Time and space resolved imaging of electron tunneling from molecules.
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Transcript of Time and space resolved imaging of electron tunneling from molecules.
![Page 1: Time and space resolved imaging of electron tunneling from molecules.](https://reader038.fdocuments.net/reader038/viewer/2022103123/56649d7e5503460f94a60d5d/html5/thumbnails/1.jpg)
Time and space resolved imaging
of electron tunneling
from molecules
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Olga Smirnova, Max-Born Institute, Berlin
Serguei Patchkovskii, NRC, Ottawa
Misha Ivanov, Imperial College, London
Yann Mairesse, CELIA, Université Bordeaux I
Nirit Dudovich, Weizmann Institute, Rehovot
David Villeneuve, NRC, Ottawa
Paul Corkum, NRC, Ottawa
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Strong Field Ionization: Optical Tunneling
+
V(x)+xE cost
Field free atom/molecule
Tunnel ionization in strong laser fields
V(x)
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• We can remove an electron from different orbitals
• Ion can be left in excited states
Many electrons and multiple orbitals
Ion Ion*
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Ionization from molecules
O OC
HOMO
HOMO-1
HOMO-2
+ -
Tunnel ionization is exponentially sensitive to Ip
E
IW p
3
)2(2exp~
2/3
X 2g~A 2u~
B 2u
~
Ip~13.8 eV
4.3eV3.5 eV
There is more to ionization than IThere is more to ionization than Ipp
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Ionization from different orbitals: leaving the ion in excited states
O OC
HOMO
HOMO-1
HOMO-2
+ -
Our calculations show that 3 channels are important in CO2
X 2g~A 2u~
B 2u
~
Ip~13.8 eV
4.3eV3.5 eV
Multiple ionization channels are important in molecules
Key reasons: Proximity of electronic states in the ion
Geometry of Dyson orbitals
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Main message
1. Channel coupling during ionization (laser-induced)
2. Interaction between the departing electron and hole
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Main message
1. Channel coupling during ionization (laser-induced)
2. Interaction between the departing electron and hole
1. Affects ionization rates into each channel
2. 2. New parameter: phasephase between channels
Reflected in the shape and location of the hole, its recoil from the electron during ionization
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Main message
1. Channel coupling during ionization (laser-induced)
2. Interaction between the departing electron and hole
1. Affects the magnitude of each channel
2. 2. New parameter: phasephase between channels
Reflected in the shape and location of the hole, its recoil from the electron during ionization
How can we image the hole dynamics during tunneling?
Can we measure the phase of ionization?
Consider CO2
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Ionization from different orbitals: leaving the ion in excited states
O OC
HOMO
HOMO-1
HOMO-2
+ -
X 2g~A 2u~
B 2u
~
Ip~13.8 eV
Interference suppression of SF ionization
A. Becker et al, 2000, C.D. Lin et al 2002
Suppression at both 0o and 90o
X2g
~
xz
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Angular dependence: channel X, I=2.1014 W/cm2
HOMO
|aT|2=4.5 10-3
Interference suppression of SF ionization
A. Becker et al, 2000
Suppression at both 0o and 90o
X2g
~
~
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X 2g~A 2u~ B 2
u~
O OC
HOMO
HOMO-1
HOMO-2+ -
3.5 eV
Ionization from different orbitals: leaving the ion in excited states
A2u
~
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Ionization: channel A, I=2.1014 W/cm2
|aA|2=9 10-5= |aX|2/50
θ=90o: |aA|2/|aX|2=1/5
Suppression at 0o
A2u
~
~ ~
~ ~
~
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O OC
HOMO
HOMO-1
HOMO-2 + -X 2g~A 2u~ B 2
u~
4.3eV
Ionization from different orbitals: leaving the ion in excited states
B2u+
~
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Ionization: channel , I=2.1014 W/cm2
|aX|2/128|aB|2=3.5 10-5=
|aB|2/|aX|2=1/28Suppression at 90o
B2u+
~
B
~
~~
~
~
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Ionization: intermediate conclusions
•Strong-field ionization almost always creates dynamics in the ion (Not specific for CO2)
•This dynamics is different for different orientations of the molecule with respect to the laser field
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Ionization: intermediate conclusions
•Strong-field ionization almost always creates dynamics in the ion (Not specific for CO2)
•This dynamics is different for different orientations of the molecule with respect to the laser field
Visualization of hole dynamics X,A channels~ ~
X,B channels~ ~
xz
xz
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• Visualization of hole dynamics for
|X-B|2~ ~
Where does the hole begin its motion after tunnel ionization, and how does it move?
We need to record relative phase between different channels
Direction of tunneling
X,B channels~ ~
|X+B|2~~
|X-iB|2~ ~x
z
xz
xz
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High harmonic spectroscopy
3. Recombination
1. Ionization
2. Propagation
-xEL
Same initial and final states: ground state of the neutral
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Multiple channels in HHG
Different ionization channels-Different ionization channels-different HHG channelsdifferent HHG channels
Ion Ion*
Interference records relative phase between the channels by mapping it into harmonic amplitude
modulations!
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High harmonics: temporal resolution
Atto-second temporal resolutionAtto-second temporal resolution
t - time delay between ionization and recombination
t1 t2
1.75
N1
N2Ee(t)+Ip
0 2.7 t,fs
~e.g. 60 eV
2fs/20 odd harmonics~100 asec
Each harmonic takes snapshot of the system at a
particular time delay between ionization and recombination
M. Lein,
S. Baker et al
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Getting initial phase
H29X
BTotal
Destructive interference at XB(*)=(2n+1)
XB(=0)= rec+ion
H29
XB=(EX-EB) + rec+ion
Dynamical minimum is tied to *, not
harmonic number!
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I=1.1*1014W/cm2
Amplitude Minima in CO2
I=2.0*1014W/cm2
Minimum shifts with intensity
It is a signature of dynamical minimum and channel interference
HH
inte
nsity
H31H25
HH
inte
nsity
800nm 40fs800nm 40fs
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Intensity dependence of the dynamical minimum
=1.17±0.1fs
1.1014
2.1014
3.1014
Ele
ctro
n e
nerg
y,
eV
Delay , fs Laser Intensity, 1014 W/cm2H
arm
on
ic n
um
ber cos4()
cos6()
N*= Ee()+Ip
N*∞ (1.7±0.2)Up
*
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Theory vs experiment
Laser Intensity, 1014 W/cm2
Harm
on
ic n
um
ber
cos4()cos6()cos4()cos6()
Experiment: Yann Mairesse, Nirit Dudovich, David Villeneuve, Paul Corkum
cos4()cos6()cos4()cos6()cos4()cos6()exp
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The harmonic movie decoded
• Visualization of hole dynamics for aligned CO2:X,B channels~ ~
• In tunneling regime, the initial phase between and is zero, see frame 1: maximum extension in the direction of tunneling.
Direction of tunneling
1
2
3
B~
X~
|X+B|2~~
|X-iB|2~ ~
|X-B|2~ ~
xz
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Theory vs experiment
Laser Intensity, 1014 W/cm2
Harm
on
ic n
um
ber
cos4()cos6()cos4()cos6()
Experiment: Yann Mairesse, Nirit Dudovich, David Villeneuve, Paul Corkum
cos4()cos6()cos4()cos6()cos4()cos6()exp
=1
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Hole delocalization in multiphoton regime?
• Visualization of hole dynamics for aligned CO2:X,B channels~ ~
1
2
3Multiphoton regime
|X-B|2~~
|X-iB|2~ ~
|X+iB|2~ ~
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Tracking hole dynamics at longer wavelength
Each harmonic is a frame of an “attosecond movie” (M. Lein; S. Baker et al)
Longer wavelength - longer movie (~),
more frames per fs (~)
=1200nm
HH
inte
nsity
X,A channels~ ~
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Mapping the period of hole motion
One can monitor separately the length of the period of hole motion and initial phase for each intensity.
X,A channels~ ~
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Mapping the period of hole motion
One can monitor separately the length of the period of hole motion and initial phase for each intensity.
X,B channels
Constructive
Destructive
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Conclusions
New questions for theory and experiment:New questions for theory and experiment:
• Channel coupling during strong-field ionization
• Relative phase of strong-field ionization between channels, in tunneling and multi-photon regimes.
In simple terms:In simple terms:
• How does the hole recoil from the departing electron?
• How does the hole left in the ion records attosecond dynamics of core re-arrangement during strong field ionization?
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Dynamical origin of the minimum
=1.17±0.1fs
N= Ee()+Ip
Up=E2L/42
N∞ (1.7±0.2)Up
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Dynamical origin of the minimum
=1.8 fs
1.1014
2.1014
3.1014
Ele
ctro
n e
nerg
y,
eV
Delay , fs
N= Ee()+Ip
Up=E2L/42
N∞ 3.17Up
Laser Intensity, 1014 W/cm2
Harm
on
ic n
um
ber cos4()
cos6()
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HHG – multichannel interference
NN
Ion
Neutral
Ion*
Interference records relative phase between the channels by mapping it into harmonic amplitude
modulations
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Amplitude Minima in CO2, cut of the spectrum for =0o
Harm
on
ic in
ten
sity
I=1.1 1014W/cm2
Harmonic number
H25
Interplay of the channels depends on intensity
dominates for high harmonics, dominates for low harmonics
X~
X~
B~
B~B
~
X~ Total Total
800nm 40fs800nm 40fs
Harmonic number
H33
I=2.0*1014W/cm2
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HH spectroscopy: the promise (?)
dtetN tiN )(D)(E
Temporal and spatial information about • electron density in the neutral • electron density in the ion• continuum electron: scattering phase
cctttt CONTNION
NNEUT )()(A|d|)()(D )1()(
HHG Observables • photon energy• harmonic amplitude (intensity)• harmonic phase• harmonic polarization
Temporal and spatial information- how it is encoded?
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n
npR
2
)12(cos
2
)(2
NpIN p
M. Lein et al, 2002
Potential to obtain structural information
- gerade
- ungerade
Structure –related interference minima in HHG
R
Rcos
M. Lein et al, 2002, 2D H2+
HHG spectroscopy: spatial resolution
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Example: HHG in CO2
D
Kanai et al, Nature 435, 2005
minimum2cos pR
pINNp
2
)(2
NB: Molecules are pre-aligned for HHG experiments!
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CO2 is different in Tokyo and Milano
Harmonic number
2cos)( RNp
25-27C. Vozzi, PRL 95, 153902 (2005)
Tokyo Milano
CO2
Kanai et al, Nature 435, 2005
33-35
CO2
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CO2 is different in Tokyo and Milano
Harmonic number
2cos)( RNp
25-27C. Vozzi, PRL 95, 153902 (2005)
Tokyo Milano
CO2
Kanai et al, Nature 435, 2005
33-35
CO2
Ottawa: Mairesse, Dudovich, Villeneuve, Corkum –
The minimum shifts with intensity
> 2. 10 14 W/cm2< 2.10 14 W/cm2
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Main message
Theory and Experiment in CO2
•HHG spectra for molecules reflect the contribution of different electronic states of the ion
•The positions of minima in HHG spectrum are related to
•Structure: geometry of participating Dyson orbitals
•Dynamics: the interplay of different states of the ion
•How to tell them apart?
•What can we learn from positions of dynamical minima?
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Ionization: intermediate conclusions
•Strong-field ionization almost always creates dynamics in the ion (Not specific for CO2)
•This dynamics is different for different orientations of the molecule with respect to the laser field
•This dynamics can be further modified by the laser field (Not the case for CO2 in IR field)
•This dynamics is reflected in HHG spectra and we shall see how X, A channels~ ~
X,B channels~ ~
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Amplitude minima in harmonic spectra
@ N. Rerikh
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Theory vs experiment
Laser Intensity, 1014 W/cm2
Harm
on
ic n
um
ber
cos4()cos6()cos4()cos6()
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The harmonic movie decoded
• Visualization of hole dynamics for aligned CO2:X,B channels~ ~
1
2
3Multiphoton regime
|X-B|2~~
|X-iB|2~ ~
|X+iB|2~ ~
Low intensity measurement (multiphoton regime) is consistent with maximum delocalization
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I=1.7*1014 W/cm2I=1.26*1014 W/cm2
Theory vs experiment: HHG spectra
Alignment angle-50 0 50
Alignment angle-50 0 5017 25 31 37
HH
order
Inte
nsity -6
-7
17 21 25 29 33
HH
order
Inte
nsity -6
-7
17 21 25 29
HH
order
Inte
nsity -6
-7
17 21 25 29 37
HH
order
Inte
nsity -6
-7
Alignment angle-50 0 50
Alignment angle-50 0 50
I~1.0*1014 W/cm2 I~1.8*1014 W/cm2
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Conclusions
• There are several HHG channels in CO2 molecule
• Interference between the channels records attosecond dynamics of ionic states
• Dynamical minimum is tied to recombination time and is strongly dependent on intensity
• Structural minimum is tied to electron energy and is intensity-independent.
• The comparison of theory and experiment has allowed us to ask and answer fundamental question: Where is the hole created and how does it recoil from the departing electron?
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Harmonic phases near dynamical minimum
Structural minimum: -phase jumps
Dynamical minimum:
H43
H43
Ab-initio, 2D H2+, Lein et al, 2002
Inte
nsit
yP
hase
Angle
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phase jumps near dynamical minima
I=2.0*1014W/cm2
H33
Molecular alignment angle,
Harmonic Phase, units of
X~
B~
A~
Total
X~
B~
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I=2.0*1014W/cm2
H33
Molecular alignment angle,
Harmonic Phase, units of
X~
B~
A~
H33
A~
X~
B~
Molecular alignment angle,
Harmonic Phase, units of
I=1.3*1014W/cm2
Intensity dependence of the phase
Total
Total
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Circular dichroism
=
Mc
|ER|2- |EL|2
|ER|2+ |EL|2=
Circular dichroism means that system responds differently to left and right circularly
polarized light:
no left-right symmetry
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Circular dichroism of harmonic emission: why?
1. Anisotropy of molecular potential: returning electron does not have to move along the field
OO C
-
Elaser
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Circular dichroism of harmonic emission: how?
ElaserHHG||HHG┴
Laser field dominates the motion of continuum
electron and HHG┴<<HHG||
Conditions of high circularity:
1. Suppress HHG|| -> HHG||~ HHG┴
. /2 relative phase between HHG|| and HHG┴
Conditions are naturally met both in the vicinity of structural and dynamical minima
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Circular dichroism “marks” dynamical minima in CO2
Circularity, calculated from recombination dipole for HOMO, no
angle averaging
Max circularity marks the positions of structural
minimumAfter averaging the min shifts from H25 to H37-39
HHG spectra, after averaging
HHG circularity
Max circularity marks the positions
of dynamical minima
I=2.0*1014W/cm2
![Page 56: Time and space resolved imaging of electron tunneling from molecules.](https://reader038.fdocuments.net/reader038/viewer/2022103123/56649d7e5503460f94a60d5d/html5/thumbnails/56.jpg)
Circular dichroism “marks” dynamical minima in CO2
H35: Harmonic phase for each channel
H35: HHG amplitudes for each
channel
H35: Circularity for each channel
Circularity indicates “switching” between different channels, and positions of
“dynamical” minima
I=2.0*1014W/cm2
![Page 57: Time and space resolved imaging of electron tunneling from molecules.](https://reader038.fdocuments.net/reader038/viewer/2022103123/56649d7e5503460f94a60d5d/html5/thumbnails/57.jpg)
Circularity of harmonics in CO2
– maximal number of harmonics with high circularity
I=2.0*1014W/cm2 I=1.5*1014W/cm2
High values of Mc shift to lower harmonic orders for lower intensity
Mc=(|Ez||Ex|sin(z-x))/ |Ex|2+ |Ez|2
![Page 58: Time and space resolved imaging of electron tunneling from molecules.](https://reader038.fdocuments.net/reader038/viewer/2022103123/56649d7e5503460f94a60d5d/html5/thumbnails/58.jpg)
Circularly polarized attosecond pulses
Mc
|ER|2- |EL|2
|ER|2+ |EL|2= |ER|- |EL|
|ER|+ |EL|=
150 asec pulse with Mc=0.7
I=2.0*1014W/cm2:
![Page 59: Time and space resolved imaging of electron tunneling from molecules.](https://reader038.fdocuments.net/reader038/viewer/2022103123/56649d7e5503460f94a60d5d/html5/thumbnails/59.jpg)
Conclusions
1. High circularity of harmonic light marks the positions of dynamical minima, background –free measurement
2. Structural minima can be hard to observe in polarization measurement
3. If the amplitude minimum is not accompanied by high circularity it is neither structural, no dynamical, but reflects switching from one dominant channel to another without destructive interference between them
4. Multichannel nature of HHG in molecules allow to shape polarization of asec pulses
![Page 60: Time and space resolved imaging of electron tunneling from molecules.](https://reader038.fdocuments.net/reader038/viewer/2022103123/56649d7e5503460f94a60d5d/html5/thumbnails/60.jpg)
Dynamical minimum in HH spectra
XB=(EX-EB) (N)+ rec+ion
1.1014
2.1014
3.1014
Ele
ctro
n e
nerg
y,
eV
N= Ee()+Ip
N= 3.17 Up
Delay , fs
1.8 fs
1.8 fs
Dynamical minimum shifts linearly with the intensity
![Page 61: Time and space resolved imaging of electron tunneling from molecules.](https://reader038.fdocuments.net/reader038/viewer/2022103123/56649d7e5503460f94a60d5d/html5/thumbnails/61.jpg)
Conclusions & Outlook
• HH spectroscopy
-identifies different molecular orbitals (electronic continua)
-records the interference between different electronic continua
-records attosecond dynamics of the hole left in the molecule via interference between different electronic continua (HH channels)
• HH spectroscopy: additional observables
-harmonic phases,
-harmonic polarizations circularity
Circular dichroism in HHG: Max circularity marks the positions of dynamical minima (background –free measurement)
I=2.0 1014 W/cm2
![Page 62: Time and space resolved imaging of electron tunneling from molecules.](https://reader038.fdocuments.net/reader038/viewer/2022103123/56649d7e5503460f94a60d5d/html5/thumbnails/62.jpg)
• HH spectroscopy can be used to study
-Multielctron dynamics in polyatomic molecules in strong fields
-Reconstruction of individual contributions of different orbitals vs intensity gives insight into the largely
unknown dynamics of strong field ionization in multielectron systems.
-Where is the hole created and how does it recoil from the departing electron? (done for CO2)
-How non-adiabatic laser induced transitions affect the dynamics of the hole? (current work - N2).
- Towards strong –field control of the hole shape and motion in polyatomic molecules (possibly leading to control of
fragmentation, charge transfer)
Conclusions & Outlook
![Page 63: Time and space resolved imaging of electron tunneling from molecules.](https://reader038.fdocuments.net/reader038/viewer/2022103123/56649d7e5503460f94a60d5d/html5/thumbnails/63.jpg)
Non-linear optical wave-mixing (e.g.
CARS)
Ip
pump
HH-probe
Conclusions & Outlook
Time-resolved PES
• HH spectroscopy can be used to study
-Field-free coupled electronic and nuclear dynamics in polyatomic molecules via pump-HH probe schemes
![Page 64: Time and space resolved imaging of electron tunneling from molecules.](https://reader038.fdocuments.net/reader038/viewer/2022103123/56649d7e5503460f94a60d5d/html5/thumbnails/64.jpg)
Conclusions & Outlook
• HH spectroscopy can be used to study
-Field-free coupled electronic and nuclear dynamics in polyatomic molecules via UV pump-HH probe schemes
•Stimulated Raman Pumping of N-N stretch•HHG probing after t (800 nm strong field)
rNN
RAMANPUMP
HHGPROBE
trNN
N
O
O
N
O
O
Wen Li et al, Science 2008
![Page 65: Time and space resolved imaging of electron tunneling from molecules.](https://reader038.fdocuments.net/reader038/viewer/2022103123/56649d7e5503460f94a60d5d/html5/thumbnails/65.jpg)
IonIon*
e- e-
Ip
IonIon*
e- e-
Ip
PES HHS
HHS Observables: -amplitudes (spectra) -phases (!) -polarizations (!)Asec resolution
Selectivity: same initial and final state
HHS is inverse of PES +coherence in continuum
![Page 66: Time and space resolved imaging of electron tunneling from molecules.](https://reader038.fdocuments.net/reader038/viewer/2022103123/56649d7e5503460f94a60d5d/html5/thumbnails/66.jpg)
Harmonic phases near dynamical minimum
Structural minimum: -phase jumps
Dynamical minimum:
H43
H43
Ab-initio, 2D H2+, Lein et al, 2002
Inte
nsit
yP
hase
Angle
![Page 67: Time and space resolved imaging of electron tunneling from molecules.](https://reader038.fdocuments.net/reader038/viewer/2022103123/56649d7e5503460f94a60d5d/html5/thumbnails/67.jpg)
phase jumps near dynamical minima
I=2.0*1014W/cm2
H33
Molecular alignment angle,
Harmonic Phase, units of
X~
B~
A~
Total
X~
B~
![Page 68: Time and space resolved imaging of electron tunneling from molecules.](https://reader038.fdocuments.net/reader038/viewer/2022103123/56649d7e5503460f94a60d5d/html5/thumbnails/68.jpg)
I=2.0*1014W/cm2
H33
Molecular alignment angle,
Harmonic Phase, units of
X~
B~
A~
H33
A~
X~
B~
Molecular alignment angle,
Harmonic Phase, units of
I=1.3*1014W/cm2
Intensity dependence of the phase
Total
Total
![Page 69: Time and space resolved imaging of electron tunneling from molecules.](https://reader038.fdocuments.net/reader038/viewer/2022103123/56649d7e5503460f94a60d5d/html5/thumbnails/69.jpg)
Circular dichroism in HHG emission from aligned molecules
=
Mc
|ER|2- |EL|2
|ER|2+ |EL|2=
![Page 70: Time and space resolved imaging of electron tunneling from molecules.](https://reader038.fdocuments.net/reader038/viewer/2022103123/56649d7e5503460f94a60d5d/html5/thumbnails/70.jpg)
High circularity identifies switching between the channels
Mc
|ER|2- |EL|2
|ER|2+ |EL|2=
![Page 71: Time and space resolved imaging of electron tunneling from molecules.](https://reader038.fdocuments.net/reader038/viewer/2022103123/56649d7e5503460f94a60d5d/html5/thumbnails/71.jpg)
Circularity of harmonics in CO2
Mc indicates “switching” between different channels, and positions of “structural”
minima
Mc
|ER|2- |EL|2
|ER|2+ |EL|2=
![Page 72: Time and space resolved imaging of electron tunneling from molecules.](https://reader038.fdocuments.net/reader038/viewer/2022103123/56649d7e5503460f94a60d5d/html5/thumbnails/72.jpg)
Circularity of harmonics in CO2
![Page 73: Time and space resolved imaging of electron tunneling from molecules.](https://reader038.fdocuments.net/reader038/viewer/2022103123/56649d7e5503460f94a60d5d/html5/thumbnails/73.jpg)
Circularity of harmonics in CO2
![Page 74: Time and space resolved imaging of electron tunneling from molecules.](https://reader038.fdocuments.net/reader038/viewer/2022103123/56649d7e5503460f94a60d5d/html5/thumbnails/74.jpg)
Circular dichroism in HHG emission from aligned molecules
=
Mc
|ER|2- |EL|2
|ER|2+ |EL|2=
![Page 75: Time and space resolved imaging of electron tunneling from molecules.](https://reader038.fdocuments.net/reader038/viewer/2022103123/56649d7e5503460f94a60d5d/html5/thumbnails/75.jpg)
High circularity identifies switching between the channels
Mc
|ER|2- |EL|2
|ER|2+ |EL|2=
![Page 76: Time and space resolved imaging of electron tunneling from molecules.](https://reader038.fdocuments.net/reader038/viewer/2022103123/56649d7e5503460f94a60d5d/html5/thumbnails/76.jpg)
Circularity of harmonics in CO2
Mc indicates “switching” between different channels, and positions of “structural”
minima
Mc
|ER|2- |EL|2
|ER|2+ |EL|2=
![Page 77: Time and space resolved imaging of electron tunneling from molecules.](https://reader038.fdocuments.net/reader038/viewer/2022103123/56649d7e5503460f94a60d5d/html5/thumbnails/77.jpg)
Disentangling structural and dynamical information
Structural minimum:
Position of minimum is tied to the De-Broglie wavelength and hence energy of the continuum electron
(approximately intensity independent)
Dynamical minimum:
Position of minimum is tied to the time of recombination
(approximately linearly depends on intensity)
![Page 78: Time and space resolved imaging of electron tunneling from molecules.](https://reader038.fdocuments.net/reader038/viewer/2022103123/56649d7e5503460f94a60d5d/html5/thumbnails/78.jpg)
Modeling HHG: including different channels
j – labels different states of the ion
)(|d|)()(D )(Ie
)( ttt NNNEUT
jjCONT
NjIONb
ionj
N ttttt )()(A)]([a)( ,)1(
,)(
Ie
![Page 79: Time and space resolved imaging of electron tunneling from molecules.](https://reader038.fdocuments.net/reader038/viewer/2022103123/56649d7e5503460f94a60d5d/html5/thumbnails/79.jpg)
Modeling HHG: including different channels
• NEUT (t) – MC SCF, quasi-static field, for all relevant electrons (CAS)
• ION, j (t)
• MC SCF for all (j=1..5) essential stationary ionic states, field-free
• Calculate all dipole couplings between these states
• Do TDSE dynamics in restricted basis of these ionic states
•Channel-specific Hartree potential : Hartree [ION,J]
• aion : syb-cycle YudinIvanov* orbital-dependent angular factor (CC-VGSFA)
• CONT , j (t) from SF EVA (Smirnova, Spanner, Ivanov PRA (2008))
j – labels different states of the ion
)(|d|)()(D )(Ie
)( ttt NNNEUT
jjCONT
NjIONb
ionj
N ttttt )()(A)]([a)( ,)1(
,)(
Ie
![Page 80: Time and space resolved imaging of electron tunneling from molecules.](https://reader038.fdocuments.net/reader038/viewer/2022103123/56649d7e5503460f94a60d5d/html5/thumbnails/80.jpg)
Recombination matrix element: amplitude
k2/2+Ip=N
Harmonic order
Log scale
B~
X~
X~
B~
Harmonic order
Log scale
=20o
=30o
B~
A~
X~
|dB|2 >> |dX|2
is not accidental – same nodal planes are at fault!
General whenever Dyson orbitals have nodal planes
|drec|2
![Page 81: Time and space resolved imaging of electron tunneling from molecules.](https://reader038.fdocuments.net/reader038/viewer/2022103123/56649d7e5503460f94a60d5d/html5/thumbnails/81.jpg)
Outlook
Each harmonic is a frame of an “attosecond movie” (M. Lein; S. Baker et al)
Longer wavelength - longer movie (~),
more frames per fs (~)
=1200nm
HH
inte
nsity
X,A channels~ ~
![Page 82: Time and space resolved imaging of electron tunneling from molecules.](https://reader038.fdocuments.net/reader038/viewer/2022103123/56649d7e5503460f94a60d5d/html5/thumbnails/82.jpg)
Contributions to XB~~
XB=(EB-EX) (N)+ rec~~ ~~
X≈B≈~ ~
if(EB-EX) << N
Recombination time, fs
X- B~~
Harm
on
ic n
um
ber
~~
B~
X~
N=Ee()+Ip
![Page 83: Time and space resolved imaging of electron tunneling from molecules.](https://reader038.fdocuments.net/reader038/viewer/2022103123/56649d7e5503460f94a60d5d/html5/thumbnails/83.jpg)
Destructive interference: XB=(2n+1) ~~
Harmonic number
rec,
un
its
of
X~
B~
XB=(EX-EB) (N)+ rec~~ ~~
Evolution of phase
![Page 84: Time and space resolved imaging of electron tunneling from molecules.](https://reader038.fdocuments.net/reader038/viewer/2022103123/56649d7e5503460f94a60d5d/html5/thumbnails/84.jpg)
Conclusions I -amplitudes
• There are several HHG channels in CO2 molecule
• Position of the HHG minimum is intensity dependent and is determined by the interplay of different channels
• Structural minimum is not easy to observe in HHG spectrum – the minimum is “filled” by the HH emission associated with other orbitals (other channels)
![Page 85: Time and space resolved imaging of electron tunneling from molecules.](https://reader038.fdocuments.net/reader038/viewer/2022103123/56649d7e5503460f94a60d5d/html5/thumbnails/85.jpg)
Conclusions II -phases
• Phase measurements can be very useful to
disentangle the contribution of different orbitals
• Phase jumps are often related to the switch
between the channels and do not have to be =
• Recombination matrix elements give the
dominant contribution into harmonic phases in
the case of CO2
![Page 86: Time and space resolved imaging of electron tunneling from molecules.](https://reader038.fdocuments.net/reader038/viewer/2022103123/56649d7e5503460f94a60d5d/html5/thumbnails/86.jpg)
phase jumps near interference minima
H33
I=2.0*1014W/cm2
H33
Molecular alignment angle, Molecular alignment angle,
Harmonic Phase, units of Harmonic Amplitude
X~
X~
B~
B~
A~
A~
![Page 87: Time and space resolved imaging of electron tunneling from molecules.](https://reader038.fdocuments.net/reader038/viewer/2022103123/56649d7e5503460f94a60d5d/html5/thumbnails/87.jpg)
Intensity dependence of the phase
H33
I=1.3*1014W/cm2
H33
A~
A~
X~
X~
B~
B~
Molecular alignment angle, Molecular alignment angle,
Harmonic Phase, units of Harmonic Amplitude
![Page 88: Time and space resolved imaging of electron tunneling from molecules.](https://reader038.fdocuments.net/reader038/viewer/2022103123/56649d7e5503460f94a60d5d/html5/thumbnails/88.jpg)
Role of electron-ion entanglement
Norm:
Norm:
Low degree of entanglement:
![Page 89: Time and space resolved imaging of electron tunneling from molecules.](https://reader038.fdocuments.net/reader038/viewer/2022103123/56649d7e5503460f94a60d5d/html5/thumbnails/89.jpg)
Eikonal vs exact, hydrogen atom
![Page 90: Time and space resolved imaging of electron tunneling from molecules.](https://reader038.fdocuments.net/reader038/viewer/2022103123/56649d7e5503460f94a60d5d/html5/thumbnails/90.jpg)
Eikonal vs plane wave
=20o =20o
=30o =30o
=40o =40o
Harmonic numberHarmonic number
|d|2 |d|2
Eikonal Plane wave
![Page 91: Time and space resolved imaging of electron tunneling from molecules.](https://reader038.fdocuments.net/reader038/viewer/2022103123/56649d7e5503460f94a60d5d/html5/thumbnails/91.jpg)
Contributions to XB
Harmonic number
rec,
un
its
of
~~
~ ~
DTOT= Dx(N)+ DB(N~~
~
X~
B~
Dx(N)=exp{-iV-iEXX(N)-irec,X}~
~DB(N)=exp{-iV-iEBB(N)-irec,B}
~ ~ ~
Destructive interference
XB=(2n+1) ~~
V<< XB if (N)<<(N~~
XB=(EX-EB) (N)+ rec~~ ~~
![Page 92: Time and space resolved imaging of electron tunneling from molecules.](https://reader038.fdocuments.net/reader038/viewer/2022103123/56649d7e5503460f94a60d5d/html5/thumbnails/92.jpg)
I=1014W/cm2
Angle of molecular alignment, deg
Harm
on
ic p
hase
, u
nit
s of
Switching orbitals: harmonic phases
![Page 93: Time and space resolved imaging of electron tunneling from molecules.](https://reader038.fdocuments.net/reader038/viewer/2022103123/56649d7e5503460f94a60d5d/html5/thumbnails/93.jpg)
Interpretation of NRC phase measurements
Yann Mairesse, Nirit Dudovich, Paul Corkum & David Villeneuve
Phase measurements @ NRC:
H19
H21 H23
H17
![Page 94: Time and space resolved imaging of electron tunneling from molecules.](https://reader038.fdocuments.net/reader038/viewer/2022103123/56649d7e5503460f94a60d5d/html5/thumbnails/94.jpg)
I=1014W/cm2Experiment vs TheoryH
arm
on
ic p
hase
, u
nit
s of
Angle of molecular alignment, deg
Harm
onic
phase
, ra
d
Harm
onic
phase
, ra
d
0.6
4
0.4
H21 H23
0.6
0.9
![Page 95: Time and space resolved imaging of electron tunneling from molecules.](https://reader038.fdocuments.net/reader038/viewer/2022103123/56649d7e5503460f94a60d5d/html5/thumbnails/95.jpg)
I=1014W/cm2Experiment vs Theory
Angle of molecular alignment, deg
H17
Harm
on
ic p
hase
, u
nit
s of Harm
onic
phase
, ra
d
0.4
0.6
H21H
arm
onic
phase
, ra
d
0.1
0.1
![Page 96: Time and space resolved imaging of electron tunneling from molecules.](https://reader038.fdocuments.net/reader038/viewer/2022103123/56649d7e5503460f94a60d5d/html5/thumbnails/96.jpg)
Conclusions I -amplitudes
• There are several HHG channels in CO2 molecule
• Position of the HHG minimum is intensity dependent and is determined by the interplay of different channels
• Structural minimum is not easy to observe in HHG spectrum – the minimum is “filled” by the HH emission associated with other orbitals (other channels)
![Page 97: Time and space resolved imaging of electron tunneling from molecules.](https://reader038.fdocuments.net/reader038/viewer/2022103123/56649d7e5503460f94a60d5d/html5/thumbnails/97.jpg)
Conclusions II -phases
• Phase measurements can be very useful to
disentangle the contribution of different orbitals
• Phase jumps are often related to the switch
between the channels and do not have to be =
• Recombination matrix elements give the
dominant contribution into harmonic phases in
the case of CO2
![Page 98: Time and space resolved imaging of electron tunneling from molecules.](https://reader038.fdocuments.net/reader038/viewer/2022103123/56649d7e5503460f94a60d5d/html5/thumbnails/98.jpg)
Main message
•HHG spectra for molecules reflect the contribution of different channels related to different states of the ion
•The relative contributions of these channels change with the intensity
•The positions of minima in HHG spectrum and phase jumps are often determined by the interplay of different channels
•The channels can be distinguished by looking at harmonics:
• amplitude,
• phase,
•photon energy
vs molecular orientation
(Example: CO2 molecule)
![Page 99: Time and space resolved imaging of electron tunneling from molecules.](https://reader038.fdocuments.net/reader038/viewer/2022103123/56649d7e5503460f94a60d5d/html5/thumbnails/99.jpg)
Modeling HHG: including different channels
j – labels different states of the ion
)(|d|)()(D )(Ie
)( ttt NNNEUT
jjCONT
NjIONb
ionj
N ttttt )()(A)]([a)( ,)1(
,)(
Ie
Visualization of hole dynamics X+A channels~ ~
X+B channels~ ~
Question: Where does the hole begin its motion?
![Page 100: Time and space resolved imaging of electron tunneling from molecules.](https://reader038.fdocuments.net/reader038/viewer/2022103123/56649d7e5503460f94a60d5d/html5/thumbnails/100.jpg)
Where does the hole start its motion?
Laser Intensity, 1014 W/cm2
Harm
on
ic n
um
ber cos4()
cos6()
The position of the minimum depends on the initial phase between the X and B channels: Xei+B
![Page 101: Time and space resolved imaging of electron tunneling from molecules.](https://reader038.fdocuments.net/reader038/viewer/2022103123/56649d7e5503460f94a60d5d/html5/thumbnails/101.jpg)
Where does the hole start its motion?
Laser Intensity, 1014 W/cm2
Harm
on
ic n
um
ber cos4()
cos6()
The position of the minimum depends on the initial phase between the X and B channels: Xei+B
![Page 102: Time and space resolved imaging of electron tunneling from molecules.](https://reader038.fdocuments.net/reader038/viewer/2022103123/56649d7e5503460f94a60d5d/html5/thumbnails/102.jpg)
Ionization: intermediate conclusions
•Strong-field ionization almost always creates dynamics in the ion (Not specific for CO2)
•This dynamics is different for different orientations of the molecule with respect to the laser field
•This dynamics can be further modified by the laser field (Not the case for CO2 in IR field)
•This dynamics is reflected in HHG spectra and we shall see how
![Page 103: Time and space resolved imaging of electron tunneling from molecules.](https://reader038.fdocuments.net/reader038/viewer/2022103123/56649d7e5503460f94a60d5d/html5/thumbnails/103.jpg)
High harmonic generation in molecules: a new spectroscopic toolLes entrées
•The basics of High Harmonic Generation• Attosecond measurements without attosecond pulses • Combining atto-second temporal and sub-A spatial resolution
Les plats
CO2
•Attosecond hole dynamics after tunnel ionization
Les desserts (add 7’)
Circular dichroism spectroscopy with high harmonics
Formule du Midi - 49’
49’
![Page 104: Time and space resolved imaging of electron tunneling from molecules.](https://reader038.fdocuments.net/reader038/viewer/2022103123/56649d7e5503460f94a60d5d/html5/thumbnails/104.jpg)
Where does the hole start its motion?
Laser Intensity, 1014 W/cm2
Harm
on
ic n
um
ber cos4()
cos6()X&B channels~ ~
Direction of ionization
=0
=
![Page 105: Time and space resolved imaging of electron tunneling from molecules.](https://reader038.fdocuments.net/reader038/viewer/2022103123/56649d7e5503460f94a60d5d/html5/thumbnails/105.jpg)
Dynamical origin of the minimum
Laser Intensity, 1014 W/cm2
Harm
on
ic n
um
ber X+B channels
~ ~
Direction of ionization
cos4()cos6()cos4()cos6()cos4()cos6()exp
At low intensity the hole starts in the middle between the turning points: Xei/2+B
![Page 106: Time and space resolved imaging of electron tunneling from molecules.](https://reader038.fdocuments.net/reader038/viewer/2022103123/56649d7e5503460f94a60d5d/html5/thumbnails/106.jpg)
Ionization: intermediate conclusions
•Strong-field ionization almost always creates dynamics in the ion (Not specific for CO2)
j
jCONTjIONN ttt )()(A)( ,,
)(Ie
BIONtiE
BXIONtiE
X
BCONTtiE
BIONXCONTtiE
XION
BX
XX
eaea
ee
,,
,,,,
||
|p
•Wave-packet for CO2 molecules aligned along laser field
![Page 107: Time and space resolved imaging of electron tunneling from molecules.](https://reader038.fdocuments.net/reader038/viewer/2022103123/56649d7e5503460f94a60d5d/html5/thumbnails/107.jpg)
Recollision as a probe
+
V(x)+xELcost
X~EL/2 ~ 10-100 Å
Energy E~102 eV
DeBroglie< 1 Å
Electron probes the parent ion
•Elastic scattering
•Inelastic scattering
•Radiative recombination
)(|d|)()(D )(Ie
)( ttt NNNEUT
jjCONT
NjIONb
ionj
N ttttt )()(A)]([a)( ,)1(
,)(
Ie
![Page 108: Time and space resolved imaging of electron tunneling from molecules.](https://reader038.fdocuments.net/reader038/viewer/2022103123/56649d7e5503460f94a60d5d/html5/thumbnails/108.jpg)
Recollision after Tunnel Ionization
Corkum,1993, Schafer, Krause & Kulander, 1993
+
V(x)+xELcost
ionization
return
-eEL
-eEL
![Page 109: Time and space resolved imaging of electron tunneling from molecules.](https://reader038.fdocuments.net/reader038/viewer/2022103123/56649d7e5503460f94a60d5d/html5/thumbnails/109.jpg)
Ionization: intermediate conclusions
•Strong-field ionization almost always creates dynamics in the ion (Not specific for CO2)
•This dynamics is different for different orientations of the molecule with respect to the laser field
•This dynamics can be further modified by the laser field
(Not the case for CO2 in IR field)
•This dynamics is reflected in HHG spectra and we shall see how
![Page 110: Time and space resolved imaging of electron tunneling from molecules.](https://reader038.fdocuments.net/reader038/viewer/2022103123/56649d7e5503460f94a60d5d/html5/thumbnails/110.jpg)
HHG – multichannel interference
NN
Neutral
Interference of light records relative phase between the channels
Let us look @ HHG spectra for different intensities
B~
~X
j – labels different states of the ion
)()(D tDtj
j
)()(A|d|)()(D ,)1(
,)(
j tttt jCONTN
jIONNNEUT
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Disentangling structural and dynamical information
Structural minimum:
Position of minimum is tied to the De-Broglie wavelength and hence energy of the continuum electron
(approximately intensity independent)
Dynamical minimum:
Position of minimum is tied to the time of recombination
(approximately linearly depends on intensity)
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Theory vs experiment: HHG spectra
Experiment: Yann Mairesse, Nirit Dudovich, David Villeneuve, Paul Corkum
-6
-5
-4
17
2125
29
21
25
29
27
3131
27
I~1*1014 W/cm2
-50
500
I=1.26*1014 W/cm2
Alignment angle
Alignment angle
HH
inte
nsity
HH
inte
nsity
Harm
onic order
Harm
onic order
![Page 113: Time and space resolved imaging of electron tunneling from molecules.](https://reader038.fdocuments.net/reader038/viewer/2022103123/56649d7e5503460f94a60d5d/html5/thumbnails/113.jpg)
Kinematics of Electron recollisionE
rec/
Up
,
Up=
E2 /
4 Recollision energy
Time
X
3.17Up Up~10 eV
Scheme: Rev.Mod. Phys, Krausz, Ivanov
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The harmonic movie decoded
• Visualization of hole dynamics for aligned CO2:X,B channels~ ~
• In tunneling regime, the initial phase between and is zero, see frame 1: maximum extension in the direction of tunneling.
• Low intensity measurement (multiphoton regime) is consistent with frame 2: maximum delocalization
Direction of tunneling
1
2
3
B~
X~
|X+B|2~~
|X-iB|2~ ~
|X-B|2~ ~
![Page 115: Time and space resolved imaging of electron tunneling from molecules.](https://reader038.fdocuments.net/reader038/viewer/2022103123/56649d7e5503460f94a60d5d/html5/thumbnails/115.jpg)
HH spectroscopy: Non-linear Optics perspective
N
Ion
Neutral
HH generation as a wave-mixing process
![Page 116: Time and space resolved imaging of electron tunneling from molecules.](https://reader038.fdocuments.net/reader038/viewer/2022103123/56649d7e5503460f94a60d5d/html5/thumbnails/116.jpg)
The harmonic movie decoded
• Visualization of hole dynamics for aligned CO2:X,B channels~ ~
1
2
3Multiphoton regime
|X-B|2~~
|X-iB|2~ ~
|X+iB|2~ ~
![Page 117: Time and space resolved imaging of electron tunneling from molecules.](https://reader038.fdocuments.net/reader038/viewer/2022103123/56649d7e5503460f94a60d5d/html5/thumbnails/117.jpg)
Getting initial phase
H29X
BTotal
Destructive interference at
XB(*)=(2n+1)
* 2.6
H29
Ee(+Ip=N
0fs
XB(=0)=?
![Page 118: Time and space resolved imaging of electron tunneling from molecules.](https://reader038.fdocuments.net/reader038/viewer/2022103123/56649d7e5503460f94a60d5d/html5/thumbnails/118.jpg)
Time scale
1 as = 1/1000 fs
Time10 sec100 as 10 billion years
We can apply strong laser fields to drive electrons and use them to image their own motion
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• We can remove an electron from different orbitals
• Ion can be left in excited states
Many electrons and multiple orbitals
Ion Ion*
Different ionization channels-different HHG channelsDifferent ionization channels-different HHG channels
![Page 120: Time and space resolved imaging of electron tunneling from molecules.](https://reader038.fdocuments.net/reader038/viewer/2022103123/56649d7e5503460f94a60d5d/html5/thumbnails/120.jpg)
High harmonics: temporal resolution
Many different N are emitted at different times within 2 fsec
Atto-second temporal resolutionAtto-second temporal resolution
t1 t2
1.8
N1
N2Ee(t)+Ip
0 2.6 t,fs
t - time delay between ionization and recombination
~e.g. 60 eV
2fs/20 odd harmonics~100 asec