Generation of short pulses
2.7 fs
Ultrashort pulse generation
15 fs pulse
Single cycle pulse
Time [fs]
Wavelength [m]
Time [fs]
Wavelength [m]
Raman scattering and attosecond pulses
Input two frequencies nearly resonant with
a Raman resonance.
At high intensity, the process cascades many times.
Input
pulses
Output pulse
as input to a
second
process
Output pulse of
second process as
input to a
third
process
Output pulse of
third process as
input to a
fourth
process
Etc.
1
0
Raman processes can cascade many times, yielding a
series of equally spaced modes
=1+/- n0
S. E. Harris and A. V. Sokolov PRL 81, 2894
frequency
Cascaded Raman generation
A. V. Sokolov et al.
PRL 85, 85 562
Dba =
2994 cm-1
This can be done with nanosecond laser pulses!
Experimental demonstration of cascaded
Raman scattering
2994 cm-1
Detuning from
2-photon resonance
- 400MHz
+ 100MHz
+ 700MHz
75,000 cm-1 (2.3 x 1015 Hz) of bandwidth has been created!
A. V. Sokolov et al. PRL 85, 562
Experimental demonstration of cascaded
Raman scattering
The different frequencies are locked
Pulses with 1 fs duration are measured
The spectrum is discrete: the pulses are emitted in a pulse train, separated by
the vibrational period.
The main advantage of this process: high efficiency
The main drawback: the carrier frequency is in the visible regime
We cannot produce an isolated pulse.
A. V. Sokolov et al. PRL 85, 562
Breaking the femtosecond limit
2001: First observation of an attosecond pulse (650 as)
M. Hentschel et al., Nature 414, 509-513 (2001)
G. Sansone et al., Science 314, 443 (2006)
2006: (130 as)
Our main tool: intense laser pulses
Field Intensity: 1014 –1015 W/cm2
2.7 fs
The force is comparable to the force binding the electrons in the
atom or molecule.
Attosecond pulse generation process
Re-collision
E>100eV
Acceleration by the electric field
Tunnel ionization
  I p  Ek
With I~1014 W/cm2
 ~ 1000
cutoff
Fundamental frequency
E2
 Ip 3
2
40
Attosecond pulse generation process
Acceleration by the electric field
Tunnel ionization
Optical radiation with
attoseconds duration
Attosecond pulse generation process
Classical model
F  ma  eE
E t   E cos0t 
vt0 , t  
eE
sin 0t   sin 0t0 
me0
eE
cos0t0   cos0t   0 sin 0t0 t  t0 
xt0 , t  
me0
Ek t , t0   2U p sin 0t   sin 0t0 
2
e2 E 2
Up 
4me02
Attosecond pulse generation process
Classical model
vt0 , t  
eE
sin 0t   sin 0t0 
me0
eE
cos0t0   cos0t   0 sin 0t0 t  t0 
xt0 , t  
me0
Attosecond pulse generation process
Classical model
The return times are determined such that x0(t,t0)=0
Ek t , t0   2U p sin 0t   sin 0t0 
2
Long trajectories
Short trajectories
Ek is the instantaneous frequency of the attosecond pulse
Attosecond pulse generation process
Quantum model
 1

i  x, t     2  V  x   E cos0t x    x, t 
 2

The electron’s wavefunction
 t , x    g x   c x, t 
The induced dipole moment
xt    g x  c
The dynamics of the free electron is
mapped into the optical field
I    FFTxt 
Electron wave packet dynamic
Attosecond pulse
Electron wave packet dynamic
XUV field:
Husimi reprsentation
H  , t   F  xx    e  t  

2
/ b2


Attosecond pulse generation process
Classical model
Elliptically polarized light:
eE
sin 0t   sin 0t0 
v x t0 , t  
me0
v y t0 , t  
eE
cos0t   cos0t0 
me0
The electron is shifted in the lateral
direction: the recollision probability
reduces significantly
Isolating a single attosecond pulse
The multi-cycle
regime




E t    E  t   E  t  0.5 0   t  n 0    E  t   E  t  0.5 0   t  n 0 
n
n
E     E    E   exp i 0.5 0    n0    E  1  exp in     n0 
n
 E     n0 
 
n 0
n
odd
harmonics
even harmonics
Isolating a single attosecond pulse
The multi-cycle
regime
Femtosecond pulse
High
harmonics
20 fs, 800nm
I~1014 W/cm2
H15
23.3eV
H21
32.6eV
H27
41.9eV
H39
60.5eV
Attosecond pulse generation process
M. Hentschel et al., Nature 414, 509-513 (2001)
Attosecond pulse generation process
G. Sansone et al., Science 314, 443 (2006)
Time resolved measurements in the
attosecond regime
Attosecond pulses
generation
Measurement
How to measure an attosecond pulse?
XUV Autocorrelation
NLO effects:
2-photon absorption
2-photon ionization

focusing
NL
Problems:
low XUV flux
small sabs
Kobayashi et al., Opt. Lett. 23, 64 (1998)
Attosecond streak camera
F  ma

momentum
Dpti   e  El t dt  eAl ti 
ti
E t  
A
t
Laser field
Photo-electrons
Attosecond pulse
M. Hentschel et al., Nature 414, 509-513 (2001)
Electron release time
Momentum transfer depends on instant of
electron release within the wave cycle


Dp (t )  e EL (t )dt 
Mapping time to momentum
Momentum
change along
the EL vector
800-nm laser
electric field
Δp(t7)
Δp(t6)
Δp(t5)
t1
t2
t3
t4
t5
t6
t7
instant of
electron
release
Δp(t4)
Δp(t3)
Δp(t2)
Δp(t1)
Incident X-ray
intensity
-500 as
0
Δpi
500 as
Optical-field-driven streak camera
J. Itatani et al., Phys. Rev. Lett. 88, 173903 (2002)
M. Kitzler et al., Phys. Rev. Lett. 88, 173904 (2002)
Electron
counts per bin
Electron
countsper
per
bin counts
Electron counts
counts per
per
bin
Electron
bin
Electron
counts
bin
Electron
per bin
Full characterization of a sub-fs,
~100-eV XUV pulse
2
1
1
xuv = 250as
0
-1
-2
0
-3
-0.4
-0.2
0.0
Time [fs]
0.2
-0.4
Instantaneous
energy shift [eV]
Intensity [arb. u.]
Reconstructed temporal
intensity profile
and chirp of the xuv
excitation pulse:
00
100
100
100
100
Measurement
Measurement
Measurement
Simulation
Simulation
Simulation
50
50
50
50
000
100
100
100
100
100
100
100
Measurement
Measurement
Simulation
Simulation
Field-free
spectrum
50
50
50
50
50
50
000
00
100
100
100
100
t60
= -T0/4
60
d60
70
70
70
80
80
80
90
90
90
100
100
100
t60
60= +T0/4
d
70
70
80
80
90
90
100
100
Measurement
Measurement
Electron
[eV]
Electron
Electronkinetic
kinetic
kineticenergy
energy
energySimulation
[eV]
[eV]
Simulation
50
50
50
0
0
0
100
100
100
Electron
Electron kinetic
kinetic energy
energy [eV]
[eV]
50
50
0
0
60
60
70
70
80
80
90
90
Electron kinetic energy [eV]
 = 250
attoseconds!!
100
100
Energy shift of sub-fs electron
wave-packet
As we vary the relative delay between the XUV pulse and the 800-nm
field, the direction of the emitted electron packet will vary.
ΔW
+10 eV
0
-10 eV
tD
dN/dW
Photoelectron kinetic energy [eV]
Attosecond streak camera
trace
90
80
70
60
50
0
2
4
6
8
10
12
14
16
18
20 22
Delay Dt [fs]
E. Goulielmakis et al., Science 305, 1267 (2004)
RABITT (Reconstruction of Attosecond
Beating by Interference of Two-photon
Transition)

q2
xuv
Narrow one photon
transition
 xuv  0
 xuv
 xuv  0
q
q 2
Two photon transition The different paths interfere with a
relative phase of:
q 1  20   q   q  2
RABITT
RABITT (Reconstruction of
Attosecond Beating by Interference of
Two-photon Transition)
RABBITT takes advantage of the
interference of the even-harmonic
sidebands created when the XUV
pulse interacts with the intense IR
laser pulse.
RABITT results for a 250-as pulse
Time resolved measurements
Can we performed an attosecond pump probe measurement?
The main problem is the low photon flax

focusing
NL
One solution is to use the strong IR field as either the pump or the
probe
Attosecond streaking spectroscopy
Valence level
ionization
M. Drescher et al, Nature 419, 803 (2002)
Core level ionization
Auger Decay
Time resolved atomic
inner shell
spectroscopy
Time resolved atomic inner shell
spectroscopy
Time resolved atomic inner shell
spectroscopy
Oscillating dipole
The attosecond pulses contains the spatial information of the
ground and the free electron wavefunctions.
Imaging the ground state
c ~1A
d(t)= a(k) <g|er|eikx-()t>
The free electron act as a probe - the re-collision step maps the
ground state wave function to the spectrum
Harmonic intensities
5
9
0
22
45
67
90
8
7
Harmonic Intensity
Harmonic
intensities from
N2 at different
molecular angles
x 10
6
5
4
3
2
1
0
15
EL
20
25
30
Harmonic Number
35
40
45
Tomographic image reconstruction
Reconstructed Molecular
Orbital - N2
Reconstructed orbital
Calculated orbital
J. Itatani, et al., Nature 432, 867 (2004).