Abstract

In high-order harmonic generation by an intense laser, intrinsic phases can develop at the atomic level between the laser field and the individual emitted harmonics. Because intrinsic phases can vary rapidly with the laser intensity, they can strongly influence phase matching to the extent that the laser intensity varies within the generating medium. Previously reported measurements of broad far-field harmonic emission patterns as well as measured asymmetries in the emission with respect to the axial positioning of the medium in the focus can be explained by intrinsic phases. An experimental method for further study of intrinsic phases is proposed that involves harmonic generation in two counterpropagating laser beams. The periodic intensity modulation created by the two beams coupled with the intensity-dependent intrinsic phases allows harmonic light to propagate in directions with otherwise extremely poor phase-matching conditions.

© 1995 Optical Society of America

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  1. W. Becker, S. Long, and J. K. McIver, “Higher-harmonic production in a model atom with short-range potential,” Phys. Rev. A 41, 4112–4115 (1990).
    [Crossref] [PubMed]
  2. B. Sundaram and P. W. Milonni, “High-order harmonic generation: simplified model and relevance of single-atom theories to experiment,” Phys. Rev. A 41, 6571–6573 (1990).
    [Crossref] [PubMed]
  3. L. Plaja and L. Roso-Franco, “Adiabatic theory for high-order harmonic generation in a two-level atom,” J. Opt. Soc. Am. B 9, 2210–2213 (1992).
    [Crossref]
  4. A. L’Huillier, L. A. Lompre, G. Mainfray, and C. Manus, “Multiple harmonic conversion in rare gases in strong laser fields,” in Proceedings of the 5th International Conference on Multiphoton Processes, G. Mainfray and P. Agostini, eds. (Le Commissarial à l’Energie Atomique, Paris, 1990), pp. 45–55.
  5. K. C. Kulander, K. J. Schafer, and J. L. Krause, “Dynamics of short-pulse excitation, ionization and harmonic conversion,” in Super Intense Laser–Atom Physics, B. Piraux, A. L’Huillier, and K. Rz¸żewski, eds., Vol. 316 of NATO ASI Series (Plenum, New York, 1993), pp. 95–110.
    [Crossref]
  6. M. Lewenstein, Ph. 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]
  7. K. C. Kulander and B. W. Shore, “Calculations of multiple-harmonic conversion of 1064-nm radiation in Xe,” Phys. Rev. Lett. 62, 524–526 (1989).
    [Crossref] [PubMed]
  8. K. C. Kulander and B. W. Shore, “Generation of optical harmonics by intense pulses of laser radiation. II. Singleatom spectrum for xenon,” J. Opt. Soc. Am. B 7, 502–508 (1990).
    [Crossref]
  9. A. L’Huillier, K. J. Schafer, and K. C. Kulander, “Theoretical aspects of intense field harmonic generation,” J. Phys. B 24, 3315–3341 (1991).
    [Crossref]
  10. A. L’Huillier, Ph. Balcou, S. Candel, K. J. Schafer, and K. C. Kulander, “Calculations of high-order harmonic-generation processes in xenon at 1064 nm,” Phys. Rev. A 46, 2778–2790 (1992).
    [Crossref]
  11. J. Peatross and D. D. Meyerhofer, “Measurement of the angular distribution of high-order harmonics emitted from rare gases,” in Short Wavelength V, Vol. 17 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1993).
  12. J. Peatross and D. D. Meyerhofer, “Angular distribution of high-order harmonics emitted from rare gases at low density,” Phys. Rev. A 51, R906 (1995).
    [Crossref] [PubMed]
  13. Ph. Balcou and A. L’Huillier, “Phase-matching effects in strong-field harmonic generation,” Phys. Rev. A 47, 1447–1459 (1993).
    [Crossref] [PubMed]
  14. S. Augst, C. I. Moore, J. Peatross, and D. D. Meyerhofer, “Spatial distribution of high-order harmonics generated in the tunneling regime,” in Short Wavelength Coherent Radiation, P. H. Bucksbaum and N. M. Ceglio, eds., Vol. 11 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1991), pp. 23–27.
  15. J. W. G. Tisch, R. A. Smith, J. E. Muffett, M. Ciarrocca, J. P. Marangos, and M. H. R. Hutchinson, “Angularly resolved high-order harmonic generation in helium,” Phys. Rev. A 49, R28–R31 (1994).
    [Crossref] [PubMed]
  16. P. Salieres, T. Ditmire, K S. Budil, M. D. Perry, and A. L’Huillier, “Spatial profiles of high-order harmonics generated by a femtosecond Cr:LiSAF laser,” J. Phys. B 27, L217–L222 (1994).
    [Crossref]
  17. B. W. Shore and K. C. Kulander, “Generation of optical harmonics by intense pulses of laser radiation. I. Propagation effects,” J. Mod. Opt. 36, 857–875 (1989).
    [Crossref]
  18. J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975), p. 395, Eq. (9.19).
  19. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 61.
  20. P. W. Milonni and J. H. Eberly, Lasers (Wiley, New York, 1988), p. 490.
  21. A. L’Huillier, Ph. Balcou, and L. A. Lompre, “Coherence and resonance effects in high-order harmonic generation,” Phys. Rev. Lett. 68, 166–169 (1992).
    [Crossref]
  22. X. F. Li, A. L’Huillier, M. Ferray, L. A. Lompre, and G. Mainfray, “Multiple-harmonic generation in rare gases at high laser intensity,” Phys. Rev. A 39, 5751–5761 (1989).
    [Crossref] [PubMed]
  23. J. Peatross, J. Chaloupka, and D. D. Meyerhofer, “High-order harmonic generation with an annular laser beam,” Opt. Lett. 19, 942–944 (1994).
    [Crossref] [PubMed]

1995 (1)

J. Peatross and D. D. Meyerhofer, “Angular distribution of high-order harmonics emitted from rare gases at low density,” Phys. Rev. A 51, R906 (1995).
[Crossref] [PubMed]

1994 (4)

J. W. G. Tisch, R. A. Smith, J. E. Muffett, M. Ciarrocca, J. P. Marangos, and M. H. R. Hutchinson, “Angularly resolved high-order harmonic generation in helium,” Phys. Rev. A 49, R28–R31 (1994).
[Crossref] [PubMed]

P. Salieres, T. Ditmire, K S. Budil, M. D. Perry, and A. L’Huillier, “Spatial profiles of high-order harmonics generated by a femtosecond Cr:LiSAF laser,” J. Phys. B 27, L217–L222 (1994).
[Crossref]

J. Peatross, J. Chaloupka, and D. D. Meyerhofer, “High-order harmonic generation with an annular laser beam,” Opt. Lett. 19, 942–944 (1994).
[Crossref] [PubMed]

M. Lewenstein, Ph. 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]

1993 (1)

Ph. Balcou and A. L’Huillier, “Phase-matching effects in strong-field harmonic generation,” Phys. Rev. A 47, 1447–1459 (1993).
[Crossref] [PubMed]

1992 (3)

A. L’Huillier, Ph. Balcou, and L. A. Lompre, “Coherence and resonance effects in high-order harmonic generation,” Phys. Rev. Lett. 68, 166–169 (1992).
[Crossref]

L. Plaja and L. Roso-Franco, “Adiabatic theory for high-order harmonic generation in a two-level atom,” J. Opt. Soc. Am. B 9, 2210–2213 (1992).
[Crossref]

A. L’Huillier, Ph. Balcou, S. Candel, K. J. Schafer, and K. C. Kulander, “Calculations of high-order harmonic-generation processes in xenon at 1064 nm,” Phys. Rev. A 46, 2778–2790 (1992).
[Crossref]

1991 (1)

A. L’Huillier, K. J. Schafer, and K. C. Kulander, “Theoretical aspects of intense field harmonic generation,” J. Phys. B 24, 3315–3341 (1991).
[Crossref]

1990 (3)

K. C. Kulander and B. W. Shore, “Generation of optical harmonics by intense pulses of laser radiation. II. Singleatom spectrum for xenon,” J. Opt. Soc. Am. B 7, 502–508 (1990).
[Crossref]

W. Becker, S. Long, and J. K. McIver, “Higher-harmonic production in a model atom with short-range potential,” Phys. Rev. A 41, 4112–4115 (1990).
[Crossref] [PubMed]

B. Sundaram and P. W. Milonni, “High-order harmonic generation: simplified model and relevance of single-atom theories to experiment,” Phys. Rev. A 41, 6571–6573 (1990).
[Crossref] [PubMed]

1989 (3)

K. C. Kulander and B. W. Shore, “Calculations of multiple-harmonic conversion of 1064-nm radiation in Xe,” Phys. Rev. Lett. 62, 524–526 (1989).
[Crossref] [PubMed]

X. F. Li, A. L’Huillier, M. Ferray, L. A. Lompre, and G. Mainfray, “Multiple-harmonic generation in rare gases at high laser intensity,” Phys. Rev. A 39, 5751–5761 (1989).
[Crossref] [PubMed]

B. W. Shore and K. C. Kulander, “Generation of optical harmonics by intense pulses of laser radiation. I. Propagation effects,” J. Mod. Opt. 36, 857–875 (1989).
[Crossref]

Augst, S.

S. Augst, C. I. Moore, J. Peatross, and D. D. Meyerhofer, “Spatial distribution of high-order harmonics generated in the tunneling regime,” in Short Wavelength Coherent Radiation, P. H. Bucksbaum and N. M. Ceglio, eds., Vol. 11 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1991), pp. 23–27.

Balcou, Ph.

M. Lewenstein, Ph. 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]

Ph. Balcou and A. L’Huillier, “Phase-matching effects in strong-field harmonic generation,” Phys. Rev. A 47, 1447–1459 (1993).
[Crossref] [PubMed]

A. L’Huillier, Ph. Balcou, S. Candel, K. J. Schafer, and K. C. Kulander, “Calculations of high-order harmonic-generation processes in xenon at 1064 nm,” Phys. Rev. A 46, 2778–2790 (1992).
[Crossref]

A. L’Huillier, Ph. Balcou, and L. A. Lompre, “Coherence and resonance effects in high-order harmonic generation,” Phys. Rev. Lett. 68, 166–169 (1992).
[Crossref]

Becker, W.

W. Becker, S. Long, and J. K. McIver, “Higher-harmonic production in a model atom with short-range potential,” Phys. Rev. A 41, 4112–4115 (1990).
[Crossref] [PubMed]

Budil, K S.

P. Salieres, T. Ditmire, K S. Budil, M. D. Perry, and A. L’Huillier, “Spatial profiles of high-order harmonics generated by a femtosecond Cr:LiSAF laser,” J. Phys. B 27, L217–L222 (1994).
[Crossref]

Candel, S.

A. L’Huillier, Ph. Balcou, S. Candel, K. J. Schafer, and K. C. Kulander, “Calculations of high-order harmonic-generation processes in xenon at 1064 nm,” Phys. Rev. A 46, 2778–2790 (1992).
[Crossref]

Chaloupka, J.

Ciarrocca, M.

J. W. G. Tisch, R. A. Smith, J. E. Muffett, M. Ciarrocca, J. P. Marangos, and M. H. R. Hutchinson, “Angularly resolved high-order harmonic generation in helium,” Phys. Rev. A 49, R28–R31 (1994).
[Crossref] [PubMed]

Corkum, P. B.

M. Lewenstein, Ph. 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]

Ditmire, T.

P. Salieres, T. Ditmire, K S. Budil, M. D. Perry, and A. L’Huillier, “Spatial profiles of high-order harmonics generated by a femtosecond Cr:LiSAF laser,” J. Phys. B 27, L217–L222 (1994).
[Crossref]

Eberly, J. H.

P. W. Milonni and J. H. Eberly, Lasers (Wiley, New York, 1988), p. 490.

Ferray, M.

X. F. Li, A. L’Huillier, M. Ferray, L. A. Lompre, and G. Mainfray, “Multiple-harmonic generation in rare gases at high laser intensity,” Phys. Rev. A 39, 5751–5761 (1989).
[Crossref] [PubMed]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 61.

Hutchinson, M. H. R.

J. W. G. Tisch, R. A. Smith, J. E. Muffett, M. Ciarrocca, J. P. Marangos, and M. H. R. Hutchinson, “Angularly resolved high-order harmonic generation in helium,” Phys. Rev. A 49, R28–R31 (1994).
[Crossref] [PubMed]

Ivanov, M. Yu.

M. Lewenstein, Ph. 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]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975), p. 395, Eq. (9.19).

Krause, J. L.

K. C. Kulander, K. J. Schafer, and J. L. Krause, “Dynamics of short-pulse excitation, ionization and harmonic conversion,” in Super Intense Laser–Atom Physics, B. Piraux, A. L’Huillier, and K. Rz¸żewski, eds., Vol. 316 of NATO ASI Series (Plenum, New York, 1993), pp. 95–110.
[Crossref]

Kulander, K. C.

A. L’Huillier, Ph. Balcou, S. Candel, K. J. Schafer, and K. C. Kulander, “Calculations of high-order harmonic-generation processes in xenon at 1064 nm,” Phys. Rev. A 46, 2778–2790 (1992).
[Crossref]

A. L’Huillier, K. J. Schafer, and K. C. Kulander, “Theoretical aspects of intense field harmonic generation,” J. Phys. B 24, 3315–3341 (1991).
[Crossref]

K. C. Kulander and B. W. Shore, “Generation of optical harmonics by intense pulses of laser radiation. II. Singleatom spectrum for xenon,” J. Opt. Soc. Am. B 7, 502–508 (1990).
[Crossref]

K. C. Kulander and B. W. Shore, “Calculations of multiple-harmonic conversion of 1064-nm radiation in Xe,” Phys. Rev. Lett. 62, 524–526 (1989).
[Crossref] [PubMed]

B. W. Shore and K. C. Kulander, “Generation of optical harmonics by intense pulses of laser radiation. I. Propagation effects,” J. Mod. Opt. 36, 857–875 (1989).
[Crossref]

K. C. Kulander, K. J. Schafer, and J. L. Krause, “Dynamics of short-pulse excitation, ionization and harmonic conversion,” in Super Intense Laser–Atom Physics, B. Piraux, A. L’Huillier, and K. Rz¸żewski, eds., Vol. 316 of NATO ASI Series (Plenum, New York, 1993), pp. 95–110.
[Crossref]

L’Huillier, A.

M. Lewenstein, Ph. 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. Salieres, T. Ditmire, K S. Budil, M. D. Perry, and A. L’Huillier, “Spatial profiles of high-order harmonics generated by a femtosecond Cr:LiSAF laser,” J. Phys. B 27, L217–L222 (1994).
[Crossref]

Ph. Balcou and A. L’Huillier, “Phase-matching effects in strong-field harmonic generation,” Phys. Rev. A 47, 1447–1459 (1993).
[Crossref] [PubMed]

A. L’Huillier, Ph. Balcou, S. Candel, K. J. Schafer, and K. C. Kulander, “Calculations of high-order harmonic-generation processes in xenon at 1064 nm,” Phys. Rev. A 46, 2778–2790 (1992).
[Crossref]

A. L’Huillier, Ph. Balcou, and L. A. Lompre, “Coherence and resonance effects in high-order harmonic generation,” Phys. Rev. Lett. 68, 166–169 (1992).
[Crossref]

A. L’Huillier, K. J. Schafer, and K. C. Kulander, “Theoretical aspects of intense field harmonic generation,” J. Phys. B 24, 3315–3341 (1991).
[Crossref]

X. F. Li, A. L’Huillier, M. Ferray, L. A. Lompre, and G. Mainfray, “Multiple-harmonic generation in rare gases at high laser intensity,” Phys. Rev. A 39, 5751–5761 (1989).
[Crossref] [PubMed]

A. L’Huillier, L. A. Lompre, G. Mainfray, and C. Manus, “Multiple harmonic conversion in rare gases in strong laser fields,” in Proceedings of the 5th International Conference on Multiphoton Processes, G. Mainfray and P. Agostini, eds. (Le Commissarial à l’Energie Atomique, Paris, 1990), pp. 45–55.

Lewenstein, M.

M. Lewenstein, Ph. 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]

Li, X. F.

X. F. Li, A. L’Huillier, M. Ferray, L. A. Lompre, and G. Mainfray, “Multiple-harmonic generation in rare gases at high laser intensity,” Phys. Rev. A 39, 5751–5761 (1989).
[Crossref] [PubMed]

Lompre, L. A.

A. L’Huillier, Ph. Balcou, and L. A. Lompre, “Coherence and resonance effects in high-order harmonic generation,” Phys. Rev. Lett. 68, 166–169 (1992).
[Crossref]

X. F. Li, A. L’Huillier, M. Ferray, L. A. Lompre, and G. Mainfray, “Multiple-harmonic generation in rare gases at high laser intensity,” Phys. Rev. A 39, 5751–5761 (1989).
[Crossref] [PubMed]

A. L’Huillier, L. A. Lompre, G. Mainfray, and C. Manus, “Multiple harmonic conversion in rare gases in strong laser fields,” in Proceedings of the 5th International Conference on Multiphoton Processes, G. Mainfray and P. Agostini, eds. (Le Commissarial à l’Energie Atomique, Paris, 1990), pp. 45–55.

Long, S.

W. Becker, S. Long, and J. K. McIver, “Higher-harmonic production in a model atom with short-range potential,” Phys. Rev. A 41, 4112–4115 (1990).
[Crossref] [PubMed]

Mainfray, G.

X. F. Li, A. L’Huillier, M. Ferray, L. A. Lompre, and G. Mainfray, “Multiple-harmonic generation in rare gases at high laser intensity,” Phys. Rev. A 39, 5751–5761 (1989).
[Crossref] [PubMed]

A. L’Huillier, L. A. Lompre, G. Mainfray, and C. Manus, “Multiple harmonic conversion in rare gases in strong laser fields,” in Proceedings of the 5th International Conference on Multiphoton Processes, G. Mainfray and P. Agostini, eds. (Le Commissarial à l’Energie Atomique, Paris, 1990), pp. 45–55.

Manus, C.

A. L’Huillier, L. A. Lompre, G. Mainfray, and C. Manus, “Multiple harmonic conversion in rare gases in strong laser fields,” in Proceedings of the 5th International Conference on Multiphoton Processes, G. Mainfray and P. Agostini, eds. (Le Commissarial à l’Energie Atomique, Paris, 1990), pp. 45–55.

Marangos, J. P.

J. W. G. Tisch, R. A. Smith, J. E. Muffett, M. Ciarrocca, J. P. Marangos, and M. H. R. Hutchinson, “Angularly resolved high-order harmonic generation in helium,” Phys. Rev. A 49, R28–R31 (1994).
[Crossref] [PubMed]

McIver, J. K.

W. Becker, S. Long, and J. K. McIver, “Higher-harmonic production in a model atom with short-range potential,” Phys. Rev. A 41, 4112–4115 (1990).
[Crossref] [PubMed]

Meyerhofer, D. D.

J. Peatross and D. D. Meyerhofer, “Angular distribution of high-order harmonics emitted from rare gases at low density,” Phys. Rev. A 51, R906 (1995).
[Crossref] [PubMed]

J. Peatross, J. Chaloupka, and D. D. Meyerhofer, “High-order harmonic generation with an annular laser beam,” Opt. Lett. 19, 942–944 (1994).
[Crossref] [PubMed]

S. Augst, C. I. Moore, J. Peatross, and D. D. Meyerhofer, “Spatial distribution of high-order harmonics generated in the tunneling regime,” in Short Wavelength Coherent Radiation, P. H. Bucksbaum and N. M. Ceglio, eds., Vol. 11 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1991), pp. 23–27.

J. Peatross and D. D. Meyerhofer, “Measurement of the angular distribution of high-order harmonics emitted from rare gases,” in Short Wavelength V, Vol. 17 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1993).

Milonni, P. W.

B. Sundaram and P. W. Milonni, “High-order harmonic generation: simplified model and relevance of single-atom theories to experiment,” Phys. Rev. A 41, 6571–6573 (1990).
[Crossref] [PubMed]

P. W. Milonni and J. H. Eberly, Lasers (Wiley, New York, 1988), p. 490.

Moore, C. I.

S. Augst, C. I. Moore, J. Peatross, and D. D. Meyerhofer, “Spatial distribution of high-order harmonics generated in the tunneling regime,” in Short Wavelength Coherent Radiation, P. H. Bucksbaum and N. M. Ceglio, eds., Vol. 11 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1991), pp. 23–27.

Muffett, J. E.

J. W. G. Tisch, R. A. Smith, J. E. Muffett, M. Ciarrocca, J. P. Marangos, and M. H. R. Hutchinson, “Angularly resolved high-order harmonic generation in helium,” Phys. Rev. A 49, R28–R31 (1994).
[Crossref] [PubMed]

Peatross, J.

J. Peatross and D. D. Meyerhofer, “Angular distribution of high-order harmonics emitted from rare gases at low density,” Phys. Rev. A 51, R906 (1995).
[Crossref] [PubMed]

J. Peatross, J. Chaloupka, and D. D. Meyerhofer, “High-order harmonic generation with an annular laser beam,” Opt. Lett. 19, 942–944 (1994).
[Crossref] [PubMed]

S. Augst, C. I. Moore, J. Peatross, and D. D. Meyerhofer, “Spatial distribution of high-order harmonics generated in the tunneling regime,” in Short Wavelength Coherent Radiation, P. H. Bucksbaum and N. M. Ceglio, eds., Vol. 11 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1991), pp. 23–27.

J. Peatross and D. D. Meyerhofer, “Measurement of the angular distribution of high-order harmonics emitted from rare gases,” in Short Wavelength V, Vol. 17 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1993).

Perry, M. D.

P. Salieres, T. Ditmire, K S. Budil, M. D. Perry, and A. L’Huillier, “Spatial profiles of high-order harmonics generated by a femtosecond Cr:LiSAF laser,” J. Phys. B 27, L217–L222 (1994).
[Crossref]

Plaja, L.

Roso-Franco, L.

Salieres, P.

P. Salieres, T. Ditmire, K S. Budil, M. D. Perry, and A. L’Huillier, “Spatial profiles of high-order harmonics generated by a femtosecond Cr:LiSAF laser,” J. Phys. B 27, L217–L222 (1994).
[Crossref]

Schafer, K. J.

A. L’Huillier, Ph. Balcou, S. Candel, K. J. Schafer, and K. C. Kulander, “Calculations of high-order harmonic-generation processes in xenon at 1064 nm,” Phys. Rev. A 46, 2778–2790 (1992).
[Crossref]

A. L’Huillier, K. J. Schafer, and K. C. Kulander, “Theoretical aspects of intense field harmonic generation,” J. Phys. B 24, 3315–3341 (1991).
[Crossref]

K. C. Kulander, K. J. Schafer, and J. L. Krause, “Dynamics of short-pulse excitation, ionization and harmonic conversion,” in Super Intense Laser–Atom Physics, B. Piraux, A. L’Huillier, and K. Rz¸żewski, eds., Vol. 316 of NATO ASI Series (Plenum, New York, 1993), pp. 95–110.
[Crossref]

Shore, B. W.

K. C. Kulander and B. W. Shore, “Generation of optical harmonics by intense pulses of laser radiation. II. Singleatom spectrum for xenon,” J. Opt. Soc. Am. B 7, 502–508 (1990).
[Crossref]

K. C. Kulander and B. W. Shore, “Calculations of multiple-harmonic conversion of 1064-nm radiation in Xe,” Phys. Rev. Lett. 62, 524–526 (1989).
[Crossref] [PubMed]

B. W. Shore and K. C. Kulander, “Generation of optical harmonics by intense pulses of laser radiation. I. Propagation effects,” J. Mod. Opt. 36, 857–875 (1989).
[Crossref]

Smith, R. A.

J. W. G. Tisch, R. A. Smith, J. E. Muffett, M. Ciarrocca, J. P. Marangos, and M. H. R. Hutchinson, “Angularly resolved high-order harmonic generation in helium,” Phys. Rev. A 49, R28–R31 (1994).
[Crossref] [PubMed]

Sundaram, B.

B. Sundaram and P. W. Milonni, “High-order harmonic generation: simplified model and relevance of single-atom theories to experiment,” Phys. Rev. A 41, 6571–6573 (1990).
[Crossref] [PubMed]

Tisch, J. W. G.

J. W. G. Tisch, R. A. Smith, J. E. Muffett, M. Ciarrocca, J. P. Marangos, and M. H. R. Hutchinson, “Angularly resolved high-order harmonic generation in helium,” Phys. Rev. A 49, R28–R31 (1994).
[Crossref] [PubMed]

J. Mod. Opt. (1)

B. W. Shore and K. C. Kulander, “Generation of optical harmonics by intense pulses of laser radiation. I. Propagation effects,” J. Mod. Opt. 36, 857–875 (1989).
[Crossref]

J. Opt. Soc. Am. B (2)

J. Phys. B (2)

A. L’Huillier, K. J. Schafer, and K. C. Kulander, “Theoretical aspects of intense field harmonic generation,” J. Phys. B 24, 3315–3341 (1991).
[Crossref]

P. Salieres, T. Ditmire, K S. Budil, M. D. Perry, and A. L’Huillier, “Spatial profiles of high-order harmonics generated by a femtosecond Cr:LiSAF laser,” J. Phys. B 27, L217–L222 (1994).
[Crossref]

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Phys. Rev. A (8)

J. W. G. Tisch, R. A. Smith, J. E. Muffett, M. Ciarrocca, J. P. Marangos, and M. H. R. Hutchinson, “Angularly resolved high-order harmonic generation in helium,” Phys. Rev. A 49, R28–R31 (1994).
[Crossref] [PubMed]

X. F. Li, A. L’Huillier, M. Ferray, L. A. Lompre, and G. Mainfray, “Multiple-harmonic generation in rare gases at high laser intensity,” Phys. Rev. A 39, 5751–5761 (1989).
[Crossref] [PubMed]

A. L’Huillier, Ph. Balcou, S. Candel, K. J. Schafer, and K. C. Kulander, “Calculations of high-order harmonic-generation processes in xenon at 1064 nm,” Phys. Rev. A 46, 2778–2790 (1992).
[Crossref]

W. Becker, S. Long, and J. K. McIver, “Higher-harmonic production in a model atom with short-range potential,” Phys. Rev. A 41, 4112–4115 (1990).
[Crossref] [PubMed]

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[Crossref] [PubMed]

M. Lewenstein, Ph. 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]

J. Peatross and D. D. Meyerhofer, “Angular distribution of high-order harmonics emitted from rare gases at low density,” Phys. Rev. A 51, R906 (1995).
[Crossref] [PubMed]

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[Crossref] [PubMed]

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Other (7)

S. Augst, C. I. Moore, J. Peatross, and D. D. Meyerhofer, “Spatial distribution of high-order harmonics generated in the tunneling regime,” in Short Wavelength Coherent Radiation, P. H. Bucksbaum and N. M. Ceglio, eds., Vol. 11 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1991), pp. 23–27.

J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975), p. 395, Eq. (9.19).

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A. L’Huillier, L. A. Lompre, G. Mainfray, and C. Manus, “Multiple harmonic conversion in rare gases in strong laser fields,” in Proceedings of the 5th International Conference on Multiphoton Processes, G. Mainfray and P. Agostini, eds. (Le Commissarial à l’Energie Atomique, Paris, 1990), pp. 45–55.

K. C. Kulander, K. J. Schafer, and J. L. Krause, “Dynamics of short-pulse excitation, ionization and harmonic conversion,” in Super Intense Laser–Atom Physics, B. Piraux, A. L’Huillier, and K. Rz¸żewski, eds., Vol. 316 of NATO ASI Series (Plenum, New York, 1993), pp. 95–110.
[Crossref]

J. Peatross and D. D. Meyerhofer, “Measurement of the angular distribution of high-order harmonics emitted from rare gases,” in Short Wavelength V, Vol. 17 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1993).

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Figures (9)

Fig. 1
Fig. 1

(a) Single-atom response for the 13th harmonic generated in Xe plotted as a function of laser intensity. (b) Single-atom response for the 13th harmonic generated in Xe plotted in a polar format where the azimuthal coordinate corresponds to the phase of harmonic emission relative to the laser’s phase.

Fig. 2
Fig. 2

Schematic depicting how an intensity-dependent phase variation of the qth-harmonic emission can cause the harmonic light to scatter into angles off axis. A change of Δr in radius corresponds to a change of ΔI in laser intensity. The associated change in the harmonic phase Δϕq causes the light to scatter into an angle θ ∼ Δϕq/(kqΔr).

Fig. 3
Fig. 3

(a) Single-atom response for the 13th harmonic generated in Xe plotted as a function of radius in a Gaussian laser focus with peak intensity 4.5 × 1013 W/cm2 (solid curve). The dotted curve is the phase of harmonic emission relative to the laser’s phase indicated on the right vertical axis. (b) Far-field intensity distribution calculated from the planar emission distribution of (a). The dotted curve is a repeat of the calculation performed with the intrinsic phase held constant. The dotted curve has been divided by a factor of 10. The dashed curve depicts the laser intensity profile. The units on the horizontal axis can also be written as ρ/w(z), where w(z) ≅ w0z/z0.

Fig. 4
Fig. 4

Far-field intensity distribution of the 13th harmonic generated in a medium of thickness z0/5 centered in a laser focus with peak intensity 4.5 × 1013 W/cm2 (solid curve). The dotted curve is a repeat of the calculation in which the temporal integration over a Gaussian laser pulse has been performed to yield the accumulated energy as indicated on the right vertical axis.

Fig. 5
Fig. 5

Schematic showing the phase error that occurs as a result of the thickness of the generating medium when the harmonics emerge into angles off the laser axis.

Fig. 6
Fig. 6

Far-field intensity distribution corresponding to emission of the 13th harmonic generated in a medium of thickness z0 centered in a laser focus with peak intensity 4.5 × 1013 W/cm2 (solid curve). The dotted curve is a repeat of the calculation performed with the intrinsic phase held constant. The dotted curve has been divided by a factor of 4.

Fig. 7
Fig. 7

Far-field axial intensity of the 13th-harmonic emission as a function of the longitudinal position of the gas distribution in the laser focus. The dotted curve is a repeat of the calculation performed with the relative phase held constant. The dotted curve has been divided by a factor of 4.

Fig. 8
Fig. 8

Proposed experimental setup for studying intensity-dependent intrinsic phases. Harmonics are generated in counterpropagating beams focused off mirrors with holes in their centers.

Fig. 9
Fig. 9

Effective emission for the 13th harmonic in the direction of the weak beam when two beams of intensities I1 and I2 = I1/100 are counterpropagated (solid curve). The dotted curve is the effective emission in the direction of the strong beam. The dashed curve is the single-atom response identical to that shown in Fig. 1(a).

Equations (11)

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E q ( r , t + r / c ) = k q 2 8 π 0 τ exp ( i q ω t ) | d q [ I L ( t ) ] | × exp { i ϕ q [ I L ( t ) ] + i q ϕ L } + c.c. ,
E q ( r , t + r / c ) = k q 2 N 0 4 0 r exp ( i q ω t ) 0 d ρ ρ J 0 ( k q ρ ρ z ) × | d q [ I L ( ρ , t ) ] | exp { i ϕ q [ I L ( ρ , t ) ] + i q ϕ L } + c.c. ,
I L ( ρ , t ) = I 0 exp ( 2 ρ 2 w 0 2 t 2 τ 2 ) ,
Δ ϕ q / Δ r k q θ ,
E q ( r , t + r / c ) = k q 2 N 0 4 0 r exp ( i q ω t ) z 1 z 2 d z 0 d ρ ρ J 0 ( k q ρ ρ z ) × | d q [ I L ( ρ , z , t ) ] | × exp { i ϕ q [ I L ( ρ , z , t ) ] + i q ϕ L ( ρ , z ) + i k q ρ 2 z 2 z 2 } + c.c. ,
I L ( ρ , z , t ) = I 0 1 + z 2 / z 0 2 × exp [ 2 ρ 2 w 0 2 ( 1 + z 2 / z 0 2 ) ( t z / c τ ) 2 ] ,
ϕ L ( ρ , z ) = k L ρ 2 / 2 R ( z ) tan 1 ( z / z 0 ) z d z Δ k ( z ) / q ,
E 1 ( z , t ) = E 1 2 exp ( i ω t + i k z ) + E 2 2 exp ( i ω t i k z ) + c.c.
I t ( z ) = I 1 [ ( 1 I 2 / I 1 ) 2 + 4 I 2 / I 1 cos 2 k z ] .
Φ ( z ) = k z tan 1 ( 1 I 2 / I 1 1 + I 2 / I 1 tan k z ) n π ,
d q Eff ( I 1 , I 2 ) = 2 λ λ / 4 λ / 4 d z | d q { I t ( z ) } | × exp { i ϕ q { I t ( z ) } + i q Φ ( z ) } .

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