Post on 12-Jan-2016
description
Alignment dependence of HHG from N2, O2 and CO2
Dept. of Physics, KSU
Oct. 19, 2005
A.T. Le, X.M. Tong, and C.D. Lin
Outlines
• Introduction
• MO-ADK: a simplified picture
• HHG in N2 and O2: a comparison
• Minima in HHG: interference effect
• Case of CO2
• Summary and outlook
Ionization
23rd HHG
N2
O2
CO2
N2 and O2: HHG and ionization are in phase
CO2 is different!!!
N2 and O2: HHG and ionization are in phase
CO2 is different!!!
Kanai et al, Nature, 435, 470 (2005)
Laser parameters: 50fs, 800nm, 2x1014W/cm2
Temperature ~ 80K
Vozzi et al, PRL 2005Vozzi et al, PRL 2005
800nm, 30fs
250 J
Inversion found at harmonic 33
Inversion found at harmonic 33
Two-Point Emitter model
MO-ADK ionization rates of O2 and N2
• Strong dependence on alignment;
• For N2 good agreement with Litvinyuk et al, PRL 2003;
• Agrees well with recent experiments at KSU;
• Strong dependence on alignment;
• For N2 good agreement with Litvinyuk et al, PRL 2003;
• Agrees well with recent experiments at KSU;
Our initial goals
• Analytic form for angular dependence (both ionization and HHG)?
• Why CO2 is different?
Pn(-x)=(-1)n Pn(x)
For homonuclear diatomic molecules:
HHG: Three-Step model
1. Tunneling ionization: depends on orientation
2. Propagation in laser field
3. Recombination: depends on orientation
Question:
Is the alignment dependence of ionization is more important?
Question:
Is the alignment dependence of ionization is more important?
Ionization: MO-ADK theory
Main contribution from m’=0 Main contribution from m’=0
Tong et al, PRA 2002
0.25 0.5 0.75 1 1.25 1.5
1
2
3
4
5
6
7
)(cos78.02
02.2)0'( 22
5 PmB
N2
Numerical results from Zhao et al, PRA 2003
N2 case
0.25 0.5 0.75 1 1.25 1.5
0.1
0.2
0.3
0.4
0.5
0.25 0.5 0.75 1 1.25 1.5
2.5
5
7.5
10
12.5
15
17.5
O2
CO2
0max 40
0max 30
Numerical resultsZhao et al, PRA 2003
Numerical resultsZhao et al, PRA 2003
Analytical result with only m’=0
Molecular Orbital from GAMESS
Molecular Orbital from GAMESS
HHG: Lewenstein model
)coscos()2/.cos(
)cossin()2/.sin(
21
21
pRRp
pRRp
)(cos)()coscos(
)(cos)()cossin(
22
1212
ll
ll
PaBa
PaAa
)(cos)()coscos(
)(cos)()cossin(
22
1212
ll
ll
PaBa
PaAa
0.5 1 1.5 2 2.5 3
-0.75
-0.5
-0.25
0.25
0.5
0.75
0.5 1 1.5 2 2.5 3
0.2
0.4
0.6
0.8
1sin(1*cos(θ)),
with 1 term
cos(1.5*cos(θ)),
with 2 terms
Present results Zhou et al (PRA 2005)
Discrepancies foundDiscrepancies found
Numerical results
Comparison for different intensities
Need to include depletion for high intensity
cutoff ~ 47
N2
• 800nm;
• 30fs, Gaussian envelope;
• 3x1014 W/cm2
N2
• 800nm;
• 30fs, Gaussian envelope;
• 3x1014 W/cm2
Typical result of HHG
Note the even orders
Note the even orders
Evidence of interference effect
Now odd orders!
Symmetry
Now odd orders!
Symmetry
Go one step further: ionization OR recombination at one center.
What are the results?
Go one step further: ionization OR recombination at one center.
What are the results?
Note the even orders
Note the even orders
More evidence
N2
800nm; 30fs
3x1014 W/cm2
cutoff ~ 47
Dependence on the alignment angle
N2
800nm, 30fs
5x1014 W/cm2
cutoff ~ 71
Positions of the minima not changed
Positions of the minima not changed
High intensity
N2
1064nm, 30fs
3x1014 W/cm2
Minima scale with wavelength
Minima scale with wavelength
Long wavelength
N2
800nm; 30fs
3x1014 W/cm2
N2
800nm; 30fs
3x1014 W/cm2
Position of the minima moved towards higher order, as orientation angle increases
Minima moving away
Lein et al, PRL 2002Lein et al, PRL 2002
Solved numerically 2D Schrodinger equation for H2
+
Lein et al, PRA 2002Lein et al, PRA 2002
Positions of the Max & Min are given by:
Two-point emitter model
Numerical data from 2D H2+ and H2
NOTE:
• Min & Max are interchanged for different symmetries
• Controversy about
NOTE:
• Min & Max are interchanged for different symmetries
• Controversy about
Blue: without atomic potential
Red: with atomic potential
N2
Blue: without atomic potential
Red: with atomic potential
O2
Problem with large angles?
Problem with large angles?
Zimmermann et al, PRA 2005Zimmermann et al, PRA 2005
Weak-field approx. for recombination
0
1
2
0 2 4
Minima: x
Maxima: +
N2
Very complicatedVery complicated
CO2 O2
R=0.232nm R=0.121nm
Quantum chemistry GAMESS code & MOLEKEL plotQuantum chemistry GAMESS code & MOLEKEL plot
CO2
Almost no contribution from C-center (small polarization term)
Almost no contribution from C-center (small polarization term)
cutoff ~ 31
Preliminary results
No significant differences between these molecules!??
No significant differences between these molecules!??
Summary & Outlook
1. HHG is max at 0o for N2 and 45o for O2
2. Minima in HHG due to interference effect
• Resolve the discrepancies
• Case of CO2
• Finish analytical approach
Next:
N2 HOMO in momentum spaceN2 HOMO
N2 HOMO in momentum space
s-wave contribution
N2 HOMO: s-wave contribution
N2 HOMO in momentum space
p-wave contributionN2 HOMO: p-wave contribution
dy dz
Higher intensity:
N2
800nm, 30fs
5x1014 W/cm2
Higher intensity:
N2
800nm, 30fs
5x1014 W/cm2