Abstract

The generation of harmonics from two mixed laser fields of noncommensurate frequencies is analyzed. We address the case of the hydrogen atom irradiated both by a laser field of wavelength λ0=1231 nm with an intensity I0=4×1013 W cm-2 and by a tunable laser field of wavelength approximately λ1=2071 nm with an intensity I1I0. We study the temporal profile and the efficiency of two-color harmonic generation far from the saturation regime. We focus on situations in which an even number of photons ω0 are absorbed in association with the emission or absorption of one photon ω1 of the second laser. The influence of the second laser on the production of the main harmonic spectrum is also analyzed.

© 1999 Optical Society of America

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    [CrossRef] [PubMed]
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  3. M. B. Gaarde, P. Antoine, A. Persson, B. Carre, A. L’Huillier, and C. G. Wahlstrom, “High-order tunable sum and difference frequency mixing in the xuv region,” J. Phys. B 29, L163–L168 (1996).
    [CrossRef]
  4. H. Eichmann, S. Meyer, K. Riepl, C. Momma, and B. Wellegehausen, “Generation of short-pulse tunable xuv radiation by high-order frequency mixing,” Phys. Rev. A 50, R2834–R2836 (1994).
    [CrossRef] [PubMed]
  5. H. Eichmann, A. Egbert, S. Nolte, C. Momma, B. Welleghausen, W. Becker, S. Long, and J. K. McIver, “Polarization-dependent high-order two color mixing,” Phys. Rev. A 51, R3414–R3417 (1995).
    [CrossRef]
  6. M. D. Perry and J. K. Crane, “High-order harmonic emission from mixed fields,” Phys. Rev. A 48, R4051–R4054 (1993).
    [CrossRef]
  7. M. Protopapas, P. L. Knight, and K. Burnett, “Phase dependence in two color excitation of a model atom by intense fields,” Phys. Rev. A 49, 1945–1949 (1994).
    [CrossRef] [PubMed]
  8. M. Protopapas, A. Sanpera, P. L. Knight, and K. Burnett, “High intensity two color interactions in the tunneling and stabilization regimes,” Phys. Rev. A 52, R2527–R2530 (1995).
    [CrossRef]
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    [CrossRef] [PubMed]
  10. E. Cormier and P. Lambropoulos, “Above-threshold ioniza- tion spectrum of hydrogen using b-spline functions,” J. Phys. B 30, 77–91 (1997).
    [CrossRef]
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  12. P. Antoine, B. Piraux, and A. Maquet, “Time profile of harmonics generated by a single atom in strong electromagnetic field,” Phys. Rev. A 51, R1750–R1753 (1995).
    [CrossRef]
  13. S. C. Rae, K. Burnett, and J. Cooper, “Generation and propagation of high-order harmonics in a rapidly ionizing medium,” Phys. Rev. A 50, 3438–3446 (1994).
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    [CrossRef]
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    [CrossRef] [PubMed]
  17. K. J. Schafer and K. C. Kulander, “High harmonic generation from ultrafast pump lasers,” Phys. Rev. Lett. 78, 638–641 (1997).
    [CrossRef]
  18. C. Figueira de Morisson Faria, M. Dörr, and W. Sandner, “Time profile of harmonic generation,” Phys. Rev. A 55, 3961–3963 (1997).
    [CrossRef]
  19. S. G. Preston and J. B. Watson, “Generation of harmonic quasi-continuum from beating laser fields,” J. Phys. B 31, 2247–2257 (1998).
    [CrossRef]
  20. M. Lewenstein, P. Balcou, M. Yu Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high harmonic generation by low-frequency laser fields,” Phys. Rev. A 49, 2117–2132 (1994).
    [CrossRef] [PubMed]
  21. M. Lewenstein, P. Salieres, and A. L’Huillier, “Phase of the atomic polarization in high-order harmonic generation,” Phys. Rev. A 52, 4747–4754 (1995).
    [CrossRef] [PubMed]

1998 (1)

S. G. Preston and J. B. Watson, “Generation of harmonic quasi-continuum from beating laser fields,” J. Phys. B 31, 2247–2257 (1998).
[CrossRef]

1997 (4)

E. Cormier and P. Lambropoulos, “Above-threshold ioniza- tion spectrum of hydrogen using b-spline functions,” J. Phys. B 30, 77–91 (1997).
[CrossRef]

E. Cormier and P. Lambropoulos, “Effect of strong dressing field on the polarizability of atomic helium at harmonic frequencies,” J. Phys. B 30, 3095–3106 (1997).
[CrossRef]

K. J. Schafer and K. C. Kulander, “High harmonic generation from ultrafast pump lasers,” Phys. Rev. Lett. 78, 638–641 (1997).
[CrossRef]

C. Figueira de Morisson Faria, M. Dörr, and W. Sandner, “Time profile of harmonic generation,” Phys. Rev. A 55, 3961–3963 (1997).
[CrossRef]

1996 (3)

Ph. Antoine, B. Piraux, D. B. Milosevic, and M. Gadja, “Generation of ultrashort pulses of harmonics,” Phys. Rev. A 54, R1761–R1764 (1996).
[CrossRef] [PubMed]

M. B. Gaarde, P. Antoine, A. Persson, B. Carre, A. L’Huillier, and C. G. Wahlstrom, “High-order tunable sum and difference frequency mixing in the xuv region,” J. Phys. B 29, L163–L168 (1996).
[CrossRef]

M. B. Gaarde, A. L’Huillier, and M. Lewenstein, “Theory of high-order sum and difference frequency mixing in a strong bichromatic laser field,” Phys. Rev. A 54, 4236–4248 (1996).
[CrossRef] [PubMed]

1995 (4)

M. Protopapas, A. Sanpera, P. L. Knight, and K. Burnett, “High intensity two color interactions in the tunneling and stabilization regimes,” Phys. Rev. A 52, R2527–R2530 (1995).
[CrossRef]

H. Eichmann, A. Egbert, S. Nolte, C. Momma, B. Welleghausen, W. Becker, S. Long, and J. K. McIver, “Polarization-dependent high-order two color mixing,” Phys. Rev. A 51, R3414–R3417 (1995).
[CrossRef]

P. Antoine, B. Piraux, and A. Maquet, “Time profile of harmonics generated by a single atom in strong electromagnetic field,” Phys. Rev. A 51, R1750–R1753 (1995).
[CrossRef]

M. Lewenstein, P. Salieres, and A. L’Huillier, “Phase of the atomic polarization in high-order harmonic generation,” Phys. Rev. A 52, 4747–4754 (1995).
[CrossRef] [PubMed]

1994 (4)

M. Lewenstein, P. Balcou, M. Yu Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high harmonic generation by low-frequency laser fields,” Phys. Rev. A 49, 2117–2132 (1994).
[CrossRef] [PubMed]

S. C. Rae, K. Burnett, and J. Cooper, “Generation and propagation of high-order harmonics in a rapidly ionizing medium,” Phys. Rev. A 50, 3438–3446 (1994).
[CrossRef] [PubMed]

H. Eichmann, S. Meyer, K. Riepl, C. Momma, and B. Wellegehausen, “Generation of short-pulse tunable xuv radiation by high-order frequency mixing,” Phys. Rev. A 50, R2834–R2836 (1994).
[CrossRef] [PubMed]

M. Protopapas, P. L. Knight, and K. Burnett, “Phase dependence in two color excitation of a model atom by intense fields,” Phys. Rev. A 49, 1945–1949 (1994).
[CrossRef] [PubMed]

1993 (2)

P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71, 1994–1997 (1993).
[CrossRef] [PubMed]

M. D. Perry and J. K. Crane, “High-order harmonic emission from mixed fields,” Phys. Rev. A 48, R4051–R4054 (1993).
[CrossRef]

1992 (1)

K. Burnett, V. C. Reed, J. Cooper, and P. L. Knight, “Calculation of the background emitted during high-harmonic generation,” Phys. Rev. A 45, 3347–3349 (1992).
[CrossRef] [PubMed]

Antoine, P.

M. B. Gaarde, P. Antoine, A. Persson, B. Carre, A. L’Huillier, and C. G. Wahlstrom, “High-order tunable sum and difference frequency mixing in the xuv region,” J. Phys. B 29, L163–L168 (1996).
[CrossRef]

P. Antoine, B. Piraux, and A. Maquet, “Time profile of harmonics generated by a single atom in strong electromagnetic field,” Phys. Rev. A 51, R1750–R1753 (1995).
[CrossRef]

Antoine, Ph.

Ph. Antoine, B. Piraux, D. B. Milosevic, and M. Gadja, “Generation of ultrashort pulses of harmonics,” Phys. Rev. A 54, R1761–R1764 (1996).
[CrossRef] [PubMed]

Balcou, P.

M. Lewenstein, P. Balcou, M. Yu Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high harmonic generation by low-frequency laser fields,” Phys. Rev. A 49, 2117–2132 (1994).
[CrossRef] [PubMed]

Becker, W.

H. Eichmann, A. Egbert, S. Nolte, C. Momma, B. Welleghausen, W. Becker, S. Long, and J. K. McIver, “Polarization-dependent high-order two color mixing,” Phys. Rev. A 51, R3414–R3417 (1995).
[CrossRef]

Burnett, K.

M. Protopapas, A. Sanpera, P. L. Knight, and K. Burnett, “High intensity two color interactions in the tunneling and stabilization regimes,” Phys. Rev. A 52, R2527–R2530 (1995).
[CrossRef]

M. Protopapas, P. L. Knight, and K. Burnett, “Phase dependence in two color excitation of a model atom by intense fields,” Phys. Rev. A 49, 1945–1949 (1994).
[CrossRef] [PubMed]

S. C. Rae, K. Burnett, and J. Cooper, “Generation and propagation of high-order harmonics in a rapidly ionizing medium,” Phys. Rev. A 50, 3438–3446 (1994).
[CrossRef] [PubMed]

K. Burnett, V. C. Reed, J. Cooper, and P. L. Knight, “Calculation of the background emitted during high-harmonic generation,” Phys. Rev. A 45, 3347–3349 (1992).
[CrossRef] [PubMed]

Carre, B.

M. B. Gaarde, P. Antoine, A. Persson, B. Carre, A. L’Huillier, and C. G. Wahlstrom, “High-order tunable sum and difference frequency mixing in the xuv region,” J. Phys. B 29, L163–L168 (1996).
[CrossRef]

Cooper, J.

S. C. Rae, K. Burnett, and J. Cooper, “Generation and propagation of high-order harmonics in a rapidly ionizing medium,” Phys. Rev. A 50, 3438–3446 (1994).
[CrossRef] [PubMed]

K. Burnett, V. C. Reed, J. Cooper, and P. L. Knight, “Calculation of the background emitted during high-harmonic generation,” Phys. Rev. A 45, 3347–3349 (1992).
[CrossRef] [PubMed]

Corkum, P. B.

M. Lewenstein, P. Balcou, M. Yu Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high harmonic generation by low-frequency laser fields,” Phys. Rev. A 49, 2117–2132 (1994).
[CrossRef] [PubMed]

P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71, 1994–1997 (1993).
[CrossRef] [PubMed]

Cormier, E.

E. Cormier and P. Lambropoulos, “Above-threshold ioniza- tion spectrum of hydrogen using b-spline functions,” J. Phys. B 30, 77–91 (1997).
[CrossRef]

E. Cormier and P. Lambropoulos, “Effect of strong dressing field on the polarizability of atomic helium at harmonic frequencies,” J. Phys. B 30, 3095–3106 (1997).
[CrossRef]

Crane, J. K.

M. D. Perry and J. K. Crane, “High-order harmonic emission from mixed fields,” Phys. Rev. A 48, R4051–R4054 (1993).
[CrossRef]

Dörr, M.

C. Figueira de Morisson Faria, M. Dörr, and W. Sandner, “Time profile of harmonic generation,” Phys. Rev. A 55, 3961–3963 (1997).
[CrossRef]

Egbert, A.

H. Eichmann, A. Egbert, S. Nolte, C. Momma, B. Welleghausen, W. Becker, S. Long, and J. K. McIver, “Polarization-dependent high-order two color mixing,” Phys. Rev. A 51, R3414–R3417 (1995).
[CrossRef]

Eichmann, H.

H. Eichmann, A. Egbert, S. Nolte, C. Momma, B. Welleghausen, W. Becker, S. Long, and J. K. McIver, “Polarization-dependent high-order two color mixing,” Phys. Rev. A 51, R3414–R3417 (1995).
[CrossRef]

H. Eichmann, S. Meyer, K. Riepl, C. Momma, and B. Wellegehausen, “Generation of short-pulse tunable xuv radiation by high-order frequency mixing,” Phys. Rev. A 50, R2834–R2836 (1994).
[CrossRef] [PubMed]

Figueira de Morisson Faria, C.

C. Figueira de Morisson Faria, M. Dörr, and W. Sandner, “Time profile of harmonic generation,” Phys. Rev. A 55, 3961–3963 (1997).
[CrossRef]

Gaarde, M. B.

M. B. Gaarde, P. Antoine, A. Persson, B. Carre, A. L’Huillier, and C. G. Wahlstrom, “High-order tunable sum and difference frequency mixing in the xuv region,” J. Phys. B 29, L163–L168 (1996).
[CrossRef]

M. B. Gaarde, A. L’Huillier, and M. Lewenstein, “Theory of high-order sum and difference frequency mixing in a strong bichromatic laser field,” Phys. Rev. A 54, 4236–4248 (1996).
[CrossRef] [PubMed]

Gadja, M.

Ph. Antoine, B. Piraux, D. B. Milosevic, and M. Gadja, “Generation of ultrashort pulses of harmonics,” Phys. Rev. A 54, R1761–R1764 (1996).
[CrossRef] [PubMed]

Ivanov, M. Yu

M. Lewenstein, P. Balcou, M. Yu Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high harmonic generation by low-frequency laser fields,” Phys. Rev. A 49, 2117–2132 (1994).
[CrossRef] [PubMed]

Knight, P. L.

M. Protopapas, A. Sanpera, P. L. Knight, and K. Burnett, “High intensity two color interactions in the tunneling and stabilization regimes,” Phys. Rev. A 52, R2527–R2530 (1995).
[CrossRef]

M. Protopapas, P. L. Knight, and K. Burnett, “Phase dependence in two color excitation of a model atom by intense fields,” Phys. Rev. A 49, 1945–1949 (1994).
[CrossRef] [PubMed]

K. Burnett, V. C. Reed, J. Cooper, and P. L. Knight, “Calculation of the background emitted during high-harmonic generation,” Phys. Rev. A 45, 3347–3349 (1992).
[CrossRef] [PubMed]

Kulander, K. C.

K. J. Schafer and K. C. Kulander, “High harmonic generation from ultrafast pump lasers,” Phys. Rev. Lett. 78, 638–641 (1997).
[CrossRef]

L’Huillier, A.

M. B. Gaarde, A. L’Huillier, and M. Lewenstein, “Theory of high-order sum and difference frequency mixing in a strong bichromatic laser field,” Phys. Rev. A 54, 4236–4248 (1996).
[CrossRef] [PubMed]

M. B. Gaarde, P. Antoine, A. Persson, B. Carre, A. L’Huillier, and C. G. Wahlstrom, “High-order tunable sum and difference frequency mixing in the xuv region,” J. Phys. B 29, L163–L168 (1996).
[CrossRef]

M. Lewenstein, P. Salieres, and A. L’Huillier, “Phase of the atomic polarization in high-order harmonic generation,” Phys. Rev. A 52, 4747–4754 (1995).
[CrossRef] [PubMed]

M. Lewenstein, P. Balcou, M. Yu Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high harmonic generation by low-frequency laser fields,” Phys. Rev. A 49, 2117–2132 (1994).
[CrossRef] [PubMed]

Lambropoulos, P.

E. Cormier and P. Lambropoulos, “Effect of strong dressing field on the polarizability of atomic helium at harmonic frequencies,” J. Phys. B 30, 3095–3106 (1997).
[CrossRef]

E. Cormier and P. Lambropoulos, “Above-threshold ioniza- tion spectrum of hydrogen using b-spline functions,” J. Phys. B 30, 77–91 (1997).
[CrossRef]

Lewenstein, M.

M. B. Gaarde, A. L’Huillier, and M. Lewenstein, “Theory of high-order sum and difference frequency mixing in a strong bichromatic laser field,” Phys. Rev. A 54, 4236–4248 (1996).
[CrossRef] [PubMed]

M. Lewenstein, P. Salieres, and A. L’Huillier, “Phase of the atomic polarization in high-order harmonic generation,” Phys. Rev. A 52, 4747–4754 (1995).
[CrossRef] [PubMed]

M. Lewenstein, P. Balcou, M. Yu Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high harmonic generation by low-frequency laser fields,” Phys. Rev. A 49, 2117–2132 (1994).
[CrossRef] [PubMed]

Long, S.

H. Eichmann, A. Egbert, S. Nolte, C. Momma, B. Welleghausen, W. Becker, S. Long, and J. K. McIver, “Polarization-dependent high-order two color mixing,” Phys. Rev. A 51, R3414–R3417 (1995).
[CrossRef]

Maquet, A.

P. Antoine, B. Piraux, and A. Maquet, “Time profile of harmonics generated by a single atom in strong electromagnetic field,” Phys. Rev. A 51, R1750–R1753 (1995).
[CrossRef]

McIver, J. K.

H. Eichmann, A. Egbert, S. Nolte, C. Momma, B. Welleghausen, W. Becker, S. Long, and J. K. McIver, “Polarization-dependent high-order two color mixing,” Phys. Rev. A 51, R3414–R3417 (1995).
[CrossRef]

Meyer, S.

H. Eichmann, S. Meyer, K. Riepl, C. Momma, and B. Wellegehausen, “Generation of short-pulse tunable xuv radiation by high-order frequency mixing,” Phys. Rev. A 50, R2834–R2836 (1994).
[CrossRef] [PubMed]

Milosevic, D. B.

Ph. Antoine, B. Piraux, D. B. Milosevic, and M. Gadja, “Generation of ultrashort pulses of harmonics,” Phys. Rev. A 54, R1761–R1764 (1996).
[CrossRef] [PubMed]

Momma, C.

H. Eichmann, A. Egbert, S. Nolte, C. Momma, B. Welleghausen, W. Becker, S. Long, and J. K. McIver, “Polarization-dependent high-order two color mixing,” Phys. Rev. A 51, R3414–R3417 (1995).
[CrossRef]

H. Eichmann, S. Meyer, K. Riepl, C. Momma, and B. Wellegehausen, “Generation of short-pulse tunable xuv radiation by high-order frequency mixing,” Phys. Rev. A 50, R2834–R2836 (1994).
[CrossRef] [PubMed]

Nolte, S.

H. Eichmann, A. Egbert, S. Nolte, C. Momma, B. Welleghausen, W. Becker, S. Long, and J. K. McIver, “Polarization-dependent high-order two color mixing,” Phys. Rev. A 51, R3414–R3417 (1995).
[CrossRef]

Perry, M. D.

M. D. Perry and J. K. Crane, “High-order harmonic emission from mixed fields,” Phys. Rev. A 48, R4051–R4054 (1993).
[CrossRef]

Persson, A.

M. B. Gaarde, P. Antoine, A. Persson, B. Carre, A. L’Huillier, and C. G. Wahlstrom, “High-order tunable sum and difference frequency mixing in the xuv region,” J. Phys. B 29, L163–L168 (1996).
[CrossRef]

Piraux, B.

Ph. Antoine, B. Piraux, D. B. Milosevic, and M. Gadja, “Generation of ultrashort pulses of harmonics,” Phys. Rev. A 54, R1761–R1764 (1996).
[CrossRef] [PubMed]

P. Antoine, B. Piraux, and A. Maquet, “Time profile of harmonics generated by a single atom in strong electromagnetic field,” Phys. Rev. A 51, R1750–R1753 (1995).
[CrossRef]

Preston, S. G.

S. G. Preston and J. B. Watson, “Generation of harmonic quasi-continuum from beating laser fields,” J. Phys. B 31, 2247–2257 (1998).
[CrossRef]

Protopapas, M.

M. Protopapas, A. Sanpera, P. L. Knight, and K. Burnett, “High intensity two color interactions in the tunneling and stabilization regimes,” Phys. Rev. A 52, R2527–R2530 (1995).
[CrossRef]

M. Protopapas, P. L. Knight, and K. Burnett, “Phase dependence in two color excitation of a model atom by intense fields,” Phys. Rev. A 49, 1945–1949 (1994).
[CrossRef] [PubMed]

Rae, S. C.

S. C. Rae, K. Burnett, and J. Cooper, “Generation and propagation of high-order harmonics in a rapidly ionizing medium,” Phys. Rev. A 50, 3438–3446 (1994).
[CrossRef] [PubMed]

Reed, V. C.

K. Burnett, V. C. Reed, J. Cooper, and P. L. Knight, “Calculation of the background emitted during high-harmonic generation,” Phys. Rev. A 45, 3347–3349 (1992).
[CrossRef] [PubMed]

Riepl, K.

H. Eichmann, S. Meyer, K. Riepl, C. Momma, and B. Wellegehausen, “Generation of short-pulse tunable xuv radiation by high-order frequency mixing,” Phys. Rev. A 50, R2834–R2836 (1994).
[CrossRef] [PubMed]

Salieres, P.

M. Lewenstein, P. Salieres, and A. L’Huillier, “Phase of the atomic polarization in high-order harmonic generation,” Phys. Rev. A 52, 4747–4754 (1995).
[CrossRef] [PubMed]

Sandner, W.

C. Figueira de Morisson Faria, M. Dörr, and W. Sandner, “Time profile of harmonic generation,” Phys. Rev. A 55, 3961–3963 (1997).
[CrossRef]

Sanpera, A.

M. Protopapas, A. Sanpera, P. L. Knight, and K. Burnett, “High intensity two color interactions in the tunneling and stabilization regimes,” Phys. Rev. A 52, R2527–R2530 (1995).
[CrossRef]

Schafer, K. J.

K. J. Schafer and K. C. Kulander, “High harmonic generation from ultrafast pump lasers,” Phys. Rev. Lett. 78, 638–641 (1997).
[CrossRef]

Wahlstrom, C. G.

M. B. Gaarde, P. Antoine, A. Persson, B. Carre, A. L’Huillier, and C. G. Wahlstrom, “High-order tunable sum and difference frequency mixing in the xuv region,” J. Phys. B 29, L163–L168 (1996).
[CrossRef]

Watson, J. B.

S. G. Preston and J. B. Watson, “Generation of harmonic quasi-continuum from beating laser fields,” J. Phys. B 31, 2247–2257 (1998).
[CrossRef]

Wellegehausen, B.

H. Eichmann, S. Meyer, K. Riepl, C. Momma, and B. Wellegehausen, “Generation of short-pulse tunable xuv radiation by high-order frequency mixing,” Phys. Rev. A 50, R2834–R2836 (1994).
[CrossRef] [PubMed]

Welleghausen, B.

H. Eichmann, A. Egbert, S. Nolte, C. Momma, B. Welleghausen, W. Becker, S. Long, and J. K. McIver, “Polarization-dependent high-order two color mixing,” Phys. Rev. A 51, R3414–R3417 (1995).
[CrossRef]

J. Phys. B (4)

M. B. Gaarde, P. Antoine, A. Persson, B. Carre, A. L’Huillier, and C. G. Wahlstrom, “High-order tunable sum and difference frequency mixing in the xuv region,” J. Phys. B 29, L163–L168 (1996).
[CrossRef]

E. Cormier and P. Lambropoulos, “Above-threshold ioniza- tion spectrum of hydrogen using b-spline functions,” J. Phys. B 30, 77–91 (1997).
[CrossRef]

E. Cormier and P. Lambropoulos, “Effect of strong dressing field on the polarizability of atomic helium at harmonic frequencies,” J. Phys. B 30, 3095–3106 (1997).
[CrossRef]

S. G. Preston and J. B. Watson, “Generation of harmonic quasi-continuum from beating laser fields,” J. Phys. B 31, 2247–2257 (1998).
[CrossRef]

Phys. Rev. A (13)

M. Lewenstein, P. Balcou, M. Yu Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high harmonic generation by low-frequency laser fields,” Phys. Rev. A 49, 2117–2132 (1994).
[CrossRef] [PubMed]

M. Lewenstein, P. Salieres, and A. L’Huillier, “Phase of the atomic polarization in high-order harmonic generation,” Phys. Rev. A 52, 4747–4754 (1995).
[CrossRef] [PubMed]

C. Figueira de Morisson Faria, M. Dörr, and W. Sandner, “Time profile of harmonic generation,” Phys. Rev. A 55, 3961–3963 (1997).
[CrossRef]

K. Burnett, V. C. Reed, J. Cooper, and P. L. Knight, “Calculation of the background emitted during high-harmonic generation,” Phys. Rev. A 45, 3347–3349 (1992).
[CrossRef] [PubMed]

Ph. Antoine, B. Piraux, D. B. Milosevic, and M. Gadja, “Generation of ultrashort pulses of harmonics,” Phys. Rev. A 54, R1761–R1764 (1996).
[CrossRef] [PubMed]

P. Antoine, B. Piraux, and A. Maquet, “Time profile of harmonics generated by a single atom in strong electromagnetic field,” Phys. Rev. A 51, R1750–R1753 (1995).
[CrossRef]

S. C. Rae, K. Burnett, and J. Cooper, “Generation and propagation of high-order harmonics in a rapidly ionizing medium,” Phys. Rev. A 50, 3438–3446 (1994).
[CrossRef] [PubMed]

H. Eichmann, S. Meyer, K. Riepl, C. Momma, and B. Wellegehausen, “Generation of short-pulse tunable xuv radiation by high-order frequency mixing,” Phys. Rev. A 50, R2834–R2836 (1994).
[CrossRef] [PubMed]

H. Eichmann, A. Egbert, S. Nolte, C. Momma, B. Welleghausen, W. Becker, S. Long, and J. K. McIver, “Polarization-dependent high-order two color mixing,” Phys. Rev. A 51, R3414–R3417 (1995).
[CrossRef]

M. D. Perry and J. K. Crane, “High-order harmonic emission from mixed fields,” Phys. Rev. A 48, R4051–R4054 (1993).
[CrossRef]

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[CrossRef] [PubMed]

M. Protopapas, A. Sanpera, P. L. Knight, and K. Burnett, “High intensity two color interactions in the tunneling and stabilization regimes,” Phys. Rev. A 52, R2527–R2530 (1995).
[CrossRef]

M. B. Gaarde, A. L’Huillier, and M. Lewenstein, “Theory of high-order sum and difference frequency mixing in a strong bichromatic laser field,” Phys. Rev. A 54, 4236–4248 (1996).
[CrossRef] [PubMed]

Phys. Rev. Lett. (2)

K. J. Schafer and K. C. Kulander, “High harmonic generation from ultrafast pump lasers,” Phys. Rev. Lett. 78, 638–641 (1997).
[CrossRef]

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Other (2)

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Figures (10)

Fig. 1
Fig. 1

Harmonic spectrum in hydrogen. I0=4.0×1013 W cm-2, ω0=1.0 eV.

Fig. 2
Fig. 2

Time profile of harmonic 15 with a flat pulse (see the text) obtained with Eq. (4). I0=4.0×1013 W cm-2, ω0=1.0 eV.

Fig. 3
Fig. 3

Harmonic spectrum obtained with a hydrogen atom irradiated by two lasers. The first laser has the same characteristics as in Fig. 1. The second laser is much less intense: I1=10-4 I0 and with a frequency ω1=0.6 eV.

Fig. 4
Fig. 4

Harmonic spectrum obtained with a hydrogen atom irradiated by two lasers. The laser-field parameters are the same as in Fig. 3 except that I1=10-3 I0 here.

Fig. 5
Fig. 5

Time profile of two-color harmonic 16 ω0-ω1 [Eq. (4)]. See parameters in Fig. 3.

Fig. 6
Fig. 6

Time-profile envelope obtained with Eq. (5) (frequency-dependent dipole) for harmonics 37, 38+1, 38-1, and 39. The harmonic orders are shown in the figure. See parameters in Fig. 3.

Fig. 7
Fig. 7

Harmonic amplitude versus the ratio between weak-field and strong-field intensities (I1/I0) in the cutoff region. I0=4.0×1013 W cm-2.

Fig. 8
Fig. 8

Harmonic amplitude versus I1/I0 in the middle of the plateau region.

Fig. 9
Fig. 9

Time-profile envelope obtained with Eq. (5) (frequency-dependent dipole) for harmonic 37. The second laser (I1, ω1) is off from t=-3000 to t=0 a.u. In the right-hand side (t>0) of the graph the upper and lower profiles correspond to I1=0 and I1=10-4I0, respectively. See other parameters in Fig. 3.

Fig. 10
Fig. 10

Harmonic amplitude versus I1/I0 in the cutoff region.

Equations (6)

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i tΨ(r, t)=(Hat+Hint)Ψ(r, t),
Ψ(r, t)=ilmcilm(t) Bik(r)ry lm(θ, φ),
a(t)=2t2d(t)=2t2r·=Ψ(r, t)|-rV(r)+E(t)sin ωt|Ψ(r, t),
a˜(ω, t0)=- exp(-iωt)exp-(t-t0)22σ02a(t)dt,
a˜(ω0, t)=- exp(-iωt)exp-(ω-ω0)22σ02a˜(ω)dω.
E(t)=E0(t)cos(ω0t)+E1(t)cos(ω1t),

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