Alignment dependence of HHG from N2, O2 and CO2

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Alignment dependence of HHG from N2, O2 and CO2
A.T. Le, X.M. Tong, and C.D. Lin

• Dept. of Physics, KSU
• Oct. 19, 2005

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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

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Kanai et al, Nature, 435, 470 (2005)
Ionization
N2
23rd HHG
Laser parameters 50fs, 800nm, 2x1014W/cm2 Tempera
ture 80K
O2
N2 and O2 HHG and ionization are in phase CO2 is
different!!!
CO2
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Vozzi et al, PRL 2005
800nm, 30fs 250 ?J
Inversion found at harmonic 33
Two-Point Emitter model
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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

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Our initial goals

• Analytic form for angular dependence (both
  ionization and HHG)?
• Why CO2 is different?

For homonuclear diatomic molecules
Pn(-x)(-1)n Pn(x)
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HHG Three-Step model

• Tunneling ionization depends on orientation
• Propagation in laser field
• Recombination depends on orientation

Question Is the alignment dependence of
ionization is more important?
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Ionization MO-ADK theory
Tong et al, PRA 2002
Main contribution from m0
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N2
N2 case
Numerical results from Zhao et al, PRA 2003
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Numerical results Zhao et al, PRA 2003
Analytical result with only m0
O2
CO2
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HHG Lewenstein model
Molecular Orbital from GAMESS
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sin(1cos(?)), with 1 term
cos(1.5cos(?)), with 2 terms
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Numerical results
Present results
Zhou et al (PRA 2005)
Discrepancies found
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Comparison for different intensities
Need to include depletion for high intensity
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Typical result of HHG

• N2
• 800nm
• 30fs, Gaussian envelope
• 3x1014 W/cm2

cutoff 47
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Evidence of interference effect
Note the even orders
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Now odd orders! Symmetry
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Go one step further ionization OR recombination
at one center. What are the results?
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More evidence
Note the even orders
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Dependence on the alignment angle
N2 800nm 30fs 3x1014 W/cm2
cutoff 47
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High intensity
N2 800nm, 30fs 5x1014 W/cm2
cutoff 71
Positions of the minima not changed
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Long wavelength
N2 1064nm, 30fs 3x1014 W/cm2
Minima scale with wavelength
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Minima moving away
N2 800nm 30fs 3x1014 W/cm2
Position of the minima moved towards higher
order, as orientation angle increases
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Lein et al, PRL 2002
Solved numerically 2D Schrodinger equation for H2
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Two-point emitter model
Lein et al, PRA 2002
Numerical data from 2D H2 and H2
Positions of the Max Min are given by

• NOTE
• Min Max are interchanged for different
  symmetries
• Controversy about ?

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N2
Blue without atomic potential Red with atomic
potential
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O2
Blue without atomic potential Red with atomic
potential
Problem with large angles?
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Zimmermann et al, PRA 2005
N2
Weak-field approx. for recombination
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Very complicated
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Minima x Maxima
0
0
2
4
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CO2
O2
R0.232nm
R0.121nm
Quantum chemistry GAMESS code MOLEKEL plot
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CO2
Almost no contribution from C-center (small
polarization term)
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Preliminary results
cutoff 31
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No significant differences between these
molecules!??
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Summary Outlook

• HHG is max at 0o for N2 and 45o for O2
• Minima in HHG due to interference effect

Next

• Resolve the discrepancies
• Case of CO2
• Finish analytical approach

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N2 HOMO in momentum space
N2 HOMO
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N2 HOMO in momentum space s-wave contribution
N2 HOMO s-wave contribution
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N2 HOMO in momentum space p-wave contribution
N2 HOMO p-wave contribution
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dy
dz
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Higher intensity N2 800nm, 30fs 5x1014 W/cm2