Abstract

We report the observation of conical diffraction induced by cross-phase modulation when a strong beam is copropagating with a weak beam through a cell containing dimethylsulfoxide. Pulsed laser beams at 1064 and 597 nm, in the transparency window of the material, were used. The phenomenon is attributed to third-order nonlinear susceptibility, and the ring observed at the far-field region is theoretically predicted by use of the Fresnel–Kirchhoff diffraction formalism.

© 2003 Optical Society of America

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References

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  1. Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).
  2. J. F. Valley, G. Khitrova, H. M. Gibbs, J. W. Granthan, and J. J. Xu, “Cw conical emission: first comparison and agreement between theory and experiment,” Phys. Rev. Lett. 64, 2362–2365 (1990).
    [CrossRef] [PubMed]
  3. B. DeBoo, D. F. Kimball, C. H. Li, and D. Budker, “Multichannel conical emission and parametric and nonparametric nonlinear optical processes in ytterbium vapor,” J. Opt. Soc. Am. B 18, 639–645 (2001), and references therein.
    [CrossRef]
  4. G. Khitrova, H. M. Gibbs, Y. Kawamura, H. Iwamura, T. Ikegami, J. E. Sipe, and L. Ming, “Spatial solitons in a self-focusing semiconductor gain medium,” Phys. Rev. Lett. 70, 920–923 (1993).
    [CrossRef] [PubMed]
  5. W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
    [CrossRef] [PubMed]
  6. H. S. Eisenberg, R. Morandotti, Y. Silberberg, S. Bar-Ad, D. Ross, and J. S. Aitchison, “Kerr spatiotemporal self-focusing in a planar glass waveguide,” Phys. Rev. Lett. 87, 043902 (2001).
    [CrossRef] [PubMed]
  7. S. Tzortzakis, L. Sudrie, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and L. Bergé, “Self-guided propagation of ultrashort IR laser pulses in fused silica,” Phys. Rev. Lett. 87, 213902 (2001), and references therein.
    [CrossRef] [PubMed]
  8. 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]
  9. M. Kauranen, A. L. Gaeta, and C. J. McKinstrie, “Transverse instabilities of two intersecting laser beams in a nonlinear Kerr medium,” J. Opt. Soc. Am. B 10, 2298–2305 (1993).
    [CrossRef]
  10. S. Saltiel, K. Koynov, K. Kirov, and K. Petrova, “Cross-phase modulation caused by cascading of third-order processes,” J. Opt. Soc. Am. B 16, 262–266 (1999), and references therein.
    [CrossRef]
  11. M. Schwab, C. Denz, and M. Saffman, “Transverse modulational instability in counterpropagating two-wave mixing with frequency-detuned pump beams,” J. Opt. Soc. Am. B 18, 628–638 (2001), and references therein.
    [CrossRef]
  12. 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]
  13. A. E. Kaplan, “Bending of trajectories of asymmetrical light beams in nonlinear media,” Pis'ma Zh. Eksp. Teor. Fiz. 9, 58–60 (1969) [JETP Lett. 9, 33–35 (1969)].
  14. H. Ma, A. S. L. Gomes, and C. B. de Araújo, “Measurements of nondegenerate optical nonlinearity using a two-color single beam method,” Appl. Phys. Lett. 59, 2666–2668 (1991).
    [CrossRef]
  15. M. Sheik-Bahae, J. Wang, R. DeSalvo, D. J. Hagan, and E. W. Van Stryland, “Measurement of nondegenerate nonlinearities using a two-color Z-scan,” Opt. Lett. 17, 258–260 (1992).
    [CrossRef] [PubMed]
  16. J. A. Riddick, W. B. Bunger, and T. K. Sukano, Handbook of Organic Solvents, D. R. Lide, ed. (CRC Press, Boca Raton, Fla., 1995), Vol. 2.
  17. V. P. Kozich, F. E. Hernandez, and A. Marcano, “Pulse-induced thermal lensing in Kerr media,” Appl. Spectrosc. 49, 1804–1808 (1995).
    [CrossRef]
  18. H. Toda and C. M. Verber, “Simple technique to reveal a slow nonlinear mechanism in a Z-scan-like n2 measurement,” Opt. Lett. 17, 1379–1381 (1992).
    [CrossRef]
  19. V. Pilla, G. G. G. Costa, and T. Catunda, “Applications of Fresnel–Kirchhoff diffraction integral in linear and nonlinear optics: a didactic introduction,” in Proceedings of the 4th IberoAmerican Meeting on Optics and 7th Latin American Meeting on Optics, Lasers and their Applications, V. L. Brudny, S. A. Ledesma, and M. C. Marconi, eds., Proc. SPIE 4419, 728–731 (2001).

2001 (4)

B. DeBoo, D. F. Kimball, C. H. Li, and D. Budker, “Multichannel conical emission and parametric and nonparametric nonlinear optical processes in ytterbium vapor,” J. Opt. Soc. Am. B 18, 639–645 (2001), and references therein.
[CrossRef]

H. S. Eisenberg, R. Morandotti, Y. Silberberg, S. Bar-Ad, D. Ross, and J. S. Aitchison, “Kerr spatiotemporal self-focusing in a planar glass waveguide,” Phys. Rev. Lett. 87, 043902 (2001).
[CrossRef] [PubMed]

S. Tzortzakis, L. Sudrie, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and L. Bergé, “Self-guided propagation of ultrashort IR laser pulses in fused silica,” Phys. Rev. Lett. 87, 213902 (2001), and references therein.
[CrossRef] [PubMed]

M. Schwab, C. Denz, and M. Saffman, “Transverse modulational instability in counterpropagating two-wave mixing with frequency-detuned pump beams,” J. Opt. Soc. Am. B 18, 628–638 (2001), and references therein.
[CrossRef]

1999 (1)

1995 (3)

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[CrossRef] [PubMed]

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]

V. P. Kozich, F. E. Hernandez, and A. Marcano, “Pulse-induced thermal lensing in Kerr media,” Appl. Spectrosc. 49, 1804–1808 (1995).
[CrossRef]

1993 (2)

G. Khitrova, H. M. Gibbs, Y. Kawamura, H. Iwamura, T. Ikegami, J. E. Sipe, and L. Ming, “Spatial solitons in a self-focusing semiconductor gain medium,” Phys. Rev. Lett. 70, 920–923 (1993).
[CrossRef] [PubMed]

M. Kauranen, A. L. Gaeta, and C. J. McKinstrie, “Transverse instabilities of two intersecting laser beams in a nonlinear Kerr medium,” J. Opt. Soc. Am. B 10, 2298–2305 (1993).
[CrossRef]

1992 (3)

1991 (1)

H. Ma, A. S. L. Gomes, and C. B. de Araújo, “Measurements of nondegenerate optical nonlinearity using a two-color single beam method,” Appl. Phys. Lett. 59, 2666–2668 (1991).
[CrossRef]

1990 (1)

J. F. Valley, G. Khitrova, H. M. Gibbs, J. W. Granthan, and J. J. Xu, “Cw conical emission: first comparison and agreement between theory and experiment,” Phys. Rev. Lett. 64, 2362–2365 (1990).
[CrossRef] [PubMed]

Aitchison, J. S.

H. S. Eisenberg, R. Morandotti, Y. Silberberg, S. Bar-Ad, D. Ross, and J. S. Aitchison, “Kerr spatiotemporal self-focusing in a planar glass waveguide,” Phys. Rev. Lett. 87, 043902 (2001).
[CrossRef] [PubMed]

Bar-Ad, S.

H. S. Eisenberg, R. Morandotti, Y. Silberberg, S. Bar-Ad, D. Ross, and J. S. Aitchison, “Kerr spatiotemporal self-focusing in a planar glass waveguide,” Phys. Rev. Lett. 87, 043902 (2001).
[CrossRef] [PubMed]

Bergé, L.

S. Tzortzakis, L. Sudrie, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and L. Bergé, “Self-guided propagation of ultrashort IR laser pulses in fused silica,” Phys. Rev. Lett. 87, 213902 (2001), and references therein.
[CrossRef] [PubMed]

Budker, D.

Couairon, A.

S. Tzortzakis, L. Sudrie, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and L. Bergé, “Self-guided propagation of ultrashort IR laser pulses in fused silica,” Phys. Rev. Lett. 87, 213902 (2001), and references therein.
[CrossRef] [PubMed]

de Araújo, C. B.

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, “Measurements of nondegenerate optical nonlinearity using a two-color single beam method,” Appl. Phys. Lett. 59, 2666–2668 (1991).
[CrossRef]

DeBoo, B.

Denz, C.

DeSalvo, R.

Eisenberg, H. S.

H. S. Eisenberg, R. Morandotti, Y. Silberberg, S. Bar-Ad, D. Ross, and J. S. Aitchison, “Kerr spatiotemporal self-focusing in a planar glass waveguide,” Phys. Rev. Lett. 87, 043902 (2001).
[CrossRef] [PubMed]

Franco, M.

S. Tzortzakis, L. Sudrie, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and L. Bergé, “Self-guided propagation of ultrashort IR laser pulses in fused silica,” Phys. Rev. Lett. 87, 213902 (2001), and references therein.
[CrossRef] [PubMed]

Gaeta, A. L.

Gibbs, H. M.

G. Khitrova, H. M. Gibbs, Y. Kawamura, H. Iwamura, T. Ikegami, J. E. Sipe, and L. Ming, “Spatial solitons in a self-focusing semiconductor gain medium,” Phys. Rev. Lett. 70, 920–923 (1993).
[CrossRef] [PubMed]

J. F. Valley, G. Khitrova, H. M. Gibbs, J. W. Granthan, and J. J. Xu, “Cw conical emission: first comparison and agreement between theory and experiment,” Phys. Rev. Lett. 64, 2362–2365 (1990).
[CrossRef] [PubMed]

Gomes, A. S. L.

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, “Measurements of nondegenerate optical nonlinearity using a two-color single beam method,” Appl. Phys. Lett. 59, 2666–2668 (1991).
[CrossRef]

Granthan, J. W.

J. F. Valley, G. Khitrova, H. M. Gibbs, J. W. Granthan, and J. J. Xu, “Cw conical emission: first comparison and agreement between theory and experiment,” Phys. Rev. Lett. 64, 2362–2365 (1990).
[CrossRef] [PubMed]

Hagan, D. J.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[CrossRef] [PubMed]

M. Sheik-Bahae, J. Wang, R. DeSalvo, D. J. Hagan, and E. W. Van Stryland, “Measurement of nondegenerate nonlinearities using a two-color Z-scan,” Opt. Lett. 17, 258–260 (1992).
[CrossRef] [PubMed]

Hernandez, F. E.

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]

Ikegami, T.

G. Khitrova, H. M. Gibbs, Y. Kawamura, H. Iwamura, T. Ikegami, J. E. Sipe, and L. Ming, “Spatial solitons in a self-focusing semiconductor gain medium,” Phys. Rev. Lett. 70, 920–923 (1993).
[CrossRef] [PubMed]

Iwamura, H.

G. Khitrova, H. M. Gibbs, Y. Kawamura, H. Iwamura, T. Ikegami, J. E. Sipe, and L. Ming, “Spatial solitons in a self-focusing semiconductor gain medium,” Phys. Rev. Lett. 70, 920–923 (1993).
[CrossRef] [PubMed]

Kauranen, M.

Kawamura, Y.

G. Khitrova, H. M. Gibbs, Y. Kawamura, H. Iwamura, T. Ikegami, J. E. Sipe, and L. Ming, “Spatial solitons in a self-focusing semiconductor gain medium,” Phys. Rev. Lett. 70, 920–923 (1993).
[CrossRef] [PubMed]

Khitrova, G.

G. Khitrova, H. M. Gibbs, Y. Kawamura, H. Iwamura, T. Ikegami, J. E. Sipe, and L. Ming, “Spatial solitons in a self-focusing semiconductor gain medium,” Phys. Rev. Lett. 70, 920–923 (1993).
[CrossRef] [PubMed]

J. F. Valley, G. Khitrova, H. M. Gibbs, J. W. Granthan, and J. J. Xu, “Cw conical emission: first comparison and agreement between theory and experiment,” Phys. Rev. Lett. 64, 2362–2365 (1990).
[CrossRef] [PubMed]

Kimball, D. F.

Kirov, K.

Koynov, K.

Kozich, V. P.

Li, C. H.

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, “Measurements of nondegenerate optical nonlinearity using a two-color single beam method,” Appl. Phys. Lett. 59, 2666–2668 (1991).
[CrossRef]

Marcano, A.

McKinstrie, C. J.

Menyuk, C. R.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[CrossRef] [PubMed]

Ming, L.

G. Khitrova, H. M. Gibbs, Y. Kawamura, H. Iwamura, T. Ikegami, J. E. Sipe, and L. Ming, “Spatial solitons in a self-focusing semiconductor gain medium,” Phys. Rev. Lett. 70, 920–923 (1993).
[CrossRef] [PubMed]

Morandotti, R.

H. S. Eisenberg, R. Morandotti, Y. Silberberg, S. Bar-Ad, D. Ross, and J. S. Aitchison, “Kerr spatiotemporal self-focusing in a planar glass waveguide,” Phys. Rev. Lett. 87, 043902 (2001).
[CrossRef] [PubMed]

Mysyrowicz, A.

S. Tzortzakis, L. Sudrie, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and L. Bergé, “Self-guided propagation of ultrashort IR laser pulses in fused silica,” Phys. Rev. Lett. 87, 213902 (2001), and references therein.
[CrossRef] [PubMed]

Petrova, K.

Prade, B.

S. Tzortzakis, L. Sudrie, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and L. Bergé, “Self-guided propagation of ultrashort IR laser pulses in fused silica,” Phys. Rev. Lett. 87, 213902 (2001), and references therein.
[CrossRef] [PubMed]

Ross, D.

H. S. Eisenberg, R. Morandotti, Y. Silberberg, S. Bar-Ad, D. Ross, and J. S. Aitchison, “Kerr spatiotemporal self-focusing in a planar glass waveguide,” Phys. Rev. Lett. 87, 043902 (2001).
[CrossRef] [PubMed]

Saffman, M.

Saltiel, S.

Schwab, M.

Sheik-Bahae, M.

Silberberg, Y.

H. S. Eisenberg, R. Morandotti, Y. Silberberg, S. Bar-Ad, D. Ross, and J. S. Aitchison, “Kerr spatiotemporal self-focusing in a planar glass waveguide,” Phys. Rev. Lett. 87, 043902 (2001).
[CrossRef] [PubMed]

Sipe, J. E.

G. Khitrova, H. M. Gibbs, Y. Kawamura, H. Iwamura, T. Ikegami, J. E. Sipe, and L. Ming, “Spatial solitons in a self-focusing semiconductor gain medium,” Phys. Rev. Lett. 70, 920–923 (1993).
[CrossRef] [PubMed]

Stegeman, G. I.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[CrossRef] [PubMed]

Sudrie, L.

S. Tzortzakis, L. Sudrie, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and L. Bergé, “Self-guided propagation of ultrashort IR laser pulses in fused silica,” Phys. Rev. Lett. 87, 213902 (2001), and references therein.
[CrossRef] [PubMed]

Toda, H.

Torner, L.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[CrossRef] [PubMed]

Torruellas, W. E.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[CrossRef] [PubMed]

Tzortzakis, S.

S. Tzortzakis, L. Sudrie, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and L. Bergé, “Self-guided propagation of ultrashort IR laser pulses in fused silica,” Phys. Rev. Lett. 87, 213902 (2001), and references therein.
[CrossRef] [PubMed]

Valley, J. F.

J. F. Valley, G. Khitrova, H. M. Gibbs, J. W. Granthan, and J. J. Xu, “Cw conical emission: first comparison and agreement between theory and experiment,” Phys. Rev. Lett. 64, 2362–2365 (1990).
[CrossRef] [PubMed]

Van Stryland, E. W.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[CrossRef] [PubMed]

M. Sheik-Bahae, J. Wang, R. DeSalvo, D. J. Hagan, and E. W. Van Stryland, “Measurement of nondegenerate nonlinearities using a two-color Z-scan,” Opt. Lett. 17, 258–260 (1992).
[CrossRef] [PubMed]

Verber, C. M.

Wang, J.

Wang, Z.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[CrossRef] [PubMed]

Xu, J. J.

J. F. Valley, G. Khitrova, H. M. Gibbs, J. W. Granthan, and J. J. Xu, “Cw conical emission: first comparison and agreement between theory and experiment,” Phys. Rev. Lett. 64, 2362–2365 (1990).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

H. Ma, A. S. L. Gomes, and C. B. de Araújo, “Measurements of nondegenerate optical nonlinearity using a two-color single beam method,” Appl. Phys. Lett. 59, 2666–2668 (1991).
[CrossRef]

Appl. Spectrosc. (1)

J. Opt. Soc. Am. B (4)

Opt. Lett. (2)

Phys. Rev. A (1)

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]

Phys. Rev. Lett. (6)

G. Khitrova, H. M. Gibbs, Y. Kawamura, H. Iwamura, T. Ikegami, J. E. Sipe, and L. Ming, “Spatial solitons in a self-focusing semiconductor gain medium,” Phys. Rev. Lett. 70, 920–923 (1993).
[CrossRef] [PubMed]

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[CrossRef] [PubMed]

H. S. Eisenberg, R. Morandotti, Y. Silberberg, S. Bar-Ad, D. Ross, and J. S. Aitchison, “Kerr spatiotemporal self-focusing in a planar glass waveguide,” Phys. Rev. Lett. 87, 043902 (2001).
[CrossRef] [PubMed]

S. Tzortzakis, L. Sudrie, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and L. Bergé, “Self-guided propagation of ultrashort IR laser pulses in fused silica,” Phys. Rev. Lett. 87, 213902 (2001), and references therein.
[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]

J. F. Valley, G. Khitrova, H. M. Gibbs, J. W. Granthan, and J. J. Xu, “Cw conical emission: first comparison and agreement between theory and experiment,” Phys. Rev. Lett. 64, 2362–2365 (1990).
[CrossRef] [PubMed]

Other (4)

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

J. A. Riddick, W. B. Bunger, and T. K. Sukano, Handbook of Organic Solvents, D. R. Lide, ed. (CRC Press, Boca Raton, Fla., 1995), Vol. 2.

V. Pilla, G. G. G. Costa, and T. Catunda, “Applications of Fresnel–Kirchhoff diffraction integral in linear and nonlinear optics: a didactic introduction,” in Proceedings of the 4th IberoAmerican Meeting on Optics and 7th Latin American Meeting on Optics, Lasers and their Applications, V. L. Brudny, S. A. Ledesma, and M. C. Marconi, eds., Proc. SPIE 4419, 728–731 (2001).

A. E. Kaplan, “Bending of trajectories of asymmetrical light beams in nonlinear media,” Pis'ma Zh. Eksp. Teor. Fiz. 9, 58–60 (1969) [JETP Lett. 9, 33–35 (1969)].

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Figures (4)

Fig. 1
Fig. 1

Probe beam profile of the dye laser used with an intensity smaller than 4×106 W/cm2. Two cases are illustrated: in (a) and (c) the pump beam is absent; in (b) and (d) a pump beam at 1064 nm, with an intensity of 4×109 W/cm2, is present, with polarization perpendicular to the probe beam.

Fig. 2
Fig. 2

Behavior of the ring intensity as function of the lasers’ intensities: dependence of the signal on (a) the probe beam’s intensity and (b) the pump beam’s intensity.

Fig. 3
Fig. 3

(a) Two-color Z-scan profile in DMSO. The pump intensity was 2×109 W/cm2, and its polarization was parallel to the probe beam, whose intensity was smaller than 4×106 W/cm2. (b) Temporal profile of the probe beam after transmission through the sample when it is located at positions 1–3 and the pump beam is present. The pulse duration changes by less than 5% along the three positions.

Fig. 4
Fig. 4

Numerical predictions of the probe beam’s intensity profile, l(ρ2), as a function of ρ2=r2/w2, where w2 is the probe beam’s waist at the observation plane. The curves are normalized to values that correspond to ρ2=0 and Δϕ=0. The polarizations of the two incident beams are (a) perpendicular and (b) parallel.

Equations (1)

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ε(r2)=ikdexp-ikd+r222d0×exp-ikr122dεS(r1)J0kr1r2dr1dr1,

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