Abstract

The response of a hydrogen atom to an intense nonresonant laser field is investigated by direct numerical solution of the time-dependent Schrodinger equation. This calculation is nonperturbative and does not involve the eigenstates of the field-free atom. An ionization rate for three-photon ionization is calculated and found to be in excellent agreement with previous values. The time-dependent electric dipole moment is calculated; its Fourier transform yields the spectrum of scattered light. Odd-order harmonic peaks through at least the 25th order are present in the spectrum.

© 1990 Optical Society of America

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References

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  1. J. Javanainen, Q. Su, and J. H. Eberly, Phys. Rev. A 38, 3430 (1988).
    [Crossref] [PubMed]
  2. K. C. Kulander, Phys. Rev. A 35, 445 (1987).
    [Crossref] [PubMed]
  3. K. C. Kulander, Phys. Rev. A 36, 2726 (1987).
    [Crossref] [PubMed]
  4. K. C. Kulander, Phys. Rev. A 38, 778 (1988).
    [Crossref] [PubMed]
  5. M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompré, G. Mainfray, and C. Manus, J. Phys. B 21, L31 (1988).
    [Crossref]
  6. K. C. Kulander and B. W. Shore, Phys. Rev. Lett. 62, 524 (1989).
    [Crossref] [PubMed]
  7. J. H. Eberly, Q. Su, and J. Javanainen, Phys. Rev. Lett. 62, 881 (1989).
    [Crossref] [PubMed]
  8. S. I. Chu and J. Cooper, Phys. Rev. A 32, 2769 (1985).
    [Crossref] [PubMed]
  9. J. A. Fleck, J. R. Morris, and M. D. Feit, Appl. Phys. 10, 129 (1976).
    [Crossref]
  10. M. R. Herman and J. A. Fleck, Phys. Rev. A 38, 6000 (1988).
    [Crossref]
  11. H. De Raedt, Comput. Phys. Rep. 7, 1 (1987).
    [Crossref]
  12. P. J. Davis and P. Rabinowitz, Methods of Numerical Integration (Academic, New York, 1975).

1989 (2)

K. C. Kulander and B. W. Shore, Phys. Rev. Lett. 62, 524 (1989).
[Crossref] [PubMed]

J. H. Eberly, Q. Su, and J. Javanainen, Phys. Rev. Lett. 62, 881 (1989).
[Crossref] [PubMed]

1988 (4)

J. Javanainen, Q. Su, and J. H. Eberly, Phys. Rev. A 38, 3430 (1988).
[Crossref] [PubMed]

K. C. Kulander, Phys. Rev. A 38, 778 (1988).
[Crossref] [PubMed]

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompré, G. Mainfray, and C. Manus, J. Phys. B 21, L31 (1988).
[Crossref]

M. R. Herman and J. A. Fleck, Phys. Rev. A 38, 6000 (1988).
[Crossref]

1987 (3)

H. De Raedt, Comput. Phys. Rep. 7, 1 (1987).
[Crossref]

K. C. Kulander, Phys. Rev. A 35, 445 (1987).
[Crossref] [PubMed]

K. C. Kulander, Phys. Rev. A 36, 2726 (1987).
[Crossref] [PubMed]

1985 (1)

S. I. Chu and J. Cooper, Phys. Rev. A 32, 2769 (1985).
[Crossref] [PubMed]

1976 (1)

J. A. Fleck, J. R. Morris, and M. D. Feit, Appl. Phys. 10, 129 (1976).
[Crossref]

Chu, S. I.

S. I. Chu and J. Cooper, Phys. Rev. A 32, 2769 (1985).
[Crossref] [PubMed]

Cooper, J.

S. I. Chu and J. Cooper, Phys. Rev. A 32, 2769 (1985).
[Crossref] [PubMed]

Davis, P. J.

P. J. Davis and P. Rabinowitz, Methods of Numerical Integration (Academic, New York, 1975).

De Raedt, H.

H. De Raedt, Comput. Phys. Rep. 7, 1 (1987).
[Crossref]

Eberly, J. H.

J. H. Eberly, Q. Su, and J. Javanainen, Phys. Rev. Lett. 62, 881 (1989).
[Crossref] [PubMed]

J. Javanainen, Q. Su, and J. H. Eberly, Phys. Rev. A 38, 3430 (1988).
[Crossref] [PubMed]

Feit, M. D.

J. A. Fleck, J. R. Morris, and M. D. Feit, Appl. Phys. 10, 129 (1976).
[Crossref]

Ferray, M.

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompré, G. Mainfray, and C. Manus, J. Phys. B 21, L31 (1988).
[Crossref]

Fleck, J. A.

M. R. Herman and J. A. Fleck, Phys. Rev. A 38, 6000 (1988).
[Crossref]

J. A. Fleck, J. R. Morris, and M. D. Feit, Appl. Phys. 10, 129 (1976).
[Crossref]

Herman, M. R.

M. R. Herman and J. A. Fleck, Phys. Rev. A 38, 6000 (1988).
[Crossref]

Javanainen, J.

J. H. Eberly, Q. Su, and J. Javanainen, Phys. Rev. Lett. 62, 881 (1989).
[Crossref] [PubMed]

J. Javanainen, Q. Su, and J. H. Eberly, Phys. Rev. A 38, 3430 (1988).
[Crossref] [PubMed]

Kulander, K. C.

K. C. Kulander and B. W. Shore, Phys. Rev. Lett. 62, 524 (1989).
[Crossref] [PubMed]

K. C. Kulander, Phys. Rev. A 38, 778 (1988).
[Crossref] [PubMed]

K. C. Kulander, Phys. Rev. A 35, 445 (1987).
[Crossref] [PubMed]

K. C. Kulander, Phys. Rev. A 36, 2726 (1987).
[Crossref] [PubMed]

L’Huillier, A.

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompré, G. Mainfray, and C. Manus, J. Phys. B 21, L31 (1988).
[Crossref]

Li, X. F.

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompré, G. Mainfray, and C. Manus, J. Phys. B 21, L31 (1988).
[Crossref]

Lompré, L. A.

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompré, G. Mainfray, and C. Manus, J. Phys. B 21, L31 (1988).
[Crossref]

Mainfray, G.

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompré, G. Mainfray, and C. Manus, J. Phys. B 21, L31 (1988).
[Crossref]

Manus, C.

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompré, G. Mainfray, and C. Manus, J. Phys. B 21, L31 (1988).
[Crossref]

Morris, J. R.

J. A. Fleck, J. R. Morris, and M. D. Feit, Appl. Phys. 10, 129 (1976).
[Crossref]

Rabinowitz, P.

P. J. Davis and P. Rabinowitz, Methods of Numerical Integration (Academic, New York, 1975).

Shore, B. W.

K. C. Kulander and B. W. Shore, Phys. Rev. Lett. 62, 524 (1989).
[Crossref] [PubMed]

Su, Q.

J. H. Eberly, Q. Su, and J. Javanainen, Phys. Rev. Lett. 62, 881 (1989).
[Crossref] [PubMed]

J. Javanainen, Q. Su, and J. H. Eberly, Phys. Rev. A 38, 3430 (1988).
[Crossref] [PubMed]

Appl. Phys. (1)

J. A. Fleck, J. R. Morris, and M. D. Feit, Appl. Phys. 10, 129 (1976).
[Crossref]

Comput. Phys. Rep. (1)

H. De Raedt, Comput. Phys. Rep. 7, 1 (1987).
[Crossref]

J. Phys. B (1)

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompré, G. Mainfray, and C. Manus, J. Phys. B 21, L31 (1988).
[Crossref]

Phys. Rev. A (6)

M. R. Herman and J. A. Fleck, Phys. Rev. A 38, 6000 (1988).
[Crossref]

J. Javanainen, Q. Su, and J. H. Eberly, Phys. Rev. A 38, 3430 (1988).
[Crossref] [PubMed]

K. C. Kulander, Phys. Rev. A 35, 445 (1987).
[Crossref] [PubMed]

K. C. Kulander, Phys. Rev. A 36, 2726 (1987).
[Crossref] [PubMed]

K. C. Kulander, Phys. Rev. A 38, 778 (1988).
[Crossref] [PubMed]

S. I. Chu and J. Cooper, Phys. Rev. A 32, 2769 (1985).
[Crossref] [PubMed]

Phys. Rev. Lett. (2)

K. C. Kulander and B. W. Shore, Phys. Rev. Lett. 62, 524 (1989).
[Crossref] [PubMed]

J. H. Eberly, Q. Su, and J. Javanainen, Phys. Rev. Lett. 62, 881 (1989).
[Crossref] [PubMed]

Other (1)

P. J. Davis and P. Rabinowitz, Methods of Numerical Integration (Academic, New York, 1975).

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Figures (3)

Fig. 1
Fig. 1

Population of the s state plotted versus time, in atomic units. The laser field reaches its maximum at about 314 time units, after which it is constant. The population varies in concert with the applied radiation, with peaks in the population occurring every half optical cycle as the electron distribution is driven through the origin.

Fig. 2
Fig. 2

Population P0 of the s state averaged over one optical cycle and plotted on a logarithmic scale. The dashed line indicates an exponential decay at the rate of 3.5 × 1014 sec−1.

Fig. 3
Fig. 3

Photon spectrum, obtained as the square of the Fourier transform of d(t) and plotted on a logarithmic scale. Harmonics of the 0.2 hartree incident radiation are present through the 23rd order at relative intensities greater than 10−8.

Equations (12)

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i Ψ ( r , t ) t = H Ψ ( r , t ) ,
H = 1 2 2 1 r z E ( t ) sin ω t .
Ψ ( r , t ) = U ( t , t 0 ) Ψ ( r , t 0 ) ,
U ( t , t 0 ) = exp ( i H ¯ δ ) ,
U ( t , t 0 ) exp ( i H atom δ / 2 ) exp ( H ¯ int δ ) exp ( i H atom δ / 2 ) .
Ψ ( r , t ) = l , m R l m ( r , t ) Y l m ( θ , ϕ ) ,
exp ( i H atom δ / 2 ) Ψ ( r , t ) = lm exp { i [ 1 2 r 2 d d r ( r 2 d d r ) + l ( l + 1 ) 2 r 2 1 r ] δ / 2 } R lm ( r , t ) Y lm ( θ , ϕ ) .
exp ( i H l δ / 2 ) 1 i H l δ / 4 1 + i H l δ / 4 .
l m | zE ( t ¯ ) sin ω t ¯ | lm = rE ( t ¯ ) sin ω t ¯ l m | cos θ | lm ,
S cos θ S = C ,
exp ( i H ¯ int δ ) = S S exp ( i H ¯ int δ ) S S = S exp [ i ( r E ( t ¯ ) sin ω t ¯ C ) δ ] S .
d ( t ) = Ψ ( r , t ) z Ψ ( r , t ) d r

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