Abstract

Conical diffraction was observed when two beams of the same or different frequencies intersect as they pass through a cell containing a transparent liquid. Light is emitted along the surfaces of cones centered in each of the two beams with an angular extent equal to twice the crossing angle between the two incident beams. The origin of this effect is attributed to a combination of modulational instability, two-beam emission, and nonlinear Bragg diffraction.

© 2006 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  3. J. H. Marburger, ed., Special Issue on Transverse Effects in Nonlinear Optics, J. Opt. Soc. Am. B 7 (1990).
  4. L. Bergé, "Wave collapse in physics: principles and applications in light and plasma waves," Phys. Rep. 303, 259-370 (1998).
    [CrossRef]
  5. S. Tzortzakis, L. Bergé, M. Franco, B. Prade, and A. Mysyrowicz, "Breakup and fusion of self-guided femtosecond light pulses in air," Phys. Rev. Lett. 86, 5470-5473 (2001).
    [CrossRef] [PubMed]
  6. S. Shwartz, M. Segev, and U. El-Hanany, "Self-deflection and all-optical beam steering in CdZnTe," Opt. Lett. 29, 760-762 (2004).
    [CrossRef] [PubMed]
  7. G. I. Stegeman and M. Segev, "Self-trapping of optical beams: spatial solitons," Phys. Today 51, 42-48 (1998).
    [CrossRef]
  8. K. D. Moll, A. L. Gaeta, and G. Fibich, "Self-similar optical wave collapse: observation of the townes profile," Phys. Rev. Lett. 90, 203902 (2003).
    [CrossRef] [PubMed]
  9. D. J. Harter, P. Narum, M. G. Raymer, and R. W. Boyd, "Four-wave parametric amplification of Rabi sidebands in sodium," Phys. Rev. Lett. 46, 1192-1195 (1981).
    [CrossRef]
  10. 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 29, 739-748 (1984).
    [CrossRef]
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    [PubMed]
  12. W. Du and S. Liu, "Single beam self-interaction in Langmuir-Blodgett films," Opt. Commun. 98, 117-119 (1993).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  15. K. D. Moll, D. Homoelle, A. Gaeta, and R. W. Boyd, "Conical harmonic generation in isotropic materials," Phys. Rev. Lett. 88, 153901 (2002).
    [CrossRef] [PubMed]
  16. H. Zeng, J. Wu, X. Hu, K. Wu, and E. Wu, "Colored conical emission by means of second harmonic generation in a quadratically nonlinear medium," Phys. Rev. Lett. 92, 143903 (2004).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  20. A. J. Stentz, M. KauranenJ. J. Maki, G. P. Agrawal, and R. W. Boyd, "Induced focusing and spatial wave breaking from cross-phase modulation in a self-defocusing medium," Opt. Lett. 17, 19-21 (1992).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  22. M. Y. Shverdin, D. D. Yavuz, and D. R. Walker, "(2+1)-dimensional stable spatial Raman solitons," Phys. Rev. A 69, 031801 (2004).
    [CrossRef]
  23. M. Kauranen, J. J. Maki, A. L. Gaeta, and R. W. Boyd, "Two-beam-excited conical emission," Opt. Lett. 16, 943-945 (1991).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  26. H. Lotem and R. T. Lynch, Jr., "Destructive interference of imaginary resonant contributions to chi(3)," Phys. Rev. Lett. 37, 334-337 (1976).
    [CrossRef]
  27. H. Ma, A. S. L. Gomes, and C. B. de Araújo, "Raman-assisted polarization beats in time-delayed four-wave mixing," Opt. Lett. 17, 1052-1054 (1992).
    [CrossRef] [PubMed]
  28. G. Grynberg, "Mirrorless four-wave mixing oscillation in atomic vapors," Opt. Commun. 66, 321-324 (1988).
    [CrossRef]
  29. T. Honda, "Hexagonal pattern formation due to counterpropagation in KNbO3," Opt. Lett. 18, 598-600 (1993).
    [CrossRef] [PubMed]

2004

S. Shwartz, M. Segev, and U. El-Hanany, "Self-deflection and all-optical beam steering in CdZnTe," Opt. Lett. 29, 760-762 (2004).
[CrossRef] [PubMed]

H. Zeng, J. Wu, X. Hu, K. Wu, and E. Wu, "Colored conical emission by means of second harmonic generation in a quadratically nonlinear medium," Phys. Rev. Lett. 92, 143903 (2004).
[CrossRef] [PubMed]

M. Y. Shverdin, D. D. Yavuz, and D. R. Walker, "(2+1)-dimensional stable spatial Raman solitons," Phys. Rev. A 69, 031801 (2004).
[CrossRef]

2003

V. Pilla, L. de S. Menezes, M. A. R. C. Alencar, and C. B. de Araújo, "Laser-induced conical diffraction due to cross-phase modulation in a transparent medium," J. Opt. Soc. Am. B 20, 1269-1272 (2003).
[CrossRef]

D. Salerno, S. Minardi, J. Trull, A. Varanavicius, G. Tamosauskas, G. Valiulis, A. Dubietis, D. Caironi, S. Trillo, A. Piskarskas, and P. Di Traponi, "Spatial versus temporal deterministic wave breakup of nonlinearly coupled light waves," Phys. Rev. Lett. 91, 143905 (2003).
[CrossRef] [PubMed]

K. D. Moll, A. L. Gaeta, and G. Fibich, "Self-similar optical wave collapse: observation of the townes profile," Phys. Rev. Lett. 90, 203902 (2003).
[CrossRef] [PubMed]

2002

K. D. Moll, D. Homoelle, A. Gaeta, and R. W. Boyd, "Conical harmonic generation in isotropic materials," Phys. Rev. Lett. 88, 153901 (2002).
[CrossRef] [PubMed]

2001

S. Tzortzakis, L. Bergé, M. Franco, B. Prade, and A. Mysyrowicz, "Breakup and fusion of self-guided femtosecond light pulses in air," Phys. Rev. Lett. 86, 5470-5473 (2001).
[CrossRef] [PubMed]

2000

1998

L. Bergé, "Wave collapse in physics: principles and applications in light and plasma waves," Phys. Rep. 303, 259-370 (1998).
[CrossRef]

G. I. Stegeman and M. Segev, "Self-trapping of optical beams: spatial solitons," Phys. Today 51, 42-48 (1998).
[CrossRef]

1995

H. Ma and C. B. de Araújo, "Raman-assisted spatial cross phase modulation in carbon disulfide," Phys. Rev. A 51, 4910-4912 (1995).
[CrossRef] [PubMed]

1993

1992

1991

1990

G. P. Agrawal, "Induced focusing of optical beams in self-defocusing nonlinear media," Phys. Rev. Lett. 64, 2487-2490 (1990).
[CrossRef] [PubMed]

G. P. Agrawal, "Transverse modulation instability of copropagating optical beams in nonlinear Kerr media," J. Opt. Soc. Am. B 7, 1072-1078 (1990).
[CrossRef]

1988

G. Grynberg, "Mirrorless four-wave mixing oscillation in atomic vapors," Opt. Commun. 66, 321-324 (1988).
[CrossRef]

1984

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 29, 739-748 (1984).
[CrossRef]

1981

S. D. Durbin, S. M. Arakelian, and Y. R. Shen, "Laser-induced diffraction rings from a nematic-liquid-crystal film," Opt. Lett. 6, 411-413 (1981).
[PubMed]

D. J. Harter, P. Narum, M. G. Raymer, and R. W. Boyd, "Four-wave parametric amplification of Rabi sidebands in sodium," Phys. Rev. Lett. 46, 1192-1195 (1981).
[CrossRef]

1976

H. Lotem and R. T. Lynch, Jr., "Destructive interference of imaginary resonant contributions to chi(3)," Phys. Rev. Lett. 37, 334-337 (1976).
[CrossRef]

1975

For a review of earlier studies, see Y. R. Shen, "Self-focusing: experimental," Prog. Quantum Electron. 4, 1-35 (1975).
[CrossRef]

J. H. Marburger, "Self-focusing: theory," Prog. Quantum Electron. 4, 35-110 (1975).
[CrossRef]

Agrawal, G. P.

Alencar, M. A.

Arakelian, S. M.

Bergé, L.

S. Tzortzakis, L. Bergé, M. Franco, B. Prade, and A. Mysyrowicz, "Breakup and fusion of self-guided femtosecond light pulses in air," Phys. Rev. Lett. 86, 5470-5473 (2001).
[CrossRef] [PubMed]

L. Bergé, "Wave collapse in physics: principles and applications in light and plasma waves," Phys. Rep. 303, 259-370 (1998).
[CrossRef]

Bourhill, G.

Boyd, R. W.

K. D. Moll, D. Homoelle, A. Gaeta, and R. W. Boyd, "Conical harmonic generation in isotropic materials," Phys. Rev. Lett. 88, 153901 (2002).
[CrossRef] [PubMed]

A. J. Stentz, M. KauranenJ. J. Maki, G. P. Agrawal, and R. W. Boyd, "Induced focusing and spatial wave breaking from cross-phase modulation in a self-defocusing medium," Opt. Lett. 17, 19-21 (1992).
[CrossRef] [PubMed]

M. Kauranen, J. J. Maki, A. L. Gaeta, and R. W. Boyd, "Two-beam-excited conical emission," Opt. Lett. 16, 943-945 (1991).
[CrossRef] [PubMed]

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 29, 739-748 (1984).
[CrossRef]

D. J. Harter, P. Narum, M. G. Raymer, and R. W. Boyd, "Four-wave parametric amplification of Rabi sidebands in sodium," Phys. Rev. Lett. 46, 1192-1195 (1981).
[CrossRef]

Caironi, D.

D. Salerno, S. Minardi, J. Trull, A. Varanavicius, G. Tamosauskas, G. Valiulis, A. Dubietis, D. Caironi, S. Trillo, A. Piskarskas, and P. Di Traponi, "Spatial versus temporal deterministic wave breakup of nonlinearly coupled light waves," Phys. Rev. Lett. 91, 143905 (2003).
[CrossRef] [PubMed]

de Araújo, C. B.

V. Pilla, L. de S. Menezes, M. A. R. C. Alencar, and C. B. de Araújo, "Laser-induced conical diffraction due to cross-phase modulation in a transparent medium," J. Opt. Soc. Am. B 20, 1269-1272 (2003).
[CrossRef]

H. Ma and C. B. de Araújo, "Raman-assisted spatial cross phase modulation in carbon disulfide," Phys. Rev. A 51, 4910-4912 (1995).
[CrossRef] [PubMed]

J. M. Hickmann, A. S. L. Gomes, and C. B. de Araújo, "Observation of spatial cross-phase modulation effects in a self-defocusing nonlinear medium," Phys. Rev. Lett. 68, 3547-3550 (1992).
[CrossRef] [PubMed]

H. Ma, A. S. L. Gomes, and C. B. de Araújo, "Raman-assisted polarization beats in time-delayed four-wave mixing," Opt. Lett. 17, 1052-1054 (1992).
[CrossRef] [PubMed]

de S. Menezes, L.

Di Traponi, P.

D. Salerno, S. Minardi, J. Trull, A. Varanavicius, G. Tamosauskas, G. Valiulis, A. Dubietis, D. Caironi, S. Trillo, A. Piskarskas, and P. Di Traponi, "Spatial versus temporal deterministic wave breakup of nonlinearly coupled light waves," Phys. Rev. Lett. 91, 143905 (2003).
[CrossRef] [PubMed]

Du, W.

W. Du and S. Liu, "Single beam self-interaction in Langmuir-Blodgett films," Opt. Commun. 98, 117-119 (1993).
[CrossRef]

Dubietis, A.

D. Salerno, S. Minardi, J. Trull, A. Varanavicius, G. Tamosauskas, G. Valiulis, A. Dubietis, D. Caironi, S. Trillo, A. Piskarskas, and P. Di Traponi, "Spatial versus temporal deterministic wave breakup of nonlinearly coupled light waves," Phys. Rev. Lett. 91, 143905 (2003).
[CrossRef] [PubMed]

Duignan, J.

Durbin, S. D.

El-Hanany, U.

Fibich, G.

K. D. Moll, A. L. Gaeta, and G. Fibich, "Self-similar optical wave collapse: observation of the townes profile," Phys. Rev. Lett. 90, 203902 (2003).
[CrossRef] [PubMed]

Franco, M.

S. Tzortzakis, L. Bergé, M. Franco, B. Prade, and A. Mysyrowicz, "Breakup and fusion of self-guided femtosecond light pulses in air," Phys. Rev. Lett. 86, 5470-5473 (2001).
[CrossRef] [PubMed]

Gaeta, A.

K. D. Moll, D. Homoelle, A. Gaeta, and R. W. Boyd, "Conical harmonic generation in isotropic materials," Phys. Rev. Lett. 88, 153901 (2002).
[CrossRef] [PubMed]

Gaeta, A. L.

Gomes, A. S.

J. M. Hickmann, A. S. L. Gomes, and C. B. de Araújo, "Observation of spatial cross-phase modulation effects in a self-defocusing nonlinear medium," Phys. Rev. Lett. 68, 3547-3550 (1992).
[CrossRef] [PubMed]

H. Ma, A. S. L. Gomes, and C. B. de Araújo, "Raman-assisted polarization beats in time-delayed four-wave mixing," Opt. Lett. 17, 1052-1054 (1992).
[CrossRef] [PubMed]

Grynberg, G.

G. Grynberg, "Mirrorless four-wave mixing oscillation in atomic vapors," Opt. Commun. 66, 321-324 (1988).
[CrossRef]

Harter, D. J.

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 29, 739-748 (1984).
[CrossRef]

D. J. Harter, P. Narum, M. G. Raymer, and R. W. Boyd, "Four-wave parametric amplification of Rabi sidebands in sodium," Phys. Rev. Lett. 46, 1192-1195 (1981).
[CrossRef]

Hickmann, J. M.

J. M. Hickmann, A. S. L. Gomes, and C. B. de Araújo, "Observation of spatial cross-phase modulation effects in a self-defocusing nonlinear medium," Phys. Rev. Lett. 68, 3547-3550 (1992).
[CrossRef] [PubMed]

Homoelle, D.

K. D. Moll, D. Homoelle, A. Gaeta, and R. W. Boyd, "Conical harmonic generation in isotropic materials," Phys. Rev. Lett. 88, 153901 (2002).
[CrossRef] [PubMed]

Honda, T.

Hu, X.

H. Zeng, J. Wu, X. Hu, K. Wu, and E. Wu, "Colored conical emission by means of second harmonic generation in a quadratically nonlinear medium," Phys. Rev. Lett. 92, 143903 (2004).
[CrossRef] [PubMed]

Kauranen, M.

Liu, S.

W. Du and S. Liu, "Single beam self-interaction in Langmuir-Blodgett films," Opt. Commun. 98, 117-119 (1993).
[CrossRef]

Lotem, H.

H. Lotem and R. T. Lynch, Jr., "Destructive interference of imaginary resonant contributions to chi(3)," Phys. Rev. Lett. 37, 334-337 (1976).
[CrossRef]

Lynch, R. T.

H. Lotem and R. T. Lynch, Jr., "Destructive interference of imaginary resonant contributions to chi(3)," Phys. Rev. Lett. 37, 334-337 (1976).
[CrossRef]

Ma, H.

H. Ma and C. B. de Araújo, "Raman-assisted spatial cross phase modulation in carbon disulfide," Phys. Rev. A 51, 4910-4912 (1995).
[CrossRef] [PubMed]

H. Ma, A. S. L. Gomes, and C. B. de Araújo, "Raman-assisted polarization beats in time-delayed four-wave mixing," Opt. Lett. 17, 1052-1054 (1992).
[CrossRef] [PubMed]

Maki, J. J.

Marburger, J. H.

J. H. Marburger, "Self-focusing: theory," Prog. Quantum Electron. 4, 35-110 (1975).
[CrossRef]

J. H. Marburger, ed., Special Issue on Transverse Effects in Nonlinear Optics, J. Opt. Soc. Am. B 7 (1990).

McKinstrie, C. J.

Milsom, P.

Minardi, S.

D. Salerno, S. Minardi, J. Trull, A. Varanavicius, G. Tamosauskas, G. Valiulis, A. Dubietis, D. Caironi, S. Trillo, A. Piskarskas, and P. Di Traponi, "Spatial versus temporal deterministic wave breakup of nonlinearly coupled light waves," Phys. Rev. Lett. 91, 143905 (2003).
[CrossRef] [PubMed]

Moll, K. D.

K. D. Moll, A. L. Gaeta, and G. Fibich, "Self-similar optical wave collapse: observation of the townes profile," Phys. Rev. Lett. 90, 203902 (2003).
[CrossRef] [PubMed]

K. D. Moll, D. Homoelle, A. Gaeta, and R. W. Boyd, "Conical harmonic generation in isotropic materials," Phys. Rev. Lett. 88, 153901 (2002).
[CrossRef] [PubMed]

Mysyrowicz, A.

S. Tzortzakis, L. Bergé, M. Franco, B. Prade, and A. Mysyrowicz, "Breakup and fusion of self-guided femtosecond light pulses in air," Phys. Rev. Lett. 86, 5470-5473 (2001).
[CrossRef] [PubMed]

Narum, P.

D. J. Harter, P. Narum, M. G. Raymer, and R. W. Boyd, "Four-wave parametric amplification of Rabi sidebands in sodium," Phys. Rev. Lett. 46, 1192-1195 (1981).
[CrossRef]

Pilla, V.

Piskarskas, A.

D. Salerno, S. Minardi, J. Trull, A. Varanavicius, G. Tamosauskas, G. Valiulis, A. Dubietis, D. Caironi, S. Trillo, A. Piskarskas, and P. Di Traponi, "Spatial versus temporal deterministic wave breakup of nonlinearly coupled light waves," Phys. Rev. Lett. 91, 143905 (2003).
[CrossRef] [PubMed]

Prade, B.

S. Tzortzakis, L. Bergé, M. Franco, B. Prade, and A. Mysyrowicz, "Breakup and fusion of self-guided femtosecond light pulses in air," Phys. Rev. Lett. 86, 5470-5473 (2001).
[CrossRef] [PubMed]

Raymer, M. G.

D. J. Harter, P. Narum, M. G. Raymer, and R. W. Boyd, "Four-wave parametric amplification of Rabi sidebands in sodium," Phys. Rev. Lett. 46, 1192-1195 (1981).
[CrossRef]

Robertson, J.

Salerno, D.

D. Salerno, S. Minardi, J. Trull, A. Varanavicius, G. Tamosauskas, G. Valiulis, A. Dubietis, D. Caironi, S. Trillo, A. Piskarskas, and P. Di Traponi, "Spatial versus temporal deterministic wave breakup of nonlinearly coupled light waves," Phys. Rev. Lett. 91, 143905 (2003).
[CrossRef] [PubMed]

Segev, M.

S. Shwartz, M. Segev, and U. El-Hanany, "Self-deflection and all-optical beam steering in CdZnTe," Opt. Lett. 29, 760-762 (2004).
[CrossRef] [PubMed]

G. I. Stegeman and M. Segev, "Self-trapping of optical beams: spatial solitons," Phys. Today 51, 42-48 (1998).
[CrossRef]

Shen, Y. R.

S. D. Durbin, S. M. Arakelian, and Y. R. Shen, "Laser-induced diffraction rings from a nematic-liquid-crystal film," Opt. Lett. 6, 411-413 (1981).
[PubMed]

For a review of earlier studies, see Y. R. Shen, "Self-focusing: experimental," Prog. Quantum Electron. 4, 1-35 (1975).
[CrossRef]

Shverdin, M. Y.

M. Y. Shverdin, D. D. Yavuz, and D. R. Walker, "(2+1)-dimensional stable spatial Raman solitons," Phys. Rev. A 69, 031801 (2004).
[CrossRef]

Shwartz, S.

Stegeman, G. I.

G. I. Stegeman and M. Segev, "Self-trapping of optical beams: spatial solitons," Phys. Today 51, 42-48 (1998).
[CrossRef]

Stentz, A. J.

Tamosauskas, G.

D. Salerno, S. Minardi, J. Trull, A. Varanavicius, G. Tamosauskas, G. Valiulis, A. Dubietis, D. Caironi, S. Trillo, A. Piskarskas, and P. Di Traponi, "Spatial versus temporal deterministic wave breakup of nonlinearly coupled light waves," Phys. Rev. Lett. 91, 143905 (2003).
[CrossRef] [PubMed]

Trillo, S.

D. Salerno, S. Minardi, J. Trull, A. Varanavicius, G. Tamosauskas, G. Valiulis, A. Dubietis, D. Caironi, S. Trillo, A. Piskarskas, and P. Di Traponi, "Spatial versus temporal deterministic wave breakup of nonlinearly coupled light waves," Phys. Rev. Lett. 91, 143905 (2003).
[CrossRef] [PubMed]

Trull, J.

D. Salerno, S. Minardi, J. Trull, A. Varanavicius, G. Tamosauskas, G. Valiulis, A. Dubietis, D. Caironi, S. Trillo, A. Piskarskas, and P. Di Traponi, "Spatial versus temporal deterministic wave breakup of nonlinearly coupled light waves," Phys. Rev. Lett. 91, 143905 (2003).
[CrossRef] [PubMed]

Tzortzakis, S.

S. Tzortzakis, L. Bergé, M. Franco, B. Prade, and A. Mysyrowicz, "Breakup and fusion of self-guided femtosecond light pulses in air," Phys. Rev. Lett. 86, 5470-5473 (2001).
[CrossRef] [PubMed]

Valiulis, G.

D. Salerno, S. Minardi, J. Trull, A. Varanavicius, G. Tamosauskas, G. Valiulis, A. Dubietis, D. Caironi, S. Trillo, A. Piskarskas, and P. Di Traponi, "Spatial versus temporal deterministic wave breakup of nonlinearly coupled light waves," Phys. Rev. Lett. 91, 143905 (2003).
[CrossRef] [PubMed]

Varanavicius, A.

D. Salerno, S. Minardi, J. Trull, A. Varanavicius, G. Tamosauskas, G. Valiulis, A. Dubietis, D. Caironi, S. Trillo, A. Piskarskas, and P. Di Traponi, "Spatial versus temporal deterministic wave breakup of nonlinearly coupled light waves," Phys. Rev. Lett. 91, 143905 (2003).
[CrossRef] [PubMed]

Walker, D. R.

M. Y. Shverdin, D. D. Yavuz, and D. R. Walker, "(2+1)-dimensional stable spatial Raman solitons," Phys. Rev. A 69, 031801 (2004).
[CrossRef]

Wu, E.

H. Zeng, J. Wu, X. Hu, K. Wu, and E. Wu, "Colored conical emission by means of second harmonic generation in a quadratically nonlinear medium," Phys. Rev. Lett. 92, 143903 (2004).
[CrossRef] [PubMed]

Wu, J.

H. Zeng, J. Wu, X. Hu, K. Wu, and E. Wu, "Colored conical emission by means of second harmonic generation in a quadratically nonlinear medium," Phys. Rev. Lett. 92, 143903 (2004).
[CrossRef] [PubMed]

Wu, K.

H. Zeng, J. Wu, X. Hu, K. Wu, and E. Wu, "Colored conical emission by means of second harmonic generation in a quadratically nonlinear medium," Phys. Rev. Lett. 92, 143903 (2004).
[CrossRef] [PubMed]

Yavuz, D. D.

M. Y. Shverdin, D. D. Yavuz, and D. R. Walker, "(2+1)-dimensional stable spatial Raman solitons," Phys. Rev. A 69, 031801 (2004).
[CrossRef]

Zeng, H.

H. Zeng, J. Wu, X. Hu, K. Wu, and E. Wu, "Colored conical emission by means of second harmonic generation in a quadratically nonlinear medium," Phys. Rev. Lett. 92, 143903 (2004).
[CrossRef] [PubMed]

J. Opt. Soc. Am. B

Opt. Commun.

G. Grynberg, "Mirrorless four-wave mixing oscillation in atomic vapors," Opt. Commun. 66, 321-324 (1988).
[CrossRef]

W. Du and S. Liu, "Single beam self-interaction in Langmuir-Blodgett films," Opt. Commun. 98, 117-119 (1993).
[CrossRef]

Opt. Lett.

Phys. Rep.

L. Bergé, "Wave collapse in physics: principles and applications in light and plasma waves," Phys. Rep. 303, 259-370 (1998).
[CrossRef]

Phys. Rev. A

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 29, 739-748 (1984).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Schematic of the experimental configuration. λ and λ are the wavelengths of the laser beams.

Fig. 2
Fig. 2

CD as observed on a screen located about 30 cm from the sample. (a) The two incident beams have different frequencies (incident powers: 30 kW). (b) The intensity profile recorded with a digital camera (accumulation of four shots). The two incident beams, around ( x r , y r ) equal to (0,0) and ( 1.0 , 0), were blocked to prevent saturation of the camera.

Fig. 3
Fig. 3

(a) Hexagonal geometry of the interacting beams. (b) Intensity pattern calculated assuming four-wave-mixing processes involving the input beams and Rayleigh-scattered light.

Fig. 4
Fig. 4

CD intensity as a function of the probe beam and the pump beam power. Theoretical results are given by solid curves, and the points represent the experimental data. (a) Total intensity of the ring. (b) Intensity corresponding to a selected spatial region of the ring.

Fig. 5
Fig. 5

CD signal intensity as a function of the transverse coordinate x. The solid curve is the theoretical result considering the dependence of the NL Bragg diffraction and TBE on the interaction length. The inset shows the orientation of the coordinate system used.

Equations (17)

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P NL = 3 χ ( 3 ) E p 2 E p + 6 χ ( 3 ) E p 2 E w + 3 χ ( 3 ) E p 2 E w * + 6 χ ( 3 ) E w 2 E p + 3 χ ( 3 ) E w 2 E w .
d A j d z = i 2 π k j P j .
A j ( z ) = A j ( 0 ) exp [ i β ( A j 2 + 2 A m 2 ) z ] ,
d A 3 d z = i 2 β { ( A 1 2 + A 2 2 ) A 3 + A 1 [ A 2 A 4 * exp ( i Δ k 1 z ) + A 5 A 7 * exp ( i Δ k 2 z ) ] + A 1 * A 2 A 5 exp ( i Δ k 2 z ) + A 6 * [ A 4 A 5 + A 2 A 7 exp ( i Δ k 3 z ) + 1 2 A 1 2 exp ( i Δ k 4 z ) ] } ,
d A 4 d z = i 2 β { ( A 1 2 + A 2 2 ) A 4 + A 1 [ A 2 A 3 * exp ( i Δ k 1 z ) + A 6 A 7 * exp ( i Δ k 2 z ) ] + A 1 * A 2 A 6 exp ( i Δ k 2 z ) + A 5 * [ A 3 A 6 + A 2 A 7 exp ( i Δ k 3 z ) + 1 2 A 1 2 exp ( i Δ k 4 z ) ] } ,
d A 5 d z = i 2 β { ( A 1 2 + A 2 2 ) A 5 + A 1 [ A 7 A 6 * exp ( i Δ k 1 z ) + A 3 A 2 * exp ( i Δ k 2 z ) ] + A 1 * A 3 A 7 exp ( i Δ k 2 z ) + A 4 * [ A 3 A 6 + A 2 A 7 exp ( i Δ k 3 z ) + 1 2 A 1 2 exp ( i Δ k 4 z ) ] } ,
d A 6 d z = i 2 β { ( A 1 2 + A 2 2 ) A 6 + A 1 [ A 7 A 5 * exp ( i Δ k 1 z ) + A 4 A 2 * exp ( i Δ k 2 z ) ] + A 1 * A 4 A 7 exp ( i Δ k 2 z ) + A 3 * [ A 4 A 5 + A 2 A 7 exp ( i Δ k 3 z ) + 1 2 A 1 2 exp ( i Δ k 4 z ) ] } ,
d A 7 d z = i 2 β { ( A 1 2 + A 2 2 ) A 7 + A 1 ( A 5 A 3 * + A 6 A 4 * ) exp ( i Δ k 2 z ) + A 1 * A 5 A 6 exp ( i Δ k 1 z ) + A 2 * [ ( A 3 A 6 + A 4 A 5 ) exp ( i Δ k 3 z ) + 1 2 A 1 2 exp ( i 2 Δ k 2 z ) ] } .
Δ k 1 = k ( 1 + cos θ ) 2 k z ,
Δ k 2 = k ( 1 cos θ ) ,
Δ k 3 = 2 ( k cos θ k z ) ,
Δ k 4 = 2 ( k k z ) .
d A 3 d z = i 2 { ( γ A 1 2 + γ A 2 2 ) A 3 + γ [ A 1 A 2 A 4 * exp ( i Δ k 1 z ) + A 1 A 5 A 7 * exp ( i Δ k 2 z ) + A 1 * A 2 A 5 exp ( i Δ k 2 z ) ] } ,
d A 4 d z = i 2 { ( γ A 1 2 + γ A 2 2 ) A 4 + γ A 5 * A 2 A 7 exp ( i Δ k 3 z ) + γ [ A 1 A 2 A 3 * exp ( i Δ k 1 z ) + 1 2 A 5 * A 1 2 exp ( i Δ k 4 z ) ] } ,
d A 5 d z = i 2 { ( γ A 1 2 + γ A 2 2 ) A 5 + γ A 4 * A 2 A 7 exp ( i Δ k 3 z ) + γ [ A 1 * A 3 A 7 exp ( i Δ k 2 z ) + A 1 A 3 A 2 * exp ( i Δ k 2 z ) + 1 2 A 4 * A 1 2 exp ( i Δ k 4 z ) ] } ,
d A 6 d z = i 2 [ ( γ A 1 2 + γ A 2 2 ) A 6 ] ,
d A 7 d z = i 2 { ( γ A 1 2 + γ A 2 2 ) A 7 + γ A 2 * A 4 A 5 exp ( i Δ k 3 z ) + γ [ A 1 A 5 A 3 * exp ( i Δ k 2 z ) + 1 2 A 2 * A 1 2 exp ( i 2 Δ k 2 z ) ] } ,

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