## Magnetic-field effect in atomic ionization by intense laser fields

Optics Express, Vol. 5, Issue 7, pp. 144-148 (1999)

http://dx.doi.org/10.1364/OE.5.000144

Acrobat PDF (202 KB)

### Abstract

Numerical integrations of the two-dimensional Schrödinger equation that describes a flat atom interacting with an intense and linearly polarized laser field are presented. Simulations show the influence of the drift that is due to the magnetic field in situations in which a strong dichotomy of the wave function would otherwise have been expected.

© Optical Society of America

3. Q. Su, A. Sanpera, and L. Roso-Franco, “Atomic stabilization in the presence of intense laser pulses,” Int. J. Mod. Phys. B **8**, 1655 (1994). [CrossRef]

5. M. Protopapas, C. H. Keitel, and P. L. Knight, “Atomic physics with super-high intensity lasers,” Rep. Prog. Phys. **60**, 389–486 (1997), and references therein. [CrossRef]

6. A. Patel, N. J. Kylstra, and P. L. Knight, “Ellipticity and pulse shape dependence of localised wavepackets,” Opt. Express **4**, 496–537 (1999). [CrossRef] [PubMed]

*e*=

*m*=1

*au*,

*c*=137

*au*) are used throughout this paper. Because of computer limitations we work with a two-dimensional model, considering a flat atom in the

*xy*plane with a soft-core Coulomb potential:

*a*is a parameter that avoids singularity at the origin and was chosen to be

*a*=1

*au*in our calculations. The spatial grid where the Schrödinger equation is solved has 1300×3000 equally separated points, with a step size of Δ

*x*=Δ

*y*=0.2

*au*. In this grid and for the chosen value of

*a*, the ground-state energy of the model is

*E*

_{B}=-0.43

*au*, as determined by the standard imaginary-time propagation method.

*xy*plane we assume that the electric field is linearly polarized along the

*y*axis and that the pulse propagates along the

*x*axis. Then the magnetic field is parallel to the

*z*axis. Therefore the classic Lorentz force will drive the electron (initially at rest) inside the

*z*=0 plane. The electric field is

*f*(

*x*,

*t*) is the laser turn-on, which is chosen to be linear and to last four cycles of the field. The vector potential is defined by

5. M. Protopapas, C. H. Keitel, and P. L. Knight, “Atomic physics with super-high intensity lasers,” Rep. Prog. Phys. **60**, 389–486 (1997), and references therein. [CrossRef]

*t*+Δ

*t*is calculated from the wave function in the previous time step

*t*[10

10. A. D. Bandrauk and H. Shen, “Exponential split operator methods for solving coupled time-dependent Schrödinger equations,” J. Chem. Phys. **99**, 1185–1193 (1993). [CrossRef]

*A*

_{y}(

*x*,

*t*)(

*∂*/

*∂y*) mixes momentum and space coordinates.

*E*

_{y}(

*x*,

*t*)≃

*E*

_{y}(

*t*)=

*E*

_{0}

*f*(

*t*) sin(

*ω*

_{L}

*t*)] with the same laser parameters. Figure 1 corresponds to a laser field of amplitude

*E*

_{0}=15

*au*(intensity, 7.9×10

^{18}

*W*=

*cm*

^{2}) and frequency

*ω*

_{L}=1

*au*(photon energy, 27

*eV*). This is a set of parameters for which a nonrelativistic study is reasonable but the first order correction

*υ*/

*c*is not extremely small. We selected these parameters because they were also selected for a recent paper in this journal [6

6. A. Patel, N. J. Kylstra, and P. L. Knight, “Ellipticity and pulse shape dependence of localised wavepackets,” Opt. Express **4**, 496–537 (1999). [CrossRef] [PubMed]

*nm*(or 861

*au*), which is still much bigger than the atomic size. But the dipole approximation is not valid because of the influence of the magnetic field. Figure 1(b) shows the computation for the same laser parameters with the space dependence of the fields retained. The ionized population that reaches the boundaries of the integration surface in both cases is negligible (less than 10

^{-6}anytime).

*ω*

_{L}; this is the origin of the drift shown in Fig. 1(b). Obviously, in the case of the numerical simulation presented here, the laser turn-on and the atomic potential reduce the magnitude of the drift.

## Acknowledgments

## References

1. | J. H. Eberly, R. Grobe, C. K. Law, and Q. Su, “Numerical experiments in strong and super-strong fields,” in |

2. | K. C. Kulander, K. J. Schafer, and J. L. Krause, “Time-dependent studies of multiphoton processes,” in |

3. | Q. Su, A. Sanpera, and L. Roso-Franco, “Atomic stabilization in the presence of intense laser pulses,” Int. J. Mod. Phys. B |

4. | M. Gavrila, “Atomic structure and decay in high frequency fields,” in |

5. | M. Protopapas, C. H. Keitel, and P. L. Knight, “Atomic physics with super-high intensity lasers,” Rep. Prog. Phys. |

6. | A. Patel, N. J. Kylstra, and P. L. Knight, “Ellipticity and pulse shape dependence of localised wavepackets,” Opt. Express |

7. | M. Protopapas, C. H. Keitel, and P. L. Knight, “Relativistic mass shift effects in adiabatic intense laser field stabilization of atoms,” J. Phys. B |

8. | C. H. Keitel and P. L. Knight, “Monte Carlo classical simulations of ionization and harmonic generation in the relativistic domain,” Phys. Rev. A |

9. | P. Moreno, “Harmonic generation by |

10. | A. D. Bandrauk and H. Shen, “Exponential split operator methods for solving coupled time-dependent Schrödinger equations,” J. Chem. Phys. |

**OCIS Codes**

(020.4180) Atomic and molecular physics : Multiphoton processes

(300.6410) Spectroscopy : Spectroscopy, multiphoton

**ToC Category:**

Research Papers

**History**

Original Manuscript: July 12, 1999

Published: September 27, 1999

**Citation**

J. Vazquez de Aldana and Luis Roso, "Magnetic-field effect in atomic ionization by intense laser fields.," Opt. Express **5**, 144-148 (1999)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-5-7-144

Sort: Journal | Reset

### References

- J. H. Eberly, R. Grobe, C. K. Law and Q. Su, "Numerical experiments in strong and super-strong fields," in Atoms in Intense Laser Fields, M. Gavrila, ed. (Academic, San Diego, Calif., 1992).
- K. C. Kulander, K. J. Schafer and J. L. Krause, "Time-dependent studies of multiphoton processes," in Atoms in Intense Laser Fields, M. Gavrila, ed. (Academic, San Diego, Calif., 1992).
- Q. Su, A. Sanpera and L. Roso-Franco, "Atomic stabilization in the presence of intense laser pulses," Int. J. Mod. Phys. B 8, 1655 (1994). [CrossRef]
- M. Gavrila, "Atomic structure and decay in high frequency fields," in Atoms in Intense Laser Fields, M. Gavrila, ed. (Academic, San Diego, Calif., 1992), and references therein.
- M. Protopapas, C. H. Keitel and P. L. Knight,"Atomic physics with super-high intensity lasers," Rep. Prog. Phys. 60, 389-486 (1997), and references therein. [CrossRef]
- A. Patel, N. J. Kylstra and P. L. Knight, "Ellipticity and pulse shape dependence of localised wavepackets," Opt. Express 4, 496-537 (1999), http://www.opticsexpress.org/oearchive/source/10164.htm [CrossRef] [PubMed]
- M. Protopapas, C. H. Keitel and P. L. Knight, "Relativistic mass shift effects in adiabatic intense laser field stabilization of atoms," J. Phys. B 29, L591-L598 (1996). [CrossRef]
- C. H. Keitel and P. L. Knight, "Monte Carlo classical simulations of ionization and harmonic generation in the relativistic domain," Phys. Rev. A 51, 1420-1430 (1995). [CrossRef] [PubMed]
- P. Moreno, "Harmonic generation by H and H + 2 in intense laser pulses," Ph. D. dissertation, (Universidad de Salamanca, Salamanca, Spain, 1997).
- A. D. Bandrauk and H. Shen, "Exponential split operator methods for solving coupled time-dependent Schr�dinger equations," J. Chem. Phys. 99, 1185-1193 (1993). [CrossRef]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

### Figures

Figure 1. |

OSA is a member of CrossRef.