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R-Matrix Theory of Atomic Collisions pp 433–491Cite as

Multiphoton Processes: Floquet Theory

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Part of the book series: Springer Series on Atomic, Optical, and Plasma Physics ((SSAOPP,volume 61))

Abstract

The study of the interaction of intense laser fields with atoms and molecules has attracted considerable attention in recent years. In particular, the availability of increasingly intense lasers has made possible the observation of a wide variety of multiphoton processes, including multiphoton ionization, laser-assisted electron–atom collisions and harmonic generation. Also, in the case of molecules, the loss of spherical symmetry and the degrees of freedom associated with the nuclear motion give rise to additional computational difficulties and new effects including multiphoton dissociation. Many reviews of these processes have been written and we mention here comprehensive overviews by Gavrila [365], Burnett et al. [194], Mason [639], Protopapas et al. [759] and Joachain et al. [504] where the emphasis is on atomic multiphoton processes, and by Bandrauk et al. [50, 51], Giusti-Suzor et al. [378] and Posthumus [751], where the emphasis is on molecular multiphoton processes.

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Notes

  1. 1.

    Explicit expressions for the potential matrices \(\textbf{ V}^{E\gamma}\), V Dγ and \(\textbf{V}^{P\gamma}\) in (9.41) are derived in Appendix D.2.

  2. 2.

    See Sect. 9.2.3 for a further discussion of LICS states.

References

  1. M.V. Ammosov, N.B. Delone, V.P. Krainov, Sov. Phys. JETP 64, 1191 (1986)

    Google Scholar 

  2. A.D. Bandrauk (ed.) Molecules in Laser Fields (Dekker, New York, NY, 1994)

    Google Scholar 

  3. A.D. Bandrauk, E.E. Aubanel, J.-J. Gauthier, in Molecules in Laser Fields, ed. by A.D. Bandrauk (Dekker, New York, NY, 1994), p. 109

    Google Scholar 

  4. W. Becker, S. Long, J.K. McIver, Phys. Rev. A 41, 4112 (1990)

    Article  ADS  Google Scholar 

  5. W. Becker, S. Long, J.K. McIver, Phys. Rev. A 50, 1540 (1994)

    Article  ADS  Google Scholar 

  6. P.G. Burke, P. Francken, C.J. Joachain, Europhys. Lett. 13, 617 (1990)

    Article  ADS  Google Scholar 

  7. P.G. Burke, P. Francken, C.J. Joachain, J. Phys. B At. Mol. Opt. Phys. 24, 761 (1991)

    Article  ADS  Google Scholar 

  8. K. Burnett, V.C. Reed, P.L. Knight, J. Phys. B At. Mol. Opt. Phys. 26, 561 (1993)

    Article  ADS  Google Scholar 

  9. D. Charlo, M. Tereo-Dunseath, K.M. Dunseath, J.-M. Launay, J. Phys. B At. Mol. Opt. Phys. 31, L539 (1998)

    Article  ADS  Google Scholar 

  10. S.-I. Chu, Adv. At. Mol. Phys. 21, 197 (1985)

    Article  Google Scholar 

  11. P.B. Corkum, Phys. Rev. Lett. 71, 1994 (1993)

    Article  ADS  Google Scholar 

  12. A. Cyr, O. Latinne, P.G. Burke, J. Phys. B At. Mol. Opt. Phys. 30, 659 (1997)

    Article  ADS  Google Scholar 

  13. H.C. Day, A.S. Fearnside, R.M. Potvliege, Phys. Rev. A 56, 2447 (1997)

    Article  ADS  Google Scholar 

  14. H.C. Day, B. Piraux, R.M. Potvliege, Phys. Rev. A 61, 031402(R) (2000)

    Article  ADS  Google Scholar 

  15. M. Dörr, M. Terao-Dunseath, J. Purvis, C.J. Noble, P.G. Burke, C.J. Joachain, J. Phys. B At. Mol. Opt. Phys. 25, 2809 (1992)

    Article  ADS  Google Scholar 

  16. K.M. Dunseath, M. Terao-Dunseath, J. Phys. B At. Mol. Opt. Phys. 37, 1305 (2004)

    Article  ADS  Google Scholar 

  17. K.M. Dunseath, M. Terao-Dunseath, Phys. Rev. A 73, 053407 (2006)

    Article  ADS  Google Scholar 

  18. K.M. Dunseath, M. Terao-Dunseath, G. Bourhis, Phys. Rev. A 72, 033410 (2005)

    Article  ADS  Google Scholar 

  19. J.H. Eberly, Q. Su, J. Javanainen, Phys. Rev. Lett. 62, 881 (1989)

    Article  ADS  Google Scholar 

  20. J.H. Eberly, Q. Su, J. Javanainen, J. Opt. Soc. Am. B 6, 1289 (1989)

    Article  ADS  Google Scholar 

  21. G. Floquet, Ann. Ec. Norm. 13(2), 47 (1883)

    MathSciNet  Google Scholar 

  22. R. Frahm, K. Liang, G. Williams (eds.), Synchrotron Radiation News 20(6) (Taylor and Francis Group, Boca Raton, FL, 2007)

    Google Scholar 

  23. M. Gavrila, (ed.) Adv. At. Mol. Opt. Phys. Suppl. 1, Atoms in Intense Laser Fields (Academic Press, New York, NY, 1992)

    Google Scholar 

  24. R. Gȩbarowski, P.G. Burke, K.T. Taylor, M. Dörr, M. Bensaid, C.J. Joachain, J. Phys. B At. Mol. Opt. Phys. 30, 1837 (1997)

    Article  ADS  Google Scholar 

  25. R. Gȩbarowski, K.T. Taylor, P.G. Burke, J. Phys. B At. Mol. Opt. Phys. 30, 2505 (1997)

    Article  ADS  Google Scholar 

  26. A. Giusti-Suzor, F.H. Mies, L.F. DiMauro, E. Charron, B. Yang, J. Phys. B At. Mol. Opt. Phys. 28, 309 (1995)

    Article  ADS  Google Scholar 

  27. D.H. Glass, P.G. Burke, J. Phys. B At. Mol. Opt. Phys. 33, 407 (2000)

    Article  ADS  Google Scholar 

  28. M.L. Goldberger, K.M. Watson, Collision Theory (Wiley, New York, NY, 1964)

    MATH  Google Scholar 

  29. T.W. Gorczyca, O. Zatsarinny, H.-L. Zhou, S.T. Manson, Z. Felfli, A.Z. Msezane, Phys. Rev. A 68, 050703(R) (2003)

    Article  ADS  Google Scholar 

  30. F.E. Harris, H.H. Michels, J. Chem. Phys. 43, 5165 (1965)

    MathSciNet  Google Scholar 

  31. W.C. Henneberger, Phys. Rev. Lett. 21, 838 (1968)

    Article  ADS  Google Scholar 

  32. T.-S. Ho, S.-I. Chu, Chem. Phys. Lett. 141, 315 (1987)

    Article  ADS  Google Scholar 

  33. C.J. Joachain, M. Dörr, N.J. Kylstra, Adv. At. Mol. Opt. Phys. 42, 225 (2000)

    Article  Google Scholar 

  34. P.L. Knight, Comm. At. Mol. Phys. 15, 193 (1984)

    MathSciNet  Google Scholar 

  35. P.L. Knight, M.A. Lauder, B.J. Dalton, Phys. Rep. 190, 1 (1990)

    Article  ADS  Google Scholar 

  36. H.A. Kramers, Collected Scientific Papers (North Holland, Amsterdam, 1956), p. 272

    Google Scholar 

  37. J.L. Krause, K.J. Schafer, K.C. Kulander, Phys. Rev. Lett. 68, 3535 (1992)

    Article  ADS  Google Scholar 

  38. J.L. Krause, K.J. Schafer, K.C. Kulander, Phys. Rev. A 45, 4998 (1992)

    Article  ADS  Google Scholar 

  39. N.M. Kroll, K.M. Watson, Phys. Rev. A 8, 804 (1973)

    Article  ADS  Google Scholar 

  40. K.C. Kulander, B.W. Shore, Phys. Rev. Lett. 62, 524 (1989)

    Article  ADS  Google Scholar 

  41. K.C. Kulander, K.J. Schafer, J.L. Krause, in Adv. At. Mol. Opt. Phys. Suppl. 1, Atoms in Intense Laser Fields, ed. by M. Gavrila (Academic Press, New York, 1992), p. 247

    Google Scholar 

  42. K.C. Kulander, K.J. Shafer, J.L. Krause, in Super-Intense Laser–Atom Physics, ed. by B. Piraux, A. L’Huillier, K. Rzazewski (Plenum Press, New York, NY, 1993), p. 95

    Google Scholar 

  43. N.J. Kylstra, C.J. Joachain, Phys. Rev. A 57, 412 (1998)

    Article  ADS  Google Scholar 

  44. O. Latinne, N.J. Kylstra, M. Dörr, J. Purvis, M. Terao-Dunseath, C.J. Joachain, P.G. Burke, Phys. Rev. Lett. 74, 46 (1995)

    Article  ADS  Google Scholar 

  45. M. Lewenstein, P. Balcou, M.Yu. Ivanov, A. L’Huillier, P.B. Corkum, Phys. Rev. A 49, 2117 (1994)

    Article  ADS  Google Scholar 

  46. A. L’Huillier, P. Balcou, Phys. Rev. Lett. 70, 774 (1993)

    Article  ADS  Google Scholar 

  47. A. L’Huillier, K.J. Schafer, K.C. Kulander, J. Phys. B At. Mol. Opt. Phys. 24, 3315 (1991)

    Article  ADS  Google Scholar 

  48. A. L’Huillier, L.-A. Lombré, G. Mainfray, C. Manus, in Adv. At. Mol. Opt. Phys. Suppl. 1, Atoms in Intense Laser Fields, ed. by M. Gavrila (Academic Press, New York, NY, 1992), p. 139

    Google Scholar 

  49. C. McKenna, H.W. van der Hart, J. Phys. B At. Mol. Opt. Phys. 36, 1627 (2003)

    Article  ADS  Google Scholar 

  50. C. McKenna, H.W. van der Hart, J. Phys. B At. Mol. Opt. Phys. 37, 457 (2004)

    Article  ADS  Google Scholar 

  51. J.J. Macklin, J.D. Kmetec, C.L. Gordon, Phys. Rev. Lett. 70, 766 (1993)

    Article  ADS  Google Scholar 

  52. A. McPherson, G. Gibson, H. Jara, U. Johann, T.S. Luk, I.A. McIntyre, K. Boyer, C.K. Rhodes, J. Opt. Soc. Am. B 4, 595 (1987)

    Article  ADS  Google Scholar 

  53. A. Maquet, S.-I. Chu, W.P. Reinhardt, Phys. Rev. A 27, 2946 (1983)

    Article  ADS  Google Scholar 

  54. N.J. Mason, Rep. Prog. Phys. 56, 1275 (1993)

    Article  ADS  Google Scholar 

  55. N.J. Mason, W.R. Newell, J. Phys. B At. Mol. Phys. 20, L323 (1987)

    Article  ADS  Google Scholar 

  56. N.J. Mason, W.R. Newell, J. Phys. B At. Mol. Phys. 22, 777 (1987)

    ADS  Google Scholar 

  57. G.G. Newton, Scattering Theory of Waves and Particles (McGraw-Hill Inc., New York, NY, 1966)

    Google Scholar 

  58. J. Parker, K.T. Taylor, C.W. Clark, S. Blodgett-Ford, J. Phys. B At. Mol. Opt. Phys. 29, L33 (1996)

    Article  ADS  Google Scholar 

  59. A.M. Perelomov, V.S. Popov, M.V. Terent’ev, Sov. Phys. JETP, 23, 924 (1966)

    ADS  Google Scholar 

  60. B. Piraux, R. Shakeshaft, Phys. Rev. A 49, 3903 (1994)

    Article  ADS  Google Scholar 

  61. M. Plummer, J.F. McCann, J. Phys. B At. Mol. Opt. Phys. 29, 4625 (1996)

    Article  ADS  Google Scholar 

  62. M. Plummer, C.J. Noble, J. Phys. B At. Mol. Opt. Phys. 33, L807 (2000)

    Article  ADS  Google Scholar 

  63. M. Plummer, C.J. Noble, J. Phys. B At. Mol. Opt. Phys. 35, L51 (2002)

    Article  ADS  Google Scholar 

  64. M. Plummer, C.J. Noble, J. Phys. B At. Mol. Opt. Phys. 36, L219 (2003)

    Article  ADS  Google Scholar 

  65. J.H. Posthumus, Molecules and Clusters in Intense Laser Fields (Cambridge University Press, Cambridge, UK, 2001)

    Book  Google Scholar 

  66. R.M. Potvliege, R. Shakeshaft, Phys. Rev. A 38, 4597 (1988)

    Article  ADS  Google Scholar 

  67. R.M. Potvliege, R. Shakeshaft, Phys. Rev. A 40, 3061 (1989)

    Article  ADS  Google Scholar 

  68. S.G. Preston, A. Sanpera, M. Zepf, W.J. Blyth, C.G. Smith, J.S. Wark, M.H. Key, K. Burnett, N. Nakai, D. Neely, A.A. Offenberger, Phys. Rev. A 53, R31 (1996)

    Article  ADS  Google Scholar 

  69. M. Protopapas, C.H. Keitel, P.L. Knight, Rep. Prog. Phys. 60, 389 (1997)

    Article  ADS  Google Scholar 

  70. G.J. Schulz, Phys. Rev. Lett. 10, 104 (1963)

    Article  ADS  Google Scholar 

  71. J.H. Shirley, Phys. Rev. B 138, 979 (1965)

    Article  ADS  Google Scholar 

  72. A.J.F. Siegert, Phys. Rev. 56, 750 (1939)

    Article  ADS  Google Scholar 

  73. D. Strickland, G. Mourou, Opt. Commun. 56, 219 (1985)

    Article  ADS  Google Scholar 

  74. E.C.G. Stückelberg, Helv. Phys. Acta. 5, 369 (1932)

    MATH  Google Scholar 

  75. M. Terao-Dunseath, K.M. Dunseath, J. Phys. B At. Mol. Opt. Phys. 35, 125 (2002)

    Article  ADS  Google Scholar 

  76. M. Terao-Dunseath, K.M. Dunseath, D. Charlo, A. Hibbert, R.J. Allan, J. Phys. B At. Mol. Opt. Phys. 34, L263 (2001)

    Article  ADS  Google Scholar 

  77. H.W. van der Hart, Phys. Rev. Lett. 95, 153001 (2005)

    Article  ADS  Google Scholar 

  78. H.W. van der Hart, Phys. Rev. A 73, 023417 (2006)

    Article  ADS  Google Scholar 

  79. H.W. van der Hart, B.J.S. Doherty, J.S. Parker, K.T. Taylor, J. Phys. B At. Mol. Opt. Phys. 38, L207 (2005)

    Article  Google Scholar 

  80. B. Wallbank, J.K. Holmes, Phys. Rev. A 48, R2515 (1993)

    Article  ADS  Google Scholar 

  81. B. Wallbank, J.K. Holmes, J. Phys. B At. Mol. Opt. Phys. 27, 5405 (1994)

    Article  ADS  Google Scholar 

  82. B. Wallbank, J.K. Holmes, A. Weingartshofer, J. Phys. B At. Mol. Opt. Phys. 23, 2997 (1990)

    Article  ADS  Google Scholar 

  83. B. Wallbank, J.K. Holmes, L. LeBranc, A. Weingartshofer, Zeits. Phys. D 10, 467 (1998)

    Article  ADS  Google Scholar 

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    Professor Philip G. Burke

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Burke, P.G. (2011). Multiphoton Processes: Floquet Theory. In: R-Matrix Theory of Atomic Collisions. Springer Series on Atomic, Optical, and Plasma Physics, vol 61. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15931-2_9

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