Alignment dependence of HHG from N2, O2 and CO2

1. 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

2. 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

3. 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

4. Vozzi et al, PRL 2005 800nm, 30fs 250 J Inversion found at harmonic 33 Two-Point Emitter model

5. 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;

6. 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)

7. 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?

8. Ionization: MO-ADK theory Tong et al, PRA 2002 Main contribution from m’=0

9. N2 case N2 Numerical results from Zhao et al, PRA 2003

10. Numerical results Zhao et al, PRA 2003 Analytical result with only m’=0 O2 CO2

11. HHG: Lewenstein model Molecular Orbital from GAMESS

12. sin(1*cos(θ)), with 1 term cos(1.5*cos(θ)), with 2 terms

13. Numerical results Present results Zhou et al (PRA 2005) Discrepancies found

14. Comparison for different intensities Need to include depletion for high intensity

15. Typical result of HHG • N2 • 800nm; • 30fs, Gaussian envelope; • 3x1014 W/cm2 cutoff ~ 47

16. Evidence of interference effect Note the even orders

17. Now odd orders! Symmetry

18. Go one step further: ionization OR recombination at one center. What are the results?

19. More evidence Note the even orders

20. Dependence on the alignment angle N2 800nm; 30fs 3x1014 W/cm2 cutoff ~ 47

21. High intensity N2 800nm, 30fs 5x1014 W/cm2 cutoff ~ 71 Positions of the minima not changed

22. Long wavelength N2 1064nm, 30fs 3x1014 W/cm2 Minima scale with wavelength

23. Minima moving away N2 800nm; 30fs 3x1014 W/cm2 Position of the minima moved towards higher order, as orientation angle increases

24. Lein et al, PRL 2002 Solved numerically 2D Schrodinger equation for H2+

25. 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 

26. N2 Blue: without atomic potential Red: with atomic potential

27. O2 Blue: without atomic potential Red: with atomic potential Problem with large angles?

28. Zimmermann et al, PRA 2005 N2 Weak-field approx. for recombination 2 Very complicated 1 Minima: x Maxima: + 0 0 2 4

29. CO2 O2 R=0.232nm R=0.121nm Quantum chemistry GAMESS code & MOLEKEL plot

30. CO2 Almost no contribution from C-center (small polarization term)

31. Preliminary results cutoff ~ 31

32. No significant differences between these molecules!??

33. 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

34. N2 HOMO in momentum space N2 HOMO

35. N2 HOMO: s-wave contribution N2 HOMO in momentum space s-wave contribution

36. N2 HOMO in momentum space p-wave contribution N2 HOMO: p-wave contribution

37. dy dz

38. Higher intensity: N2 800nm, 30fs 5x1014 W/cm2