Abstract

We have investigated the laser-assisted radiative recombination in the presence of a few-cycle pulse with the aim of demonstrating means of controlling such process. Within the Coulomb-Volkov approach already employed to describe the radiative recombination assisted by a monochromatic laser field, we have found that the emitted photon spectrum is affected by both the cycle number nc and the carrier-envelope relative phase φ. In particular, it has been shown that the minimum and the maximum values of the emitted photon energy may be controlled by varying nc and φ. Finally, it has been found that the enhancement of radiative recombination occurring in the presence of a monochromatic field, takes place also by using a few-cycle laser pulse.

© 2006 Optical Society of America

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  1. Y. Hahn, "Electron -ion recombination process - an overview," Rep. Prog. Phys. 60, 691-759 (1997).
    [CrossRef]
  2. R. Neumann, H. Poth, A. Winnacker, and A. Wolf, "Laser-enhanced electron-ion capture and antihydrogen formation," Z. Physik. A 313, 253-262 (1983).
    [CrossRef]
  3. U. Schramm, J. Berger, M. Grieser, D. Habs, E. Jaeschke, G. Kilgus, D. Schwalm, A. Wolf, R. Neumann, and R. Schuch, "Observation of laser-induced recombination in merged electron and proton-beams," Phys. Rev. Lett. 67, 22-25 (1991).
    [CrossRef] [PubMed]
  4. F. B. Yousif, P. Vanderdonk, Z. Kucherovsky, J. Reis, E. Brannen, J. B. A. Mitchell, and T. J. Morgan, "Experimental-observation of laser-stimulated radiative recombination," Phys. Rev. Lett. 67, 26-29 (1991).
    [CrossRef] [PubMed]
  5. S. Borneis, F. Bosch, T. Engel, M. Jung, I. Klaft, O. Klepper, T. Kuhl, D. Marx, R. Moshammer, R. Neumann, S. Schroder, P. Seelig, and L. Volker, "Laser-stimulated two-step recombination of highly charged ions and electrons in a storage ring," Phys. Rev. Lett. 72, 207-209 (1994).
    [CrossRef] [PubMed]
  6. U. Schramm, T. Schussler, D. Habs, D. Schwalm, and A. Wolf, "Laser-induced recombination studies with the adiabatically expanded electron beam of the Heidelberg TSR," Hyperfine Interact. 99,309-316 (1996).
    [CrossRef]
  7. S. Pastuszka, U. Schramm, M. Grieser, C. Broude, R. Grimm, D. Habs, J. Kenntner, H. J. Miesner, T. Schussler, D. Schwalm and A. Wolf, "Electron cooling and recombination experiments with an adiabatically expanded electron beam, " Nucl. Instrum. Methods Phys. Res. A 369, 11-22 (1996).
    [CrossRef]
  8. S. Asp, S. R. Schuch, D. R. DeWitt, C. Biedermann, H. Gao, W. Zong, G. Andler, and E. Ustiniano, "Laser-induced recombination of D+," Nucl. Instrum. Methods: Phys. Res. B 117, 31-37 (1996).
    [CrossRef]
  9. M. L. Rogelstad, F. B. Yousif, T. J. Morgan, and J. B. A. Mitchell, "Stimulated radiative recombination of H+ and He+," J. Phys. B 30, 3913-3931 (1997).
    [CrossRef]
  10. M. Yu Kuchiev and V. N. Ostrovsky, "Multiphoton radiative recombination of electron assisted by a laser field," Phys. Rev. A 61, 033414 (2000).
    [CrossRef]
  11. D. B. Milosevic and F. Ehlotzky, "Rescattering effects in soft-x-ray generation by laser-assisted electron-ion recombination," Phys. Rev. A 65, 042504 (2002).
    [CrossRef]
  12. C. Leone, S. Bivona, R. Burlon, and G. Ferrante, "Strong-field and plasma aspects of multiphoton radiative recombination," Phys. Rev. A 66, 051403 (2002).
    [CrossRef]
  13. S. Bivona, R. Burlon, G. Ferrante, and C. Leone, "Strong field effects of multiphoton radiative recombination," Laser Phys. 13, 1077-1082 (2003).
  14. S. Bivona, R. Burlon, G. Ferrante, and C. Leone, "Influence of a plasma medium on laser assisted radiative recombination," Laser Phys. Lett. 1, 86-92 (2004).
    [CrossRef]
  15. S. Bivona, R. Burlon, G. Ferrante, and C. Leone, "Control of multiphoton radiative recombination through the action of two-frequency fields," Laser Phys. Lett. 1, 118-123 (2004).
    [CrossRef]
  16. S. Bivona, R. Burlon, G. Ferrante, and C. Leone, "Control of radiative recombination by a strong laser field," Appl. Phys. B 78, 809-812 (2004).
    [CrossRef]
  17. S. Bivona, R. Burlon, G. Ferrante, and C. Leone, "Radiative recombination in a strong laser field. Low frequency approximation," J. Opt. Soc. Am. B 22, 2076-2082 (2005).
    [CrossRef]
  18. S. X. Hu and L. A. Collins, "Phase control of the inverse above-threshold-ionization processes with few-cycle pulses," Phys. Rev A 70, 013407 (2004).
    [CrossRef]
  19. J. Z. Kaminski and F. Ehlotzky, "Time-frequency analysis of x-ray generation by recombination in short laser pulses," Phys. Rev. A 71, 043402 (2005).
    [CrossRef]
  20. M. Jain and N. Tzoar, "Compton scattering in the presence of coherent electromagnetic radiation," Phys. Rev. A 18, 538-545 (1978).
    [CrossRef]
  21. C. Leone, S. Bivona, R. Burlon, and G. Ferrante, "Two-frequency multiphoton ionization of hydrogen atoms," Phys. Rev. A 38,5642-5651 (1988).
    [CrossRef] [PubMed]
  22. F. Ehlotzky, A. Jaron, and J. Z. Kaminsky, "Electron-atom collisions in a laser field," Phys. Rep. Rev. Section of Phys. Lett. 297, 64-153 (1998)
  23. D. B. Milosevic and F. Ehlotzky, "Scattering and reaction processes in powerful laser fields," Adv. At. Mol., Opt. Phys. 49, 373-532 (2003).
    [CrossRef]
  24. A. Maquet, R. Taieb, and V. Veniard, "Two-color infrared-UV atomic photoionization," in Fundamental of laser-matter interaction, K.N. Drabovich and N. I. Koroteev, eds., Proc. SPIE 2796, 31-38 (1995).
    [CrossRef]
  25. N. M. Kroll and K. M. Watson, "Charged-particle scattering in the presence of a strong electromagnetic wave," Phys. Rev. A 8, 804-809 (1973).
    [CrossRef]

2005

J. Z. Kaminski and F. Ehlotzky, "Time-frequency analysis of x-ray generation by recombination in short laser pulses," Phys. Rev. A 71, 043402 (2005).
[CrossRef]

S. Bivona, R. Burlon, G. Ferrante, and C. Leone, "Radiative recombination in a strong laser field. Low frequency approximation," J. Opt. Soc. Am. B 22, 2076-2082 (2005).
[CrossRef]

2004

S. Bivona, R. Burlon, G. Ferrante, and C. Leone, "Influence of a plasma medium on laser assisted radiative recombination," Laser Phys. Lett. 1, 86-92 (2004).
[CrossRef]

S. Bivona, R. Burlon, G. Ferrante, and C. Leone, "Control of multiphoton radiative recombination through the action of two-frequency fields," Laser Phys. Lett. 1, 118-123 (2004).
[CrossRef]

S. Bivona, R. Burlon, G. Ferrante, and C. Leone, "Control of radiative recombination by a strong laser field," Appl. Phys. B 78, 809-812 (2004).
[CrossRef]

S. X. Hu and L. A. Collins, "Phase control of the inverse above-threshold-ionization processes with few-cycle pulses," Phys. Rev A 70, 013407 (2004).
[CrossRef]

2003

S. Bivona, R. Burlon, G. Ferrante, and C. Leone, "Strong field effects of multiphoton radiative recombination," Laser Phys. 13, 1077-1082 (2003).

D. B. Milosevic and F. Ehlotzky, "Scattering and reaction processes in powerful laser fields," Adv. At. Mol., Opt. Phys. 49, 373-532 (2003).
[CrossRef]

2002

D. B. Milosevic and F. Ehlotzky, "Rescattering effects in soft-x-ray generation by laser-assisted electron-ion recombination," Phys. Rev. A 65, 042504 (2002).
[CrossRef]

C. Leone, S. Bivona, R. Burlon, and G. Ferrante, "Strong-field and plasma aspects of multiphoton radiative recombination," Phys. Rev. A 66, 051403 (2002).
[CrossRef]

2000

M. Yu Kuchiev and V. N. Ostrovsky, "Multiphoton radiative recombination of electron assisted by a laser field," Phys. Rev. A 61, 033414 (2000).
[CrossRef]

1998

F. Ehlotzky, A. Jaron, and J. Z. Kaminsky, "Electron-atom collisions in a laser field," Phys. Rep. Rev. Section of Phys. Lett. 297, 64-153 (1998)

1997

Y. Hahn, "Electron -ion recombination process - an overview," Rep. Prog. Phys. 60, 691-759 (1997).
[CrossRef]

M. L. Rogelstad, F. B. Yousif, T. J. Morgan, and J. B. A. Mitchell, "Stimulated radiative recombination of H+ and He+," J. Phys. B 30, 3913-3931 (1997).
[CrossRef]

1996

U. Schramm, T. Schussler, D. Habs, D. Schwalm, and A. Wolf, "Laser-induced recombination studies with the adiabatically expanded electron beam of the Heidelberg TSR," Hyperfine Interact. 99,309-316 (1996).
[CrossRef]

S. Pastuszka, U. Schramm, M. Grieser, C. Broude, R. Grimm, D. Habs, J. Kenntner, H. J. Miesner, T. Schussler, D. Schwalm and A. Wolf, "Electron cooling and recombination experiments with an adiabatically expanded electron beam, " Nucl. Instrum. Methods Phys. Res. A 369, 11-22 (1996).
[CrossRef]

S. Asp, S. R. Schuch, D. R. DeWitt, C. Biedermann, H. Gao, W. Zong, G. Andler, and E. Ustiniano, "Laser-induced recombination of D+," Nucl. Instrum. Methods: Phys. Res. B 117, 31-37 (1996).
[CrossRef]

1994

S. Borneis, F. Bosch, T. Engel, M. Jung, I. Klaft, O. Klepper, T. Kuhl, D. Marx, R. Moshammer, R. Neumann, S. Schroder, P. Seelig, and L. Volker, "Laser-stimulated two-step recombination of highly charged ions and electrons in a storage ring," Phys. Rev. Lett. 72, 207-209 (1994).
[CrossRef] [PubMed]

1991

U. Schramm, J. Berger, M. Grieser, D. Habs, E. Jaeschke, G. Kilgus, D. Schwalm, A. Wolf, R. Neumann, and R. Schuch, "Observation of laser-induced recombination in merged electron and proton-beams," Phys. Rev. Lett. 67, 22-25 (1991).
[CrossRef] [PubMed]

F. B. Yousif, P. Vanderdonk, Z. Kucherovsky, J. Reis, E. Brannen, J. B. A. Mitchell, and T. J. Morgan, "Experimental-observation of laser-stimulated radiative recombination," Phys. Rev. Lett. 67, 26-29 (1991).
[CrossRef] [PubMed]

1988

C. Leone, S. Bivona, R. Burlon, and G. Ferrante, "Two-frequency multiphoton ionization of hydrogen atoms," Phys. Rev. A 38,5642-5651 (1988).
[CrossRef] [PubMed]

1983

R. Neumann, H. Poth, A. Winnacker, and A. Wolf, "Laser-enhanced electron-ion capture and antihydrogen formation," Z. Physik. A 313, 253-262 (1983).
[CrossRef]

1978

M. Jain and N. Tzoar, "Compton scattering in the presence of coherent electromagnetic radiation," Phys. Rev. A 18, 538-545 (1978).
[CrossRef]

1973

N. M. Kroll and K. M. Watson, "Charged-particle scattering in the presence of a strong electromagnetic wave," Phys. Rev. A 8, 804-809 (1973).
[CrossRef]

Andler, G.

S. Asp, S. R. Schuch, D. R. DeWitt, C. Biedermann, H. Gao, W. Zong, G. Andler, and E. Ustiniano, "Laser-induced recombination of D+," Nucl. Instrum. Methods: Phys. Res. B 117, 31-37 (1996).
[CrossRef]

Asp, S.

S. Asp, S. R. Schuch, D. R. DeWitt, C. Biedermann, H. Gao, W. Zong, G. Andler, and E. Ustiniano, "Laser-induced recombination of D+," Nucl. Instrum. Methods: Phys. Res. B 117, 31-37 (1996).
[CrossRef]

Berger, J.

U. Schramm, J. Berger, M. Grieser, D. Habs, E. Jaeschke, G. Kilgus, D. Schwalm, A. Wolf, R. Neumann, and R. Schuch, "Observation of laser-induced recombination in merged electron and proton-beams," Phys. Rev. Lett. 67, 22-25 (1991).
[CrossRef] [PubMed]

Biedermann, C.

S. Asp, S. R. Schuch, D. R. DeWitt, C. Biedermann, H. Gao, W. Zong, G. Andler, and E. Ustiniano, "Laser-induced recombination of D+," Nucl. Instrum. Methods: Phys. Res. B 117, 31-37 (1996).
[CrossRef]

Bivona, S.

S. Bivona, R. Burlon, G. Ferrante, and C. Leone, "Radiative recombination in a strong laser field. Low frequency approximation," J. Opt. Soc. Am. B 22, 2076-2082 (2005).
[CrossRef]

S. Bivona, R. Burlon, G. Ferrante, and C. Leone, "Control of multiphoton radiative recombination through the action of two-frequency fields," Laser Phys. Lett. 1, 118-123 (2004).
[CrossRef]

S. Bivona, R. Burlon, G. Ferrante, and C. Leone, "Control of radiative recombination by a strong laser field," Appl. Phys. B 78, 809-812 (2004).
[CrossRef]

S. Bivona, R. Burlon, G. Ferrante, and C. Leone, "Influence of a plasma medium on laser assisted radiative recombination," Laser Phys. Lett. 1, 86-92 (2004).
[CrossRef]

S. Bivona, R. Burlon, G. Ferrante, and C. Leone, "Strong field effects of multiphoton radiative recombination," Laser Phys. 13, 1077-1082 (2003).

C. Leone, S. Bivona, R. Burlon, and G. Ferrante, "Strong-field and plasma aspects of multiphoton radiative recombination," Phys. Rev. A 66, 051403 (2002).
[CrossRef]

C. Leone, S. Bivona, R. Burlon, and G. Ferrante, "Two-frequency multiphoton ionization of hydrogen atoms," Phys. Rev. A 38,5642-5651 (1988).
[CrossRef] [PubMed]

Borneis, S.

S. Borneis, F. Bosch, T. Engel, M. Jung, I. Klaft, O. Klepper, T. Kuhl, D. Marx, R. Moshammer, R. Neumann, S. Schroder, P. Seelig, and L. Volker, "Laser-stimulated two-step recombination of highly charged ions and electrons in a storage ring," Phys. Rev. Lett. 72, 207-209 (1994).
[CrossRef] [PubMed]

Bosch, F.

S. Borneis, F. Bosch, T. Engel, M. Jung, I. Klaft, O. Klepper, T. Kuhl, D. Marx, R. Moshammer, R. Neumann, S. Schroder, P. Seelig, and L. Volker, "Laser-stimulated two-step recombination of highly charged ions and electrons in a storage ring," Phys. Rev. Lett. 72, 207-209 (1994).
[CrossRef] [PubMed]

Brannen, E.

F. B. Yousif, P. Vanderdonk, Z. Kucherovsky, J. Reis, E. Brannen, J. B. A. Mitchell, and T. J. Morgan, "Experimental-observation of laser-stimulated radiative recombination," Phys. Rev. Lett. 67, 26-29 (1991).
[CrossRef] [PubMed]

Broude, C.

S. Pastuszka, U. Schramm, M. Grieser, C. Broude, R. Grimm, D. Habs, J. Kenntner, H. J. Miesner, T. Schussler, D. Schwalm and A. Wolf, "Electron cooling and recombination experiments with an adiabatically expanded electron beam, " Nucl. Instrum. Methods Phys. Res. A 369, 11-22 (1996).
[CrossRef]

Burlon, R.

S. Bivona, R. Burlon, G. Ferrante, and C. Leone, "Radiative recombination in a strong laser field. Low frequency approximation," J. Opt. Soc. Am. B 22, 2076-2082 (2005).
[CrossRef]

S. Bivona, R. Burlon, G. Ferrante, and C. Leone, "Control of radiative recombination by a strong laser field," Appl. Phys. B 78, 809-812 (2004).
[CrossRef]

S. Bivona, R. Burlon, G. Ferrante, and C. Leone, "Control of multiphoton radiative recombination through the action of two-frequency fields," Laser Phys. Lett. 1, 118-123 (2004).
[CrossRef]

S. Bivona, R. Burlon, G. Ferrante, and C. Leone, "Influence of a plasma medium on laser assisted radiative recombination," Laser Phys. Lett. 1, 86-92 (2004).
[CrossRef]

S. Bivona, R. Burlon, G. Ferrante, and C. Leone, "Strong field effects of multiphoton radiative recombination," Laser Phys. 13, 1077-1082 (2003).

C. Leone, S. Bivona, R. Burlon, and G. Ferrante, "Strong-field and plasma aspects of multiphoton radiative recombination," Phys. Rev. A 66, 051403 (2002).
[CrossRef]

C. Leone, S. Bivona, R. Burlon, and G. Ferrante, "Two-frequency multiphoton ionization of hydrogen atoms," Phys. Rev. A 38,5642-5651 (1988).
[CrossRef] [PubMed]

Collins, L. A.

S. X. Hu and L. A. Collins, "Phase control of the inverse above-threshold-ionization processes with few-cycle pulses," Phys. Rev A 70, 013407 (2004).
[CrossRef]

DeWitt, D. R.

S. Asp, S. R. Schuch, D. R. DeWitt, C. Biedermann, H. Gao, W. Zong, G. Andler, and E. Ustiniano, "Laser-induced recombination of D+," Nucl. Instrum. Methods: Phys. Res. B 117, 31-37 (1996).
[CrossRef]

Ehlotzky, F.

J. Z. Kaminski and F. Ehlotzky, "Time-frequency analysis of x-ray generation by recombination in short laser pulses," Phys. Rev. A 71, 043402 (2005).
[CrossRef]

D. B. Milosevic and F. Ehlotzky, "Scattering and reaction processes in powerful laser fields," Adv. At. Mol., Opt. Phys. 49, 373-532 (2003).
[CrossRef]

D. B. Milosevic and F. Ehlotzky, "Rescattering effects in soft-x-ray generation by laser-assisted electron-ion recombination," Phys. Rev. A 65, 042504 (2002).
[CrossRef]

F. Ehlotzky, A. Jaron, and J. Z. Kaminsky, "Electron-atom collisions in a laser field," Phys. Rep. Rev. Section of Phys. Lett. 297, 64-153 (1998)

Engel, T.

S. Borneis, F. Bosch, T. Engel, M. Jung, I. Klaft, O. Klepper, T. Kuhl, D. Marx, R. Moshammer, R. Neumann, S. Schroder, P. Seelig, and L. Volker, "Laser-stimulated two-step recombination of highly charged ions and electrons in a storage ring," Phys. Rev. Lett. 72, 207-209 (1994).
[CrossRef] [PubMed]

Ferrante, G.

S. Bivona, R. Burlon, G. Ferrante, and C. Leone, "Radiative recombination in a strong laser field. Low frequency approximation," J. Opt. Soc. Am. B 22, 2076-2082 (2005).
[CrossRef]

S. Bivona, R. Burlon, G. Ferrante, and C. Leone, "Control of multiphoton radiative recombination through the action of two-frequency fields," Laser Phys. Lett. 1, 118-123 (2004).
[CrossRef]

S. Bivona, R. Burlon, G. Ferrante, and C. Leone, "Control of radiative recombination by a strong laser field," Appl. Phys. B 78, 809-812 (2004).
[CrossRef]

S. Bivona, R. Burlon, G. Ferrante, and C. Leone, "Influence of a plasma medium on laser assisted radiative recombination," Laser Phys. Lett. 1, 86-92 (2004).
[CrossRef]

S. Bivona, R. Burlon, G. Ferrante, and C. Leone, "Strong field effects of multiphoton radiative recombination," Laser Phys. 13, 1077-1082 (2003).

C. Leone, S. Bivona, R. Burlon, and G. Ferrante, "Strong-field and plasma aspects of multiphoton radiative recombination," Phys. Rev. A 66, 051403 (2002).
[CrossRef]

C. Leone, S. Bivona, R. Burlon, and G. Ferrante, "Two-frequency multiphoton ionization of hydrogen atoms," Phys. Rev. A 38,5642-5651 (1988).
[CrossRef] [PubMed]

Gao, H.

S. Asp, S. R. Schuch, D. R. DeWitt, C. Biedermann, H. Gao, W. Zong, G. Andler, and E. Ustiniano, "Laser-induced recombination of D+," Nucl. Instrum. Methods: Phys. Res. B 117, 31-37 (1996).
[CrossRef]

Grieser, M.

S. Pastuszka, U. Schramm, M. Grieser, C. Broude, R. Grimm, D. Habs, J. Kenntner, H. J. Miesner, T. Schussler, D. Schwalm and A. Wolf, "Electron cooling and recombination experiments with an adiabatically expanded electron beam, " Nucl. Instrum. Methods Phys. Res. A 369, 11-22 (1996).
[CrossRef]

U. Schramm, J. Berger, M. Grieser, D. Habs, E. Jaeschke, G. Kilgus, D. Schwalm, A. Wolf, R. Neumann, and R. Schuch, "Observation of laser-induced recombination in merged electron and proton-beams," Phys. Rev. Lett. 67, 22-25 (1991).
[CrossRef] [PubMed]

Grimm, R.

S. Pastuszka, U. Schramm, M. Grieser, C. Broude, R. Grimm, D. Habs, J. Kenntner, H. J. Miesner, T. Schussler, D. Schwalm and A. Wolf, "Electron cooling and recombination experiments with an adiabatically expanded electron beam, " Nucl. Instrum. Methods Phys. Res. A 369, 11-22 (1996).
[CrossRef]

Habs, D.

S. Pastuszka, U. Schramm, M. Grieser, C. Broude, R. Grimm, D. Habs, J. Kenntner, H. J. Miesner, T. Schussler, D. Schwalm and A. Wolf, "Electron cooling and recombination experiments with an adiabatically expanded electron beam, " Nucl. Instrum. Methods Phys. Res. A 369, 11-22 (1996).
[CrossRef]

U. Schramm, T. Schussler, D. Habs, D. Schwalm, and A. Wolf, "Laser-induced recombination studies with the adiabatically expanded electron beam of the Heidelberg TSR," Hyperfine Interact. 99,309-316 (1996).
[CrossRef]

U. Schramm, J. Berger, M. Grieser, D. Habs, E. Jaeschke, G. Kilgus, D. Schwalm, A. Wolf, R. Neumann, and R. Schuch, "Observation of laser-induced recombination in merged electron and proton-beams," Phys. Rev. Lett. 67, 22-25 (1991).
[CrossRef] [PubMed]

Hahn, Y.

Y. Hahn, "Electron -ion recombination process - an overview," Rep. Prog. Phys. 60, 691-759 (1997).
[CrossRef]

Hu, S. X.

S. X. Hu and L. A. Collins, "Phase control of the inverse above-threshold-ionization processes with few-cycle pulses," Phys. Rev A 70, 013407 (2004).
[CrossRef]

Jaeschke, E.

U. Schramm, J. Berger, M. Grieser, D. Habs, E. Jaeschke, G. Kilgus, D. Schwalm, A. Wolf, R. Neumann, and R. Schuch, "Observation of laser-induced recombination in merged electron and proton-beams," Phys. Rev. Lett. 67, 22-25 (1991).
[CrossRef] [PubMed]

Jain, M.

M. Jain and N. Tzoar, "Compton scattering in the presence of coherent electromagnetic radiation," Phys. Rev. A 18, 538-545 (1978).
[CrossRef]

Jaron, A.

F. Ehlotzky, A. Jaron, and J. Z. Kaminsky, "Electron-atom collisions in a laser field," Phys. Rep. Rev. Section of Phys. Lett. 297, 64-153 (1998)

Jung, M.

S. Borneis, F. Bosch, T. Engel, M. Jung, I. Klaft, O. Klepper, T. Kuhl, D. Marx, R. Moshammer, R. Neumann, S. Schroder, P. Seelig, and L. Volker, "Laser-stimulated two-step recombination of highly charged ions and electrons in a storage ring," Phys. Rev. Lett. 72, 207-209 (1994).
[CrossRef] [PubMed]

Kaminski, J. Z.

J. Z. Kaminski and F. Ehlotzky, "Time-frequency analysis of x-ray generation by recombination in short laser pulses," Phys. Rev. A 71, 043402 (2005).
[CrossRef]

Kaminsky, J. Z.

F. Ehlotzky, A. Jaron, and J. Z. Kaminsky, "Electron-atom collisions in a laser field," Phys. Rep. Rev. Section of Phys. Lett. 297, 64-153 (1998)

Kenntner, J.

S. Pastuszka, U. Schramm, M. Grieser, C. Broude, R. Grimm, D. Habs, J. Kenntner, H. J. Miesner, T. Schussler, D. Schwalm and A. Wolf, "Electron cooling and recombination experiments with an adiabatically expanded electron beam, " Nucl. Instrum. Methods Phys. Res. A 369, 11-22 (1996).
[CrossRef]

Kilgus, G.

U. Schramm, J. Berger, M. Grieser, D. Habs, E. Jaeschke, G. Kilgus, D. Schwalm, A. Wolf, R. Neumann, and R. Schuch, "Observation of laser-induced recombination in merged electron and proton-beams," Phys. Rev. Lett. 67, 22-25 (1991).
[CrossRef] [PubMed]

Klaft, I.

S. Borneis, F. Bosch, T. Engel, M. Jung, I. Klaft, O. Klepper, T. Kuhl, D. Marx, R. Moshammer, R. Neumann, S. Schroder, P. Seelig, and L. Volker, "Laser-stimulated two-step recombination of highly charged ions and electrons in a storage ring," Phys. Rev. Lett. 72, 207-209 (1994).
[CrossRef] [PubMed]

Klepper, O.

S. Borneis, F. Bosch, T. Engel, M. Jung, I. Klaft, O. Klepper, T. Kuhl, D. Marx, R. Moshammer, R. Neumann, S. Schroder, P. Seelig, and L. Volker, "Laser-stimulated two-step recombination of highly charged ions and electrons in a storage ring," Phys. Rev. Lett. 72, 207-209 (1994).
[CrossRef] [PubMed]

Kroll, N. M.

N. M. Kroll and K. M. Watson, "Charged-particle scattering in the presence of a strong electromagnetic wave," Phys. Rev. A 8, 804-809 (1973).
[CrossRef]

Kucherovsky, Z.

F. B. Yousif, P. Vanderdonk, Z. Kucherovsky, J. Reis, E. Brannen, J. B. A. Mitchell, and T. J. Morgan, "Experimental-observation of laser-stimulated radiative recombination," Phys. Rev. Lett. 67, 26-29 (1991).
[CrossRef] [PubMed]

Kuhl, T.

S. Borneis, F. Bosch, T. Engel, M. Jung, I. Klaft, O. Klepper, T. Kuhl, D. Marx, R. Moshammer, R. Neumann, S. Schroder, P. Seelig, and L. Volker, "Laser-stimulated two-step recombination of highly charged ions and electrons in a storage ring," Phys. Rev. Lett. 72, 207-209 (1994).
[CrossRef] [PubMed]

Leone, C.

S. Bivona, R. Burlon, G. Ferrante, and C. Leone, "Radiative recombination in a strong laser field. Low frequency approximation," J. Opt. Soc. Am. B 22, 2076-2082 (2005).
[CrossRef]

S. Bivona, R. Burlon, G. Ferrante, and C. Leone, "Control of radiative recombination by a strong laser field," Appl. Phys. B 78, 809-812 (2004).
[CrossRef]

S. Bivona, R. Burlon, G. Ferrante, and C. Leone, "Control of multiphoton radiative recombination through the action of two-frequency fields," Laser Phys. Lett. 1, 118-123 (2004).
[CrossRef]

S. Bivona, R. Burlon, G. Ferrante, and C. Leone, "Influence of a plasma medium on laser assisted radiative recombination," Laser Phys. Lett. 1, 86-92 (2004).
[CrossRef]

S. Bivona, R. Burlon, G. Ferrante, and C. Leone, "Strong field effects of multiphoton radiative recombination," Laser Phys. 13, 1077-1082 (2003).

C. Leone, S. Bivona, R. Burlon, and G. Ferrante, "Strong-field and plasma aspects of multiphoton radiative recombination," Phys. Rev. A 66, 051403 (2002).
[CrossRef]

C. Leone, S. Bivona, R. Burlon, and G. Ferrante, "Two-frequency multiphoton ionization of hydrogen atoms," Phys. Rev. A 38,5642-5651 (1988).
[CrossRef] [PubMed]

Marx, D.

S. Borneis, F. Bosch, T. Engel, M. Jung, I. Klaft, O. Klepper, T. Kuhl, D. Marx, R. Moshammer, R. Neumann, S. Schroder, P. Seelig, and L. Volker, "Laser-stimulated two-step recombination of highly charged ions and electrons in a storage ring," Phys. Rev. Lett. 72, 207-209 (1994).
[CrossRef] [PubMed]

Miesner, H. J.

S. Pastuszka, U. Schramm, M. Grieser, C. Broude, R. Grimm, D. Habs, J. Kenntner, H. J. Miesner, T. Schussler, D. Schwalm and A. Wolf, "Electron cooling and recombination experiments with an adiabatically expanded electron beam, " Nucl. Instrum. Methods Phys. Res. A 369, 11-22 (1996).
[CrossRef]

Milosevic, D. B.

D. B. Milosevic and F. Ehlotzky, "Scattering and reaction processes in powerful laser fields," Adv. At. Mol., Opt. Phys. 49, 373-532 (2003).
[CrossRef]

D. B. Milosevic and F. Ehlotzky, "Rescattering effects in soft-x-ray generation by laser-assisted electron-ion recombination," Phys. Rev. A 65, 042504 (2002).
[CrossRef]

Mitchell, J. B. A.

M. L. Rogelstad, F. B. Yousif, T. J. Morgan, and J. B. A. Mitchell, "Stimulated radiative recombination of H+ and He+," J. Phys. B 30, 3913-3931 (1997).
[CrossRef]

F. B. Yousif, P. Vanderdonk, Z. Kucherovsky, J. Reis, E. Brannen, J. B. A. Mitchell, and T. J. Morgan, "Experimental-observation of laser-stimulated radiative recombination," Phys. Rev. Lett. 67, 26-29 (1991).
[CrossRef] [PubMed]

Morgan, T. J.

M. L. Rogelstad, F. B. Yousif, T. J. Morgan, and J. B. A. Mitchell, "Stimulated radiative recombination of H+ and He+," J. Phys. B 30, 3913-3931 (1997).
[CrossRef]

F. B. Yousif, P. Vanderdonk, Z. Kucherovsky, J. Reis, E. Brannen, J. B. A. Mitchell, and T. J. Morgan, "Experimental-observation of laser-stimulated radiative recombination," Phys. Rev. Lett. 67, 26-29 (1991).
[CrossRef] [PubMed]

Moshammer, R.

S. Borneis, F. Bosch, T. Engel, M. Jung, I. Klaft, O. Klepper, T. Kuhl, D. Marx, R. Moshammer, R. Neumann, S. Schroder, P. Seelig, and L. Volker, "Laser-stimulated two-step recombination of highly charged ions and electrons in a storage ring," Phys. Rev. Lett. 72, 207-209 (1994).
[CrossRef] [PubMed]

Neumann, R.

S. Borneis, F. Bosch, T. Engel, M. Jung, I. Klaft, O. Klepper, T. Kuhl, D. Marx, R. Moshammer, R. Neumann, S. Schroder, P. Seelig, and L. Volker, "Laser-stimulated two-step recombination of highly charged ions and electrons in a storage ring," Phys. Rev. Lett. 72, 207-209 (1994).
[CrossRef] [PubMed]

U. Schramm, J. Berger, M. Grieser, D. Habs, E. Jaeschke, G. Kilgus, D. Schwalm, A. Wolf, R. Neumann, and R. Schuch, "Observation of laser-induced recombination in merged electron and proton-beams," Phys. Rev. Lett. 67, 22-25 (1991).
[CrossRef] [PubMed]

R. Neumann, H. Poth, A. Winnacker, and A. Wolf, "Laser-enhanced electron-ion capture and antihydrogen formation," Z. Physik. A 313, 253-262 (1983).
[CrossRef]

Ostrovsky, V. N.

M. Yu Kuchiev and V. N. Ostrovsky, "Multiphoton radiative recombination of electron assisted by a laser field," Phys. Rev. A 61, 033414 (2000).
[CrossRef]

Pastuszka, S.

S. Pastuszka, U. Schramm, M. Grieser, C. Broude, R. Grimm, D. Habs, J. Kenntner, H. J. Miesner, T. Schussler, D. Schwalm and A. Wolf, "Electron cooling and recombination experiments with an adiabatically expanded electron beam, " Nucl. Instrum. Methods Phys. Res. A 369, 11-22 (1996).
[CrossRef]

Poth, H.

R. Neumann, H. Poth, A. Winnacker, and A. Wolf, "Laser-enhanced electron-ion capture and antihydrogen formation," Z. Physik. A 313, 253-262 (1983).
[CrossRef]

Reis, J.

F. B. Yousif, P. Vanderdonk, Z. Kucherovsky, J. Reis, E. Brannen, J. B. A. Mitchell, and T. J. Morgan, "Experimental-observation of laser-stimulated radiative recombination," Phys. Rev. Lett. 67, 26-29 (1991).
[CrossRef] [PubMed]

Rogelstad, M. L.

M. L. Rogelstad, F. B. Yousif, T. J. Morgan, and J. B. A. Mitchell, "Stimulated radiative recombination of H+ and He+," J. Phys. B 30, 3913-3931 (1997).
[CrossRef]

Schramm, U.

S. Pastuszka, U. Schramm, M. Grieser, C. Broude, R. Grimm, D. Habs, J. Kenntner, H. J. Miesner, T. Schussler, D. Schwalm and A. Wolf, "Electron cooling and recombination experiments with an adiabatically expanded electron beam, " Nucl. Instrum. Methods Phys. Res. A 369, 11-22 (1996).
[CrossRef]

U. Schramm, T. Schussler, D. Habs, D. Schwalm, and A. Wolf, "Laser-induced recombination studies with the adiabatically expanded electron beam of the Heidelberg TSR," Hyperfine Interact. 99,309-316 (1996).
[CrossRef]

U. Schramm, J. Berger, M. Grieser, D. Habs, E. Jaeschke, G. Kilgus, D. Schwalm, A. Wolf, R. Neumann, and R. Schuch, "Observation of laser-induced recombination in merged electron and proton-beams," Phys. Rev. Lett. 67, 22-25 (1991).
[CrossRef] [PubMed]

Schroder, S.

S. Borneis, F. Bosch, T. Engel, M. Jung, I. Klaft, O. Klepper, T. Kuhl, D. Marx, R. Moshammer, R. Neumann, S. Schroder, P. Seelig, and L. Volker, "Laser-stimulated two-step recombination of highly charged ions and electrons in a storage ring," Phys. Rev. Lett. 72, 207-209 (1994).
[CrossRef] [PubMed]

Schuch, R.

U. Schramm, J. Berger, M. Grieser, D. Habs, E. Jaeschke, G. Kilgus, D. Schwalm, A. Wolf, R. Neumann, and R. Schuch, "Observation of laser-induced recombination in merged electron and proton-beams," Phys. Rev. Lett. 67, 22-25 (1991).
[CrossRef] [PubMed]

Schuch, S. R.

S. Asp, S. R. Schuch, D. R. DeWitt, C. Biedermann, H. Gao, W. Zong, G. Andler, and E. Ustiniano, "Laser-induced recombination of D+," Nucl. Instrum. Methods: Phys. Res. B 117, 31-37 (1996).
[CrossRef]

Schussler, T.

U. Schramm, T. Schussler, D. Habs, D. Schwalm, and A. Wolf, "Laser-induced recombination studies with the adiabatically expanded electron beam of the Heidelberg TSR," Hyperfine Interact. 99,309-316 (1996).
[CrossRef]

S. Pastuszka, U. Schramm, M. Grieser, C. Broude, R. Grimm, D. Habs, J. Kenntner, H. J. Miesner, T. Schussler, D. Schwalm and A. Wolf, "Electron cooling and recombination experiments with an adiabatically expanded electron beam, " Nucl. Instrum. Methods Phys. Res. A 369, 11-22 (1996).
[CrossRef]

Schwalm, D.

S. Pastuszka, U. Schramm, M. Grieser, C. Broude, R. Grimm, D. Habs, J. Kenntner, H. J. Miesner, T. Schussler, D. Schwalm and A. Wolf, "Electron cooling and recombination experiments with an adiabatically expanded electron beam, " Nucl. Instrum. Methods Phys. Res. A 369, 11-22 (1996).
[CrossRef]

U. Schramm, T. Schussler, D. Habs, D. Schwalm, and A. Wolf, "Laser-induced recombination studies with the adiabatically expanded electron beam of the Heidelberg TSR," Hyperfine Interact. 99,309-316 (1996).
[CrossRef]

U. Schramm, J. Berger, M. Grieser, D. Habs, E. Jaeschke, G. Kilgus, D. Schwalm, A. Wolf, R. Neumann, and R. Schuch, "Observation of laser-induced recombination in merged electron and proton-beams," Phys. Rev. Lett. 67, 22-25 (1991).
[CrossRef] [PubMed]

Seelig, P.

S. Borneis, F. Bosch, T. Engel, M. Jung, I. Klaft, O. Klepper, T. Kuhl, D. Marx, R. Moshammer, R. Neumann, S. Schroder, P. Seelig, and L. Volker, "Laser-stimulated two-step recombination of highly charged ions and electrons in a storage ring," Phys. Rev. Lett. 72, 207-209 (1994).
[CrossRef] [PubMed]

Tzoar, N.

M. Jain and N. Tzoar, "Compton scattering in the presence of coherent electromagnetic radiation," Phys. Rev. A 18, 538-545 (1978).
[CrossRef]

Ustiniano, E.

S. Asp, S. R. Schuch, D. R. DeWitt, C. Biedermann, H. Gao, W. Zong, G. Andler, and E. Ustiniano, "Laser-induced recombination of D+," Nucl. Instrum. Methods: Phys. Res. B 117, 31-37 (1996).
[CrossRef]

Vanderdonk, P.

F. B. Yousif, P. Vanderdonk, Z. Kucherovsky, J. Reis, E. Brannen, J. B. A. Mitchell, and T. J. Morgan, "Experimental-observation of laser-stimulated radiative recombination," Phys. Rev. Lett. 67, 26-29 (1991).
[CrossRef] [PubMed]

Volker, L.

S. Borneis, F. Bosch, T. Engel, M. Jung, I. Klaft, O. Klepper, T. Kuhl, D. Marx, R. Moshammer, R. Neumann, S. Schroder, P. Seelig, and L. Volker, "Laser-stimulated two-step recombination of highly charged ions and electrons in a storage ring," Phys. Rev. Lett. 72, 207-209 (1994).
[CrossRef] [PubMed]

Watson, K. M.

N. M. Kroll and K. M. Watson, "Charged-particle scattering in the presence of a strong electromagnetic wave," Phys. Rev. A 8, 804-809 (1973).
[CrossRef]

Winnacker, A.

R. Neumann, H. Poth, A. Winnacker, and A. Wolf, "Laser-enhanced electron-ion capture and antihydrogen formation," Z. Physik. A 313, 253-262 (1983).
[CrossRef]

Wolf, A.

S. Pastuszka, U. Schramm, M. Grieser, C. Broude, R. Grimm, D. Habs, J. Kenntner, H. J. Miesner, T. Schussler, D. Schwalm and A. Wolf, "Electron cooling and recombination experiments with an adiabatically expanded electron beam, " Nucl. Instrum. Methods Phys. Res. A 369, 11-22 (1996).
[CrossRef]

U. Schramm, T. Schussler, D. Habs, D. Schwalm, and A. Wolf, "Laser-induced recombination studies with the adiabatically expanded electron beam of the Heidelberg TSR," Hyperfine Interact. 99,309-316 (1996).
[CrossRef]

U. Schramm, J. Berger, M. Grieser, D. Habs, E. Jaeschke, G. Kilgus, D. Schwalm, A. Wolf, R. Neumann, and R. Schuch, "Observation of laser-induced recombination in merged electron and proton-beams," Phys. Rev. Lett. 67, 22-25 (1991).
[CrossRef] [PubMed]

R. Neumann, H. Poth, A. Winnacker, and A. Wolf, "Laser-enhanced electron-ion capture and antihydrogen formation," Z. Physik. A 313, 253-262 (1983).
[CrossRef]

Yousif, F. B.

M. L. Rogelstad, F. B. Yousif, T. J. Morgan, and J. B. A. Mitchell, "Stimulated radiative recombination of H+ and He+," J. Phys. B 30, 3913-3931 (1997).
[CrossRef]

F. B. Yousif, P. Vanderdonk, Z. Kucherovsky, J. Reis, E. Brannen, J. B. A. Mitchell, and T. J. Morgan, "Experimental-observation of laser-stimulated radiative recombination," Phys. Rev. Lett. 67, 26-29 (1991).
[CrossRef] [PubMed]

Yu Kuchiev, M.

M. Yu Kuchiev and V. N. Ostrovsky, "Multiphoton radiative recombination of electron assisted by a laser field," Phys. Rev. A 61, 033414 (2000).
[CrossRef]

Zong, W.

S. Asp, S. R. Schuch, D. R. DeWitt, C. Biedermann, H. Gao, W. Zong, G. Andler, and E. Ustiniano, "Laser-induced recombination of D+," Nucl. Instrum. Methods: Phys. Res. B 117, 31-37 (1996).
[CrossRef]

Appl. Phys. B

S. Bivona, R. Burlon, G. Ferrante, and C. Leone, "Control of radiative recombination by a strong laser field," Appl. Phys. B 78, 809-812 (2004).
[CrossRef]

Hyperfine Interact.

U. Schramm, T. Schussler, D. Habs, D. Schwalm, and A. Wolf, "Laser-induced recombination studies with the adiabatically expanded electron beam of the Heidelberg TSR," Hyperfine Interact. 99,309-316 (1996).
[CrossRef]

J. Opt. Soc. Am. B

J. Phys. B

M. L. Rogelstad, F. B. Yousif, T. J. Morgan, and J. B. A. Mitchell, "Stimulated radiative recombination of H+ and He+," J. Phys. B 30, 3913-3931 (1997).
[CrossRef]

Laser Phys.

S. Bivona, R. Burlon, G. Ferrante, and C. Leone, "Strong field effects of multiphoton radiative recombination," Laser Phys. 13, 1077-1082 (2003).

Laser Phys. Lett.

S. Bivona, R. Burlon, G. Ferrante, and C. Leone, "Influence of a plasma medium on laser assisted radiative recombination," Laser Phys. Lett. 1, 86-92 (2004).
[CrossRef]

S. Bivona, R. Burlon, G. Ferrante, and C. Leone, "Control of multiphoton radiative recombination through the action of two-frequency fields," Laser Phys. Lett. 1, 118-123 (2004).
[CrossRef]

Nucl. Instrum. Methods Phys. Res. A

S. Pastuszka, U. Schramm, M. Grieser, C. Broude, R. Grimm, D. Habs, J. Kenntner, H. J. Miesner, T. Schussler, D. Schwalm and A. Wolf, "Electron cooling and recombination experiments with an adiabatically expanded electron beam, " Nucl. Instrum. Methods Phys. Res. A 369, 11-22 (1996).
[CrossRef]

Nucl. Instrum. Methods: Phys. Res. B

S. Asp, S. R. Schuch, D. R. DeWitt, C. Biedermann, H. Gao, W. Zong, G. Andler, and E. Ustiniano, "Laser-induced recombination of D+," Nucl. Instrum. Methods: Phys. Res. B 117, 31-37 (1996).
[CrossRef]

Opt. Phys.

D. B. Milosevic and F. Ehlotzky, "Scattering and reaction processes in powerful laser fields," Adv. At. Mol., Opt. Phys. 49, 373-532 (2003).
[CrossRef]

Phys. Rep. Rev. Section of Phys. Lett.

F. Ehlotzky, A. Jaron, and J. Z. Kaminsky, "Electron-atom collisions in a laser field," Phys. Rep. Rev. Section of Phys. Lett. 297, 64-153 (1998)

Phys. Rev A

S. X. Hu and L. A. Collins, "Phase control of the inverse above-threshold-ionization processes with few-cycle pulses," Phys. Rev A 70, 013407 (2004).
[CrossRef]

Phys. Rev. A

J. Z. Kaminski and F. Ehlotzky, "Time-frequency analysis of x-ray generation by recombination in short laser pulses," Phys. Rev. A 71, 043402 (2005).
[CrossRef]

M. Jain and N. Tzoar, "Compton scattering in the presence of coherent electromagnetic radiation," Phys. Rev. A 18, 538-545 (1978).
[CrossRef]

C. Leone, S. Bivona, R. Burlon, and G. Ferrante, "Two-frequency multiphoton ionization of hydrogen atoms," Phys. Rev. A 38,5642-5651 (1988).
[CrossRef] [PubMed]

M. Yu Kuchiev and V. N. Ostrovsky, "Multiphoton radiative recombination of electron assisted by a laser field," Phys. Rev. A 61, 033414 (2000).
[CrossRef]

D. B. Milosevic and F. Ehlotzky, "Rescattering effects in soft-x-ray generation by laser-assisted electron-ion recombination," Phys. Rev. A 65, 042504 (2002).
[CrossRef]

C. Leone, S. Bivona, R. Burlon, and G. Ferrante, "Strong-field and plasma aspects of multiphoton radiative recombination," Phys. Rev. A 66, 051403 (2002).
[CrossRef]

N. M. Kroll and K. M. Watson, "Charged-particle scattering in the presence of a strong electromagnetic wave," Phys. Rev. A 8, 804-809 (1973).
[CrossRef]

Phys. Rev. Lett.

U. Schramm, J. Berger, M. Grieser, D. Habs, E. Jaeschke, G. Kilgus, D. Schwalm, A. Wolf, R. Neumann, and R. Schuch, "Observation of laser-induced recombination in merged electron and proton-beams," Phys. Rev. Lett. 67, 22-25 (1991).
[CrossRef] [PubMed]

F. B. Yousif, P. Vanderdonk, Z. Kucherovsky, J. Reis, E. Brannen, J. B. A. Mitchell, and T. J. Morgan, "Experimental-observation of laser-stimulated radiative recombination," Phys. Rev. Lett. 67, 26-29 (1991).
[CrossRef] [PubMed]

S. Borneis, F. Bosch, T. Engel, M. Jung, I. Klaft, O. Klepper, T. Kuhl, D. Marx, R. Moshammer, R. Neumann, S. Schroder, P. Seelig, and L. Volker, "Laser-stimulated two-step recombination of highly charged ions and electrons in a storage ring," Phys. Rev. Lett. 72, 207-209 (1994).
[CrossRef] [PubMed]

Rep. Prog. Phys.

Y. Hahn, "Electron -ion recombination process - an overview," Rep. Prog. Phys. 60, 691-759 (1997).
[CrossRef]

Z. Physik. A

R. Neumann, H. Poth, A. Winnacker, and A. Wolf, "Laser-enhanced electron-ion capture and antihydrogen formation," Z. Physik. A 313, 253-262 (1983).
[CrossRef]

Other

A. Maquet, R. Taieb, and V. Veniard, "Two-color infrared-UV atomic photoionization," in Fundamental of laser-matter interaction, K.N. Drabovich and N. I. Koroteev, eds., Proc. SPIE 2796, 31-38 (1995).
[CrossRef]

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Figures (3)

Fig. 1.
Fig. 1.

Double differential probability (DDP) at the end of the laser pulse as a function of the X-ray energy ωx for three different values of the carrier envelope relative phase (φ= -90°, 0°, 90°), at the energy of the incoming electron εq =90 eV. Red line: DDP calculated in the framework of the quantum theory, Eq. (6). Blue line: the corresponding quantity obtained by the semiclassical model, Eq. (13). Left panel: nc =2. Right panel: nc =3

Fig. 2.
Fig. 2.

The evolution of the double differential probability when the laser pulse is on for the photon energies corresponding to the maxima of the curve of Fig. 1 corresponding to nc =2 and ϕ=-90°. The red curve corresponds to ωX =437.5 eV, the blue curve to ωX =101.4 eV and the green curve to ωX =62.4 eV. In the insert we report the time dependence of the X- ray emitted photon ωX (t), Eq. (10), evaluated classically.

Fig. 3
Fig. 3

The single differential probability at the end of the pulse SDP (τ) as a function of the incoming electron energy when the laser pulse is off for nc =2 and 6 at three different values of φ (blue curve φ=-90°, red curve φ=0°, green curve φ=90°)

Equations (16)

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

E(t)={ ε ^ L E 0 sin 2 ( πt τ )cos(ωt+ϕ) t[0,τ] 0 otherwise
T fi ( t ) = i 0 t d t ´ Ψ 0 ( r , t ´ ) E x ( t ) r Ψ q + ( r , t ´ )
E x ( t ) = 2 π ω x V ε ̂ x exp [ i ( k x r ω x t ) ]
Ψ 0 ( r , t ) = u 0 ( r ) exp ( i I 0 t )
Ψ q + ( r , t ) = χ q + ( r , t ) u q + ( r )
χ q + ( r , t ) = exp { i [ q + k L ( t ) ] r i 2 0 t d t ´ [ q + k L ( t ´ ) ] 2 }
u q + ( r ) = exp ( 1 2 πv ) ( 2 π ) 3 2 Γ ( 1 v ) 1 F 1 [ i v , 1 , i ( q r qr ) ] .
DP ( t ) = d 2 P ( t ) d Ω x d ω x = ω x 3 ( 2 π ) 2 c 3 × 0 t dt ´ exp { i [ ( ω x + I 0 ) t ´ ] i 2 0 t ´ dt " [ q + k L ( t " ) ] 2 } M q ( t ´ ) 2
M q ( t ) = u 0 ( r ) ε ̂ x r exp ( i k x r ) exp { i [ q + k L ( t ) ] r } u q + ( r )
SP ( t ) = dP ( t ) d Ω x = 0 d ω x DP ( t )
q ( t ) = q + k L ( t )
ω x ( t ) = 1 2 q 2 ( t ) + I 0
dP = P dt τ
P τ ω x 3 M q ( t ) 2 2 π c 3 δ [ ω x ω x ( t ) ] ,
CDP ( t ) = 0 t d t ´ P τ = l ω x 3 2 π c 3 M ( t 1 ) 2 E ( t 1 ) [ q + k L ( t ) ]
CSP ( t ) = 0 t d t ´ ω x 3 ( t ´ ) 2 π c 3 M q ( t ´ )

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