time-resolved spectra. From the spectra, we can either obtain the cross-correlation function of two pulses or probe the atomic dynamics.
We don’t have to do the time delay, we may find the time information of the pump pulse from the spectra at one time by comparing with that in laser-free case.
Cross-correlation
Probe atomic dynamics
Time-resolved spectra

6. Theory of laser-assisted photoionizaton

7. Quantum mechanical model
Strong field approximation: neglect Coulomb field
Assuming no depletion of ground state, no structure
Assume :
XUV: ionization
Laser: modify energy
Stationary phase equation:
ts: Saddle point
The amplitude of coming out electron with momentum p is given by LAPI formula.

8. Linear polarized laser assisted photoionization
classical model:   x y
Linear polarization:
Considering photoionization of atoms by x-rays. Suppose electrons are freed with momentum p_0 without laser field present. If the photoionization process is assisted by laser pulse, the electron will gain additional drift velocity from the pulse. Based on energy conservation, we have $ with W0 as hw-Ip. T is electron born time. For linear polarization, one finds:$
Electron energy at observation angle :

9. Linear polarized laser assisted photoionization
XUV pulse
Laser-free
momentum
distribution t0 t1
A(t) (drift velocity)

10. Circularly polarized laser assisted photoionization  x y 
Circular polarization:
(Replace  by ’ in that of linear case and noted that the definition of  is different from PRL88,173903)

11. Circularly polarized laser assisted photoionization
Laser-free t0
t-1
XUV pulse
A(t) (drift velocity)

12. HOW to characterize attosecond pulses from
Spectra of circularly polarized laser assisted XUV
photoionization of argon?

13. Laser-free photoionization of Argon
Starting from 3P ground state, reduced dipole moment to s and d cont.:
Total cross section proportional to
Angular distribution:
ev of Ar.
Asymmetry parameter  can be calculated from R- and R+
Single active electron model of Ar:

14. Laser-free photoionization: Cross section and asymmetry parameter
Ix()
XUV:1012W/cm2,0.1-2fs, 35 ev (21HG)

15. Transform-limited vs chirped pulses
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)

16. No chirp– dependence on the phase angle of circularly polarized laser
no laser
xuv along x axis
0.1 fs for xuv

17. Dependence on the Chirp

18. Pulse retrieving

19. Procedures of pulse retrieving
1) Laser-free PI spectra as input:
2) Free guess of the phases:
3) Construct XUV pulse:
4) Calculate laser-assisted spectra:
5) Compared with measured one:
6) Find best fit of the phases:
1. genetic algorithm
2. 5 parameter fitting

20. Straightforward Genetic Algorithm
Discretize the phases:
Genetic algorithm: 15 bits, 200 parameters, 200 population, 200 generation
8 hours
1fs, chirp 10 as an example

21. 5-parameter GA
Taylor expansion of the phase:

22. Transform limited (no chirp) XUV pulses
0.2 fs
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
0.5 fs
2 fs
no laser

23. Double-pulse XUV light
(a) no laser (b),(c),(d) laser phase with 0, /4 and /2

24. mapping

25. Chirp-dependence Stationary phase equation (no chirp):
ts: Saddle point
Linearly chirped XUV pulse (, chirp parameter):
Energy center of gravity at given angles: spiral curve

26. Summary Calculated spectra
Retrieved electric field of attosecond pulse
Retrieving method can be further improved