Generation of short pulses 2.7 fs. Ultrashort pulse generation 15 fs pulse Time [fs] Wavelength [m]...
-
date post
19-Dec-2015 -
Category
Documents
-
view
218 -
download
1
Transcript of Generation of short pulses 2.7 fs. Ultrashort pulse generation 15 fs pulse Time [fs] Wavelength [m]...
Ultrashort pulse generation
15 fs pulse
Time [fs] Time [fs]
Wavelength [m]
Wavelength [m]
Single cycle pulse
Raman scattering and attosecond pulses
S. E. Harris and A. V. Sokolov PRL 81, 2894
frequency
Raman processes can cascade many times, yielding a series of equally spaced modes
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+/- n0
1
0
Cascaded Raman generation
ba= 2994 cm-1
A. V. Sokolov et al. PRL 85, 85 562
This can be done with nanosecond laser pulses!
A. V. Sokolov et al. PRL 85, 562
Experimental demonstration of cascaded Raman scattering
- 400MHz
+ 100MHz
+ 700MHz
2994 cm-1
Detuning from 2-photon resonance
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.
2001: First observation of an attosecond pulse (650 as)
2006: (130 as)
Breaking the femtosecond limitBreaking the femtosecond limit
M. Hentschel et al., Nature 414, 509-513 (2001)
G. Sansone et al., Science 314, 443 (2006)
Field Intensity: 1014 –1015 W/cm2
2.7 fs
Our main tool: intense laser pulsesOur main tool: intense laser pulses
The force is comparable to the force binding the electrons in the atom or molecule.
Attosecond pulse generation processAttosecond pulse generation process
Acceleration by the electric fieldRe-collision
Tunnel ionization
E>100eV
kp EI
0100~ With I~1014 W/cm2
Fundamental frequency
20
2
43
EI pcutoff
Attosecond pulse generation processAttosecond pulse generation process
Acceleration by the electric field
Tunnel ionization
Optical radiation with attoseconds duration
Attosecond pulse generation processAttosecond pulse generation process
eEmaF
tEtE 0cos
00000000
0
0000
0
sincoscos,
sinsin,
tttttm
eEttx
ttm
eEttv
e
e
20
22
20000
4
sinsin2,
ep
pk
m
EeU
ttUttE
Classical model
Attosecond pulse generation processAttosecond pulse generation process
00000000
0
0000
0
sincoscos,
sinsin,
tttttm
eEttx
ttm
eEttv
e
e
Classical model
Attosecond pulse generation processAttosecond pulse generation process
20000 sinsin2, ttUttE pk
Classical modelThe return times are determined such that x0(t,t0)=0
Short trajectories
Long trajectories
Ek is the instantaneous frequency of the attosecond pulse
Attosecond pulse generation processAttosecond pulse generation process
Quantum model
txxtExVtxi ,cos2
1, 0
2
txxxt cg ,,
cg xtx
The dynamics of the free electron is mapped into the optical field
txFFTI
The electron’s wavefunction
The induced dipole moment
Electron wave packet dynamicElectron wave packet dynamicXUV field:
2 2/, t bH t x e xF
Husimi reprsentation
Attosecond pulse generation processAttosecond pulse generation process
Classical model
Elliptically polarized light:
0000
0
0000
0
coscos,
sinsin,
ttm
eEttv
ttm
eEttv
ey
ex
The electron is shifted in the lateral direction: the recollision probability reduces significantly
Isolating a single attosecond pulseIsolating a single attosecond pulse
The multi-cycle regime
n
nn
n n
harmonicseven
harmonicsoddnE
ninEniEEE
nttEtEnttEtEtE
0
exp15.0exp
5.05.0
0
000
0000
H1523.3eV
H2132.6eV
H2741.9eV
H3960.5eV
Isolating a single attosecond pulseIsolating a single attosecond pulse
The multi-cycle regime
Femtosecond pulse
20 fs, 800nm
I~1014 W/cm2
High harmonics
Attosecond pulse generation processAttosecond pulse generation process
M. Hentschel et al., Nature 414, 509-513 (2001)
Attosecond pulse generation processAttosecond pulse generation process
G. Sansone et al., Science 314, 443 (2006)
Time resolved measurements in the Time resolved measurements in the attosecond regimeattosecond regime
Attosecond pulses generation
Measurement
XUV Autocorrelation
focusing NL
NLO effects:2-photon absorption
2-photon ionization
Problems:low XUV fluxsmall abs
Kobayashi et al., Opt. Lett. 23, 64 (1998)
How to measure an attosecond pulse?
t
AtE
teAdttEetp
maF
il
t
li
i
momentum
Attosecond pulse
Laser field
Electron release time
Photo-electrons
Attosecond streak cameraAttosecond streak camera
M. Hentschel et al., Nature 414, 509-513 (2001)
Momentum transfer depends on instant of electron release within the wave cycle
L( ) ( )t
p t e E t dt
Mapping time to momentum
Incident X-rayintensity
Δpi
instant ofelectronrelease
Δp(t7)
Δp(t6)
Δp(t5)
Δp(t3)
Δp(t2)
Δp(t1)
Δp(t4)
Momentumchange along the EL vector
-500 as 0 500 as
800-nm laser electric field
t7t1 t2 t3 t4 t5 t6
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)
Full characterization of a sub-fs, ~100-eV XUV pulse
= 250 attoseconds!!
td = -T0/4
td = +T0/4
Field-freespectrum
Reconstructed temporal intensity profile
and chirp of the xuv excitation pulse:
Time [fs]
Inte
ns
ity [arb
. u.] 0
1In
stan
tane
ou
s
energ
y sh
ift [eV]
-3
-2
-1
0
1
2
-0.4 -0.2 0.0 0.2 -0.4
xuv = 250as
+10 eV
-10 eV
0
ΔW
tD
Energy shift of sub-fs electron wave-packet
dN/dW
As we vary the relative delay between the XUV pulse and the 800-nm field, the direction of the emitted electron packet will vary.
Ph
oto
ele
ctro
n k
ine
tic e
ne
rgy
[eV
]
Delay t [fs]
2 4 8 10 14 18 200 6 12 16 22
50
60
70
80
90
Attosecond streak camera trace
E. Goulielmakis et al., Science 305, 1267 (2004)
RABITT (Reconstruction of Attosecond RABITT (Reconstruction of Attosecond Beating by Interference of Two-photon Beating by Interference of Two-photon
Transition)Transition)
Narrow one photon transition
xuv
Two photon transition
0 xuv
xuv0 xuv
2q
q
2q
The different paths interfere with a relative phase of:
201 2 qqq
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.
focusing NL
Time resolved measurementsTime resolved measurements
Can we performed an attosecond pump probe measurement?
The main problem is the low photon flax
One solution is to use the strong IR field as either the pump or the probe
Attosecond streaking spectroscopyAttosecond streaking spectroscopy
M. Drescher et al, Nature 419, 803 (2002)
Core level ionizationValence level ionization
Auger Decay
Oscillating dipoleOscillating dipole
The attosecond pulses contains the spatial information of the ground and the free electron wavefunctions.
The free electron act as a probe - the re-collision step maps the
ground state wave function to the spectrum
Imaging the ground stateImaging the ground state
d(t)= a(k) <g|er|eikx-()t>
c ~1A
Harmonic intensitiesHarmonic intensities
15 20 25 30 35 40 450
1
2
3
4
5
6
7
8
9x 10
5
Harmonic Number
Ha
rmo
nic
In
ten
sit
y
0
22
4567
90
Harmonic intensities from N2 at different molecular angles
EL