Abstract

The half Kapitza-Dirac effect of H2+ molecule in an intense standing-wave laser field is studied with a focus on the influence of the molecular orbital symmetry and the molecular alignment on the photo-electron angular distributions (PADs). In standing-wave laser fields, the PADs split along the scattering angle due to the momentum change of electron with photons when it escapes from the laser fields. The structures and the symmetry of PADs are severely affected by the molecular orbital symmetry and the molecular alignment. For H2+ molecule in ground state (σg), the PADs are severely changed by the molecular alignment only when the photoelectron kinetic energy is sufficiently high. For H2+ molecule in the first excited state (σμ), the molecular alignment distinctively changes the PADs, irrelevant to the kinetic energy of photoelectrons. When the molecules are aligned either parallel with or perpendicular to the laser polarization, the PADs are symmetric about an axis. In other cases, the PADs do not show any symmetry. These results indicate that the molecular alignment can be used to control the splitting in the half Kapitza-Dirac effect.

© 2011 OSA

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  1. P. H. Bucksbaum, D. W. Schumacher, and M. Bashkansky, “High-Intensity Kapitza-Dirac Effect,” Phys. Rev. Lett. 61, 1182–1185 (1988).
    [CrossRef] [PubMed]
  2. P. L. Kapitza and P. A. M. Dirac, “The reflection of electrons from standing light waves,” Proc. Cambridge, Philos. Soc. 29, 297–300 (1933).
    [CrossRef]
  3. D.-S. Guo and G. W. F. Drake, “Multiphoton ionization in circularly polarized standing waves,” Phys. Rev. A 45, 6622–6635 (1992).
    [CrossRef] [PubMed]
  4. D. L. Freimund, K. Aflatoon, and H. Batelaan, “Observation of the Kapitza-Dirac effect,” Nature (London) 413, 142–143 (2002).
    [CrossRef]
  5. H. Batelaan, “The Kapitza-Dirac effect,” Comtemp. Phys. 41, 369–381 (2000).
    [CrossRef]
  6. P. J. Martin, P. L. Gould, B. G. Oldaker, A. H. Mikllich, and D. E. Pritchard, “Diffraction of atoms moving through a standing light wave,” Phys. Rev. A 36, 2495–2498 (1987).
    [CrossRef] [PubMed]
  7. P. L. Gould, G. A. Ruff, and D. E. Pritchard, “Diffraction of atoms by light: The near-resonant Kapitza-Dirac effect,” Phys. Rev. Lett. 56, 827–830 (1986).
    [CrossRef] [PubMed]
  8. O. Smirnova, D. L. Freimund, H. Batelaan, and M. Ivanov, “Kapitza-Dirac Diffraction without Standing Waves: Diffraction without a Grating?,” Phys. Rev. Lett. 92, 223601 (2004).
    [CrossRef] [PubMed]
  9. O. Nairz, B. Brezger, M. Arndt, and A. Zeilinger, “Diffraction of Complex Molecules by Structures Made of Light,” Phys. Rev. Lett. 87, 160401 (2001).
    [CrossRef] [PubMed]
  10. C. Guo, “Multielectron Effects on Single-Electron Strong Field Ionization,” Phys. Rev. Lett. 85, 2276–2279 (2000).
    [CrossRef] [PubMed]
  11. J. Muth-Bőhm, A. Becker, and F. H. M. Faisal, “Suppressed Molecular Ionization for a Class of Diatomics in Intense Femtosecond Laser Fields,” Phys. Rev. Lett. 85, 2280–2283 (2000).
    [CrossRef]
  12. X. Ren, J. Zhang, P. Liu, Y. Wang, and Z. Xu, “Ionization suppression of diatomic molecules in strong laser fields,” Phys. Rev. A 78, 043411 (2008).
    [CrossRef]
  13. M. Foster, J. Colgan, O. Al-Hagan, J. L. Peacher, D. H. Madison, and M. S. Pindzola, “Angular distributions from photoionization of H2+,” Phys. Rev. A 75, 062707 (2007).
    [CrossRef]
  14. V. I. Usachenko, “Reply to Comment on Strong-field ionization of laser-irradiated light homonuclear diatomic molecules: A generalized strong-field approximation-linear combination of atomic orbitals model,” Phys. Rev. A 73, 047402 (2006).
    [CrossRef]
  15. A. Jaroń-Becker, A. Becker, and F. H. M. Faisal, “Ionization of N2, O2, and linear carbon clusters in a strong laser pulse,” Phys. Rev. A 69, 023410 (2004).
    [CrossRef]
  16. X. Ren, J. Zhang, Y. Wang, Z. Xu, and D.-S. Guo, “Effects of the internuclear vector on the photoelectron angular distributions of H2+,” Eur. J. Phys. D. 51, 401–407 (2009).
    [CrossRef]
  17. H. Stapelfeldt and T. Seideman, “Colloquium: Aligning molecules with strong laser pulses,” Rev. Mod. Phys. 75, 543–557 (2003).
    [CrossRef]
  18. D. Pavičić, K. F. Lee, D. M. Rayner, P. B. Corkum, and D. M. Villeneuve, “Direct Measurement of the Angular Dependence of Ionization for N2, O2, and CO2 in Intense Laser Fields,” Phys. Rev. Lett. 98, 243001 (2007).
    [CrossRef]
  19. S. Zhang, C. Lu, T. Jia, Z. Wang, and Z. Sun, “Controlling field-free molecular orientation with combined single- and dual-color laser pulses,” Phys. Rev. A 83, 043410 (2011).
    [CrossRef]
  20. D.-S. Guo, T. Åberg, and B. Crasemann, “Scattering theory of multiphoton ionization in strong fields,” Phys. Rev. A 40, 4997–5005 (1989).
    [CrossRef] [PubMed]
  21. D.-S. Guo, “Theory of the Kapitza-Dirac effect in strong radiation fields,” Phys. Rev. A 53, 4311–4319 (1996).
    [CrossRef] [PubMed]
  22. J. Gao, D.-S. Guo, and Y.-S. Wu, “Resonant above-threshold ionization at quantized laser intensities,” Phys. Rev. A 61, 043406 (2000).
    [CrossRef]
  23. X. Li, J. Zhang, Z. Xu, P. Fu, D.-S. Guo, and R. R. Freeman, “Theory of the Kapitza-Dirac Diffraction Effect,” Phys. Rev. Lett. 92, 233603 (2004).
    [CrossRef] [PubMed]
  24. H. D. Cohen and U. Fano, “Interference in the Photo-Ionization of Molecules,” Phys. Rev. 150, 30–33 (1966).
    [CrossRef]
  25. J. Zhang, W. Zhang, Z. Xu, X. Li, P. Fu, D.-S. Guo, and R. R. Freeman, “The calculation of photoelectron angular distributions with jet-like structure from scattering theory,” J. Phys. B 35, 4809–4818 (2002).
    [CrossRef]
  26. T. K. Kjeldsen, C. Z. Bisgaard, L. B. Madsen, and H. Stapelfeldt, “Role of symmetry in strong-field ionization of molecules,” Phys. Rev. A 68, 063407 (2003).
    [CrossRef]
  27. T. J. Houser, P. G. Lykos, and E. L. Mehler, “One-Center Wavefunction for the Hydrogen Molecule Ion,” J. Chem. Phys. 38, 583–585 (1963).
    [CrossRef]
  28. M. Mathholm and N. E. Henriksen, “Field-Free Orientation of Molecules,” Phys. Rev. Lett. 87, 193001 (2001).
    [CrossRef]
  29. X. H. Ren, J. T. Zhang, Z. Z. Xu, and D.-S. Guo, “Angular splitting in half Kapitza-Dirac effect of H2+ molecules,” J. Opt. Soc. Am. B 27, 714–718 (2010).
    [CrossRef]

2011 (1)

S. Zhang, C. Lu, T. Jia, Z. Wang, and Z. Sun, “Controlling field-free molecular orientation with combined single- and dual-color laser pulses,” Phys. Rev. A 83, 043410 (2011).
[CrossRef]

2010 (1)

2009 (1)

X. Ren, J. Zhang, Y. Wang, Z. Xu, and D.-S. Guo, “Effects of the internuclear vector on the photoelectron angular distributions of H2+,” Eur. J. Phys. D. 51, 401–407 (2009).
[CrossRef]

2008 (1)

X. Ren, J. Zhang, P. Liu, Y. Wang, and Z. Xu, “Ionization suppression of diatomic molecules in strong laser fields,” Phys. Rev. A 78, 043411 (2008).
[CrossRef]

2007 (2)

M. Foster, J. Colgan, O. Al-Hagan, J. L. Peacher, D. H. Madison, and M. S. Pindzola, “Angular distributions from photoionization of H2+,” Phys. Rev. A 75, 062707 (2007).
[CrossRef]

D. Pavičić, K. F. Lee, D. M. Rayner, P. B. Corkum, and D. M. Villeneuve, “Direct Measurement of the Angular Dependence of Ionization for N2, O2, and CO2 in Intense Laser Fields,” Phys. Rev. Lett. 98, 243001 (2007).
[CrossRef]

2006 (1)

V. I. Usachenko, “Reply to Comment on Strong-field ionization of laser-irradiated light homonuclear diatomic molecules: A generalized strong-field approximation-linear combination of atomic orbitals model,” Phys. Rev. A 73, 047402 (2006).
[CrossRef]

2004 (3)

A. Jaroń-Becker, A. Becker, and F. H. M. Faisal, “Ionization of N2, O2, and linear carbon clusters in a strong laser pulse,” Phys. Rev. A 69, 023410 (2004).
[CrossRef]

O. Smirnova, D. L. Freimund, H. Batelaan, and M. Ivanov, “Kapitza-Dirac Diffraction without Standing Waves: Diffraction without a Grating?,” Phys. Rev. Lett. 92, 223601 (2004).
[CrossRef] [PubMed]

X. Li, J. Zhang, Z. Xu, P. Fu, D.-S. Guo, and R. R. Freeman, “Theory of the Kapitza-Dirac Diffraction Effect,” Phys. Rev. Lett. 92, 233603 (2004).
[CrossRef] [PubMed]

2003 (2)

T. K. Kjeldsen, C. Z. Bisgaard, L. B. Madsen, and H. Stapelfeldt, “Role of symmetry in strong-field ionization of molecules,” Phys. Rev. A 68, 063407 (2003).
[CrossRef]

H. Stapelfeldt and T. Seideman, “Colloquium: Aligning molecules with strong laser pulses,” Rev. Mod. Phys. 75, 543–557 (2003).
[CrossRef]

2002 (2)

D. L. Freimund, K. Aflatoon, and H. Batelaan, “Observation of the Kapitza-Dirac effect,” Nature (London) 413, 142–143 (2002).
[CrossRef]

J. Zhang, W. Zhang, Z. Xu, X. Li, P. Fu, D.-S. Guo, and R. R. Freeman, “The calculation of photoelectron angular distributions with jet-like structure from scattering theory,” J. Phys. B 35, 4809–4818 (2002).
[CrossRef]

2001 (2)

M. Mathholm and N. E. Henriksen, “Field-Free Orientation of Molecules,” Phys. Rev. Lett. 87, 193001 (2001).
[CrossRef]

O. Nairz, B. Brezger, M. Arndt, and A. Zeilinger, “Diffraction of Complex Molecules by Structures Made of Light,” Phys. Rev. Lett. 87, 160401 (2001).
[CrossRef] [PubMed]

2000 (4)

C. Guo, “Multielectron Effects on Single-Electron Strong Field Ionization,” Phys. Rev. Lett. 85, 2276–2279 (2000).
[CrossRef] [PubMed]

J. Muth-Bőhm, A. Becker, and F. H. M. Faisal, “Suppressed Molecular Ionization for a Class of Diatomics in Intense Femtosecond Laser Fields,” Phys. Rev. Lett. 85, 2280–2283 (2000).
[CrossRef]

H. Batelaan, “The Kapitza-Dirac effect,” Comtemp. Phys. 41, 369–381 (2000).
[CrossRef]

J. Gao, D.-S. Guo, and Y.-S. Wu, “Resonant above-threshold ionization at quantized laser intensities,” Phys. Rev. A 61, 043406 (2000).
[CrossRef]

1996 (1)

D.-S. Guo, “Theory of the Kapitza-Dirac effect in strong radiation fields,” Phys. Rev. A 53, 4311–4319 (1996).
[CrossRef] [PubMed]

1992 (1)

D.-S. Guo and G. W. F. Drake, “Multiphoton ionization in circularly polarized standing waves,” Phys. Rev. A 45, 6622–6635 (1992).
[CrossRef] [PubMed]

1989 (1)

D.-S. Guo, T. Åberg, and B. Crasemann, “Scattering theory of multiphoton ionization in strong fields,” Phys. Rev. A 40, 4997–5005 (1989).
[CrossRef] [PubMed]

1988 (1)

P. H. Bucksbaum, D. W. Schumacher, and M. Bashkansky, “High-Intensity Kapitza-Dirac Effect,” Phys. Rev. Lett. 61, 1182–1185 (1988).
[CrossRef] [PubMed]

1987 (1)

P. J. Martin, P. L. Gould, B. G. Oldaker, A. H. Mikllich, and D. E. Pritchard, “Diffraction of atoms moving through a standing light wave,” Phys. Rev. A 36, 2495–2498 (1987).
[CrossRef] [PubMed]

1986 (1)

P. L. Gould, G. A. Ruff, and D. E. Pritchard, “Diffraction of atoms by light: The near-resonant Kapitza-Dirac effect,” Phys. Rev. Lett. 56, 827–830 (1986).
[CrossRef] [PubMed]

1966 (1)

H. D. Cohen and U. Fano, “Interference in the Photo-Ionization of Molecules,” Phys. Rev. 150, 30–33 (1966).
[CrossRef]

1963 (1)

T. J. Houser, P. G. Lykos, and E. L. Mehler, “One-Center Wavefunction for the Hydrogen Molecule Ion,” J. Chem. Phys. 38, 583–585 (1963).
[CrossRef]

1933 (1)

P. L. Kapitza and P. A. M. Dirac, “The reflection of electrons from standing light waves,” Proc. Cambridge, Philos. Soc. 29, 297–300 (1933).
[CrossRef]

Åberg, T.

D.-S. Guo, T. Åberg, and B. Crasemann, “Scattering theory of multiphoton ionization in strong fields,” Phys. Rev. A 40, 4997–5005 (1989).
[CrossRef] [PubMed]

Aflatoon, K.

D. L. Freimund, K. Aflatoon, and H. Batelaan, “Observation of the Kapitza-Dirac effect,” Nature (London) 413, 142–143 (2002).
[CrossRef]

Al-Hagan, O.

M. Foster, J. Colgan, O. Al-Hagan, J. L. Peacher, D. H. Madison, and M. S. Pindzola, “Angular distributions from photoionization of H2+,” Phys. Rev. A 75, 062707 (2007).
[CrossRef]

Arndt, M.

O. Nairz, B. Brezger, M. Arndt, and A. Zeilinger, “Diffraction of Complex Molecules by Structures Made of Light,” Phys. Rev. Lett. 87, 160401 (2001).
[CrossRef] [PubMed]

Bashkansky, M.

P. H. Bucksbaum, D. W. Schumacher, and M. Bashkansky, “High-Intensity Kapitza-Dirac Effect,” Phys. Rev. Lett. 61, 1182–1185 (1988).
[CrossRef] [PubMed]

Batelaan, H.

O. Smirnova, D. L. Freimund, H. Batelaan, and M. Ivanov, “Kapitza-Dirac Diffraction without Standing Waves: Diffraction without a Grating?,” Phys. Rev. Lett. 92, 223601 (2004).
[CrossRef] [PubMed]

D. L. Freimund, K. Aflatoon, and H. Batelaan, “Observation of the Kapitza-Dirac effect,” Nature (London) 413, 142–143 (2002).
[CrossRef]

H. Batelaan, “The Kapitza-Dirac effect,” Comtemp. Phys. 41, 369–381 (2000).
[CrossRef]

Becker, A.

A. Jaroń-Becker, A. Becker, and F. H. M. Faisal, “Ionization of N2, O2, and linear carbon clusters in a strong laser pulse,” Phys. Rev. A 69, 023410 (2004).
[CrossRef]

J. Muth-Bőhm, A. Becker, and F. H. M. Faisal, “Suppressed Molecular Ionization for a Class of Diatomics in Intense Femtosecond Laser Fields,” Phys. Rev. Lett. 85, 2280–2283 (2000).
[CrossRef]

Bisgaard, C. Z.

T. K. Kjeldsen, C. Z. Bisgaard, L. B. Madsen, and H. Stapelfeldt, “Role of symmetry in strong-field ionization of molecules,” Phys. Rev. A 68, 063407 (2003).
[CrossRef]

Brezger, B.

O. Nairz, B. Brezger, M. Arndt, and A. Zeilinger, “Diffraction of Complex Molecules by Structures Made of Light,” Phys. Rev. Lett. 87, 160401 (2001).
[CrossRef] [PubMed]

Bucksbaum, P. H.

P. H. Bucksbaum, D. W. Schumacher, and M. Bashkansky, “High-Intensity Kapitza-Dirac Effect,” Phys. Rev. Lett. 61, 1182–1185 (1988).
[CrossRef] [PubMed]

Cohen, H. D.

H. D. Cohen and U. Fano, “Interference in the Photo-Ionization of Molecules,” Phys. Rev. 150, 30–33 (1966).
[CrossRef]

Colgan, J.

M. Foster, J. Colgan, O. Al-Hagan, J. L. Peacher, D. H. Madison, and M. S. Pindzola, “Angular distributions from photoionization of H2+,” Phys. Rev. A 75, 062707 (2007).
[CrossRef]

Corkum, P. B.

D. Pavičić, K. F. Lee, D. M. Rayner, P. B. Corkum, and D. M. Villeneuve, “Direct Measurement of the Angular Dependence of Ionization for N2, O2, and CO2 in Intense Laser Fields,” Phys. Rev. Lett. 98, 243001 (2007).
[CrossRef]

Crasemann, B.

D.-S. Guo, T. Åberg, and B. Crasemann, “Scattering theory of multiphoton ionization in strong fields,” Phys. Rev. A 40, 4997–5005 (1989).
[CrossRef] [PubMed]

Dirac, P. A. M.

P. L. Kapitza and P. A. M. Dirac, “The reflection of electrons from standing light waves,” Proc. Cambridge, Philos. Soc. 29, 297–300 (1933).
[CrossRef]

Drake, G. W. F.

D.-S. Guo and G. W. F. Drake, “Multiphoton ionization in circularly polarized standing waves,” Phys. Rev. A 45, 6622–6635 (1992).
[CrossRef] [PubMed]

Faisal, F. H. M.

A. Jaroń-Becker, A. Becker, and F. H. M. Faisal, “Ionization of N2, O2, and linear carbon clusters in a strong laser pulse,” Phys. Rev. A 69, 023410 (2004).
[CrossRef]

J. Muth-Bőhm, A. Becker, and F. H. M. Faisal, “Suppressed Molecular Ionization for a Class of Diatomics in Intense Femtosecond Laser Fields,” Phys. Rev. Lett. 85, 2280–2283 (2000).
[CrossRef]

Fano, U.

H. D. Cohen and U. Fano, “Interference in the Photo-Ionization of Molecules,” Phys. Rev. 150, 30–33 (1966).
[CrossRef]

Foster, M.

M. Foster, J. Colgan, O. Al-Hagan, J. L. Peacher, D. H. Madison, and M. S. Pindzola, “Angular distributions from photoionization of H2+,” Phys. Rev. A 75, 062707 (2007).
[CrossRef]

Freeman, R. R.

X. Li, J. Zhang, Z. Xu, P. Fu, D.-S. Guo, and R. R. Freeman, “Theory of the Kapitza-Dirac Diffraction Effect,” Phys. Rev. Lett. 92, 233603 (2004).
[CrossRef] [PubMed]

J. Zhang, W. Zhang, Z. Xu, X. Li, P. Fu, D.-S. Guo, and R. R. Freeman, “The calculation of photoelectron angular distributions with jet-like structure from scattering theory,” J. Phys. B 35, 4809–4818 (2002).
[CrossRef]

Freimund, D. L.

O. Smirnova, D. L. Freimund, H. Batelaan, and M. Ivanov, “Kapitza-Dirac Diffraction without Standing Waves: Diffraction without a Grating?,” Phys. Rev. Lett. 92, 223601 (2004).
[CrossRef] [PubMed]

D. L. Freimund, K. Aflatoon, and H. Batelaan, “Observation of the Kapitza-Dirac effect,” Nature (London) 413, 142–143 (2002).
[CrossRef]

Fu, P.

X. Li, J. Zhang, Z. Xu, P. Fu, D.-S. Guo, and R. R. Freeman, “Theory of the Kapitza-Dirac Diffraction Effect,” Phys. Rev. Lett. 92, 233603 (2004).
[CrossRef] [PubMed]

J. Zhang, W. Zhang, Z. Xu, X. Li, P. Fu, D.-S. Guo, and R. R. Freeman, “The calculation of photoelectron angular distributions with jet-like structure from scattering theory,” J. Phys. B 35, 4809–4818 (2002).
[CrossRef]

Gao, J.

J. Gao, D.-S. Guo, and Y.-S. Wu, “Resonant above-threshold ionization at quantized laser intensities,” Phys. Rev. A 61, 043406 (2000).
[CrossRef]

Gould, P. L.

P. J. Martin, P. L. Gould, B. G. Oldaker, A. H. Mikllich, and D. E. Pritchard, “Diffraction of atoms moving through a standing light wave,” Phys. Rev. A 36, 2495–2498 (1987).
[CrossRef] [PubMed]

P. L. Gould, G. A. Ruff, and D. E. Pritchard, “Diffraction of atoms by light: The near-resonant Kapitza-Dirac effect,” Phys. Rev. Lett. 56, 827–830 (1986).
[CrossRef] [PubMed]

Guo, C.

C. Guo, “Multielectron Effects on Single-Electron Strong Field Ionization,” Phys. Rev. Lett. 85, 2276–2279 (2000).
[CrossRef] [PubMed]

Guo, D.-S.

X. H. Ren, J. T. Zhang, Z. Z. Xu, and D.-S. Guo, “Angular splitting in half Kapitza-Dirac effect of H2+ molecules,” J. Opt. Soc. Am. B 27, 714–718 (2010).
[CrossRef]

X. Ren, J. Zhang, Y. Wang, Z. Xu, and D.-S. Guo, “Effects of the internuclear vector on the photoelectron angular distributions of H2+,” Eur. J. Phys. D. 51, 401–407 (2009).
[CrossRef]

X. Li, J. Zhang, Z. Xu, P. Fu, D.-S. Guo, and R. R. Freeman, “Theory of the Kapitza-Dirac Diffraction Effect,” Phys. Rev. Lett. 92, 233603 (2004).
[CrossRef] [PubMed]

J. Zhang, W. Zhang, Z. Xu, X. Li, P. Fu, D.-S. Guo, and R. R. Freeman, “The calculation of photoelectron angular distributions with jet-like structure from scattering theory,” J. Phys. B 35, 4809–4818 (2002).
[CrossRef]

J. Gao, D.-S. Guo, and Y.-S. Wu, “Resonant above-threshold ionization at quantized laser intensities,” Phys. Rev. A 61, 043406 (2000).
[CrossRef]

D.-S. Guo, “Theory of the Kapitza-Dirac effect in strong radiation fields,” Phys. Rev. A 53, 4311–4319 (1996).
[CrossRef] [PubMed]

D.-S. Guo and G. W. F. Drake, “Multiphoton ionization in circularly polarized standing waves,” Phys. Rev. A 45, 6622–6635 (1992).
[CrossRef] [PubMed]

D.-S. Guo, T. Åberg, and B. Crasemann, “Scattering theory of multiphoton ionization in strong fields,” Phys. Rev. A 40, 4997–5005 (1989).
[CrossRef] [PubMed]

Henriksen, N. E.

M. Mathholm and N. E. Henriksen, “Field-Free Orientation of Molecules,” Phys. Rev. Lett. 87, 193001 (2001).
[CrossRef]

Houser, T. J.

T. J. Houser, P. G. Lykos, and E. L. Mehler, “One-Center Wavefunction for the Hydrogen Molecule Ion,” J. Chem. Phys. 38, 583–585 (1963).
[CrossRef]

Ivanov, M.

O. Smirnova, D. L. Freimund, H. Batelaan, and M. Ivanov, “Kapitza-Dirac Diffraction without Standing Waves: Diffraction without a Grating?,” Phys. Rev. Lett. 92, 223601 (2004).
[CrossRef] [PubMed]

Jaron-Becker, A.

A. Jaroń-Becker, A. Becker, and F. H. M. Faisal, “Ionization of N2, O2, and linear carbon clusters in a strong laser pulse,” Phys. Rev. A 69, 023410 (2004).
[CrossRef]

Jia, T.

S. Zhang, C. Lu, T. Jia, Z. Wang, and Z. Sun, “Controlling field-free molecular orientation with combined single- and dual-color laser pulses,” Phys. Rev. A 83, 043410 (2011).
[CrossRef]

Kapitza, P. L.

P. L. Kapitza and P. A. M. Dirac, “The reflection of electrons from standing light waves,” Proc. Cambridge, Philos. Soc. 29, 297–300 (1933).
[CrossRef]

Kjeldsen, T. K.

T. K. Kjeldsen, C. Z. Bisgaard, L. B. Madsen, and H. Stapelfeldt, “Role of symmetry in strong-field ionization of molecules,” Phys. Rev. A 68, 063407 (2003).
[CrossRef]

Lee, K. F.

D. Pavičić, K. F. Lee, D. M. Rayner, P. B. Corkum, and D. M. Villeneuve, “Direct Measurement of the Angular Dependence of Ionization for N2, O2, and CO2 in Intense Laser Fields,” Phys. Rev. Lett. 98, 243001 (2007).
[CrossRef]

Li, X.

X. Li, J. Zhang, Z. Xu, P. Fu, D.-S. Guo, and R. R. Freeman, “Theory of the Kapitza-Dirac Diffraction Effect,” Phys. Rev. Lett. 92, 233603 (2004).
[CrossRef] [PubMed]

J. Zhang, W. Zhang, Z. Xu, X. Li, P. Fu, D.-S. Guo, and R. R. Freeman, “The calculation of photoelectron angular distributions with jet-like structure from scattering theory,” J. Phys. B 35, 4809–4818 (2002).
[CrossRef]

Liu, P.

X. Ren, J. Zhang, P. Liu, Y. Wang, and Z. Xu, “Ionization suppression of diatomic molecules in strong laser fields,” Phys. Rev. A 78, 043411 (2008).
[CrossRef]

Lu, C.

S. Zhang, C. Lu, T. Jia, Z. Wang, and Z. Sun, “Controlling field-free molecular orientation with combined single- and dual-color laser pulses,” Phys. Rev. A 83, 043410 (2011).
[CrossRef]

Lykos, P. G.

T. J. Houser, P. G. Lykos, and E. L. Mehler, “One-Center Wavefunction for the Hydrogen Molecule Ion,” J. Chem. Phys. 38, 583–585 (1963).
[CrossRef]

Madison, D. H.

M. Foster, J. Colgan, O. Al-Hagan, J. L. Peacher, D. H. Madison, and M. S. Pindzola, “Angular distributions from photoionization of H2+,” Phys. Rev. A 75, 062707 (2007).
[CrossRef]

Madsen, L. B.

T. K. Kjeldsen, C. Z. Bisgaard, L. B. Madsen, and H. Stapelfeldt, “Role of symmetry in strong-field ionization of molecules,” Phys. Rev. A 68, 063407 (2003).
[CrossRef]

Martin, P. J.

P. J. Martin, P. L. Gould, B. G. Oldaker, A. H. Mikllich, and D. E. Pritchard, “Diffraction of atoms moving through a standing light wave,” Phys. Rev. A 36, 2495–2498 (1987).
[CrossRef] [PubMed]

Mathholm, M.

M. Mathholm and N. E. Henriksen, “Field-Free Orientation of Molecules,” Phys. Rev. Lett. 87, 193001 (2001).
[CrossRef]

Mehler, E. L.

T. J. Houser, P. G. Lykos, and E. L. Mehler, “One-Center Wavefunction for the Hydrogen Molecule Ion,” J. Chem. Phys. 38, 583–585 (1963).
[CrossRef]

Mikllich, A. H.

P. J. Martin, P. L. Gould, B. G. Oldaker, A. H. Mikllich, and D. E. Pritchard, “Diffraction of atoms moving through a standing light wave,” Phys. Rev. A 36, 2495–2498 (1987).
[CrossRef] [PubMed]

Muth-Bohm, J.

J. Muth-Bőhm, A. Becker, and F. H. M. Faisal, “Suppressed Molecular Ionization for a Class of Diatomics in Intense Femtosecond Laser Fields,” Phys. Rev. Lett. 85, 2280–2283 (2000).
[CrossRef]

Nairz, O.

O. Nairz, B. Brezger, M. Arndt, and A. Zeilinger, “Diffraction of Complex Molecules by Structures Made of Light,” Phys. Rev. Lett. 87, 160401 (2001).
[CrossRef] [PubMed]

Oldaker, B. G.

P. J. Martin, P. L. Gould, B. G. Oldaker, A. H. Mikllich, and D. E. Pritchard, “Diffraction of atoms moving through a standing light wave,” Phys. Rev. A 36, 2495–2498 (1987).
[CrossRef] [PubMed]

Pavicic, D.

D. Pavičić, K. F. Lee, D. M. Rayner, P. B. Corkum, and D. M. Villeneuve, “Direct Measurement of the Angular Dependence of Ionization for N2, O2, and CO2 in Intense Laser Fields,” Phys. Rev. Lett. 98, 243001 (2007).
[CrossRef]

Peacher, J. L.

M. Foster, J. Colgan, O. Al-Hagan, J. L. Peacher, D. H. Madison, and M. S. Pindzola, “Angular distributions from photoionization of H2+,” Phys. Rev. A 75, 062707 (2007).
[CrossRef]

Pindzola, M. S.

M. Foster, J. Colgan, O. Al-Hagan, J. L. Peacher, D. H. Madison, and M. S. Pindzola, “Angular distributions from photoionization of H2+,” Phys. Rev. A 75, 062707 (2007).
[CrossRef]

Pritchard, D. E.

P. J. Martin, P. L. Gould, B. G. Oldaker, A. H. Mikllich, and D. E. Pritchard, “Diffraction of atoms moving through a standing light wave,” Phys. Rev. A 36, 2495–2498 (1987).
[CrossRef] [PubMed]

P. L. Gould, G. A. Ruff, and D. E. Pritchard, “Diffraction of atoms by light: The near-resonant Kapitza-Dirac effect,” Phys. Rev. Lett. 56, 827–830 (1986).
[CrossRef] [PubMed]

Rayner, D. M.

D. Pavičić, K. F. Lee, D. M. Rayner, P. B. Corkum, and D. M. Villeneuve, “Direct Measurement of the Angular Dependence of Ionization for N2, O2, and CO2 in Intense Laser Fields,” Phys. Rev. Lett. 98, 243001 (2007).
[CrossRef]

Ren, X.

X. Ren, J. Zhang, Y. Wang, Z. Xu, and D.-S. Guo, “Effects of the internuclear vector on the photoelectron angular distributions of H2+,” Eur. J. Phys. D. 51, 401–407 (2009).
[CrossRef]

X. Ren, J. Zhang, P. Liu, Y. Wang, and Z. Xu, “Ionization suppression of diatomic molecules in strong laser fields,” Phys. Rev. A 78, 043411 (2008).
[CrossRef]

Ren, X. H.

Ruff, G. A.

P. L. Gould, G. A. Ruff, and D. E. Pritchard, “Diffraction of atoms by light: The near-resonant Kapitza-Dirac effect,” Phys. Rev. Lett. 56, 827–830 (1986).
[CrossRef] [PubMed]

Schumacher, D. W.

P. H. Bucksbaum, D. W. Schumacher, and M. Bashkansky, “High-Intensity Kapitza-Dirac Effect,” Phys. Rev. Lett. 61, 1182–1185 (1988).
[CrossRef] [PubMed]

Seideman, T.

H. Stapelfeldt and T. Seideman, “Colloquium: Aligning molecules with strong laser pulses,” Rev. Mod. Phys. 75, 543–557 (2003).
[CrossRef]

Smirnova, O.

O. Smirnova, D. L. Freimund, H. Batelaan, and M. Ivanov, “Kapitza-Dirac Diffraction without Standing Waves: Diffraction without a Grating?,” Phys. Rev. Lett. 92, 223601 (2004).
[CrossRef] [PubMed]

Stapelfeldt, H.

H. Stapelfeldt and T. Seideman, “Colloquium: Aligning molecules with strong laser pulses,” Rev. Mod. Phys. 75, 543–557 (2003).
[CrossRef]

T. K. Kjeldsen, C. Z. Bisgaard, L. B. Madsen, and H. Stapelfeldt, “Role of symmetry in strong-field ionization of molecules,” Phys. Rev. A 68, 063407 (2003).
[CrossRef]

Sun, Z.

S. Zhang, C. Lu, T. Jia, Z. Wang, and Z. Sun, “Controlling field-free molecular orientation with combined single- and dual-color laser pulses,” Phys. Rev. A 83, 043410 (2011).
[CrossRef]

Usachenko, V. I.

V. I. Usachenko, “Reply to Comment on Strong-field ionization of laser-irradiated light homonuclear diatomic molecules: A generalized strong-field approximation-linear combination of atomic orbitals model,” Phys. Rev. A 73, 047402 (2006).
[CrossRef]

Villeneuve, D. M.

D. Pavičić, K. F. Lee, D. M. Rayner, P. B. Corkum, and D. M. Villeneuve, “Direct Measurement of the Angular Dependence of Ionization for N2, O2, and CO2 in Intense Laser Fields,” Phys. Rev. Lett. 98, 243001 (2007).
[CrossRef]

Wang, Y.

X. Ren, J. Zhang, Y. Wang, Z. Xu, and D.-S. Guo, “Effects of the internuclear vector on the photoelectron angular distributions of H2+,” Eur. J. Phys. D. 51, 401–407 (2009).
[CrossRef]

X. Ren, J. Zhang, P. Liu, Y. Wang, and Z. Xu, “Ionization suppression of diatomic molecules in strong laser fields,” Phys. Rev. A 78, 043411 (2008).
[CrossRef]

Wang, Z.

S. Zhang, C. Lu, T. Jia, Z. Wang, and Z. Sun, “Controlling field-free molecular orientation with combined single- and dual-color laser pulses,” Phys. Rev. A 83, 043410 (2011).
[CrossRef]

Wu, Y.-S.

J. Gao, D.-S. Guo, and Y.-S. Wu, “Resonant above-threshold ionization at quantized laser intensities,” Phys. Rev. A 61, 043406 (2000).
[CrossRef]

Xu, Z.

X. Ren, J. Zhang, Y. Wang, Z. Xu, and D.-S. Guo, “Effects of the internuclear vector on the photoelectron angular distributions of H2+,” Eur. J. Phys. D. 51, 401–407 (2009).
[CrossRef]

X. Ren, J. Zhang, P. Liu, Y. Wang, and Z. Xu, “Ionization suppression of diatomic molecules in strong laser fields,” Phys. Rev. A 78, 043411 (2008).
[CrossRef]

X. Li, J. Zhang, Z. Xu, P. Fu, D.-S. Guo, and R. R. Freeman, “Theory of the Kapitza-Dirac Diffraction Effect,” Phys. Rev. Lett. 92, 233603 (2004).
[CrossRef] [PubMed]

J. Zhang, W. Zhang, Z. Xu, X. Li, P. Fu, D.-S. Guo, and R. R. Freeman, “The calculation of photoelectron angular distributions with jet-like structure from scattering theory,” J. Phys. B 35, 4809–4818 (2002).
[CrossRef]

Xu, Z. Z.

Zeilinger, A.

O. Nairz, B. Brezger, M. Arndt, and A. Zeilinger, “Diffraction of Complex Molecules by Structures Made of Light,” Phys. Rev. Lett. 87, 160401 (2001).
[CrossRef] [PubMed]

Zhang, J.

X. Ren, J. Zhang, Y. Wang, Z. Xu, and D.-S. Guo, “Effects of the internuclear vector on the photoelectron angular distributions of H2+,” Eur. J. Phys. D. 51, 401–407 (2009).
[CrossRef]

X. Ren, J. Zhang, P. Liu, Y. Wang, and Z. Xu, “Ionization suppression of diatomic molecules in strong laser fields,” Phys. Rev. A 78, 043411 (2008).
[CrossRef]

X. Li, J. Zhang, Z. Xu, P. Fu, D.-S. Guo, and R. R. Freeman, “Theory of the Kapitza-Dirac Diffraction Effect,” Phys. Rev. Lett. 92, 233603 (2004).
[CrossRef] [PubMed]

J. Zhang, W. Zhang, Z. Xu, X. Li, P. Fu, D.-S. Guo, and R. R. Freeman, “The calculation of photoelectron angular distributions with jet-like structure from scattering theory,” J. Phys. B 35, 4809–4818 (2002).
[CrossRef]

Zhang, J. T.

Zhang, S.

S. Zhang, C. Lu, T. Jia, Z. Wang, and Z. Sun, “Controlling field-free molecular orientation with combined single- and dual-color laser pulses,” Phys. Rev. A 83, 043410 (2011).
[CrossRef]

Zhang, W.

J. Zhang, W. Zhang, Z. Xu, X. Li, P. Fu, D.-S. Guo, and R. R. Freeman, “The calculation of photoelectron angular distributions with jet-like structure from scattering theory,” J. Phys. B 35, 4809–4818 (2002).
[CrossRef]

Comtemp. Phys. (1)

H. Batelaan, “The Kapitza-Dirac effect,” Comtemp. Phys. 41, 369–381 (2000).
[CrossRef]

Eur. J. Phys. D. (1)

X. Ren, J. Zhang, Y. Wang, Z. Xu, and D.-S. Guo, “Effects of the internuclear vector on the photoelectron angular distributions of H2+,” Eur. J. Phys. D. 51, 401–407 (2009).
[CrossRef]

J. Chem. Phys. (1)

T. J. Houser, P. G. Lykos, and E. L. Mehler, “One-Center Wavefunction for the Hydrogen Molecule Ion,” J. Chem. Phys. 38, 583–585 (1963).
[CrossRef]

J. Opt. Soc. Am. B (1)

J. Phys. B (1)

J. Zhang, W. Zhang, Z. Xu, X. Li, P. Fu, D.-S. Guo, and R. R. Freeman, “The calculation of photoelectron angular distributions with jet-like structure from scattering theory,” J. Phys. B 35, 4809–4818 (2002).
[CrossRef]

Nature (London) (1)

D. L. Freimund, K. Aflatoon, and H. Batelaan, “Observation of the Kapitza-Dirac effect,” Nature (London) 413, 142–143 (2002).
[CrossRef]

Phys. Rev. (1)

H. D. Cohen and U. Fano, “Interference in the Photo-Ionization of Molecules,” Phys. Rev. 150, 30–33 (1966).
[CrossRef]

Phys. Rev. A (11)

T. K. Kjeldsen, C. Z. Bisgaard, L. B. Madsen, and H. Stapelfeldt, “Role of symmetry in strong-field ionization of molecules,” Phys. Rev. A 68, 063407 (2003).
[CrossRef]

D.-S. Guo and G. W. F. Drake, “Multiphoton ionization in circularly polarized standing waves,” Phys. Rev. A 45, 6622–6635 (1992).
[CrossRef] [PubMed]

P. J. Martin, P. L. Gould, B. G. Oldaker, A. H. Mikllich, and D. E. Pritchard, “Diffraction of atoms moving through a standing light wave,” Phys. Rev. A 36, 2495–2498 (1987).
[CrossRef] [PubMed]

X. Ren, J. Zhang, P. Liu, Y. Wang, and Z. Xu, “Ionization suppression of diatomic molecules in strong laser fields,” Phys. Rev. A 78, 043411 (2008).
[CrossRef]

M. Foster, J. Colgan, O. Al-Hagan, J. L. Peacher, D. H. Madison, and M. S. Pindzola, “Angular distributions from photoionization of H2+,” Phys. Rev. A 75, 062707 (2007).
[CrossRef]

V. I. Usachenko, “Reply to Comment on Strong-field ionization of laser-irradiated light homonuclear diatomic molecules: A generalized strong-field approximation-linear combination of atomic orbitals model,” Phys. Rev. A 73, 047402 (2006).
[CrossRef]

A. Jaroń-Becker, A. Becker, and F. H. M. Faisal, “Ionization of N2, O2, and linear carbon clusters in a strong laser pulse,” Phys. Rev. A 69, 023410 (2004).
[CrossRef]

S. Zhang, C. Lu, T. Jia, Z. Wang, and Z. Sun, “Controlling field-free molecular orientation with combined single- and dual-color laser pulses,” Phys. Rev. A 83, 043410 (2011).
[CrossRef]

D.-S. Guo, T. Åberg, and B. Crasemann, “Scattering theory of multiphoton ionization in strong fields,” Phys. Rev. A 40, 4997–5005 (1989).
[CrossRef] [PubMed]

D.-S. Guo, “Theory of the Kapitza-Dirac effect in strong radiation fields,” Phys. Rev. A 53, 4311–4319 (1996).
[CrossRef] [PubMed]

J. Gao, D.-S. Guo, and Y.-S. Wu, “Resonant above-threshold ionization at quantized laser intensities,” Phys. Rev. A 61, 043406 (2000).
[CrossRef]

Phys. Rev. Lett. (9)

X. Li, J. Zhang, Z. Xu, P. Fu, D.-S. Guo, and R. R. Freeman, “Theory of the Kapitza-Dirac Diffraction Effect,” Phys. Rev. Lett. 92, 233603 (2004).
[CrossRef] [PubMed]

P. L. Gould, G. A. Ruff, and D. E. Pritchard, “Diffraction of atoms by light: The near-resonant Kapitza-Dirac effect,” Phys. Rev. Lett. 56, 827–830 (1986).
[CrossRef] [PubMed]

O. Smirnova, D. L. Freimund, H. Batelaan, and M. Ivanov, “Kapitza-Dirac Diffraction without Standing Waves: Diffraction without a Grating?,” Phys. Rev. Lett. 92, 223601 (2004).
[CrossRef] [PubMed]

O. Nairz, B. Brezger, M. Arndt, and A. Zeilinger, “Diffraction of Complex Molecules by Structures Made of Light,” Phys. Rev. Lett. 87, 160401 (2001).
[CrossRef] [PubMed]

C. Guo, “Multielectron Effects on Single-Electron Strong Field Ionization,” Phys. Rev. Lett. 85, 2276–2279 (2000).
[CrossRef] [PubMed]

J. Muth-Bőhm, A. Becker, and F. H. M. Faisal, “Suppressed Molecular Ionization for a Class of Diatomics in Intense Femtosecond Laser Fields,” Phys. Rev. Lett. 85, 2280–2283 (2000).
[CrossRef]

P. H. Bucksbaum, D. W. Schumacher, and M. Bashkansky, “High-Intensity Kapitza-Dirac Effect,” Phys. Rev. Lett. 61, 1182–1185 (1988).
[CrossRef] [PubMed]

M. Mathholm and N. E. Henriksen, “Field-Free Orientation of Molecules,” Phys. Rev. Lett. 87, 193001 (2001).
[CrossRef]

D. Pavičić, K. F. Lee, D. M. Rayner, P. B. Corkum, and D. M. Villeneuve, “Direct Measurement of the Angular Dependence of Ionization for N2, O2, and CO2 in Intense Laser Fields,” Phys. Rev. Lett. 98, 243001 (2007).
[CrossRef]

Proc. Cambridge, Philos. Soc. (1)

P. L. Kapitza and P. A. M. Dirac, “The reflection of electrons from standing light waves,” Proc. Cambridge, Philos. Soc. 29, 297–300 (1933).
[CrossRef]

Rev. Mod. Phys. (1)

H. Stapelfeldt and T. Seideman, “Colloquium: Aligning molecules with strong laser pulses,” Rev. Mod. Phys. 75, 543–557 (2003).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

(Color online) (a) Coordinate system for H 2 + molecule without laser fields. (b) Coordinate system for H 2 + molecule upon photoelectron ejection.

Fig. 2
Fig. 2

PADs for the 2nd ((a), (c) and (d)) and 10th ((b)) ATI peak at laser intensities 5.5 × 1013 ((a), (b) and (d)) and 6.4 × 1013 W/cm2 ((c)). The H 2 + molecule is prepared in an antibonding state σμ with binding energy 18.1 eV. The laser field is linearly polarized and wavelength of 800 nm. The molecules are aligned along the laser propagation. The red (grey) line in (d) is the PAD calculated by the wave function given in Ref. [27] and is up shifted by a quantity of 0.1 for clarity. Each PAD is normalized by its respective maximum.

Fig. 3
Fig. 3

(Color online) 3D plots of the PADs for different molecular alignments: (a) and (c) are for the molecular axis along the laser polarization; (b) and (d) are for the molecular axis perpendicular to the laser polarization. (a) and (b) are for the 10th ATI peak, while (c) and (d) are for the 20th ATI peak. The linearly polarized laser field is of intensity 1014 W/cm2 and wavelength of 800 nm. The molecules are prepared in a bonding state σg.

Fig. 4
Fig. 4

(Color online) 3D plots of the PADs for the molecular axis aligned in the laser polarization plane. The top two PADs are for the 2nd ATI peak and the bottom two are for the 10th ATI peak. (a) and (c) ((b) and (d)) are for molecules aligned along (perpendicular to) the laser polarization. The molecules are prepared in an antibonding state σμ. The laser field is linearly polarized, and is of intensity 1014 W/cm2 and wavelength of 800 nm.

Fig. 5
Fig. 5

(Color online) 3D plots of the PADs for the molecular axis aligned along the laser propagation: (a) the 2nd and (b) the 10th ATI peak. The molecules are prepared in an antibonding state σμ. The laser field is linearly polarized, and is of intensity 1014 W/cm2 and wavelength of 800 nm.

Fig. 6
Fig. 6

(Color online) PADs of the 2nd ATI peak for the molecular axis aligned along two arbitrary directions: (a) θR = π/2 and φR = π/4; and (b) θR = π/4 and φR = π/4. (c) and (d) are the 2D plots of the normalized PADs for the molecular alignments corresponding to (a) and (b), respectively. The molecules are prepared in an antibonding state σμ. The laser field is linearly polarized, and is of intensity 1014 W/cm2 and wavelength of 800 nm.

Equations (14)

Equations on this page are rendered with MathJax. Learn more.

Ψ ( r ) = V e 1 / 2 e i [ p r k r ( N a 1 N a 2 ) ] q | n 1 + q , n 2 c 𝒳 q ( z c , z s ) ,
c 1 = 1 2 ( a 1 + a 2 ) , c 2 = 1 2 ( a 1 a 2 ) ,
𝒳 q ( z c , z s ) = j = + X q 2 j ( z c ) X j ( z s ) ,
z c = 2 2 | e | Λ m e ω P ɛ ^ , z s = u p cos ξ ,
T f i = Ψ ( = i ) Φ f ; m 1 , m 2 | Ψ Ψ | V | Φ ( R , r ) ; l , l ,
V = i e 2 m e ( A + A ) + e 2 A 2 2 m e ,
Φ ( R , r ) = Φ 1 ( r 1 ) ± Φ 2 ( r 2 ) 2 [ 1 ± S ( R ) ] ,
d W d Ω P f = ( 2 m 3 ω 5 ) 1 / 2 ( 2 π ) 2 ( n E b / ω ) 1 / 2 × | c h ( j s = n ) ( 2 u p j ) F 𝒳 s ( ζ f , η ) 𝒳 j * ( ζ f , η ) | 2 ,
ζ f = 2 2 | e | Λ m e ω P f ɛ ^ , η = u p cos ξ .
F = Φ ( R , P + ) F + + Φ ( R , P ) F ,
F ± = 2 π ( m 2 m 1 ) ± ,
( m 2 m 1 ) ± = | P f | cos θ f ω ± [ ( P f cos θ f ω ) 2 2 m e ( 2 u p s ) ω ] 1 / 2 ,
Φ σ g ( R , P ) = 2 3 ( π a 0 3 ) 1 / 2 ( 1 + p 2 a 0 2 ) 2 2 cos ( P R / 2 ) 2 [ 1 + S ( R ) ] , Φ σ μ ( R , P ) = 2 3 ( π a 0 3 ) 1 / 2 ( 1 + p 2 a 0 2 ) 2 2 sin ( P R / 2 ) 2 [ 1 S ( R ) ] ,
α = arcsin ( 2 u p s n E b / ω ) 1 / 2 .

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