Abstract

Using a lens of focal distance 10 cm, we sent plane-polarized optical pulses of wavelength 532 nm and duration 30 ps into a transparent cell of length 1 cm, filled with carbon disulfide at standard pressure and temperature. If a pulse generates at the focus of the lens an input intensity of at least I0=0.3 GW/cm2, then stimulated light scattering takes place, and we observe a strong backward-propagating signal. By monitoring its spectrum and transverse spatial profile as a function of input intensity, we found quantitative information on the optical Kerr effect. At input intensities of I0, 1.2I0, and 1.8I0, self-focusing leads to the formation of one, two, and four filaments, respectively. Each of these is subject to self-phase modulation and thus generates in the backward spectrum a frequency band of a granular structure. The latter can be perfectly reproduced by evaluating the Fourier transform of a phase-modulated electric field on the basis of the method of stationary phase. This allows us to calculate intensity and lifetime of a filament. If the input intensity exceeds the value of 1.8I0, fluctuations in refractive index destabilize the filamentation process. Backward spectra no longer consist of separate bands, and their shape varies at random during each series of laser shots. For input intensities higher than 3I0 the combined action of stimulated scattering and self-phase modulation causes the structure of spectra to become smooth. This explains why at an input intensity of 30I0 one observes for each laser shot a continuous backward spectrum, which possesses a large band that extends to relative wave numbers of approximately -200 cm-1.

© 1998 Optical Society of America

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References

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  1. P. D. Maker, R. W. Terhune, and C. M. Savage, “Intensity-dependent changes in the refractive index of liquids,” Phys. Rev. Lett. 12, 507–509 (1964); G. Mayer and F. Gires, “Action d’une onde lumineuse intense sur l’indice de réfraction des liquides,” C. R. Acad. Sci. 258, 2039–2042 (1964).
    [CrossRef]
  2. A. Yariv, Quantum Electronics, 3rd ed. (Wiley, New York, 1989).
  3. Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).
  4. P. Lallemand and N. Bloembergen, “Self-focusing of laser beams and stimulated Raman gain in liquids,” Phys. Rev. Lett. 15, 1010–1012 (1965); Y. R. Shen and Y. J. Shaham, “Beam deterioration and stimulated Raman effect,” Phys. Rev. Lett. 15, 1008–1010 (1965); G. Hauchecorne and G. Mayer, “Effets de l’anisotropie moléculaire sur la propagation d’une lumiere intense,” C. R. Acad. Sci. COREAF 261, 4014–4017 (1965).
    [CrossRef]
  5. E. P. Ippen, “Low-power quasi-cw Raman oscillator,” Appl. Phys. Lett. 16, 303–305 (1970).
    [CrossRef]
  6. D. I. Mash, V. V. Morozov, V. S. Starunov, and I. L. Fabelinskii, “Stimulated scattering of light of the Rayleigh-line wing,” Pis’ma Zh. Eksp. Teor. Fiz. 2, 41–43 (1965) [ JETP Lett. 2, 25–27 (1965)].
  7. W. Kaiser and M. Maier, “Stimulated Rayleigh, Brillouin and Raman spectroscopy,” in Laser Handbook, F. T. Arecchi and E. O. Schulz-Dubois, eds. (North-Holland, Amsterdam, 1972), Vol. 2, pp. 1077–1150.
  8. E. J. Miller and R. W. Boyd, “Stimulated scattering of pico second optical pulses in the presence of self-focusing,” Int. J. Nonlinear Opt. Phys. 1, 765–773 (1992).
    [CrossRef]
  9. D. Wang and G. Rivoire, “Large spectral bandwidth stimulated Rayleigh-wing scattering in CS2,” J. Chem. Phys. 98, 9279–9283 (1993).
    [CrossRef]
  10. G. S. He and P. N. Prasad, “Stimulated Rayleigh–Kerr scattering in a CS2 liquid-core fiber system,” Opt. Commun. 73, 161–164 (1989); “Stimulated Kerr scattering and reorientation work of molecules in liquid CS2,” Phys. Rev. A 41, 2687–2697 (1990); “Stimulated Rayleigh–Kerr and Raman–Kerr scattering in a liquid-core hollow fiber system,” Fiber Integr. Opt. FOIOD2 9, 11–26 (1990); G. S. He, G. C. Xu, Y. Pang, and P. N. Prasad, “Temporal behavior of stimulated Kerr scattering in a CS2 liquid-core hollow-fiber system,” J. Opt. Soc. Am. B JOBPDE 8, 1907–1913 (1991); G. S. He and G. C. Xu, “Efficient amplification of a broad-band optical signal through stimulated Kerr scattering in a CS2 liquid-core fiber system,” IEEE J. Quantum Electron. IEJQA7 28, 323–329 (1992); G. S. He, M. Casstevens, R. Burzynski, and X. Li, “Broadband, multiwavelength stimulated-emission source based on stimulated Kerr and Raman scattering in a liquid-core fiber system,” Appl. Opt. APOPAI 34, 444–454 (1995).
    [CrossRef] [PubMed]
  11. J. Y. Zhou, H. Z. Wang, and Z. X. Yu, “Efficient generation of ultrafast broadband radiation in a submillimeter liquid-core waveguide,” Appl. Phys. Lett. 57, 643–644 (1990); J. Y. Zhou, H. Z. Wang, Y. C. Li, and Z. X. Yu, “Stimulated Rayleigh wing scattering and stimulated four-photon interaction in liquid-core waveguides,” J. Mod. Opt. 38, 1015–1019 (1991); J. Y. Zhou, H. Z. Wang, X. G. Huang, Z. G. Cai, and Z. X. Yu, “Generation of frequency-tunable ultrashort optical pulses with liquid-core fibers,” Opt. Lett. OPLEDP 16, 1865–1867 (1991); H. Z. Wang, X. G. Zheng, W. D. Mao, Z. X. Yu, and Z. L. Gao, “Stimulated dynamic light scattering,” Phys. Rev. A PLRAAN 52, 1740–1745 (1995).
    [CrossRef] [PubMed]
  12. A. I. Erokhin, V. S. Starunov, and A. K. Shmelev, “Time evolution of stimulated Brillouin scattering during transverse laser pumping of carbon disulfide filling a capillary,” Pis’ma Zh. Eksp. Teor. Fiz. 60, 823–828 (1994) [ JETP Lett. 60, 837–842 (1994)]; V. S. Starunov and A. K. Shmelev, “Temporal structures of stimulated Raman scattering in a capillary-filling liquid with transverse laser pumping,” Pis’ma Zh. Eksp. Teor. Fiz. 62, 844–848 (1995) [ JETP Lett. 62, 855–859 (1995)].
  13. E. J. Miller, M. S. Malcuit, and R. W. Boyd, “Simultaneous wave-front and polarization conjugation of picosecond optical pulses by stimulated Rayleigh-wing scattering,” Opt. Lett. 15, 1188–1190 (1990).
    [CrossRef] [PubMed]
  14. D. Wang, R. Barillé, and G. Rivoire, “Influence of propagation of optical pulses on stimulated Rayleigh wing scattering in a Kerr medium,” J. Opt. Soc. Am. B 14, 2584–2588 (1997).
    [CrossRef]
  15. Y. R. Shen, “Self-focusing: experimental,” Prog. Quantum. Electron. 4, 1–34 (1975); O. Svelto, “Self-focusing, self-trapping, and self-phase modulation of laser beams,” Prog. Opt. 12, 1–51 (1974).
    [CrossRef]
  16. H. Maillotte, J. Monneret, A. Barthelemy, and C. Froehly, “Laser beam self-splitting into solitons by optical Kerr nonlinearity,” Opt. Commun. 109, 265–271 (1994); H. Maillotte, J. Monneret, and C. Froehly, “Self-induced multiple soliton-like beams by stimulated scattering,” Opt. Commun. 109, 272–278 (1994).
    [CrossRef]
  17. A. Brodeur, F. A. Ilkov, and S. L. Chin, “Beam filamentation and the white light continuum divergence,” Opt. Commun. 129, 193–198 (1996).
    [CrossRef]
  18. M. L. Dowell, B. D. Paul, A. Gallagher, and J. Cooper, “Self-focused light propagation in a fully saturable medium: theory,” Phys. Rev. A 52, 3244–3253 (1995); P. K. Shukla and R. Bingham, “Filamentation instability and localization of finite amplitude optical pulses in saturable nonlinear media,” Phys. Scr. 52, 199–200 (1995); Y. Chen and J. Atai, “Solitary waves of Maxwell’s equations in nonlinear anisotropic media,” J. Mod. Opt. JMOPEW 42, 1649–1658 (1995); S. Chi and Q. Guo, “Vector theory of self-focusing of an optical beam in Kerr media,” Opt. Lett. OPLEDP 20, 1598–1600 (1995); C. S. Milsted, Jr., and C. D. Cantrell, “Vector effects in self-focusing,” Phys. Rev. A PLRAAN 53, 3536–3542 (1996); G. Fibich, “Adiabatic law for self-focusing of optical beams,” Opt. Lett. OPLEDP 21, 1735–1737 (1996).
    [CrossRef] [PubMed]
  19. F. Shimizu, “Frequency broadening in liquids by a short light pulse,” Phys. Rev. Lett. 19, 1097–1100 (1967).
    [CrossRef]
  20. G. S. He, G. C. Xu, Y. Cui, and P. N. Prasad, “Difference of spectral superbroadening behavior in Kerr-type and non-Kerr-type liquids pumped with ultrashort laser pulses,” Appl. Opt. 32, 4507–4512 (1993).
    [CrossRef] [PubMed]
  21. M. Vampouille, B. Colombeau, and C. Froehly, “Application du contro⁁le de l’autofocalisation dans CS2 au raccourcissement d’impulsions laser picoseconde,” Opt. Quantum Electron. 14, 253–261 (1982).
    [CrossRef]
  22. J. P. Boon and S. Yip, Molecular Hydrodynamics (McGraw-Hill, New York, 1980), Sect. 1.3.
  23. P. P. Ho and R. R. Alfano, “Optical Kerr effect in liquids,” Phys. Rev. A 20, 2170–2187 (1979); C. E. Barker, R. Trebino, A. G. Kostenbauder, and A. E. Siegman, “Frequency-domain observation of the ultrafast inertial response of the optical Kerr effect in CS2,” J. Chem. Phys. 92, 4740–4748 (1990). All important references can be found in these papers.
    [CrossRef]
  24. T. K. Gustafson, J. P. Taran, H. A. Haus, J. R. Lifsitz, and P. L. Kelley, “Self-modulation, self-steepening, and spectral development of light in small-scale trapped filaments,” Phys. Rev. 177, 306–313 (1969); J. Reintjes, R. L. Carman, and F. Shimizu, “Study of self-focusing and self-phase modulation in the picosecond-time regime,” Phys. Rev. A 8, 1486–1503 (1973).
    [CrossRef]
  25. R. Polloni, C. A. Sacchi, and O. Svelto, “Self-trapping with picosecond pulses and ‘rocking’ of molecules,” Phys. Rev. Lett. 23, 690–693 (1969).
    [CrossRef]
  26. R. Cubeddu, R. Polloni, C. A. Sacchi, and O. Svelto, “Self-phase modulation and ‘rocking’ of molecules in trapped filaments of light with picosecond pulses,” Phys. Rev. A 2, 1955–1963 (1970).
    [CrossRef]
  27. M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980).
  28. M. R. Topp and G. C. Orner, “Group dispersion effects in picosecond spectroscopy,” Opt. Commun. 13, 276–281 (1975).
    [CrossRef]
  29. R. R. Alfano and S. L. Shapiro, “Emission in the region 4000 to 7000 Å via four-photon coupling in glass,” Phys. Rev. Lett. 24, 584–587 (1970); “Observation of self-phase modulation and small-scale filaments in crystals and glasses,” Phys. Rev. Lett. 24, 592–594 (1970); A. Penzkofer, A. Laubereau, and W. Kaiser, “Stimulated short-wave radiation due to single-frequency resonances of χ(3),” Phys. Rev. Lett. PRLTAO 31, 863–866 (1973); D. J. Harter and R. W. Boyd, “Four-wave mixing resonantly enhanced by ac-Stark-split levels in self-trapped filaments of light,” Phys. Rev. A PLRAAN 29, 739–748 (1984).
    [CrossRef]
  30. J. K. Ranka, R. W. Schirmer, and A. L. Gaeta, “Observation of pulse splitting in nonlinear dispersive media,” Phys. Rev. Lett. 77, 3783–3786 (1996); P. Chernev and V. Petrov, “Self-focusing of short light pulses in dispersive media,” Opt. Commun. 87, 28–32 (1992); “Self-focusing of light pulses in the presence of normal group-velocity dispersion,” Opt. Lett. OPLEDP 17, 172–174 (1992); J. E. Rothenberg, “Pulse splitting during self-focusing in normally dispersive media,” Opt. Lett. OPLEDP 17, 583–585 (1992).
    [CrossRef] [PubMed]

1997 (1)

1996 (1)

A. Brodeur, F. A. Ilkov, and S. L. Chin, “Beam filamentation and the white light continuum divergence,” Opt. Commun. 129, 193–198 (1996).
[CrossRef]

1993 (2)

1992 (1)

E. J. Miller and R. W. Boyd, “Stimulated scattering of pico second optical pulses in the presence of self-focusing,” Int. J. Nonlinear Opt. Phys. 1, 765–773 (1992).
[CrossRef]

1990 (1)

1982 (1)

M. Vampouille, B. Colombeau, and C. Froehly, “Application du contro⁁le de l’autofocalisation dans CS2 au raccourcissement d’impulsions laser picoseconde,” Opt. Quantum Electron. 14, 253–261 (1982).
[CrossRef]

1975 (1)

M. R. Topp and G. C. Orner, “Group dispersion effects in picosecond spectroscopy,” Opt. Commun. 13, 276–281 (1975).
[CrossRef]

1970 (2)

R. Cubeddu, R. Polloni, C. A. Sacchi, and O. Svelto, “Self-phase modulation and ‘rocking’ of molecules in trapped filaments of light with picosecond pulses,” Phys. Rev. A 2, 1955–1963 (1970).
[CrossRef]

E. P. Ippen, “Low-power quasi-cw Raman oscillator,” Appl. Phys. Lett. 16, 303–305 (1970).
[CrossRef]

1969 (1)

R. Polloni, C. A. Sacchi, and O. Svelto, “Self-trapping with picosecond pulses and ‘rocking’ of molecules,” Phys. Rev. Lett. 23, 690–693 (1969).
[CrossRef]

1967 (1)

F. Shimizu, “Frequency broadening in liquids by a short light pulse,” Phys. Rev. Lett. 19, 1097–1100 (1967).
[CrossRef]

1965 (1)

D. I. Mash, V. V. Morozov, V. S. Starunov, and I. L. Fabelinskii, “Stimulated scattering of light of the Rayleigh-line wing,” Pis’ma Zh. Eksp. Teor. Fiz. 2, 41–43 (1965) [ JETP Lett. 2, 25–27 (1965)].

Appl. Opt. (1)

Appl. Phys. Lett. (1)

E. P. Ippen, “Low-power quasi-cw Raman oscillator,” Appl. Phys. Lett. 16, 303–305 (1970).
[CrossRef]

Int. J. Nonlinear Opt. Phys. (1)

E. J. Miller and R. W. Boyd, “Stimulated scattering of pico second optical pulses in the presence of self-focusing,” Int. J. Nonlinear Opt. Phys. 1, 765–773 (1992).
[CrossRef]

J. Chem. Phys. (1)

D. Wang and G. Rivoire, “Large spectral bandwidth stimulated Rayleigh-wing scattering in CS2,” J. Chem. Phys. 98, 9279–9283 (1993).
[CrossRef]

J. Opt. Soc. Am. B (1)

JETP Lett. (1)

D. I. Mash, V. V. Morozov, V. S. Starunov, and I. L. Fabelinskii, “Stimulated scattering of light of the Rayleigh-line wing,” Pis’ma Zh. Eksp. Teor. Fiz. 2, 41–43 (1965) [ JETP Lett. 2, 25–27 (1965)].

Opt. Commun. (2)

A. Brodeur, F. A. Ilkov, and S. L. Chin, “Beam filamentation and the white light continuum divergence,” Opt. Commun. 129, 193–198 (1996).
[CrossRef]

M. R. Topp and G. C. Orner, “Group dispersion effects in picosecond spectroscopy,” Opt. Commun. 13, 276–281 (1975).
[CrossRef]

Opt. Lett. (1)

Opt. Quantum Electron. (1)

M. Vampouille, B. Colombeau, and C. Froehly, “Application du contro⁁le de l’autofocalisation dans CS2 au raccourcissement d’impulsions laser picoseconde,” Opt. Quantum Electron. 14, 253–261 (1982).
[CrossRef]

Phys. Rev. A (1)

R. Cubeddu, R. Polloni, C. A. Sacchi, and O. Svelto, “Self-phase modulation and ‘rocking’ of molecules in trapped filaments of light with picosecond pulses,” Phys. Rev. A 2, 1955–1963 (1970).
[CrossRef]

Phys. Rev. Lett. (2)

R. Polloni, C. A. Sacchi, and O. Svelto, “Self-trapping with picosecond pulses and ‘rocking’ of molecules,” Phys. Rev. Lett. 23, 690–693 (1969).
[CrossRef]

F. Shimizu, “Frequency broadening in liquids by a short light pulse,” Phys. Rev. Lett. 19, 1097–1100 (1967).
[CrossRef]

Other (17)

M. L. Dowell, B. D. Paul, A. Gallagher, and J. Cooper, “Self-focused light propagation in a fully saturable medium: theory,” Phys. Rev. A 52, 3244–3253 (1995); P. K. Shukla and R. Bingham, “Filamentation instability and localization of finite amplitude optical pulses in saturable nonlinear media,” Phys. Scr. 52, 199–200 (1995); Y. Chen and J. Atai, “Solitary waves of Maxwell’s equations in nonlinear anisotropic media,” J. Mod. Opt. JMOPEW 42, 1649–1658 (1995); S. Chi and Q. Guo, “Vector theory of self-focusing of an optical beam in Kerr media,” Opt. Lett. OPLEDP 20, 1598–1600 (1995); C. S. Milsted, Jr., and C. D. Cantrell, “Vector effects in self-focusing,” Phys. Rev. A PLRAAN 53, 3536–3542 (1996); G. Fibich, “Adiabatic law for self-focusing of optical beams,” Opt. Lett. OPLEDP 21, 1735–1737 (1996).
[CrossRef] [PubMed]

W. Kaiser and M. Maier, “Stimulated Rayleigh, Brillouin and Raman spectroscopy,” in Laser Handbook, F. T. Arecchi and E. O. Schulz-Dubois, eds. (North-Holland, Amsterdam, 1972), Vol. 2, pp. 1077–1150.

Y. R. Shen, “Self-focusing: experimental,” Prog. Quantum. Electron. 4, 1–34 (1975); O. Svelto, “Self-focusing, self-trapping, and self-phase modulation of laser beams,” Prog. Opt. 12, 1–51 (1974).
[CrossRef]

H. Maillotte, J. Monneret, A. Barthelemy, and C. Froehly, “Laser beam self-splitting into solitons by optical Kerr nonlinearity,” Opt. Commun. 109, 265–271 (1994); H. Maillotte, J. Monneret, and C. Froehly, “Self-induced multiple soliton-like beams by stimulated scattering,” Opt. Commun. 109, 272–278 (1994).
[CrossRef]

G. S. He and P. N. Prasad, “Stimulated Rayleigh–Kerr scattering in a CS2 liquid-core fiber system,” Opt. Commun. 73, 161–164 (1989); “Stimulated Kerr scattering and reorientation work of molecules in liquid CS2,” Phys. Rev. A 41, 2687–2697 (1990); “Stimulated Rayleigh–Kerr and Raman–Kerr scattering in a liquid-core hollow fiber system,” Fiber Integr. Opt. FOIOD2 9, 11–26 (1990); G. S. He, G. C. Xu, Y. Pang, and P. N. Prasad, “Temporal behavior of stimulated Kerr scattering in a CS2 liquid-core hollow-fiber system,” J. Opt. Soc. Am. B JOBPDE 8, 1907–1913 (1991); G. S. He and G. C. Xu, “Efficient amplification of a broad-band optical signal through stimulated Kerr scattering in a CS2 liquid-core fiber system,” IEEE J. Quantum Electron. IEJQA7 28, 323–329 (1992); G. S. He, M. Casstevens, R. Burzynski, and X. Li, “Broadband, multiwavelength stimulated-emission source based on stimulated Kerr and Raman scattering in a liquid-core fiber system,” Appl. Opt. APOPAI 34, 444–454 (1995).
[CrossRef] [PubMed]

J. Y. Zhou, H. Z. Wang, and Z. X. Yu, “Efficient generation of ultrafast broadband radiation in a submillimeter liquid-core waveguide,” Appl. Phys. Lett. 57, 643–644 (1990); J. Y. Zhou, H. Z. Wang, Y. C. Li, and Z. X. Yu, “Stimulated Rayleigh wing scattering and stimulated four-photon interaction in liquid-core waveguides,” J. Mod. Opt. 38, 1015–1019 (1991); J. Y. Zhou, H. Z. Wang, X. G. Huang, Z. G. Cai, and Z. X. Yu, “Generation of frequency-tunable ultrashort optical pulses with liquid-core fibers,” Opt. Lett. OPLEDP 16, 1865–1867 (1991); H. Z. Wang, X. G. Zheng, W. D. Mao, Z. X. Yu, and Z. L. Gao, “Stimulated dynamic light scattering,” Phys. Rev. A PLRAAN 52, 1740–1745 (1995).
[CrossRef] [PubMed]

A. I. Erokhin, V. S. Starunov, and A. K. Shmelev, “Time evolution of stimulated Brillouin scattering during transverse laser pumping of carbon disulfide filling a capillary,” Pis’ma Zh. Eksp. Teor. Fiz. 60, 823–828 (1994) [ JETP Lett. 60, 837–842 (1994)]; V. S. Starunov and A. K. Shmelev, “Temporal structures of stimulated Raman scattering in a capillary-filling liquid with transverse laser pumping,” Pis’ma Zh. Eksp. Teor. Fiz. 62, 844–848 (1995) [ JETP Lett. 62, 855–859 (1995)].

P. D. Maker, R. W. Terhune, and C. M. Savage, “Intensity-dependent changes in the refractive index of liquids,” Phys. Rev. Lett. 12, 507–509 (1964); G. Mayer and F. Gires, “Action d’une onde lumineuse intense sur l’indice de réfraction des liquides,” C. R. Acad. Sci. 258, 2039–2042 (1964).
[CrossRef]

A. Yariv, Quantum Electronics, 3rd ed. (Wiley, New York, 1989).

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

P. Lallemand and N. Bloembergen, “Self-focusing of laser beams and stimulated Raman gain in liquids,” Phys. Rev. Lett. 15, 1010–1012 (1965); Y. R. Shen and Y. J. Shaham, “Beam deterioration and stimulated Raman effect,” Phys. Rev. Lett. 15, 1008–1010 (1965); G. Hauchecorne and G. Mayer, “Effets de l’anisotropie moléculaire sur la propagation d’une lumiere intense,” C. R. Acad. Sci. COREAF 261, 4014–4017 (1965).
[CrossRef]

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980).

R. R. Alfano and S. L. Shapiro, “Emission in the region 4000 to 7000 Å via four-photon coupling in glass,” Phys. Rev. Lett. 24, 584–587 (1970); “Observation of self-phase modulation and small-scale filaments in crystals and glasses,” Phys. Rev. Lett. 24, 592–594 (1970); A. Penzkofer, A. Laubereau, and W. Kaiser, “Stimulated short-wave radiation due to single-frequency resonances of χ(3),” Phys. Rev. Lett. PRLTAO 31, 863–866 (1973); D. J. Harter and R. W. Boyd, “Four-wave mixing resonantly enhanced by ac-Stark-split levels in self-trapped filaments of light,” Phys. Rev. A PLRAAN 29, 739–748 (1984).
[CrossRef]

J. K. Ranka, R. W. Schirmer, and A. L. Gaeta, “Observation of pulse splitting in nonlinear dispersive media,” Phys. Rev. Lett. 77, 3783–3786 (1996); P. Chernev and V. Petrov, “Self-focusing of short light pulses in dispersive media,” Opt. Commun. 87, 28–32 (1992); “Self-focusing of light pulses in the presence of normal group-velocity dispersion,” Opt. Lett. OPLEDP 17, 172–174 (1992); J. E. Rothenberg, “Pulse splitting during self-focusing in normally dispersive media,” Opt. Lett. OPLEDP 17, 583–585 (1992).
[CrossRef] [PubMed]

J. P. Boon and S. Yip, Molecular Hydrodynamics (McGraw-Hill, New York, 1980), Sect. 1.3.

P. P. Ho and R. R. Alfano, “Optical Kerr effect in liquids,” Phys. Rev. A 20, 2170–2187 (1979); C. E. Barker, R. Trebino, A. G. Kostenbauder, and A. E. Siegman, “Frequency-domain observation of the ultrafast inertial response of the optical Kerr effect in CS2,” J. Chem. Phys. 92, 4740–4748 (1990). All important references can be found in these papers.
[CrossRef]

T. K. Gustafson, J. P. Taran, H. A. Haus, J. R. Lifsitz, and P. L. Kelley, “Self-modulation, self-steepening, and spectral development of light in small-scale trapped filaments,” Phys. Rev. 177, 306–313 (1969); J. Reintjes, R. L. Carman, and F. Shimizu, “Study of self-focusing and self-phase modulation in the picosecond-time regime,” Phys. Rev. A 8, 1486–1503 (1973).
[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

Experimental setup. The path from cell to spectrograph has a total length of d1=24 cm. The distance d2 between lens L2 and spectrograph amounts to 12 cm.

Fig. 2
Fig. 2

Camera recordings of spatial transverse intensity distributions: upper-left picture, forward direction below threshold; upper-right picture; forward direction at threshold; lower picture, backward direction at threshold.

Fig. 3
Fig. 3

Example of a regular backward spectrum at the threshold value of I0=0.3 GW/cm2 for the input intensity. Distances are not the same as in Fig. 1; see main text. The corresponding spectral distribution of the light intensity is shown as well.

Fig. 4
Fig. 4

Example of a regular forward spectrum at threshold. The experimental setup differs from the one shown in Fig. 1. See main text for a description of the modifications.

Fig. 5
Fig. 5

Some irregular backward spectra at threshold. In the middle spectrum, fringes can be observed. Distances are the same as in Fig. 1. The reference line in the spectra corresponds to a wavelength of 532 nm.

Fig. 6
Fig. 6

Example of a regular backward spectrum at an input intensity of 1.2I0. Distances are the same as in Fig. 1. The reference line corresponds to a wavelength of 532 nm.

Fig. 7
Fig. 7

Example of a regular backward spectrum at an input intensity of 1.8I0. Distances are the same as in Fig. 1. The reference line corresponds to a wavelength of 532 nm.

Fig. 8
Fig. 8

Typical backward spectrum at an input intensity of 3I0. Distances are the same as in Fig. 1. The reference line corresponds to a wavelength of 532 nm.

Fig. 9
Fig. 9

Camera recording of a backward spectrum at an input intensity of 30I0. Distances are the same as in Fig. 1. We calculated the spectral distribution of the light intensity for 30 different laser shots and took the average. The resulting plot is shown as well.

Fig. 10
Fig. 10

Spectrum as obtained from Eqs. (3) and (6) for the choice ξ=36.2, T=3.1 ps, and α=6.5. The intensity on the vertical axis is scaled with a certain positive constant. The spectrum should be compared with the intensity distribution displayed in Fig. 3.

Equations (7)

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

E(z, t)=eˆE(t-zvg-1)exp[iω0(n0z/c-t)]+c.c.,
n0n0+n2|E(z, t)|2¯.
I(ω)=|F(ω-ω0)|2,
F(ω)=-+dxf(x)exp[iωTx+iξf2(x)].
f2(x)=-αx2+1(0xα-1)α(x-1)2/(α-1)(α-1x1),0(x1)
F(ω)=[π/(αξ)]1/2f[ωT/(2αξ)]×exp[iξ+iω2T2/(4αξ)-iπ/4]+[π(α-1)/(αξ)]1/2f[1-(α-1)ωT/(2αξ)]×exp[iωT-i(α-1)ω2T2/(4αξ)+iπ/4]+O(ξ-1),
ω(n)=ω0±2ξT±-1[1-(2π/ξ)1/2(n-1/4)1/2],

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