Strong-Field Ionization of Molecules: Simple Analytical Expressions

  • Ryan Murray
  • Serguei Patchkovskii
  • Olga Smirnova
  • Misha Yu. Ivanov
Part of the CRM Series in Mathematical Physics book series (CRM)


We use the method developed in [1] to derive simple expressions for strong-field ionization rates of molecules, as a function of their alignment with respect to the electric field. Our analytical expressions offer transparent physical interpretation, and demonstrate the connection between the geometry of the ionizing molecular orbital and alignment-dependent ionization rates, including the sensitivity of the angular patterns to the field strength. We also show how static tunnel ionization rates can be generalized to describe the subcycle ionization dynamics in oscillating laser fields.


Ionization Rate Tunneling Electron Match Point Tunneling Rate High Harmonic Generation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    R. Murray, W.K. Liu, M. Ivanov, Phys. Rev. A 81, 023413 (2010)ADSCrossRefGoogle Scholar
  2. 2.
    F. Krausz, M. Ivanov, Rev. Mod. Phys. 81, 163 (2009)ADSCrossRefGoogle Scholar
  3. 3.
    O. Smirnova, M. Spanner, M.Y. Ivanov, Phys. Rev. A 77, 33407 (2008)ADSCrossRefGoogle Scholar
  4. 4.
    S.V. Popruzhenko, G.G. Paulus, D. Bauer, Phys. Rev. A 77, 53409 (2008)ADSCrossRefGoogle Scholar
  5. 5.
    A.M. Perelomov, V.S. Popov, M.V. Terent’ev, Sov. Phys. JETP 23, 924 (1966)Google Scholar
  6. 6.
    A.M. Perelomov, V.S. Popov, M.V. Terent’ev, Sov. Phys. JETP 24, 207 (1967)Google Scholar
  7. 7.
    A.M. Perelomov, V.S. Popov, M.V. Terent’ev, Sov. Phys. JETP 25, 336 (1967)Google Scholar
  8. 8.
    G.L. Yudin, M.Y. Ivanov, Phys. Rev. A 64, 13409 (2001)ADSCrossRefGoogle Scholar
  9. 9.
    M.Y. Ivanov, M. Spanner, O. Smirnova, J. Mod. Opt. 52, 165 (2005)ADSMATHCrossRefGoogle Scholar
  10. 10.
    L.V. Keldysh, Sov. Phys. JETP 20, 1307 (1965)MathSciNetGoogle Scholar
  11. 11.
    J. Muth-Böhm, A. Becker, F.H.M. Faisal, Phys. Rev. Lett. 85, 2280 (2000)ADSCrossRefGoogle Scholar
  12. 12.
    X.M. Tong, Z.X. Zhao, C.D. Lin, Phys. Rev. A 66, 33402 (2002)ADSCrossRefGoogle Scholar
  13. 13.
    M. Awasthi, A. Saenz, J. Phys. B 39, S389 (2006)ADSCrossRefGoogle Scholar
  14. 14.
    Y.V. Vanne, A. Saenz, J. Mod. Opt. 55, 2665 (2008)ADSMATHCrossRefGoogle Scholar
  15. 15.
    S. Petretti, Y.V. Vanne, A. Saenz, P. Decleva, Phys. Rev. Lett. 104, 223001 (2010)ADSCrossRefGoogle Scholar
  16. 16.
    M. Abu-samha, L.B. Madsen, Phys. Rev. A 80, 23401 (2009)ADSCrossRefGoogle Scholar
  17. 17.
    M. Spanner, S. Patchkovskii, Phys. Rev. A 80, 063411 (2009)ADSCrossRefGoogle Scholar
  18. 18.
    I.I. Fabrikant, G.A. Gallup, Phys. Rev. A 79, 13406 (2009)ADSCrossRefGoogle Scholar
  19. 19.
    G.A. Gallup, I.I. Fabrikant, Phys. Rev. A 81, 033417 (2010)ADSCrossRefGoogle Scholar
  20. 20.
    O. Smirnova, Y. Mairesse, S. Patchkovskii, N. Dudovich, D. Villeneuve, P. Corkum, M.Y. Ivanov, Nature 460, 972 (2009)ADSCrossRefGoogle Scholar
  21. 21.
    O. Smirnova, S. Patchkovskii, Y. Mairesse, N. Dudovich, M.Y. Ivanov, Proc. Natl. Acad. Sci. U.S.A. 106, 16556 (2009)CrossRefGoogle Scholar
  22. 22.
    Y. Mairesse, J. Higuet, N. Dudovich, D. Shafir, B. Fabre, E. M?evel, E. Constant, S. Patchkovskii, Z. Walters, M.Y. Ivanov, O. Smirnova, Phys. Rev. Lett. 104, 213601 (2010)Google Scholar
  23. 23.
    A.T. Le, R.R. Lucchese, C.D. Lin, J. Phys. B 42, 211001 (2009)ADSCrossRefGoogle Scholar
  24. 24.
    S. Haessler, J. Caillat, W. Boutu, C. Giovanetti-Teixeira, T. Ruchon, T. Auguste, Z. Diveki, P. Breger, A. Maquet, B. Carr´e, R. Taïeb, P. Salières, Nature Phys. 6, 200 (2010)Google Scholar
  25. 25.
    M.V. Ammosov, N.B. Delone, V.P. Krainov, Sov. Phys. JETP 64, 1191 (1986)Google Scholar
  26. 26.
    R. Murray, M. Ivanov. In preparationGoogle Scholar
  27. 27.
    A.A. Radzig, B.M. Smirnov, Reference Data on Atoms, Molecules, and Ions, Springer Series in Chemical Physics, vol. 31 (Springer, BerlinNew York, 1985)Google Scholar
  28. 28.
    P. Salières, B. Carré, L. Le Déroff, F. Grasbon, G.G. Paulus, H.Walther, R. Kopold,W. Becker, D.B. Milošević, A. Sanpera, M. Lewenstein, Science 292, 902 (2001)ADSCrossRefGoogle Scholar
  29. 29.
    R. Kopold, W. Becker, D.B. Milošević, J. Mod. Opt. 49, 1362 (2002)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Ryan Murray
    • 1
    • 2
  • Serguei Patchkovskii
    • 3
  • Olga Smirnova
    • 3
  • Misha Yu. Ivanov
    • 2
  1. 1.Department of Physics and AstronomyUniversity of WaterlooWaterlooCanada
  2. 2.Department of PhysicsImperial College LondonLondonUK
  3. 3.Max-Born Institute for Nonlinear Optics and Short Pulse SpectroscopyBerlinGermany

Personalised recommendations