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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 N 2 and O 2 : a comparison Minima in HHG: interference effect Case of CO 2 Summary and outlook.
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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
Kanai et al, Nature, 435, 470 (2005) Ionization N2 23rd HHG Laser parameters: 50fs, 800nm, 2x1014W/cm2 Temperature ~ 80K O2 N2 and O2: HHG and ionization are in phase CO2 is different!!! CO2
Vozzi et al, PRL 2005 800nm, 30fs 250 J 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;
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)
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?
Ionization: MO-ADK theory Tong et al, PRA 2002 Main contribution from m’=0
N2 case N2 Numerical results from Zhao et al, PRA 2003
Numerical results Zhao et al, PRA 2003 Analytical result with only m’=0 O2 CO2
HHG: Lewenstein model Molecular Orbital from GAMESS
sin(1*cos(θ)), with 1 term cos(1.5*cos(θ)), with 2 terms
Numerical results Present results Zhou et al (PRA 2005) Discrepancies found
Comparison for different intensities Need to include depletion for high intensity
Typical result of HHG • N2 • 800nm; • 30fs, Gaussian envelope; • 3x1014 W/cm2 cutoff ~ 47
Evidence of interference effect Note the even orders
Now odd orders! Symmetry
Go one step further: ionization OR recombination at one center. What are the results?
More evidence Note the even orders
Dependence on the alignment angle N2 800nm; 30fs 3x1014 W/cm2 cutoff ~ 47
High intensity N2 800nm, 30fs 5x1014 W/cm2 cutoff ~ 71 Positions of the minima not changed
Long wavelength N2 1064nm, 30fs 3x1014 W/cm2 Minima scale with wavelength
Minima moving away N2 800nm; 30fs 3x1014 W/cm2 Position of the minima moved towards higher order, as orientation angle increases
Lein et al, PRL 2002 Solved numerically 2D Schrodinger equation for H2+
Two-point emitter model Numerical data from 2D H2+ and H2 Lein et al, PRA 2002 Positions of the Max & Min are given by: • NOTE: • Min & Max are interchanged for different symmetries • Controversy about
N2 Blue: without atomic potential Red: with atomic potential
O2 Blue: without atomic potential Red: with atomic potential Problem with large angles?
Zimmermann et al, PRA 2005 N2 Weak-field approx. for recombination 2 Very complicated 1 Minima: x Maxima: + 0 0 2 4
CO2 O2 R=0.232nm R=0.121nm Quantum chemistry GAMESS code & MOLEKEL plot
CO2 Almost no contribution from C-center (small polarization term)
Preliminary results cutoff ~ 31
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
N2 HOMO in momentum space N2 HOMO
N2 HOMO: s-wave contribution N2 HOMO in momentum space s-wave contribution
N2 HOMO in momentum space p-wave contribution N2 HOMO: p-wave contribution
dy dz
Higher intensity: N2 800nm, 30fs 5x1014 W/cm2