Abstract

A model of the full Raman response function of a gas mixture including rotational and vibrational motions of molecules is presented and is applied to examine the properties of the retarded optical nonlinearity of atmospheric air. For few-cycle laser pulses, broadband field waveforms, and/or high gas temperatures, both rotational and vibrational motions can significantly contribute to the Raman response of atmospheric air, with the ratio of the rotational and vibrational parts of the Raman response function controlled by the gas temperature and the temporal shape of the laser field.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. W. Hellwarth, Prog. Quantum Electron. 5, 1 (1977).
    [CrossRef]
  2. A. M. Zheltikov, J. Raman Spectrosc. 31, 653 (2000).
    [CrossRef]
  3. A. J. Druet and J.-P. E. Taran, Prog. Quantum Electron. 7, 1 (1981).
    [CrossRef]
  4. A. C. Eckbreth, Laser Diagnostic for Combustion Temperature and Species (Abacus, 1988).
  5. P. P. Radi and A. M. Zheltikov, eds., special issue of J. Raman Spectrosc. 37(6) (2006).
    [CrossRef]
  6. R. A. Bartels, T. C. Weinacht, N. Wagner, M. Baertschy, C. H. Greene, M. M. Murnane, and H. C. Kapteyn, Phys. Rev. Lett. 88, 013903 (2002).
    [CrossRef] [PubMed]
  7. S. E. Harris and A. V. Sokolov, Phys. Rev. Lett. 81, 2894 (1998).
    [CrossRef]
  8. N. Zhavoronkov and G. Korn, Phys. Rev. Lett. 88, 203901 (2002).
    [CrossRef] [PubMed]
  9. D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, Science 301, 1702 (2003).
    [CrossRef] [PubMed]
  10. A. A. Ivanov, A. A. Podshivalov, and A. M. Zheltikov, Opt. Lett. 31, 3318 (2006).
    [CrossRef] [PubMed]
  11. J.-F. Ripoche, G. Grillon, B. Prade, M. Franco, E. Nibbering, R. Lange, and A. Mysyrowicz, Opt. Commun. 135, 310 (1997).
    [CrossRef]
  12. A. Braun, G. Korn, X. Liu, D. Du, J. Squier, and G. Mourou, Opt. Lett. 20, 73 (1995).
    [CrossRef] [PubMed]
  13. D. Faccio, A. Averchi, A. Dubietis, P. Polesana, A. Piskarskas, P. D. Trapani, and A. Couairon, Opt. Lett. 32, 184 (2007).
    [CrossRef]
  14. E. T. J. Nibbering, G. Grillon, M. A. Franco, B. S. Prade, and A. Mysyrowicz, J. Opt. Soc. Am. B 14, 650 (1997).
    [CrossRef]
  15. M. Mlejnek, E. M. Wright, and J. V. Moloney, Opt. Lett. 23, 382 (1998).
    [CrossRef]
  16. R. H. Stolen, J. P. Gordon, W. J. Tomlinson, and H. A. Haus, J. Opt. Soc. Am. B 6, 1159 (1989).
    [CrossRef]
  17. D. A. Long, The Raman Effect: A Unified Treatment of the Theory of Raman Scattering by Molecules (Wiley, 2002).
  18. R. P. Lucht, R. E. Palmer, and M. A. Maris, Opt. Lett. 12, 386 (1987).
    [CrossRef] [PubMed]

2007 (1)

2006 (2)

P. P. Radi and A. M. Zheltikov, eds., special issue of J. Raman Spectrosc. 37(6) (2006).
[CrossRef]

A. A. Ivanov, A. A. Podshivalov, and A. M. Zheltikov, Opt. Lett. 31, 3318 (2006).
[CrossRef] [PubMed]

2003 (1)

D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, Science 301, 1702 (2003).
[CrossRef] [PubMed]

2002 (2)

N. Zhavoronkov and G. Korn, Phys. Rev. Lett. 88, 203901 (2002).
[CrossRef] [PubMed]

R. A. Bartels, T. C. Weinacht, N. Wagner, M. Baertschy, C. H. Greene, M. M. Murnane, and H. C. Kapteyn, Phys. Rev. Lett. 88, 013903 (2002).
[CrossRef] [PubMed]

2000 (1)

A. M. Zheltikov, J. Raman Spectrosc. 31, 653 (2000).
[CrossRef]

1998 (2)

S. E. Harris and A. V. Sokolov, Phys. Rev. Lett. 81, 2894 (1998).
[CrossRef]

M. Mlejnek, E. M. Wright, and J. V. Moloney, Opt. Lett. 23, 382 (1998).
[CrossRef]

1997 (2)

E. T. J. Nibbering, G. Grillon, M. A. Franco, B. S. Prade, and A. Mysyrowicz, J. Opt. Soc. Am. B 14, 650 (1997).
[CrossRef]

J.-F. Ripoche, G. Grillon, B. Prade, M. Franco, E. Nibbering, R. Lange, and A. Mysyrowicz, Opt. Commun. 135, 310 (1997).
[CrossRef]

1995 (1)

1989 (1)

1987 (1)

1981 (1)

A. J. Druet and J.-P. E. Taran, Prog. Quantum Electron. 7, 1 (1981).
[CrossRef]

1977 (1)

R. W. Hellwarth, Prog. Quantum Electron. 5, 1 (1977).
[CrossRef]

Ahmad, F. R.

D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, Science 301, 1702 (2003).
[CrossRef] [PubMed]

Averchi, A.

Baertschy, M.

R. A. Bartels, T. C. Weinacht, N. Wagner, M. Baertschy, C. H. Greene, M. M. Murnane, and H. C. Kapteyn, Phys. Rev. Lett. 88, 013903 (2002).
[CrossRef] [PubMed]

Bartels, R. A.

R. A. Bartels, T. C. Weinacht, N. Wagner, M. Baertschy, C. H. Greene, M. M. Murnane, and H. C. Kapteyn, Phys. Rev. Lett. 88, 013903 (2002).
[CrossRef] [PubMed]

Braun, A.

Couairon, A.

Druet, A. J.

A. J. Druet and J.-P. E. Taran, Prog. Quantum Electron. 7, 1 (1981).
[CrossRef]

Du, D.

Dubietis, A.

Eckbreth, A. C.

A. C. Eckbreth, Laser Diagnostic for Combustion Temperature and Species (Abacus, 1988).

Faccio, D.

Franco, M.

J.-F. Ripoche, G. Grillon, B. Prade, M. Franco, E. Nibbering, R. Lange, and A. Mysyrowicz, Opt. Commun. 135, 310 (1997).
[CrossRef]

Franco, M. A.

Gaeta, A. L.

D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, Science 301, 1702 (2003).
[CrossRef] [PubMed]

Gallagher, M. T.

D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, Science 301, 1702 (2003).
[CrossRef] [PubMed]

Gordon, J. P.

Greene, C. H.

R. A. Bartels, T. C. Weinacht, N. Wagner, M. Baertschy, C. H. Greene, M. M. Murnane, and H. C. Kapteyn, Phys. Rev. Lett. 88, 013903 (2002).
[CrossRef] [PubMed]

Grillon, G.

J.-F. Ripoche, G. Grillon, B. Prade, M. Franco, E. Nibbering, R. Lange, and A. Mysyrowicz, Opt. Commun. 135, 310 (1997).
[CrossRef]

E. T. J. Nibbering, G. Grillon, M. A. Franco, B. S. Prade, and A. Mysyrowicz, J. Opt. Soc. Am. B 14, 650 (1997).
[CrossRef]

Harris, S. E.

S. E. Harris and A. V. Sokolov, Phys. Rev. Lett. 81, 2894 (1998).
[CrossRef]

Haus, H. A.

Hellwarth, R. W.

R. W. Hellwarth, Prog. Quantum Electron. 5, 1 (1977).
[CrossRef]

Ivanov, A. A.

Kapteyn, H. C.

R. A. Bartels, T. C. Weinacht, N. Wagner, M. Baertschy, C. H. Greene, M. M. Murnane, and H. C. Kapteyn, Phys. Rev. Lett. 88, 013903 (2002).
[CrossRef] [PubMed]

Koch, K. W.

D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, Science 301, 1702 (2003).
[CrossRef] [PubMed]

Korn, G.

Lange, R.

J.-F. Ripoche, G. Grillon, B. Prade, M. Franco, E. Nibbering, R. Lange, and A. Mysyrowicz, Opt. Commun. 135, 310 (1997).
[CrossRef]

Liu, X.

Long, D. A.

D. A. Long, The Raman Effect: A Unified Treatment of the Theory of Raman Scattering by Molecules (Wiley, 2002).

Lucht, R. P.

Maris, M. A.

Mlejnek, M.

Moloney, J. V.

Mourou, G.

Müller, D.

D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, Science 301, 1702 (2003).
[CrossRef] [PubMed]

Murnane, M. M.

R. A. Bartels, T. C. Weinacht, N. Wagner, M. Baertschy, C. H. Greene, M. M. Murnane, and H. C. Kapteyn, Phys. Rev. Lett. 88, 013903 (2002).
[CrossRef] [PubMed]

Mysyrowicz, A.

J.-F. Ripoche, G. Grillon, B. Prade, M. Franco, E. Nibbering, R. Lange, and A. Mysyrowicz, Opt. Commun. 135, 310 (1997).
[CrossRef]

E. T. J. Nibbering, G. Grillon, M. A. Franco, B. S. Prade, and A. Mysyrowicz, J. Opt. Soc. Am. B 14, 650 (1997).
[CrossRef]

Nibbering, E.

J.-F. Ripoche, G. Grillon, B. Prade, M. Franco, E. Nibbering, R. Lange, and A. Mysyrowicz, Opt. Commun. 135, 310 (1997).
[CrossRef]

Nibbering, E. T. J.

Ouzounov, D. G.

D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, Science 301, 1702 (2003).
[CrossRef] [PubMed]

Palmer, R. E.

Piskarskas, A.

Podshivalov, A. A.

Polesana, P.

Prade, B.

J.-F. Ripoche, G. Grillon, B. Prade, M. Franco, E. Nibbering, R. Lange, and A. Mysyrowicz, Opt. Commun. 135, 310 (1997).
[CrossRef]

Prade, B. S.

Radi, P. P.

P. P. Radi and A. M. Zheltikov, eds., special issue of J. Raman Spectrosc. 37(6) (2006).
[CrossRef]

Ripoche, J.-F.

J.-F. Ripoche, G. Grillon, B. Prade, M. Franco, E. Nibbering, R. Lange, and A. Mysyrowicz, Opt. Commun. 135, 310 (1997).
[CrossRef]

Silcox, J.

D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, Science 301, 1702 (2003).
[CrossRef] [PubMed]

Sokolov, A. V.

S. E. Harris and A. V. Sokolov, Phys. Rev. Lett. 81, 2894 (1998).
[CrossRef]

Squier, J.

Stolen, R. H.

Taran, J.-P. E.

A. J. Druet and J.-P. E. Taran, Prog. Quantum Electron. 7, 1 (1981).
[CrossRef]

Thomas, M. G.

D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, Science 301, 1702 (2003).
[CrossRef] [PubMed]

Tomlinson, W. J.

Trapani, P. D.

Venkataraman, N.

D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, Science 301, 1702 (2003).
[CrossRef] [PubMed]

Wagner, N.

R. A. Bartels, T. C. Weinacht, N. Wagner, M. Baertschy, C. H. Greene, M. M. Murnane, and H. C. Kapteyn, Phys. Rev. Lett. 88, 013903 (2002).
[CrossRef] [PubMed]

Weinacht, T. C.

R. A. Bartels, T. C. Weinacht, N. Wagner, M. Baertschy, C. H. Greene, M. M. Murnane, and H. C. Kapteyn, Phys. Rev. Lett. 88, 013903 (2002).
[CrossRef] [PubMed]

Wright, E. M.

Zhavoronkov, N.

N. Zhavoronkov and G. Korn, Phys. Rev. Lett. 88, 203901 (2002).
[CrossRef] [PubMed]

Zheltikov, A. M.

P. P. Radi and A. M. Zheltikov, eds., special issue of J. Raman Spectrosc. 37(6) (2006).
[CrossRef]

A. A. Ivanov, A. A. Podshivalov, and A. M. Zheltikov, Opt. Lett. 31, 3318 (2006).
[CrossRef] [PubMed]

A. M. Zheltikov, J. Raman Spectrosc. 31, 653 (2000).
[CrossRef]

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

J. Raman Spectrosc. (2)

P. P. Radi and A. M. Zheltikov, eds., special issue of J. Raman Spectrosc. 37(6) (2006).
[CrossRef]

A. M. Zheltikov, J. Raman Spectrosc. 31, 653 (2000).
[CrossRef]

Opt. Commun. (1)

J.-F. Ripoche, G. Grillon, B. Prade, M. Franco, E. Nibbering, R. Lange, and A. Mysyrowicz, Opt. Commun. 135, 310 (1997).
[CrossRef]

Opt. Lett. (5)

Phys. Rev. Lett. (3)

R. A. Bartels, T. C. Weinacht, N. Wagner, M. Baertschy, C. H. Greene, M. M. Murnane, and H. C. Kapteyn, Phys. Rev. Lett. 88, 013903 (2002).
[CrossRef] [PubMed]

S. E. Harris and A. V. Sokolov, Phys. Rev. Lett. 81, 2894 (1998).
[CrossRef]

N. Zhavoronkov and G. Korn, Phys. Rev. Lett. 88, 203901 (2002).
[CrossRef] [PubMed]

Prog. Quantum Electron. (2)

R. W. Hellwarth, Prog. Quantum Electron. 5, 1 (1977).
[CrossRef]

A. J. Druet and J.-P. E. Taran, Prog. Quantum Electron. 7, 1 (1981).
[CrossRef]

Science (1)

D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, Science 301, 1702 (2003).
[CrossRef] [PubMed]

Other (2)

A. C. Eckbreth, Laser Diagnostic for Combustion Temperature and Species (Abacus, 1988).

D. A. Long, The Raman Effect: A Unified Treatment of the Theory of Raman Scattering by Molecules (Wiley, 2002).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

Rotational part of the Raman response function of a gas medium consisting of 80% N 2 and 20% O 2 with a gas temperature of (solid) 290 K and (dashed) 1000 K .

Fig. 2
Fig. 2

Full Raman response of a gas medium consisting of 80% N 2 and 20% O 2 with a gas temperature of (top) 290 K and (bottom) 1000 K .

Fig. 3
Fig. 3

Instantaneous frequency deviation of a probe laser pulse Δ ω normalized to the peak pump intensity I 0 in a gas medium consisting of 80% N 2 and 20% O 2 excited with a pump pulse with a pulse width of (top) 50 fs and (bottom) 10 fs . The gas temperature is 290 K . The inset shows the normalized instantaneous frequency deviation of a probe laser pulse in the same gas medium, but with a temperature of 1000 K , for a pump pulse width of 10 fs .

Fig. 4
Fig. 4

Instantaneous frequency deviation of a probe laser pulse Δ ω normalized to the peak pump intensity I 0 in a gas medium consisting of 80% N 2 and 20% O 2 excited with (top) a single pump pulse and a sequence of pump pulses consisting of (middle) three and (bottom) five pulses. The pulse width of each pulse is 10 fs . The gas temperature is 290 K . The delay time between two subsequent pulses is 10 T v , where T v is the vibration period of N 2 .

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

R ( t ) = i R r i + R v i ,
R r ( t ) = R r 1 ( t ) + R r 2 ( t ) J F 1 J sin ( ω 1 J t ) + F 2 J sin ( ω 2 J t ) ,
F 1 , 2 J = ( ρ 1 , 2 J + 1 ρ 1 , 2 J ) Z 1 , 2 J ( J + 2 ) ( J + 1 ) ( 2 J + 3 ) ,
ρ 1 , 2 J = exp [ c h B 1 , 2 J ( J + 1 ) k T ] { J Z 1 , 2 J ( 2 J + 1 ) exp [ c h B 1 , 2 J ( J + 1 ) k T ] } 1 ;
R v ( t ) = R v 1 ( t ) + R v 2 ( t ) J V 1 J sin ( Ω 1 J t ) + V 2 J sin ( Ω 2 J t ) ,

Metrics