Abstract

Broad-bandwidth light pulses with different frequencies, extending from the IR to the UV, are simultaneously generated when two noncollinear, ultrafast laser pulses from a visible dual-frequency laser propagate through bulk isotropic transparent media such as common glass. This phenomenon, which is believed to have been previously unreported, can be explained by a cascade of highly nondegenerate four-wave-mixing processes and corresponds to a coherent scattering effect with geometrically minimized phase mismatch. Frequency-upconverted beams were observed up to the 11th order.

© 2000 Optical Society of America

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  1. Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).
  2. R. R. Alfano, The Supercontinuum Laser Source (Springer-Verlag, Berlin, 1989).
    [CrossRef]
  3. S. A. Akmahnov, V. A. Martynov, S. M. Saltiel, and V. G. Tunkin, JETP Lett. 22, 65 (1975).
  4. A. Varanavicius, A. Dubietis, A. Berzanskis, R. Danielius, and A. Piskarskas, Opt. Lett. 22, 1603 (1997).
    [CrossRef]
  5. H. H. Yaffe, R. G. Waarts, E. Lichtman, and A. A. Friesem, Electron. Lett. 23, 42 (1987).
    [CrossRef]
  6. D. L. Hart, A. Judy, T. A. Brian Kennedy, R. Roy, and K. Stoev, Phys. Rev. A 50, 1807 (1994).
    [CrossRef] [PubMed]
  7. D. L. Hart, A. F. Judy, R. Roy, and J. W. Beletic, Phys. Rev. E 57, 4757 (1998).
    [CrossRef]
  8. M. Lenzner, J. Krüger, S. Sartania, Z. Cheng, Ch. Spielman, G. Mourou, W. Kautek, and F. Krausz, Phys. Rev. Lett. 80, 4076 (1998).
    [CrossRef]
  9. C. Rullière, T. Amand, and X. Marie, in Femtosecond Laser Pulses—Principles and Experiments, C. Rullière, ed. (Springer-Verlag, Berlin, 1998), pp. 243–258.
  10. H. Crespo and J. T. Mendonça, “A new method for high-harmonic generation by cascaded four-wave mixing,” Opt. Commun. (to be published).
  11. L. Xu, G. Tempea, Ch. Spielmann, F. Krausz, A. Stingl, K. Ferencz, and S. Takano, Opt. Lett. 23, 789 (1998).
    [CrossRef]
  12. T. Beddard, W. Sibbett, D. T. Reid, J. Garduno-Mejia, N. Jamasbi, and M. Mohebi, Opt. Lett. 24, 163 (1999).
    [CrossRef]
  13. A. L’Huillier, K. Shafer, and K. Kulander, Phys. Rev. Lett. 66, 2200 (1991).
    [CrossRef] [PubMed]
  14. Z. Chang, A. Rundquist, H. Wang, M. Murnane, and H. Kapteyn, Phys. Rev. Lett. 79, 2967 (1997); Ch. Spielman, N. H. Burnett, S. Sartania, R. Koppitsch, M. Schnürer, C. Kan, M. Lenzner, P. Wobrauschek, and F. Krausz, Science 278, 661 (1997).
    [CrossRef]
  15. S. Meyer, H. Eichmann, T. Menzel, S. Nolte, B. Wellegehausen, B. N. Chichkov, and C. Momma, Phys. Rev. Lett. 76, 3336 (1996).
    [CrossRef] [PubMed]

1999 (1)

1998 (3)

D. L. Hart, A. F. Judy, R. Roy, and J. W. Beletic, Phys. Rev. E 57, 4757 (1998).
[CrossRef]

M. Lenzner, J. Krüger, S. Sartania, Z. Cheng, Ch. Spielman, G. Mourou, W. Kautek, and F. Krausz, Phys. Rev. Lett. 80, 4076 (1998).
[CrossRef]

L. Xu, G. Tempea, Ch. Spielmann, F. Krausz, A. Stingl, K. Ferencz, and S. Takano, Opt. Lett. 23, 789 (1998).
[CrossRef]

1997 (2)

A. Varanavicius, A. Dubietis, A. Berzanskis, R. Danielius, and A. Piskarskas, Opt. Lett. 22, 1603 (1997).
[CrossRef]

Z. Chang, A. Rundquist, H. Wang, M. Murnane, and H. Kapteyn, Phys. Rev. Lett. 79, 2967 (1997); Ch. Spielman, N. H. Burnett, S. Sartania, R. Koppitsch, M. Schnürer, C. Kan, M. Lenzner, P. Wobrauschek, and F. Krausz, Science 278, 661 (1997).
[CrossRef]

1996 (1)

S. Meyer, H. Eichmann, T. Menzel, S. Nolte, B. Wellegehausen, B. N. Chichkov, and C. Momma, Phys. Rev. Lett. 76, 3336 (1996).
[CrossRef] [PubMed]

1994 (1)

D. L. Hart, A. Judy, T. A. Brian Kennedy, R. Roy, and K. Stoev, Phys. Rev. A 50, 1807 (1994).
[CrossRef] [PubMed]

1991 (1)

A. L’Huillier, K. Shafer, and K. Kulander, Phys. Rev. Lett. 66, 2200 (1991).
[CrossRef] [PubMed]

1987 (1)

H. H. Yaffe, R. G. Waarts, E. Lichtman, and A. A. Friesem, Electron. Lett. 23, 42 (1987).
[CrossRef]

1975 (1)

S. A. Akmahnov, V. A. Martynov, S. M. Saltiel, and V. G. Tunkin, JETP Lett. 22, 65 (1975).

Akmahnov, S. A.

S. A. Akmahnov, V. A. Martynov, S. M. Saltiel, and V. G. Tunkin, JETP Lett. 22, 65 (1975).

Alfano, R. R.

R. R. Alfano, The Supercontinuum Laser Source (Springer-Verlag, Berlin, 1989).
[CrossRef]

Amand, T.

C. Rullière, T. Amand, and X. Marie, in Femtosecond Laser Pulses—Principles and Experiments, C. Rullière, ed. (Springer-Verlag, Berlin, 1998), pp. 243–258.

Beddard, T.

Beletic, J. W.

D. L. Hart, A. F. Judy, R. Roy, and J. W. Beletic, Phys. Rev. E 57, 4757 (1998).
[CrossRef]

Berzanskis, A.

Chang, Z.

Z. Chang, A. Rundquist, H. Wang, M. Murnane, and H. Kapteyn, Phys. Rev. Lett. 79, 2967 (1997); Ch. Spielman, N. H. Burnett, S. Sartania, R. Koppitsch, M. Schnürer, C. Kan, M. Lenzner, P. Wobrauschek, and F. Krausz, Science 278, 661 (1997).
[CrossRef]

Cheng, Z.

M. Lenzner, J. Krüger, S. Sartania, Z. Cheng, Ch. Spielman, G. Mourou, W. Kautek, and F. Krausz, Phys. Rev. Lett. 80, 4076 (1998).
[CrossRef]

Chichkov, B. N.

S. Meyer, H. Eichmann, T. Menzel, S. Nolte, B. Wellegehausen, B. N. Chichkov, and C. Momma, Phys. Rev. Lett. 76, 3336 (1996).
[CrossRef] [PubMed]

Crespo, H.

H. Crespo and J. T. Mendonça, “A new method for high-harmonic generation by cascaded four-wave mixing,” Opt. Commun. (to be published).

Danielius, R.

Dubietis, A.

Eichmann, H.

S. Meyer, H. Eichmann, T. Menzel, S. Nolte, B. Wellegehausen, B. N. Chichkov, and C. Momma, Phys. Rev. Lett. 76, 3336 (1996).
[CrossRef] [PubMed]

Ferencz, K.

Friesem, A. A.

H. H. Yaffe, R. G. Waarts, E. Lichtman, and A. A. Friesem, Electron. Lett. 23, 42 (1987).
[CrossRef]

Garduno-Mejia, J.

Hart, D. L.

D. L. Hart, A. F. Judy, R. Roy, and J. W. Beletic, Phys. Rev. E 57, 4757 (1998).
[CrossRef]

D. L. Hart, A. Judy, T. A. Brian Kennedy, R. Roy, and K. Stoev, Phys. Rev. A 50, 1807 (1994).
[CrossRef] [PubMed]

Jamasbi, N.

Judy, A.

D. L. Hart, A. Judy, T. A. Brian Kennedy, R. Roy, and K. Stoev, Phys. Rev. A 50, 1807 (1994).
[CrossRef] [PubMed]

Judy, A. F.

D. L. Hart, A. F. Judy, R. Roy, and J. W. Beletic, Phys. Rev. E 57, 4757 (1998).
[CrossRef]

Kapteyn, H.

Z. Chang, A. Rundquist, H. Wang, M. Murnane, and H. Kapteyn, Phys. Rev. Lett. 79, 2967 (1997); Ch. Spielman, N. H. Burnett, S. Sartania, R. Koppitsch, M. Schnürer, C. Kan, M. Lenzner, P. Wobrauschek, and F. Krausz, Science 278, 661 (1997).
[CrossRef]

Kautek, W.

M. Lenzner, J. Krüger, S. Sartania, Z. Cheng, Ch. Spielman, G. Mourou, W. Kautek, and F. Krausz, Phys. Rev. Lett. 80, 4076 (1998).
[CrossRef]

Kennedy, T. A. Brian

D. L. Hart, A. Judy, T. A. Brian Kennedy, R. Roy, and K. Stoev, Phys. Rev. A 50, 1807 (1994).
[CrossRef] [PubMed]

Krausz, F.

M. Lenzner, J. Krüger, S. Sartania, Z. Cheng, Ch. Spielman, G. Mourou, W. Kautek, and F. Krausz, Phys. Rev. Lett. 80, 4076 (1998).
[CrossRef]

L. Xu, G. Tempea, Ch. Spielmann, F. Krausz, A. Stingl, K. Ferencz, and S. Takano, Opt. Lett. 23, 789 (1998).
[CrossRef]

Krüger, J.

M. Lenzner, J. Krüger, S. Sartania, Z. Cheng, Ch. Spielman, G. Mourou, W. Kautek, and F. Krausz, Phys. Rev. Lett. 80, 4076 (1998).
[CrossRef]

Kulander, K.

A. L’Huillier, K. Shafer, and K. Kulander, Phys. Rev. Lett. 66, 2200 (1991).
[CrossRef] [PubMed]

L’Huillier, A.

A. L’Huillier, K. Shafer, and K. Kulander, Phys. Rev. Lett. 66, 2200 (1991).
[CrossRef] [PubMed]

Lenzner, M.

M. Lenzner, J. Krüger, S. Sartania, Z. Cheng, Ch. Spielman, G. Mourou, W. Kautek, and F. Krausz, Phys. Rev. Lett. 80, 4076 (1998).
[CrossRef]

Lichtman, E.

H. H. Yaffe, R. G. Waarts, E. Lichtman, and A. A. Friesem, Electron. Lett. 23, 42 (1987).
[CrossRef]

Marie, X.

C. Rullière, T. Amand, and X. Marie, in Femtosecond Laser Pulses—Principles and Experiments, C. Rullière, ed. (Springer-Verlag, Berlin, 1998), pp. 243–258.

Martynov, V. A.

S. A. Akmahnov, V. A. Martynov, S. M. Saltiel, and V. G. Tunkin, JETP Lett. 22, 65 (1975).

Mendonça, J. T.

H. Crespo and J. T. Mendonça, “A new method for high-harmonic generation by cascaded four-wave mixing,” Opt. Commun. (to be published).

Menzel, T.

S. Meyer, H. Eichmann, T. Menzel, S. Nolte, B. Wellegehausen, B. N. Chichkov, and C. Momma, Phys. Rev. Lett. 76, 3336 (1996).
[CrossRef] [PubMed]

Meyer, S.

S. Meyer, H. Eichmann, T. Menzel, S. Nolte, B. Wellegehausen, B. N. Chichkov, and C. Momma, Phys. Rev. Lett. 76, 3336 (1996).
[CrossRef] [PubMed]

Mohebi, M.

Momma, C.

S. Meyer, H. Eichmann, T. Menzel, S. Nolte, B. Wellegehausen, B. N. Chichkov, and C. Momma, Phys. Rev. Lett. 76, 3336 (1996).
[CrossRef] [PubMed]

Mourou, G.

M. Lenzner, J. Krüger, S. Sartania, Z. Cheng, Ch. Spielman, G. Mourou, W. Kautek, and F. Krausz, Phys. Rev. Lett. 80, 4076 (1998).
[CrossRef]

Murnane, M.

Z. Chang, A. Rundquist, H. Wang, M. Murnane, and H. Kapteyn, Phys. Rev. Lett. 79, 2967 (1997); Ch. Spielman, N. H. Burnett, S. Sartania, R. Koppitsch, M. Schnürer, C. Kan, M. Lenzner, P. Wobrauschek, and F. Krausz, Science 278, 661 (1997).
[CrossRef]

Nolte, S.

S. Meyer, H. Eichmann, T. Menzel, S. Nolte, B. Wellegehausen, B. N. Chichkov, and C. Momma, Phys. Rev. Lett. 76, 3336 (1996).
[CrossRef] [PubMed]

Piskarskas, A.

Reid, D. T.

Roy, R.

D. L. Hart, A. F. Judy, R. Roy, and J. W. Beletic, Phys. Rev. E 57, 4757 (1998).
[CrossRef]

D. L. Hart, A. Judy, T. A. Brian Kennedy, R. Roy, and K. Stoev, Phys. Rev. A 50, 1807 (1994).
[CrossRef] [PubMed]

Rullière, C.

C. Rullière, T. Amand, and X. Marie, in Femtosecond Laser Pulses—Principles and Experiments, C. Rullière, ed. (Springer-Verlag, Berlin, 1998), pp. 243–258.

Rundquist, A.

Z. Chang, A. Rundquist, H. Wang, M. Murnane, and H. Kapteyn, Phys. Rev. Lett. 79, 2967 (1997); Ch. Spielman, N. H. Burnett, S. Sartania, R. Koppitsch, M. Schnürer, C. Kan, M. Lenzner, P. Wobrauschek, and F. Krausz, Science 278, 661 (1997).
[CrossRef]

Saltiel, S. M.

S. A. Akmahnov, V. A. Martynov, S. M. Saltiel, and V. G. Tunkin, JETP Lett. 22, 65 (1975).

Sartania, S.

M. Lenzner, J. Krüger, S. Sartania, Z. Cheng, Ch. Spielman, G. Mourou, W. Kautek, and F. Krausz, Phys. Rev. Lett. 80, 4076 (1998).
[CrossRef]

Shafer, K.

A. L’Huillier, K. Shafer, and K. Kulander, Phys. Rev. Lett. 66, 2200 (1991).
[CrossRef] [PubMed]

Shen, Y. R.

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).

Sibbett, W.

Spielman, Ch.

M. Lenzner, J. Krüger, S. Sartania, Z. Cheng, Ch. Spielman, G. Mourou, W. Kautek, and F. Krausz, Phys. Rev. Lett. 80, 4076 (1998).
[CrossRef]

Spielmann, Ch.

Stingl, A.

Stoev, K.

D. L. Hart, A. Judy, T. A. Brian Kennedy, R. Roy, and K. Stoev, Phys. Rev. A 50, 1807 (1994).
[CrossRef] [PubMed]

Takano, S.

Tempea, G.

Tunkin, V. G.

S. A. Akmahnov, V. A. Martynov, S. M. Saltiel, and V. G. Tunkin, JETP Lett. 22, 65 (1975).

Varanavicius, A.

Waarts, R. G.

H. H. Yaffe, R. G. Waarts, E. Lichtman, and A. A. Friesem, Electron. Lett. 23, 42 (1987).
[CrossRef]

Wang, H.

Z. Chang, A. Rundquist, H. Wang, M. Murnane, and H. Kapteyn, Phys. Rev. Lett. 79, 2967 (1997); Ch. Spielman, N. H. Burnett, S. Sartania, R. Koppitsch, M. Schnürer, C. Kan, M. Lenzner, P. Wobrauschek, and F. Krausz, Science 278, 661 (1997).
[CrossRef]

Wellegehausen, B.

S. Meyer, H. Eichmann, T. Menzel, S. Nolte, B. Wellegehausen, B. N. Chichkov, and C. Momma, Phys. Rev. Lett. 76, 3336 (1996).
[CrossRef] [PubMed]

Xu, L.

Yaffe, H. H.

H. H. Yaffe, R. G. Waarts, E. Lichtman, and A. A. Friesem, Electron. Lett. 23, 42 (1987).
[CrossRef]

Electron. Lett. (1)

H. H. Yaffe, R. G. Waarts, E. Lichtman, and A. A. Friesem, Electron. Lett. 23, 42 (1987).
[CrossRef]

JETP Lett. (1)

S. A. Akmahnov, V. A. Martynov, S. M. Saltiel, and V. G. Tunkin, JETP Lett. 22, 65 (1975).

Opt. Lett. (3)

Phys. Rev. A (1)

D. L. Hart, A. Judy, T. A. Brian Kennedy, R. Roy, and K. Stoev, Phys. Rev. A 50, 1807 (1994).
[CrossRef] [PubMed]

Phys. Rev. E (1)

D. L. Hart, A. F. Judy, R. Roy, and J. W. Beletic, Phys. Rev. E 57, 4757 (1998).
[CrossRef]

Phys. Rev. Lett. (4)

M. Lenzner, J. Krüger, S. Sartania, Z. Cheng, Ch. Spielman, G. Mourou, W. Kautek, and F. Krausz, Phys. Rev. Lett. 80, 4076 (1998).
[CrossRef]

A. L’Huillier, K. Shafer, and K. Kulander, Phys. Rev. Lett. 66, 2200 (1991).
[CrossRef] [PubMed]

Z. Chang, A. Rundquist, H. Wang, M. Murnane, and H. Kapteyn, Phys. Rev. Lett. 79, 2967 (1997); Ch. Spielman, N. H. Burnett, S. Sartania, R. Koppitsch, M. Schnürer, C. Kan, M. Lenzner, P. Wobrauschek, and F. Krausz, Science 278, 661 (1997).
[CrossRef]

S. Meyer, H. Eichmann, T. Menzel, S. Nolte, B. Wellegehausen, B. N. Chichkov, and C. Momma, Phys. Rev. Lett. 76, 3336 (1996).
[CrossRef] [PubMed]

Other (4)

C. Rullière, T. Amand, and X. Marie, in Femtosecond Laser Pulses—Principles and Experiments, C. Rullière, ed. (Springer-Verlag, Berlin, 1998), pp. 243–258.

H. Crespo and J. T. Mendonça, “A new method for high-harmonic generation by cascaded four-wave mixing,” Opt. Commun. (to be published).

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).

R. R. Alfano, The Supercontinuum Laser Source (Springer-Verlag, Berlin, 1989).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Experimental arrangement: BS, beam splitter; M1–M3, silver mirrors; M4, parabolic mirror; M5, M6, aluminum mirrors.

Fig. 2
Fig. 2

Typical image of the pattern defined by the generated beams directly projected onto a white fluorescent screen.

Fig. 3
Fig. 3

Spectra of the beams in the cascade: dashed curve, original spectra of pump beam P and the signal beam S (scaled for comparison); solid curve, spectra of the generated beams.

Fig. 4
Fig. 4

Representation of the wave vectors of all the beams in the pattern: open squares, measured points; filled circles, calculation with the cascaded processes; open circles, calculated exactly phase-matched beams, with the interaction angle given by Eq. (1) (the solid curve is a guide).

Fig. 5
Fig. 5

Wave-vector mismatch of the beams in the pattern: open squares, measured points; filled circles, calculation for the cascaded processes; dashed curve, calculation assuming collinear geometry (0°).

Equations (1)

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cosθ2=12m+1kS+mkP2-kUm2m2+mkSkP1/2,

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