Abstract

We analyze the spectral changes that occur when unfocused intense femtosecond pulses at 800 nm propagate through different atomic and molecular gases. The observed red shift in the self-phase-modulated spectra after propagation through N2, O2, and air is attributed to a delayed change of the nonlinear refractive index, a consequence of the molecular response to impulsive excitation of rotational coherences. We compare these results on the nonlinear refractive index with those obtained from Ar, Xe, and SF6.

© 1997 Optical Society of America

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  1. R. W. Hellwarth, D. M. Pennington, and M. A. Henesian, “Indices governing optical self-focusing and self-induced changes in the state of polarization in N2, O2, H2, and Ar gases,” Phys. Rev. A 41, 2766 (1990).
    [CrossRef] [PubMed]
  2. M. D. Perry and G. Mourou, “Terawatt to petawatt subpicosecond lasers,” Science 264, 917 (1994).
    [CrossRef] [PubMed]
  3. A. Braun, G. Korn, X. Liu, D. Du, J. Squier, and G. Mourou, “Self-channeling of high-peak power femtosecond laser pulses in air,” Opt. Lett. 20, 73 (1995).
    [CrossRef] [PubMed]
  4. E. T. J. Nibbering, P. F. Curley, G. Grillon, B. S. Prade, M. A. Franco, F. Salin, and A. Mysyrowicz, “Conical emission from self-guided femtosecond pulses in air,” Opt. Lett. 21, 62 (1996).
    [CrossRef] [PubMed]
  5. D. V. Vlasov, R. A. Garaev, V. V. Korobkin, and R. V. Serov, “Measurement of nonlinear polarizability of air,” Zh. Eksp. Teor. Fiz. 76, 2039 (1979) [Sov. Phys. JETP 49, 1033 (1979)].
  6. D. M. Pennington, M. A. Henesian, and R. W. Hellwarth, “Nonlinear index of air at 1.053 µm,” Phys. Rev. A 39, 3003 (1989).
    [CrossRef] [PubMed]
  7. Y. Shimoji, A. T. Fay, R. S. F. Chang, and N. Djeu, “Direct measurement of the nonlinear refractive index of air,” J. Opt. Soc. Am. B 6, 1994 (1989).
    [CrossRef]
  8. R. H. Lehmberg, C. J. Pawley, A. V. Deniz, M. Klapisch, and Y. Leng, “Two-photon resonantly-enhanced negative nonlinear refractive index in xenon at 248 nm,” Opt. Commun. 121, 78 (1995).
    [CrossRef]
  9. M. J. Shaw, C. J. Hooker, and D. C. Wilson, “Measurement of the nonlinear refractive index of air and other gases at 248 nm,” Opt. Commun. 103, 153 (1993).
    [CrossRef]
  10. B. S. Prade, J. M. Schins, E. T. J. Nibbering, M. A. Franco, and A. Mysyrowicz, “A simple method for the determination of the intensity and phase of ultrashort optical pulses,” Opt. Commun. 113, 79 (1994).
    [CrossRef]
  11. E. T. J. Nibbering, M. A. Franco, B. S. Prade, G. Grillon, C. Le Blanc, and A. Mysyrowicz, “Measurement of the nonlinear refractive index of transparent materials by spectral analysis after nonlinear propagation,” Opt. Commun. 119, 479 (1995).
    [CrossRef]
  12. E. T. J. Nibbering, M. A. Franco, B. S. Prade, G. Grillon, J.-P. Chambaret, and A. Mysyrowicz, “Spectral determination of the amplitude and the phase of intense ultrashort optical pulses,” J. Opt. Soc. Am. B 13, 317 (1996).
    [CrossRef]
  13. C. Le Blanc, G. Grillon, J. P. Chambaret, A. Migus, and A. Antonetti, “Compact and efficient multipass Ti:sapphire system for femtosecond chirped-pulse amplification at the terawatt level,” Opt. Lett. 18, 140 (1993).
    [CrossRef]
  14. R. W. Hellwarth, “Third-order optical susceptibilities of liquids and solids,” Prog. Quantum Electron. 5, 1 (1977).
    [CrossRef]
  15. V. Mizrahi and D. P. Shelton, “Dispersion of nonlinear susceptibilities of Ar, N2, and O2 measured and compared,” Phys. Rev. Lett. 55, 696 (1985).
    [CrossRef] [PubMed]
  16. S. Carusotto, E. Iacopini, E. Polacco, F. Scuri, G. Stefanini, and E. Zavattini, “Measurement of the Kerr constant of He, A, O2, N2, H2, and D2,” Nuovo Cimento 5D, 328 (1985).
    [CrossRef]
  17. M. Morgen, W. Price, L. Hunziker, P. Ludowise, M. Blackwell, and Y. Chen, “Femtosecond Raman-induced polarization spectroscopy studies of rotational coherence in O2, N2, and CO2,” Chem. Phys. Lett. 209, 1 (1993).
    [CrossRef]
  18. D. McMorrow, W. T. Lotshaw, and G. A. Kenney-Wallace, “Femtosecond optical Kerr studies on the origin of the nonlinear responses in simple liquids,” IEEE J. Quantum Electron. 24, 443 (1988).
    [CrossRef]
  19. M. Cho, M. Du, N. F. Scherer, G. R. Fleming, and S. Mukamel, “Off-resonant transient birefringence in liquids,” J. Chem. Phys. 99, 2410 (1993).
    [CrossRef]
  20. C. H. Lin, J. P. Heritage, T. K. Gustafson, R. Y. Chiao, and J. P. McTague, “Birefringence arising from the reorientation of the polarization anisotropy of molecules in collisionless gases,” Phys. Rev. A 13, 813 (1976).
    [CrossRef]
  21. M. Morgen, W. Price, P. Ludowise, and Y. Chen, “Tensor analysis of femtosecond Raman induced polarization spectroscopy: application to the study of rotational coherence,” J. Chem. Phys. 102, 8780 (1995).
    [CrossRef]
  22. J. P. Heritage, T. K. Gustafson, and C. H. Lin, “Observation of coherent transient birefringence in CS2 vapor,” Phys. Rev. Lett. 13, 1299 (1975).
    [CrossRef]
  23. H. Harde and D. Grischkowsky, “Coherent transients excited by subpicosecond pulses of terahertz radiation,” J. Opt. Soc. Am. B 8, 1642 (1991).
    [CrossRef]
  24. M. Gruebele and A. H. Zewail, “Femtosecond wave packet spectroscopy: coherences, the potential and structural determination,” J. Chem. Phys. 98, 883 (1993).
    [CrossRef]
  25. K. Tominaga and K. Yoshihara, “Fifth order optical response of liquid CS2 observed by ultrafast nonresonant six-wave mixing,” Phys. Rev. Lett. 74, 3061 (1995).
    [CrossRef] [PubMed]
  26. T. Steffen and K. Duppen, “Femtosecond two-dimensional spectroscopy of molecular motion in liquids,” Phys. Rev. Lett. 76, 1224 (1996).
    [CrossRef] [PubMed]
  27. K. A. Nelson and E. P. Ippen, “Femtosecond coherent spectroscopy,” Adv. Chem. Phys. 75, 1 (1989).
  28. S. Mukamel, Principles of Nonlinear Optical Spectroscopy, Vol. 6 of Optical and Imaging Sciences (Oxford U. Press, Oxford, 1995).

1996 (3)

1995 (5)

M. Morgen, W. Price, P. Ludowise, and Y. Chen, “Tensor analysis of femtosecond Raman induced polarization spectroscopy: application to the study of rotational coherence,” J. Chem. Phys. 102, 8780 (1995).
[CrossRef]

E. T. J. Nibbering, M. A. Franco, B. S. Prade, G. Grillon, C. Le Blanc, and A. Mysyrowicz, “Measurement of the nonlinear refractive index of transparent materials by spectral analysis after nonlinear propagation,” Opt. Commun. 119, 479 (1995).
[CrossRef]

K. Tominaga and K. Yoshihara, “Fifth order optical response of liquid CS2 observed by ultrafast nonresonant six-wave mixing,” Phys. Rev. Lett. 74, 3061 (1995).
[CrossRef] [PubMed]

A. Braun, G. Korn, X. Liu, D. Du, J. Squier, and G. Mourou, “Self-channeling of high-peak power femtosecond laser pulses in air,” Opt. Lett. 20, 73 (1995).
[CrossRef] [PubMed]

R. H. Lehmberg, C. J. Pawley, A. V. Deniz, M. Klapisch, and Y. Leng, “Two-photon resonantly-enhanced negative nonlinear refractive index in xenon at 248 nm,” Opt. Commun. 121, 78 (1995).
[CrossRef]

1994 (2)

M. D. Perry and G. Mourou, “Terawatt to petawatt subpicosecond lasers,” Science 264, 917 (1994).
[CrossRef] [PubMed]

B. S. Prade, J. M. Schins, E. T. J. Nibbering, M. A. Franco, and A. Mysyrowicz, “A simple method for the determination of the intensity and phase of ultrashort optical pulses,” Opt. Commun. 113, 79 (1994).
[CrossRef]

1993 (5)

C. Le Blanc, G. Grillon, J. P. Chambaret, A. Migus, and A. Antonetti, “Compact and efficient multipass Ti:sapphire system for femtosecond chirped-pulse amplification at the terawatt level,” Opt. Lett. 18, 140 (1993).
[CrossRef]

M. Morgen, W. Price, L. Hunziker, P. Ludowise, M. Blackwell, and Y. Chen, “Femtosecond Raman-induced polarization spectroscopy studies of rotational coherence in O2, N2, and CO2,” Chem. Phys. Lett. 209, 1 (1993).
[CrossRef]

M. J. Shaw, C. J. Hooker, and D. C. Wilson, “Measurement of the nonlinear refractive index of air and other gases at 248 nm,” Opt. Commun. 103, 153 (1993).
[CrossRef]

M. Gruebele and A. H. Zewail, “Femtosecond wave packet spectroscopy: coherences, the potential and structural determination,” J. Chem. Phys. 98, 883 (1993).
[CrossRef]

M. Cho, M. Du, N. F. Scherer, G. R. Fleming, and S. Mukamel, “Off-resonant transient birefringence in liquids,” J. Chem. Phys. 99, 2410 (1993).
[CrossRef]

1991 (1)

1990 (1)

R. W. Hellwarth, D. M. Pennington, and M. A. Henesian, “Indices governing optical self-focusing and self-induced changes in the state of polarization in N2, O2, H2, and Ar gases,” Phys. Rev. A 41, 2766 (1990).
[CrossRef] [PubMed]

1989 (3)

D. M. Pennington, M. A. Henesian, and R. W. Hellwarth, “Nonlinear index of air at 1.053 µm,” Phys. Rev. A 39, 3003 (1989).
[CrossRef] [PubMed]

Y. Shimoji, A. T. Fay, R. S. F. Chang, and N. Djeu, “Direct measurement of the nonlinear refractive index of air,” J. Opt. Soc. Am. B 6, 1994 (1989).
[CrossRef]

K. A. Nelson and E. P. Ippen, “Femtosecond coherent spectroscopy,” Adv. Chem. Phys. 75, 1 (1989).

1988 (1)

D. McMorrow, W. T. Lotshaw, and G. A. Kenney-Wallace, “Femtosecond optical Kerr studies on the origin of the nonlinear responses in simple liquids,” IEEE J. Quantum Electron. 24, 443 (1988).
[CrossRef]

1985 (2)

V. Mizrahi and D. P. Shelton, “Dispersion of nonlinear susceptibilities of Ar, N2, and O2 measured and compared,” Phys. Rev. Lett. 55, 696 (1985).
[CrossRef] [PubMed]

S. Carusotto, E. Iacopini, E. Polacco, F. Scuri, G. Stefanini, and E. Zavattini, “Measurement of the Kerr constant of He, A, O2, N2, H2, and D2,” Nuovo Cimento 5D, 328 (1985).
[CrossRef]

1979 (1)

D. V. Vlasov, R. A. Garaev, V. V. Korobkin, and R. V. Serov, “Measurement of nonlinear polarizability of air,” Zh. Eksp. Teor. Fiz. 76, 2039 (1979) [Sov. Phys. JETP 49, 1033 (1979)].

1977 (1)

R. W. Hellwarth, “Third-order optical susceptibilities of liquids and solids,” Prog. Quantum Electron. 5, 1 (1977).
[CrossRef]

1976 (1)

C. H. Lin, J. P. Heritage, T. K. Gustafson, R. Y. Chiao, and J. P. McTague, “Birefringence arising from the reorientation of the polarization anisotropy of molecules in collisionless gases,” Phys. Rev. A 13, 813 (1976).
[CrossRef]

1975 (1)

J. P. Heritage, T. K. Gustafson, and C. H. Lin, “Observation of coherent transient birefringence in CS2 vapor,” Phys. Rev. Lett. 13, 1299 (1975).
[CrossRef]

Antonetti, A.

Blackwell, M.

M. Morgen, W. Price, L. Hunziker, P. Ludowise, M. Blackwell, and Y. Chen, “Femtosecond Raman-induced polarization spectroscopy studies of rotational coherence in O2, N2, and CO2,” Chem. Phys. Lett. 209, 1 (1993).
[CrossRef]

Braun, A.

Carusotto, S.

S. Carusotto, E. Iacopini, E. Polacco, F. Scuri, G. Stefanini, and E. Zavattini, “Measurement of the Kerr constant of He, A, O2, N2, H2, and D2,” Nuovo Cimento 5D, 328 (1985).
[CrossRef]

Chambaret, J. P.

Chambaret, J.-P.

Chang, R. S. F.

Chen, Y.

M. Morgen, W. Price, P. Ludowise, and Y. Chen, “Tensor analysis of femtosecond Raman induced polarization spectroscopy: application to the study of rotational coherence,” J. Chem. Phys. 102, 8780 (1995).
[CrossRef]

M. Morgen, W. Price, L. Hunziker, P. Ludowise, M. Blackwell, and Y. Chen, “Femtosecond Raman-induced polarization spectroscopy studies of rotational coherence in O2, N2, and CO2,” Chem. Phys. Lett. 209, 1 (1993).
[CrossRef]

Chiao, R. Y.

C. H. Lin, J. P. Heritage, T. K. Gustafson, R. Y. Chiao, and J. P. McTague, “Birefringence arising from the reorientation of the polarization anisotropy of molecules in collisionless gases,” Phys. Rev. A 13, 813 (1976).
[CrossRef]

Cho, M.

M. Cho, M. Du, N. F. Scherer, G. R. Fleming, and S. Mukamel, “Off-resonant transient birefringence in liquids,” J. Chem. Phys. 99, 2410 (1993).
[CrossRef]

Curley, P. F.

Deniz, A. V.

R. H. Lehmberg, C. J. Pawley, A. V. Deniz, M. Klapisch, and Y. Leng, “Two-photon resonantly-enhanced negative nonlinear refractive index in xenon at 248 nm,” Opt. Commun. 121, 78 (1995).
[CrossRef]

Djeu, N.

Du, D.

Du, M.

M. Cho, M. Du, N. F. Scherer, G. R. Fleming, and S. Mukamel, “Off-resonant transient birefringence in liquids,” J. Chem. Phys. 99, 2410 (1993).
[CrossRef]

Duppen, K.

T. Steffen and K. Duppen, “Femtosecond two-dimensional spectroscopy of molecular motion in liquids,” Phys. Rev. Lett. 76, 1224 (1996).
[CrossRef] [PubMed]

Fay, A. T.

Fleming, G. R.

M. Cho, M. Du, N. F. Scherer, G. R. Fleming, and S. Mukamel, “Off-resonant transient birefringence in liquids,” J. Chem. Phys. 99, 2410 (1993).
[CrossRef]

Franco, M. A.

E. T. J. Nibbering, P. F. Curley, G. Grillon, B. S. Prade, M. A. Franco, F. Salin, and A. Mysyrowicz, “Conical emission from self-guided femtosecond pulses in air,” Opt. Lett. 21, 62 (1996).
[CrossRef] [PubMed]

E. T. J. Nibbering, M. A. Franco, B. S. Prade, G. Grillon, J.-P. Chambaret, and A. Mysyrowicz, “Spectral determination of the amplitude and the phase of intense ultrashort optical pulses,” J. Opt. Soc. Am. B 13, 317 (1996).
[CrossRef]

E. T. J. Nibbering, M. A. Franco, B. S. Prade, G. Grillon, C. Le Blanc, and A. Mysyrowicz, “Measurement of the nonlinear refractive index of transparent materials by spectral analysis after nonlinear propagation,” Opt. Commun. 119, 479 (1995).
[CrossRef]

B. S. Prade, J. M. Schins, E. T. J. Nibbering, M. A. Franco, and A. Mysyrowicz, “A simple method for the determination of the intensity and phase of ultrashort optical pulses,” Opt. Commun. 113, 79 (1994).
[CrossRef]

Garaev, R. A.

D. V. Vlasov, R. A. Garaev, V. V. Korobkin, and R. V. Serov, “Measurement of nonlinear polarizability of air,” Zh. Eksp. Teor. Fiz. 76, 2039 (1979) [Sov. Phys. JETP 49, 1033 (1979)].

Grillon, G.

Grischkowsky, D.

Gruebele, M.

M. Gruebele and A. H. Zewail, “Femtosecond wave packet spectroscopy: coherences, the potential and structural determination,” J. Chem. Phys. 98, 883 (1993).
[CrossRef]

Gustafson, T. K.

C. H. Lin, J. P. Heritage, T. K. Gustafson, R. Y. Chiao, and J. P. McTague, “Birefringence arising from the reorientation of the polarization anisotropy of molecules in collisionless gases,” Phys. Rev. A 13, 813 (1976).
[CrossRef]

J. P. Heritage, T. K. Gustafson, and C. H. Lin, “Observation of coherent transient birefringence in CS2 vapor,” Phys. Rev. Lett. 13, 1299 (1975).
[CrossRef]

Harde, H.

Hellwarth, R. W.

R. W. Hellwarth, D. M. Pennington, and M. A. Henesian, “Indices governing optical self-focusing and self-induced changes in the state of polarization in N2, O2, H2, and Ar gases,” Phys. Rev. A 41, 2766 (1990).
[CrossRef] [PubMed]

D. M. Pennington, M. A. Henesian, and R. W. Hellwarth, “Nonlinear index of air at 1.053 µm,” Phys. Rev. A 39, 3003 (1989).
[CrossRef] [PubMed]

R. W. Hellwarth, “Third-order optical susceptibilities of liquids and solids,” Prog. Quantum Electron. 5, 1 (1977).
[CrossRef]

Henesian, M. A.

R. W. Hellwarth, D. M. Pennington, and M. A. Henesian, “Indices governing optical self-focusing and self-induced changes in the state of polarization in N2, O2, H2, and Ar gases,” Phys. Rev. A 41, 2766 (1990).
[CrossRef] [PubMed]

D. M. Pennington, M. A. Henesian, and R. W. Hellwarth, “Nonlinear index of air at 1.053 µm,” Phys. Rev. A 39, 3003 (1989).
[CrossRef] [PubMed]

Heritage, J. P.

C. H. Lin, J. P. Heritage, T. K. Gustafson, R. Y. Chiao, and J. P. McTague, “Birefringence arising from the reorientation of the polarization anisotropy of molecules in collisionless gases,” Phys. Rev. A 13, 813 (1976).
[CrossRef]

J. P. Heritage, T. K. Gustafson, and C. H. Lin, “Observation of coherent transient birefringence in CS2 vapor,” Phys. Rev. Lett. 13, 1299 (1975).
[CrossRef]

Hooker, C. J.

M. J. Shaw, C. J. Hooker, and D. C. Wilson, “Measurement of the nonlinear refractive index of air and other gases at 248 nm,” Opt. Commun. 103, 153 (1993).
[CrossRef]

Hunziker, L.

M. Morgen, W. Price, L. Hunziker, P. Ludowise, M. Blackwell, and Y. Chen, “Femtosecond Raman-induced polarization spectroscopy studies of rotational coherence in O2, N2, and CO2,” Chem. Phys. Lett. 209, 1 (1993).
[CrossRef]

Iacopini, E.

S. Carusotto, E. Iacopini, E. Polacco, F. Scuri, G. Stefanini, and E. Zavattini, “Measurement of the Kerr constant of He, A, O2, N2, H2, and D2,” Nuovo Cimento 5D, 328 (1985).
[CrossRef]

Ippen, E. P.

K. A. Nelson and E. P. Ippen, “Femtosecond coherent spectroscopy,” Adv. Chem. Phys. 75, 1 (1989).

Kenney-Wallace, G. A.

D. McMorrow, W. T. Lotshaw, and G. A. Kenney-Wallace, “Femtosecond optical Kerr studies on the origin of the nonlinear responses in simple liquids,” IEEE J. Quantum Electron. 24, 443 (1988).
[CrossRef]

Klapisch, M.

R. H. Lehmberg, C. J. Pawley, A. V. Deniz, M. Klapisch, and Y. Leng, “Two-photon resonantly-enhanced negative nonlinear refractive index in xenon at 248 nm,” Opt. Commun. 121, 78 (1995).
[CrossRef]

Korn, G.

Korobkin, V. V.

D. V. Vlasov, R. A. Garaev, V. V. Korobkin, and R. V. Serov, “Measurement of nonlinear polarizability of air,” Zh. Eksp. Teor. Fiz. 76, 2039 (1979) [Sov. Phys. JETP 49, 1033 (1979)].

Le Blanc, C.

E. T. J. Nibbering, M. A. Franco, B. S. Prade, G. Grillon, C. Le Blanc, and A. Mysyrowicz, “Measurement of the nonlinear refractive index of transparent materials by spectral analysis after nonlinear propagation,” Opt. Commun. 119, 479 (1995).
[CrossRef]

C. Le Blanc, G. Grillon, J. P. Chambaret, A. Migus, and A. Antonetti, “Compact and efficient multipass Ti:sapphire system for femtosecond chirped-pulse amplification at the terawatt level,” Opt. Lett. 18, 140 (1993).
[CrossRef]

Lehmberg, R. H.

R. H. Lehmberg, C. J. Pawley, A. V. Deniz, M. Klapisch, and Y. Leng, “Two-photon resonantly-enhanced negative nonlinear refractive index in xenon at 248 nm,” Opt. Commun. 121, 78 (1995).
[CrossRef]

Leng, Y.

R. H. Lehmberg, C. J. Pawley, A. V. Deniz, M. Klapisch, and Y. Leng, “Two-photon resonantly-enhanced negative nonlinear refractive index in xenon at 248 nm,” Opt. Commun. 121, 78 (1995).
[CrossRef]

Lin, C. H.

C. H. Lin, J. P. Heritage, T. K. Gustafson, R. Y. Chiao, and J. P. McTague, “Birefringence arising from the reorientation of the polarization anisotropy of molecules in collisionless gases,” Phys. Rev. A 13, 813 (1976).
[CrossRef]

J. P. Heritage, T. K. Gustafson, and C. H. Lin, “Observation of coherent transient birefringence in CS2 vapor,” Phys. Rev. Lett. 13, 1299 (1975).
[CrossRef]

Liu, X.

Lotshaw, W. T.

D. McMorrow, W. T. Lotshaw, and G. A. Kenney-Wallace, “Femtosecond optical Kerr studies on the origin of the nonlinear responses in simple liquids,” IEEE J. Quantum Electron. 24, 443 (1988).
[CrossRef]

Ludowise, P.

M. Morgen, W. Price, P. Ludowise, and Y. Chen, “Tensor analysis of femtosecond Raman induced polarization spectroscopy: application to the study of rotational coherence,” J. Chem. Phys. 102, 8780 (1995).
[CrossRef]

M. Morgen, W. Price, L. Hunziker, P. Ludowise, M. Blackwell, and Y. Chen, “Femtosecond Raman-induced polarization spectroscopy studies of rotational coherence in O2, N2, and CO2,” Chem. Phys. Lett. 209, 1 (1993).
[CrossRef]

McMorrow, D.

D. McMorrow, W. T. Lotshaw, and G. A. Kenney-Wallace, “Femtosecond optical Kerr studies on the origin of the nonlinear responses in simple liquids,” IEEE J. Quantum Electron. 24, 443 (1988).
[CrossRef]

McTague, J. P.

C. H. Lin, J. P. Heritage, T. K. Gustafson, R. Y. Chiao, and J. P. McTague, “Birefringence arising from the reorientation of the polarization anisotropy of molecules in collisionless gases,” Phys. Rev. A 13, 813 (1976).
[CrossRef]

Migus, A.

Mizrahi, V.

V. Mizrahi and D. P. Shelton, “Dispersion of nonlinear susceptibilities of Ar, N2, and O2 measured and compared,” Phys. Rev. Lett. 55, 696 (1985).
[CrossRef] [PubMed]

Morgen, M.

M. Morgen, W. Price, P. Ludowise, and Y. Chen, “Tensor analysis of femtosecond Raman induced polarization spectroscopy: application to the study of rotational coherence,” J. Chem. Phys. 102, 8780 (1995).
[CrossRef]

M. Morgen, W. Price, L. Hunziker, P. Ludowise, M. Blackwell, and Y. Chen, “Femtosecond Raman-induced polarization spectroscopy studies of rotational coherence in O2, N2, and CO2,” Chem. Phys. Lett. 209, 1 (1993).
[CrossRef]

Mourou, G.

Mukamel, S.

M. Cho, M. Du, N. F. Scherer, G. R. Fleming, and S. Mukamel, “Off-resonant transient birefringence in liquids,” J. Chem. Phys. 99, 2410 (1993).
[CrossRef]

S. Mukamel, Principles of Nonlinear Optical Spectroscopy, Vol. 6 of Optical and Imaging Sciences (Oxford U. Press, Oxford, 1995).

Mysyrowicz, A.

E. T. J. Nibbering, P. F. Curley, G. Grillon, B. S. Prade, M. A. Franco, F. Salin, and A. Mysyrowicz, “Conical emission from self-guided femtosecond pulses in air,” Opt. Lett. 21, 62 (1996).
[CrossRef] [PubMed]

E. T. J. Nibbering, M. A. Franco, B. S. Prade, G. Grillon, J.-P. Chambaret, and A. Mysyrowicz, “Spectral determination of the amplitude and the phase of intense ultrashort optical pulses,” J. Opt. Soc. Am. B 13, 317 (1996).
[CrossRef]

E. T. J. Nibbering, M. A. Franco, B. S. Prade, G. Grillon, C. Le Blanc, and A. Mysyrowicz, “Measurement of the nonlinear refractive index of transparent materials by spectral analysis after nonlinear propagation,” Opt. Commun. 119, 479 (1995).
[CrossRef]

B. S. Prade, J. M. Schins, E. T. J. Nibbering, M. A. Franco, and A. Mysyrowicz, “A simple method for the determination of the intensity and phase of ultrashort optical pulses,” Opt. Commun. 113, 79 (1994).
[CrossRef]

Nelson, K. A.

K. A. Nelson and E. P. Ippen, “Femtosecond coherent spectroscopy,” Adv. Chem. Phys. 75, 1 (1989).

Nibbering, E. T. J.

E. T. J. Nibbering, M. A. Franco, B. S. Prade, G. Grillon, J.-P. Chambaret, and A. Mysyrowicz, “Spectral determination of the amplitude and the phase of intense ultrashort optical pulses,” J. Opt. Soc. Am. B 13, 317 (1996).
[CrossRef]

E. T. J. Nibbering, P. F. Curley, G. Grillon, B. S. Prade, M. A. Franco, F. Salin, and A. Mysyrowicz, “Conical emission from self-guided femtosecond pulses in air,” Opt. Lett. 21, 62 (1996).
[CrossRef] [PubMed]

E. T. J. Nibbering, M. A. Franco, B. S. Prade, G. Grillon, C. Le Blanc, and A. Mysyrowicz, “Measurement of the nonlinear refractive index of transparent materials by spectral analysis after nonlinear propagation,” Opt. Commun. 119, 479 (1995).
[CrossRef]

B. S. Prade, J. M. Schins, E. T. J. Nibbering, M. A. Franco, and A. Mysyrowicz, “A simple method for the determination of the intensity and phase of ultrashort optical pulses,” Opt. Commun. 113, 79 (1994).
[CrossRef]

Pawley, C. J.

R. H. Lehmberg, C. J. Pawley, A. V. Deniz, M. Klapisch, and Y. Leng, “Two-photon resonantly-enhanced negative nonlinear refractive index in xenon at 248 nm,” Opt. Commun. 121, 78 (1995).
[CrossRef]

Pennington, D. M.

R. W. Hellwarth, D. M. Pennington, and M. A. Henesian, “Indices governing optical self-focusing and self-induced changes in the state of polarization in N2, O2, H2, and Ar gases,” Phys. Rev. A 41, 2766 (1990).
[CrossRef] [PubMed]

D. M. Pennington, M. A. Henesian, and R. W. Hellwarth, “Nonlinear index of air at 1.053 µm,” Phys. Rev. A 39, 3003 (1989).
[CrossRef] [PubMed]

Perry, M. D.

M. D. Perry and G. Mourou, “Terawatt to petawatt subpicosecond lasers,” Science 264, 917 (1994).
[CrossRef] [PubMed]

Polacco, E.

S. Carusotto, E. Iacopini, E. Polacco, F. Scuri, G. Stefanini, and E. Zavattini, “Measurement of the Kerr constant of He, A, O2, N2, H2, and D2,” Nuovo Cimento 5D, 328 (1985).
[CrossRef]

Prade, B. S.

E. T. J. Nibbering, M. A. Franco, B. S. Prade, G. Grillon, J.-P. Chambaret, and A. Mysyrowicz, “Spectral determination of the amplitude and the phase of intense ultrashort optical pulses,” J. Opt. Soc. Am. B 13, 317 (1996).
[CrossRef]

E. T. J. Nibbering, P. F. Curley, G. Grillon, B. S. Prade, M. A. Franco, F. Salin, and A. Mysyrowicz, “Conical emission from self-guided femtosecond pulses in air,” Opt. Lett. 21, 62 (1996).
[CrossRef] [PubMed]

E. T. J. Nibbering, M. A. Franco, B. S. Prade, G. Grillon, C. Le Blanc, and A. Mysyrowicz, “Measurement of the nonlinear refractive index of transparent materials by spectral analysis after nonlinear propagation,” Opt. Commun. 119, 479 (1995).
[CrossRef]

B. S. Prade, J. M. Schins, E. T. J. Nibbering, M. A. Franco, and A. Mysyrowicz, “A simple method for the determination of the intensity and phase of ultrashort optical pulses,” Opt. Commun. 113, 79 (1994).
[CrossRef]

Price, W.

M. Morgen, W. Price, P. Ludowise, and Y. Chen, “Tensor analysis of femtosecond Raman induced polarization spectroscopy: application to the study of rotational coherence,” J. Chem. Phys. 102, 8780 (1995).
[CrossRef]

M. Morgen, W. Price, L. Hunziker, P. Ludowise, M. Blackwell, and Y. Chen, “Femtosecond Raman-induced polarization spectroscopy studies of rotational coherence in O2, N2, and CO2,” Chem. Phys. Lett. 209, 1 (1993).
[CrossRef]

Salin, F.

Scherer, N. F.

M. Cho, M. Du, N. F. Scherer, G. R. Fleming, and S. Mukamel, “Off-resonant transient birefringence in liquids,” J. Chem. Phys. 99, 2410 (1993).
[CrossRef]

Schins, J. M.

B. S. Prade, J. M. Schins, E. T. J. Nibbering, M. A. Franco, and A. Mysyrowicz, “A simple method for the determination of the intensity and phase of ultrashort optical pulses,” Opt. Commun. 113, 79 (1994).
[CrossRef]

Scuri, F.

S. Carusotto, E. Iacopini, E. Polacco, F. Scuri, G. Stefanini, and E. Zavattini, “Measurement of the Kerr constant of He, A, O2, N2, H2, and D2,” Nuovo Cimento 5D, 328 (1985).
[CrossRef]

Serov, R. V.

D. V. Vlasov, R. A. Garaev, V. V. Korobkin, and R. V. Serov, “Measurement of nonlinear polarizability of air,” Zh. Eksp. Teor. Fiz. 76, 2039 (1979) [Sov. Phys. JETP 49, 1033 (1979)].

Shaw, M. J.

M. J. Shaw, C. J. Hooker, and D. C. Wilson, “Measurement of the nonlinear refractive index of air and other gases at 248 nm,” Opt. Commun. 103, 153 (1993).
[CrossRef]

Shelton, D. P.

V. Mizrahi and D. P. Shelton, “Dispersion of nonlinear susceptibilities of Ar, N2, and O2 measured and compared,” Phys. Rev. Lett. 55, 696 (1985).
[CrossRef] [PubMed]

Shimoji, Y.

Squier, J.

Stefanini, G.

S. Carusotto, E. Iacopini, E. Polacco, F. Scuri, G. Stefanini, and E. Zavattini, “Measurement of the Kerr constant of He, A, O2, N2, H2, and D2,” Nuovo Cimento 5D, 328 (1985).
[CrossRef]

Steffen, T.

T. Steffen and K. Duppen, “Femtosecond two-dimensional spectroscopy of molecular motion in liquids,” Phys. Rev. Lett. 76, 1224 (1996).
[CrossRef] [PubMed]

Tominaga, K.

K. Tominaga and K. Yoshihara, “Fifth order optical response of liquid CS2 observed by ultrafast nonresonant six-wave mixing,” Phys. Rev. Lett. 74, 3061 (1995).
[CrossRef] [PubMed]

Vlasov, D. V.

D. V. Vlasov, R. A. Garaev, V. V. Korobkin, and R. V. Serov, “Measurement of nonlinear polarizability of air,” Zh. Eksp. Teor. Fiz. 76, 2039 (1979) [Sov. Phys. JETP 49, 1033 (1979)].

Wilson, D. C.

M. J. Shaw, C. J. Hooker, and D. C. Wilson, “Measurement of the nonlinear refractive index of air and other gases at 248 nm,” Opt. Commun. 103, 153 (1993).
[CrossRef]

Yoshihara, K.

K. Tominaga and K. Yoshihara, “Fifth order optical response of liquid CS2 observed by ultrafast nonresonant six-wave mixing,” Phys. Rev. Lett. 74, 3061 (1995).
[CrossRef] [PubMed]

Zavattini, E.

S. Carusotto, E. Iacopini, E. Polacco, F. Scuri, G. Stefanini, and E. Zavattini, “Measurement of the Kerr constant of He, A, O2, N2, H2, and D2,” Nuovo Cimento 5D, 328 (1985).
[CrossRef]

Zewail, A. H.

M. Gruebele and A. H. Zewail, “Femtosecond wave packet spectroscopy: coherences, the potential and structural determination,” J. Chem. Phys. 98, 883 (1993).
[CrossRef]

Adv. Chem. Phys. (1)

K. A. Nelson and E. P. Ippen, “Femtosecond coherent spectroscopy,” Adv. Chem. Phys. 75, 1 (1989).

Chem. Phys. Lett. (1)

M. Morgen, W. Price, L. Hunziker, P. Ludowise, M. Blackwell, and Y. Chen, “Femtosecond Raman-induced polarization spectroscopy studies of rotational coherence in O2, N2, and CO2,” Chem. Phys. Lett. 209, 1 (1993).
[CrossRef]

IEEE J. Quantum Electron. (1)

D. McMorrow, W. T. Lotshaw, and G. A. Kenney-Wallace, “Femtosecond optical Kerr studies on the origin of the nonlinear responses in simple liquids,” IEEE J. Quantum Electron. 24, 443 (1988).
[CrossRef]

J. Chem. Phys. (3)

M. Cho, M. Du, N. F. Scherer, G. R. Fleming, and S. Mukamel, “Off-resonant transient birefringence in liquids,” J. Chem. Phys. 99, 2410 (1993).
[CrossRef]

M. Gruebele and A. H. Zewail, “Femtosecond wave packet spectroscopy: coherences, the potential and structural determination,” J. Chem. Phys. 98, 883 (1993).
[CrossRef]

M. Morgen, W. Price, P. Ludowise, and Y. Chen, “Tensor analysis of femtosecond Raman induced polarization spectroscopy: application to the study of rotational coherence,” J. Chem. Phys. 102, 8780 (1995).
[CrossRef]

J. Opt. Soc. Am. B (3)

Nuovo Cimento (1)

S. Carusotto, E. Iacopini, E. Polacco, F. Scuri, G. Stefanini, and E. Zavattini, “Measurement of the Kerr constant of He, A, O2, N2, H2, and D2,” Nuovo Cimento 5D, 328 (1985).
[CrossRef]

Opt. Commun. (4)

R. H. Lehmberg, C. J. Pawley, A. V. Deniz, M. Klapisch, and Y. Leng, “Two-photon resonantly-enhanced negative nonlinear refractive index in xenon at 248 nm,” Opt. Commun. 121, 78 (1995).
[CrossRef]

M. J. Shaw, C. J. Hooker, and D. C. Wilson, “Measurement of the nonlinear refractive index of air and other gases at 248 nm,” Opt. Commun. 103, 153 (1993).
[CrossRef]

B. S. Prade, J. M. Schins, E. T. J. Nibbering, M. A. Franco, and A. Mysyrowicz, “A simple method for the determination of the intensity and phase of ultrashort optical pulses,” Opt. Commun. 113, 79 (1994).
[CrossRef]

E. T. J. Nibbering, M. A. Franco, B. S. Prade, G. Grillon, C. Le Blanc, and A. Mysyrowicz, “Measurement of the nonlinear refractive index of transparent materials by spectral analysis after nonlinear propagation,” Opt. Commun. 119, 479 (1995).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. A (3)

D. M. Pennington, M. A. Henesian, and R. W. Hellwarth, “Nonlinear index of air at 1.053 µm,” Phys. Rev. A 39, 3003 (1989).
[CrossRef] [PubMed]

C. H. Lin, J. P. Heritage, T. K. Gustafson, R. Y. Chiao, and J. P. McTague, “Birefringence arising from the reorientation of the polarization anisotropy of molecules in collisionless gases,” Phys. Rev. A 13, 813 (1976).
[CrossRef]

R. W. Hellwarth, D. M. Pennington, and M. A. Henesian, “Indices governing optical self-focusing and self-induced changes in the state of polarization in N2, O2, H2, and Ar gases,” Phys. Rev. A 41, 2766 (1990).
[CrossRef] [PubMed]

Phys. Rev. Lett. (4)

V. Mizrahi and D. P. Shelton, “Dispersion of nonlinear susceptibilities of Ar, N2, and O2 measured and compared,” Phys. Rev. Lett. 55, 696 (1985).
[CrossRef] [PubMed]

J. P. Heritage, T. K. Gustafson, and C. H. Lin, “Observation of coherent transient birefringence in CS2 vapor,” Phys. Rev. Lett. 13, 1299 (1975).
[CrossRef]

K. Tominaga and K. Yoshihara, “Fifth order optical response of liquid CS2 observed by ultrafast nonresonant six-wave mixing,” Phys. Rev. Lett. 74, 3061 (1995).
[CrossRef] [PubMed]

T. Steffen and K. Duppen, “Femtosecond two-dimensional spectroscopy of molecular motion in liquids,” Phys. Rev. Lett. 76, 1224 (1996).
[CrossRef] [PubMed]

Prog. Quantum Electron. (1)

R. W. Hellwarth, “Third-order optical susceptibilities of liquids and solids,” Prog. Quantum Electron. 5, 1 (1977).
[CrossRef]

Science (1)

M. D. Perry and G. Mourou, “Terawatt to petawatt subpicosecond lasers,” Science 264, 917 (1994).
[CrossRef] [PubMed]

Zh. Eksp. Teor. Fiz. (1)

D. V. Vlasov, R. A. Garaev, V. V. Korobkin, and R. V. Serov, “Measurement of nonlinear polarizability of air,” Zh. Eksp. Teor. Fiz. 76, 2039 (1979) [Sov. Phys. JETP 49, 1033 (1979)].

Other (1)

S. Mukamel, Principles of Nonlinear Optical Spectroscopy, Vol. 6 of Optical and Imaging Sciences (Oxford U. Press, Oxford, 1995).

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Figures (10)

Fig. 1
Fig. 1

Schematic representation of the experiment. For details see text.

Fig. 2
Fig. 2

Self-phase-modulated spectra of the center part of the beam of intense 120-fs laser pulses after propagation through a 2.5-m-long tube filled with various gases (at different pressures). The total B integral due to the nonlinearity of the windows is approximately equal to that of the gases (B integral ≅1). The small modulation in the reference spectrum is due to SPM in air during propagation over ∼2 m from the exit of the compressor to the entrance of the tube.

Fig. 3
Fig. 3

Self-phase-modulated spectra of the center part of the beam of intense 120-fs laser pulses after propagation through a 2.5-m-long tube filled with Ar, Xe, or SF6 (at different pressures). Note the relatively symmetric broadening due to SPM.

Fig. 4
Fig. 4

Self-phase-modulated spectra of the center part of the beam of intense 120-fs laser pulses after propagation through a 2.5-m-long tube filled with N2, O2, or air (at different pressures). Note the distinct red shift due to SPM.

Fig. 5
Fig. 5

Comparison of the bandwidth of a 120-fs laser pulse with the frequency differences between the input laser and the scattered Rayleigh and Raman radiation of N2. The lower graph is plotted on a logarithmic scale.

Fig. 6
Fig. 6

Calculated change of the refractive index due to rotational coherences induced by a 100-fs transform-limited pulse in (A) N2 and (B) O2. The pulse intensity profile is depicted by the thick curve; the molecular rotational response for δ-pulse excitation, by the thin curve; and the change of the refractive index, by the open circles. Note the recurrences at later times.

Fig. 7
Fig. 7

Bottom: expanded view of Fig. 6 showing the calculated change of the refractive index due to rotational coherences induced by a 100-fs transform-limited pulse in (A) N2 and (B) O2 Top: calculated spectra before (thin curve) and after (thick curve) nonlinear propagation through the gas. The magnitude of the nonlinearity is such that a B integral of π is acquired. Note that the x axis is given in the frequency scale.

Fig. 8
Fig. 8

Experimental spectra showing the pronounced red shifting during SPM when 150-fs pulses at different intensities propagate through a fused-silica cell (thickness of both windows is 1 mm) containing 1 mm of liquid CS2. Note that the initial phase is slightly different from the case of the gases described in Figs. 24.

Fig. 9
Fig. 9

Experimental (solid curve) and calculated (open circles) spectra after nonlinear propagation through 2.5 m of Ar at 1.3 bars and Xe at 0.26 bar. The spectra of the laser output and after passage through the empty tube are also depicted. Only an instantaneous electronic nonlinearity was included in the numerical procedure.

Fig. 10
Fig. 10

Experimental (solid curve) and calculated (open circles) spectra after nonlinear propagation through N2 at 1.3 bars and O2 at 0.53 bar are shown in the center. The spectrum through the empty tube is also depicted on the left, together with the initial pulse phase (thin curve). The calculated total refractive-index change for both gases is shown on the right as the open circles, together with the instantaneous (electronic and rotational Rayleigh) part (thick curve) and the time-delayed nonlinear rotational Raman component (thin curve).

Tables (3)

Tables Icon

Table 1 Experimental Values of the Nonlinear Refractive Index n2 of Gases Reported in the Literature

Tables Icon

Table 2 Values of the Nonlinear Refractive Index n2,total Together with the Electronic Contribution n2,electronic of Gases, Both Estimated from Published Data on the dc Kerr Effecta and Electric-Field-Induced Second-Harmonic Generationb (Taken from Ref. 1)

Tables Icon

Table 3 Values of the Nonlinear Refractive-Index Parameters of Gases Obtained with the Nonlinear Propagation Method by Use of 120-fs Pulses at 800 nm

Equations (22)

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P(3)(t)=E(t)0|E(t-τ)|2R(τ)dτ,
E(t)=A(t)exp(-iωt),
R(t)=σ(ω)δ(t)+(2π)/h[α(ω, t), α(ω, 0)],
[α(ω, t),α(ω, 0)]=α(ω, t)α(ω, 0)-α(ω, 0)α(ω, t).
α(ω, t)=G(t)α(ω, 0)=exp(-iHgt)α(ω)exp(+iHgt).
α(ω)=2πC(ω)hμμ,
C(ω)1ωeg+ω-iγ+1ωeg-ω-iγ.
C(ω)1ωeg+ω+1ωeg-ω.
E(t, z)=E(t, 0)exp[+iϕNL(t, z)],
ϕNL(t, z)=2πλz-tn2(τ)|E(t-τ, 0)|2dτ,
Δntotal(t)=Δninstant(t)+Δnrot-Raman(t).
Δninstant(t)=n2,instantI(t).
Δn2,rot-Raman(t)=Imn2,rot-RamanJ=0FJ×0I(t-τ)exp(-iωJτ)dτ,
n2,rot-Raman=32π2Nn0hcβ(ω).
β(ω)=α(ω)-α(ω).
FJ=(ρJ+2-ρJ)ZJ (J+2)(J+1)(2J+3).
ρJ=exp[-hcBJ(J+1)/kT]J=0ZJ(2J+1)exp[-hcBJ(J+1)/kT].
ZJ=1forJ=odd,
ZJ=2forJ=even,
ZJ=1forJ=odd,
ZJ=0forJ=even.
ωJ=4πcB(2J+3).

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