Abstract

Coherent high-order harmonic generation by an isolated two-level system is studied. A perturbative theory for the adiabatic regime is presented; the theory describes the plateau structure found experimentally in noble gases. Numerical results, without the rotating-wave approximation, are used to check the analytical predictions.

© 1992 Optical Society of America

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References

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  1. For a recent collection of papers on the subject see, for example, K. Kulander, A. L’Huillier, eds., feature on the theory of high-order processes in atoms in intense laser fields, J. Opt. Soc. Am. B7, 401–688 (1990).
  2. J. H. Eberly, Q. Su, J. Javanainen, K. C. Kulander, B. W. Shore, L. Roso-Franco, J. Mod. Opt. 36, 829 (1989).
    [CrossRef]
  3. J. H. Eberly, J. Javanainen, K. Rza̧żewski, Phys. Rep. 204, 331 (1991)
    [CrossRef]
  4. B. Sundaram, P. W. Milonni, Phys. Rev. A 41, 6571RC (1990).
  5. Although the energy difference between both states is usually indicated by ω10in the two-level atom literature, we used the symbol ωT to avoid confusion with w10, the tenth component of the Fourier expansion of the population inversion.

1991

J. H. Eberly, J. Javanainen, K. Rza̧żewski, Phys. Rep. 204, 331 (1991)
[CrossRef]

1990

B. Sundaram, P. W. Milonni, Phys. Rev. A 41, 6571RC (1990).

1989

J. H. Eberly, Q. Su, J. Javanainen, K. C. Kulander, B. W. Shore, L. Roso-Franco, J. Mod. Opt. 36, 829 (1989).
[CrossRef]

Eberly, J. H.

J. H. Eberly, J. Javanainen, K. Rza̧żewski, Phys. Rep. 204, 331 (1991)
[CrossRef]

J. H. Eberly, Q. Su, J. Javanainen, K. C. Kulander, B. W. Shore, L. Roso-Franco, J. Mod. Opt. 36, 829 (1989).
[CrossRef]

Javanainen, J.

J. H. Eberly, J. Javanainen, K. Rza̧żewski, Phys. Rep. 204, 331 (1991)
[CrossRef]

J. H. Eberly, Q. Su, J. Javanainen, K. C. Kulander, B. W. Shore, L. Roso-Franco, J. Mod. Opt. 36, 829 (1989).
[CrossRef]

Kulander, K. C.

J. H. Eberly, Q. Su, J. Javanainen, K. C. Kulander, B. W. Shore, L. Roso-Franco, J. Mod. Opt. 36, 829 (1989).
[CrossRef]

Milonni, P. W.

B. Sundaram, P. W. Milonni, Phys. Rev. A 41, 6571RC (1990).

Roso-Franco, L.

J. H. Eberly, Q. Su, J. Javanainen, K. C. Kulander, B. W. Shore, L. Roso-Franco, J. Mod. Opt. 36, 829 (1989).
[CrossRef]

Rza¸zewski, K.

J. H. Eberly, J. Javanainen, K. Rza̧żewski, Phys. Rep. 204, 331 (1991)
[CrossRef]

Shore, B. W.

J. H. Eberly, Q. Su, J. Javanainen, K. C. Kulander, B. W. Shore, L. Roso-Franco, J. Mod. Opt. 36, 829 (1989).
[CrossRef]

Su, Q.

J. H. Eberly, Q. Su, J. Javanainen, K. C. Kulander, B. W. Shore, L. Roso-Franco, J. Mod. Opt. 36, 829 (1989).
[CrossRef]

Sundaram, B.

B. Sundaram, P. W. Milonni, Phys. Rev. A 41, 6571RC (1990).

J. Mod. Opt.

J. H. Eberly, Q. Su, J. Javanainen, K. C. Kulander, B. W. Shore, L. Roso-Franco, J. Mod. Opt. 36, 829 (1989).
[CrossRef]

Phys. Rep.

J. H. Eberly, J. Javanainen, K. Rza̧żewski, Phys. Rep. 204, 331 (1991)
[CrossRef]

Phys. Rev. A

B. Sundaram, P. W. Milonni, Phys. Rev. A 41, 6571RC (1990).

Other

Although the energy difference between both states is usually indicated by ω10in the two-level atom literature, we used the symbol ωT to avoid confusion with w10, the tenth component of the Fourier expansion of the population inversion.

For a recent collection of papers on the subject see, for example, K. Kulander, A. L’Huillier, eds., feature on the theory of high-order processes in atoms in intense laser fields, J. Opt. Soc. Am. B7, 401–688 (1990).

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Figures (1)

Fig. 1
Fig. 1

Harmonic intensity spectrum, |d(ω)|2, in arbitrary units, numerically computed for the case of a frequency (ωlt = 0.1 and a laser field amplitude V/ωt = 1. The horizontal scale represents the harmonic order, i.e., ω/ωL. The boxes indicate the various harmonic intensities, |dq|2, calculated with the continued-fraction expression, Eq. (15), and the circles indicate the harmonic intensities, |dq|2, calculated with the perturbative expression, Eq. (16). For both calculations the first harmonic, |d1|2, is evaluated with use of Eq. (22). Three different envelopes are compared: a, square envelope, constant during the 100 cycles; b, smooth turn-on of 10 cycles and 90 more cycles of constant envelope; c, smooth turn-on of 50 cycles and 50 more cycles of constant envelope.

Equations (22)

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| ψ ( t ) = a 0 ( t ) | 0 + a 1 ( t ) | 1 ,
d d t a 0 = iV a 1 cos ω L t ,
d d t a 1 = i ω T a 1 iV a 0 cos ω L t ,
d ( t ) = ψ ( t ) | V | ψ ( t ) .
d ( t ) = V [ a 0 * ( t ) a 1 ( t ) + a 0 ( t ) a 1 * ( t ) ] .
d d t d ( t ) = i ω T V [ a 0 * ( t ) a 1 ( t ) a 0 ( t ) a 1 * ( t ) ] .
d 2 d t 2 d ( t ) + ω T 2 d ( t ) = 2 ω T V 2 w ( t ) cos ω L t ,
d 2 d t 2 d ( t ) + ω T 2 d ( t ) = 2 ω T V 2 cos ω L t 4 ω T V 2 cos ω L t | a 0 ( t ) | 2 .
d d t w ( t ) = 2 ω T cos ω L t d d t d ( t ) .
w ( t ) = q w q exp ( iq ω L t ) ,
d ( t ) = q d q exp ( iq ω L t ) ,
q w q = 1 ω T [ ( q 1 ) d q 1 + ( q + 1 ) d q + 1 ] ,
( q 2 ω L 2 + ω T 2 ) d q = ω T V 2 ( w q 1 + w q + 1 ) .
d q ( 2 q 2 q 2 1 + ω T 2 q 2 ω L 2 V 2 ) = d q 2 q 2 q 1 + d q + 2 q + 2 q + 1 .
z q = ( q 2 ) / ( q 1 ) { [ 2 q 2 / ( q 2 1 ) ] + [ ( ω T 2 q 2 ω L 2 ) / V 2 ] } + [ ( q + 2 ) / ( q + 1 ) ] z q + 2 .
d q 2 d q = q 1 q 2 ( 2 q 2 q 2 1 + ω T 2 q 2 ω L 2 V 2 ) .
1 = w ( t 0 ) = w 0 + | q | 0 w q exp ( i q π / 2 )
1 = w 0 + q > 0 w q cos ( q π / 2 ) ;
w 0 = 1 2 ( w 2 + w 4 w 6 + ) .
w 0 = 1 + 2 w 2 .
w 0 = 1 ( d 1 / ω T ) ,
d 1 = V 2 ω T ( ω T 2 ω L 2 ) + ( 3 / 2 ) V 2 .

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