Abstract

In this work we present a simple model that can be used to calculate the far field intensity distributions when a Gaussian beam cross a thin sample of nonlinear media but the response can be nonlocal.

©2010 Optical Society of America

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  1. W. R. Callen, B. G. Huth, and R. H. Pantell, “Optical patterns of thermally self-defocused light,” Appl. Phys. Lett. 11(3), 103–105 (1967).
    [Crossref]
  2. F. W. Dabby, T. K. Gustafson, J. R. Whinnery, and Y. Kohanzadeh, “Thermally self-induced phase modulation of laser beam,” Appl. Phys. Lett. 16(9), 362–365 (1970).
    [Crossref]
  3. S. D. Durbin, S. M. Arakelian, and Y. R. Shen, “Laser-induced diffraction rings from a nematic-liquid-crystal film,” Opt. Lett. 6(9), 411–413 (1981).
    [PubMed]
  4. E. Santamato and Y. R. Shen, “Field-curvature effect on the diffraction ring pattern of a laser beam dressed by spatial self-phase modulation in a nematic film,” Opt. Lett. 9(12), 564–566 (1984).
    [Crossref] [PubMed]
  5. R. G. Harrison, L. Dambly, D. Yu, and W. Lu, “A new self-diffraction pattern formation in defocusing liquid media,” Opt. Commun. 139(1-3), 69–72 (1997).
    [Crossref]
  6. A. Shevchenko, S. C. Buchter, N. V. Tabiryan, and M. Kaivola, “Creation of a hollow laser beam using self-phase modulation in a nematic liquid crystal,” Opt. Commun. 232(1-6), 77–82 (2004).
    [Crossref]
  7. D. Yu, W. Lu, R. G. Harrison, and N. N. Rosanov, “Analysis of dark spot formation in absorbing liquid media,” J. Mod. Opt. 45, 2597–2606 (1998).
    [Crossref]
  8. S. Brugioni and R. Meucci, “Self-phase modulation in a nematic liquid crystal film induced by a low-power CO2 laser,” Opt. Commun. 206(4-6), 445–451 (2002).
    [Crossref]
  9. L. Lucchetti, S. Suchand, and F. Simoni, “Fine structure in spatial self-phase modulation patterns: at a glance determination of the sign of optical nonlinearity in highly nonlinear films,” J. Opt. A, Pure Appl. Opt. 11(3), 034002 (2009).
    [Crossref]
  10. L. Deng, K. He, T. Zhou, and C. Li, “Formation and evolution of far-field diffraction patterns of divergent and convergent Gaussian beams passing through self-focusing and self-defocusing media,” J. Opt. A, Pure Appl. Opt. 7(8), 409–415 (2005).
    [Crossref]
  11. C. M. Nascimento, M. Alencar, S. Chávez-Cerda, M. Da Silva, M. R. Meneghetti, and J. M. Hickmann, “Experimental demonstration of novel effects on the far-field diffraction patterns of a Gaussian beam in a Kerr medium,” J. Opt. A, Pure Appl. Opt. 8(11), 947–951 (2006).
    [Crossref]
  12. F. W. Dabby and J. R. Whinnery, “Thermal self-focusing of laser beams in lead glasses,” Appl. Phys. Lett. 13(8), 284–286 (1968).
    [Crossref]
  13. M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68(7), 923–926 (1992).
    [Crossref] [PubMed]
  14. D. Suter and T. Blasberg, “Stabilization of transverse solitary waves by a nonlocal response of the nonlinear medium,” Phys. Rev. A 48(6), 4583–4587 (1993).
    [Crossref] [PubMed]
  15. W. Królikowski and O. Bang, “Solitons in nonlocal nonlinear media: Exact solutions,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 63(1), 016610 (2000).
    [Crossref]
  16. Y. R. Shen, The principles of nonlinear optics (Wiley classics library, 2003). Chap. 17.
  17. M. Born, and E. Wolf, Principles of Optics (Oxford:Pergamon, 1980). Chap. 8.
  18. W. Krolikowski, O. Bang, N. I. Nikolov, D. Neshev, J. Wyller, J. J. Rasmussen, and D. Edmundson, ““Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media,” J. Opt. B Quantum Semiclass. Opt. 6, S288–S294 (2004).
  19. E. W. Van Stryland, and D. Hagan, “Measuring nonlinear refraction and its dispersion” in Self-focusing: past and present, R.W. Boyd, S.G. Lukishova Bad, Y.R. Shen, Eds. (Springer, 2009) 573–591.
  20. S. A. Akhmanov, D. P. Krindach, A. P. Sukhorukov, and R. V. Khokhlov, “Nonlinear defocusing of laser beams,” JEPT Lett. 6, 38 (1967).

2009 (1)

L. Lucchetti, S. Suchand, and F. Simoni, “Fine structure in spatial self-phase modulation patterns: at a glance determination of the sign of optical nonlinearity in highly nonlinear films,” J. Opt. A, Pure Appl. Opt. 11(3), 034002 (2009).
[Crossref]

2006 (1)

C. M. Nascimento, M. Alencar, S. Chávez-Cerda, M. Da Silva, M. R. Meneghetti, and J. M. Hickmann, “Experimental demonstration of novel effects on the far-field diffraction patterns of a Gaussian beam in a Kerr medium,” J. Opt. A, Pure Appl. Opt. 8(11), 947–951 (2006).
[Crossref]

2005 (1)

L. Deng, K. He, T. Zhou, and C. Li, “Formation and evolution of far-field diffraction patterns of divergent and convergent Gaussian beams passing through self-focusing and self-defocusing media,” J. Opt. A, Pure Appl. Opt. 7(8), 409–415 (2005).
[Crossref]

2004 (2)

A. Shevchenko, S. C. Buchter, N. V. Tabiryan, and M. Kaivola, “Creation of a hollow laser beam using self-phase modulation in a nematic liquid crystal,” Opt. Commun. 232(1-6), 77–82 (2004).
[Crossref]

W. Krolikowski, O. Bang, N. I. Nikolov, D. Neshev, J. Wyller, J. J. Rasmussen, and D. Edmundson, ““Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media,” J. Opt. B Quantum Semiclass. Opt. 6, S288–S294 (2004).

2002 (1)

S. Brugioni and R. Meucci, “Self-phase modulation in a nematic liquid crystal film induced by a low-power CO2 laser,” Opt. Commun. 206(4-6), 445–451 (2002).
[Crossref]

2000 (1)

W. Królikowski and O. Bang, “Solitons in nonlocal nonlinear media: Exact solutions,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 63(1), 016610 (2000).
[Crossref]

1998 (1)

D. Yu, W. Lu, R. G. Harrison, and N. N. Rosanov, “Analysis of dark spot formation in absorbing liquid media,” J. Mod. Opt. 45, 2597–2606 (1998).
[Crossref]

1997 (1)

R. G. Harrison, L. Dambly, D. Yu, and W. Lu, “A new self-diffraction pattern formation in defocusing liquid media,” Opt. Commun. 139(1-3), 69–72 (1997).
[Crossref]

1993 (1)

D. Suter and T. Blasberg, “Stabilization of transverse solitary waves by a nonlocal response of the nonlinear medium,” Phys. Rev. A 48(6), 4583–4587 (1993).
[Crossref] [PubMed]

1992 (1)

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68(7), 923–926 (1992).
[Crossref] [PubMed]

1984 (1)

1981 (1)

1970 (1)

F. W. Dabby, T. K. Gustafson, J. R. Whinnery, and Y. Kohanzadeh, “Thermally self-induced phase modulation of laser beam,” Appl. Phys. Lett. 16(9), 362–365 (1970).
[Crossref]

1968 (1)

F. W. Dabby and J. R. Whinnery, “Thermal self-focusing of laser beams in lead glasses,” Appl. Phys. Lett. 13(8), 284–286 (1968).
[Crossref]

1967 (2)

S. A. Akhmanov, D. P. Krindach, A. P. Sukhorukov, and R. V. Khokhlov, “Nonlinear defocusing of laser beams,” JEPT Lett. 6, 38 (1967).

W. R. Callen, B. G. Huth, and R. H. Pantell, “Optical patterns of thermally self-defocused light,” Appl. Phys. Lett. 11(3), 103–105 (1967).
[Crossref]

Akhmanov, S. A.

S. A. Akhmanov, D. P. Krindach, A. P. Sukhorukov, and R. V. Khokhlov, “Nonlinear defocusing of laser beams,” JEPT Lett. 6, 38 (1967).

Alencar, M.

C. M. Nascimento, M. Alencar, S. Chávez-Cerda, M. Da Silva, M. R. Meneghetti, and J. M. Hickmann, “Experimental demonstration of novel effects on the far-field diffraction patterns of a Gaussian beam in a Kerr medium,” J. Opt. A, Pure Appl. Opt. 8(11), 947–951 (2006).
[Crossref]

Arakelian, S. M.

Bang, O.

W. Krolikowski, O. Bang, N. I. Nikolov, D. Neshev, J. Wyller, J. J. Rasmussen, and D. Edmundson, ““Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media,” J. Opt. B Quantum Semiclass. Opt. 6, S288–S294 (2004).

W. Królikowski and O. Bang, “Solitons in nonlocal nonlinear media: Exact solutions,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 63(1), 016610 (2000).
[Crossref]

Blasberg, T.

D. Suter and T. Blasberg, “Stabilization of transverse solitary waves by a nonlocal response of the nonlinear medium,” Phys. Rev. A 48(6), 4583–4587 (1993).
[Crossref] [PubMed]

Brugioni, S.

S. Brugioni and R. Meucci, “Self-phase modulation in a nematic liquid crystal film induced by a low-power CO2 laser,” Opt. Commun. 206(4-6), 445–451 (2002).
[Crossref]

Buchter, S. C.

A. Shevchenko, S. C. Buchter, N. V. Tabiryan, and M. Kaivola, “Creation of a hollow laser beam using self-phase modulation in a nematic liquid crystal,” Opt. Commun. 232(1-6), 77–82 (2004).
[Crossref]

Callen, W. R.

W. R. Callen, B. G. Huth, and R. H. Pantell, “Optical patterns of thermally self-defocused light,” Appl. Phys. Lett. 11(3), 103–105 (1967).
[Crossref]

Chávez-Cerda, S.

C. M. Nascimento, M. Alencar, S. Chávez-Cerda, M. Da Silva, M. R. Meneghetti, and J. M. Hickmann, “Experimental demonstration of novel effects on the far-field diffraction patterns of a Gaussian beam in a Kerr medium,” J. Opt. A, Pure Appl. Opt. 8(11), 947–951 (2006).
[Crossref]

Crosignani, B.

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68(7), 923–926 (1992).
[Crossref] [PubMed]

Da Silva, M.

C. M. Nascimento, M. Alencar, S. Chávez-Cerda, M. Da Silva, M. R. Meneghetti, and J. M. Hickmann, “Experimental demonstration of novel effects on the far-field diffraction patterns of a Gaussian beam in a Kerr medium,” J. Opt. A, Pure Appl. Opt. 8(11), 947–951 (2006).
[Crossref]

Dabby, F. W.

F. W. Dabby, T. K. Gustafson, J. R. Whinnery, and Y. Kohanzadeh, “Thermally self-induced phase modulation of laser beam,” Appl. Phys. Lett. 16(9), 362–365 (1970).
[Crossref]

F. W. Dabby and J. R. Whinnery, “Thermal self-focusing of laser beams in lead glasses,” Appl. Phys. Lett. 13(8), 284–286 (1968).
[Crossref]

Dambly, L.

R. G. Harrison, L. Dambly, D. Yu, and W. Lu, “A new self-diffraction pattern formation in defocusing liquid media,” Opt. Commun. 139(1-3), 69–72 (1997).
[Crossref]

Deng, L.

L. Deng, K. He, T. Zhou, and C. Li, “Formation and evolution of far-field diffraction patterns of divergent and convergent Gaussian beams passing through self-focusing and self-defocusing media,” J. Opt. A, Pure Appl. Opt. 7(8), 409–415 (2005).
[Crossref]

Durbin, S. D.

Edmundson, D.

W. Krolikowski, O. Bang, N. I. Nikolov, D. Neshev, J. Wyller, J. J. Rasmussen, and D. Edmundson, ““Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media,” J. Opt. B Quantum Semiclass. Opt. 6, S288–S294 (2004).

Fischer, B.

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68(7), 923–926 (1992).
[Crossref] [PubMed]

Gustafson, T. K.

F. W. Dabby, T. K. Gustafson, J. R. Whinnery, and Y. Kohanzadeh, “Thermally self-induced phase modulation of laser beam,” Appl. Phys. Lett. 16(9), 362–365 (1970).
[Crossref]

Harrison, R. G.

D. Yu, W. Lu, R. G. Harrison, and N. N. Rosanov, “Analysis of dark spot formation in absorbing liquid media,” J. Mod. Opt. 45, 2597–2606 (1998).
[Crossref]

R. G. Harrison, L. Dambly, D. Yu, and W. Lu, “A new self-diffraction pattern formation in defocusing liquid media,” Opt. Commun. 139(1-3), 69–72 (1997).
[Crossref]

He, K.

L. Deng, K. He, T. Zhou, and C. Li, “Formation and evolution of far-field diffraction patterns of divergent and convergent Gaussian beams passing through self-focusing and self-defocusing media,” J. Opt. A, Pure Appl. Opt. 7(8), 409–415 (2005).
[Crossref]

Hickmann, J. M.

C. M. Nascimento, M. Alencar, S. Chávez-Cerda, M. Da Silva, M. R. Meneghetti, and J. M. Hickmann, “Experimental demonstration of novel effects on the far-field diffraction patterns of a Gaussian beam in a Kerr medium,” J. Opt. A, Pure Appl. Opt. 8(11), 947–951 (2006).
[Crossref]

Huth, B. G.

W. R. Callen, B. G. Huth, and R. H. Pantell, “Optical patterns of thermally self-defocused light,” Appl. Phys. Lett. 11(3), 103–105 (1967).
[Crossref]

Kaivola, M.

A. Shevchenko, S. C. Buchter, N. V. Tabiryan, and M. Kaivola, “Creation of a hollow laser beam using self-phase modulation in a nematic liquid crystal,” Opt. Commun. 232(1-6), 77–82 (2004).
[Crossref]

Khokhlov, R. V.

S. A. Akhmanov, D. P. Krindach, A. P. Sukhorukov, and R. V. Khokhlov, “Nonlinear defocusing of laser beams,” JEPT Lett. 6, 38 (1967).

Kohanzadeh, Y.

F. W. Dabby, T. K. Gustafson, J. R. Whinnery, and Y. Kohanzadeh, “Thermally self-induced phase modulation of laser beam,” Appl. Phys. Lett. 16(9), 362–365 (1970).
[Crossref]

Krindach, D. P.

S. A. Akhmanov, D. P. Krindach, A. P. Sukhorukov, and R. V. Khokhlov, “Nonlinear defocusing of laser beams,” JEPT Lett. 6, 38 (1967).

Krolikowski, W.

W. Krolikowski, O. Bang, N. I. Nikolov, D. Neshev, J. Wyller, J. J. Rasmussen, and D. Edmundson, ““Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media,” J. Opt. B Quantum Semiclass. Opt. 6, S288–S294 (2004).

Królikowski, W.

W. Królikowski and O. Bang, “Solitons in nonlocal nonlinear media: Exact solutions,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 63(1), 016610 (2000).
[Crossref]

Li, C.

L. Deng, K. He, T. Zhou, and C. Li, “Formation and evolution of far-field diffraction patterns of divergent and convergent Gaussian beams passing through self-focusing and self-defocusing media,” J. Opt. A, Pure Appl. Opt. 7(8), 409–415 (2005).
[Crossref]

Lu, W.

D. Yu, W. Lu, R. G. Harrison, and N. N. Rosanov, “Analysis of dark spot formation in absorbing liquid media,” J. Mod. Opt. 45, 2597–2606 (1998).
[Crossref]

R. G. Harrison, L. Dambly, D. Yu, and W. Lu, “A new self-diffraction pattern formation in defocusing liquid media,” Opt. Commun. 139(1-3), 69–72 (1997).
[Crossref]

Lucchetti, L.

L. Lucchetti, S. Suchand, and F. Simoni, “Fine structure in spatial self-phase modulation patterns: at a glance determination of the sign of optical nonlinearity in highly nonlinear films,” J. Opt. A, Pure Appl. Opt. 11(3), 034002 (2009).
[Crossref]

Meneghetti, M. R.

C. M. Nascimento, M. Alencar, S. Chávez-Cerda, M. Da Silva, M. R. Meneghetti, and J. M. Hickmann, “Experimental demonstration of novel effects on the far-field diffraction patterns of a Gaussian beam in a Kerr medium,” J. Opt. A, Pure Appl. Opt. 8(11), 947–951 (2006).
[Crossref]

Meucci, R.

S. Brugioni and R. Meucci, “Self-phase modulation in a nematic liquid crystal film induced by a low-power CO2 laser,” Opt. Commun. 206(4-6), 445–451 (2002).
[Crossref]

Nascimento, C. M.

C. M. Nascimento, M. Alencar, S. Chávez-Cerda, M. Da Silva, M. R. Meneghetti, and J. M. Hickmann, “Experimental demonstration of novel effects on the far-field diffraction patterns of a Gaussian beam in a Kerr medium,” J. Opt. A, Pure Appl. Opt. 8(11), 947–951 (2006).
[Crossref]

Neshev, D.

W. Krolikowski, O. Bang, N. I. Nikolov, D. Neshev, J. Wyller, J. J. Rasmussen, and D. Edmundson, ““Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media,” J. Opt. B Quantum Semiclass. Opt. 6, S288–S294 (2004).

Nikolov, N. I.

W. Krolikowski, O. Bang, N. I. Nikolov, D. Neshev, J. Wyller, J. J. Rasmussen, and D. Edmundson, ““Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media,” J. Opt. B Quantum Semiclass. Opt. 6, S288–S294 (2004).

Pantell, R. H.

W. R. Callen, B. G. Huth, and R. H. Pantell, “Optical patterns of thermally self-defocused light,” Appl. Phys. Lett. 11(3), 103–105 (1967).
[Crossref]

Rasmussen, J. J.

W. Krolikowski, O. Bang, N. I. Nikolov, D. Neshev, J. Wyller, J. J. Rasmussen, and D. Edmundson, ““Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media,” J. Opt. B Quantum Semiclass. Opt. 6, S288–S294 (2004).

Rosanov, N. N.

D. Yu, W. Lu, R. G. Harrison, and N. N. Rosanov, “Analysis of dark spot formation in absorbing liquid media,” J. Mod. Opt. 45, 2597–2606 (1998).
[Crossref]

Santamato, E.

Segev, M.

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68(7), 923–926 (1992).
[Crossref] [PubMed]

Shen, Y. R.

Shevchenko, A.

A. Shevchenko, S. C. Buchter, N. V. Tabiryan, and M. Kaivola, “Creation of a hollow laser beam using self-phase modulation in a nematic liquid crystal,” Opt. Commun. 232(1-6), 77–82 (2004).
[Crossref]

Simoni, F.

L. Lucchetti, S. Suchand, and F. Simoni, “Fine structure in spatial self-phase modulation patterns: at a glance determination of the sign of optical nonlinearity in highly nonlinear films,” J. Opt. A, Pure Appl. Opt. 11(3), 034002 (2009).
[Crossref]

Suchand, S.

L. Lucchetti, S. Suchand, and F. Simoni, “Fine structure in spatial self-phase modulation patterns: at a glance determination of the sign of optical nonlinearity in highly nonlinear films,” J. Opt. A, Pure Appl. Opt. 11(3), 034002 (2009).
[Crossref]

Sukhorukov, A. P.

S. A. Akhmanov, D. P. Krindach, A. P. Sukhorukov, and R. V. Khokhlov, “Nonlinear defocusing of laser beams,” JEPT Lett. 6, 38 (1967).

Suter, D.

D. Suter and T. Blasberg, “Stabilization of transverse solitary waves by a nonlocal response of the nonlinear medium,” Phys. Rev. A 48(6), 4583–4587 (1993).
[Crossref] [PubMed]

Tabiryan, N. V.

A. Shevchenko, S. C. Buchter, N. V. Tabiryan, and M. Kaivola, “Creation of a hollow laser beam using self-phase modulation in a nematic liquid crystal,” Opt. Commun. 232(1-6), 77–82 (2004).
[Crossref]

Whinnery, J. R.

F. W. Dabby, T. K. Gustafson, J. R. Whinnery, and Y. Kohanzadeh, “Thermally self-induced phase modulation of laser beam,” Appl. Phys. Lett. 16(9), 362–365 (1970).
[Crossref]

F. W. Dabby and J. R. Whinnery, “Thermal self-focusing of laser beams in lead glasses,” Appl. Phys. Lett. 13(8), 284–286 (1968).
[Crossref]

Wyller, J.

W. Krolikowski, O. Bang, N. I. Nikolov, D. Neshev, J. Wyller, J. J. Rasmussen, and D. Edmundson, ““Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media,” J. Opt. B Quantum Semiclass. Opt. 6, S288–S294 (2004).

Yariv, A.

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68(7), 923–926 (1992).
[Crossref] [PubMed]

Yu, D.

D. Yu, W. Lu, R. G. Harrison, and N. N. Rosanov, “Analysis of dark spot formation in absorbing liquid media,” J. Mod. Opt. 45, 2597–2606 (1998).
[Crossref]

R. G. Harrison, L. Dambly, D. Yu, and W. Lu, “A new self-diffraction pattern formation in defocusing liquid media,” Opt. Commun. 139(1-3), 69–72 (1997).
[Crossref]

Zhou, T.

L. Deng, K. He, T. Zhou, and C. Li, “Formation and evolution of far-field diffraction patterns of divergent and convergent Gaussian beams passing through self-focusing and self-defocusing media,” J. Opt. A, Pure Appl. Opt. 7(8), 409–415 (2005).
[Crossref]

Appl. Phys. Lett. (3)

F. W. Dabby and J. R. Whinnery, “Thermal self-focusing of laser beams in lead glasses,” Appl. Phys. Lett. 13(8), 284–286 (1968).
[Crossref]

W. R. Callen, B. G. Huth, and R. H. Pantell, “Optical patterns of thermally self-defocused light,” Appl. Phys. Lett. 11(3), 103–105 (1967).
[Crossref]

F. W. Dabby, T. K. Gustafson, J. R. Whinnery, and Y. Kohanzadeh, “Thermally self-induced phase modulation of laser beam,” Appl. Phys. Lett. 16(9), 362–365 (1970).
[Crossref]

J. Mod. Opt. (1)

D. Yu, W. Lu, R. G. Harrison, and N. N. Rosanov, “Analysis of dark spot formation in absorbing liquid media,” J. Mod. Opt. 45, 2597–2606 (1998).
[Crossref]

J. Opt. A, Pure Appl. Opt. (3)

L. Lucchetti, S. Suchand, and F. Simoni, “Fine structure in spatial self-phase modulation patterns: at a glance determination of the sign of optical nonlinearity in highly nonlinear films,” J. Opt. A, Pure Appl. Opt. 11(3), 034002 (2009).
[Crossref]

L. Deng, K. He, T. Zhou, and C. Li, “Formation and evolution of far-field diffraction patterns of divergent and convergent Gaussian beams passing through self-focusing and self-defocusing media,” J. Opt. A, Pure Appl. Opt. 7(8), 409–415 (2005).
[Crossref]

C. M. Nascimento, M. Alencar, S. Chávez-Cerda, M. Da Silva, M. R. Meneghetti, and J. M. Hickmann, “Experimental demonstration of novel effects on the far-field diffraction patterns of a Gaussian beam in a Kerr medium,” J. Opt. A, Pure Appl. Opt. 8(11), 947–951 (2006).
[Crossref]

J. Opt. B Quantum Semiclass. Opt. (1)

W. Krolikowski, O. Bang, N. I. Nikolov, D. Neshev, J. Wyller, J. J. Rasmussen, and D. Edmundson, ““Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media,” J. Opt. B Quantum Semiclass. Opt. 6, S288–S294 (2004).

JEPT Lett. (1)

S. A. Akhmanov, D. P. Krindach, A. P. Sukhorukov, and R. V. Khokhlov, “Nonlinear defocusing of laser beams,” JEPT Lett. 6, 38 (1967).

Opt. Commun. (3)

S. Brugioni and R. Meucci, “Self-phase modulation in a nematic liquid crystal film induced by a low-power CO2 laser,” Opt. Commun. 206(4-6), 445–451 (2002).
[Crossref]

R. G. Harrison, L. Dambly, D. Yu, and W. Lu, “A new self-diffraction pattern formation in defocusing liquid media,” Opt. Commun. 139(1-3), 69–72 (1997).
[Crossref]

A. Shevchenko, S. C. Buchter, N. V. Tabiryan, and M. Kaivola, “Creation of a hollow laser beam using self-phase modulation in a nematic liquid crystal,” Opt. Commun. 232(1-6), 77–82 (2004).
[Crossref]

Opt. Lett. (2)

Phys. Rev. A (1)

D. Suter and T. Blasberg, “Stabilization of transverse solitary waves by a nonlocal response of the nonlinear medium,” Phys. Rev. A 48(6), 4583–4587 (1993).
[Crossref] [PubMed]

Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics (1)

W. Królikowski and O. Bang, “Solitons in nonlocal nonlinear media: Exact solutions,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 63(1), 016610 (2000).
[Crossref]

Phys. Rev. Lett. (1)

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68(7), 923–926 (1992).
[Crossref] [PubMed]

Other (3)

Y. R. Shen, The principles of nonlinear optics (Wiley classics library, 2003). Chap. 17.

M. Born, and E. Wolf, Principles of Optics (Oxford:Pergamon, 1980). Chap. 8.

E. W. Van Stryland, and D. Hagan, “Measuring nonlinear refraction and its dispersion” in Self-focusing: past and present, R.W. Boyd, S.G. Lukishova Bad, Y.R. Shen, Eds. (Springer, 2009) 573–591.

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Figures (14)

Fig. 1
Fig. 1 Far field intensity profiles (upper row) and cross sections (lower row) obtained for a sample with Δ φ 0 = 2π rad, set at z = −4z0 . And different values of m: a) 1, b) 2 and c) 4.

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Fig. 2
Fig. 2 Far field intensity profiles (upper row) and cross sections (lower row) obtained for a sample with Δ φ 0 = 12π rad, set at z = −4z0 . And different values of m: a) 1, b) 2 and c) 4.

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Fig. 3
Fig. 3 Far field intensity profiles (upper row) and cross sections (lower row) obtained for a sample with Δ φ 0 = 2π rad, set at z = −2z0 . And different values of m: a) 1, b) 2 and c) 4.

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Fig. 4
Fig. 4 Far field intensity profiles (upper row) and cross sections (lower row) obtained for a sample with Δ φ 0 = 12π rad, set at z = −2z0 . And different values of m: a) 1, b) 2 and c) 4.

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Fig. 5
Fig. 5 Far field intensity profiles (upper row) and cross sections (lower row) obtained for a sample with Δ φ 0 = 2π rad, set at z = -z0 . And different values of m: a) 1, b) 2 and c) 4.

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Fig. 6
Fig. 6 Far field intensity profiles (upper row) and cross sections (lower row) obtained for a sample with Δ φ 0 = 12π rad, set at z = -z0 . And different values of m: a) 1, b) 2 and c) 4.

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Fig. 7
Fig. 7 Far field intensity profiles (upper row) and cross sections (lower row) obtained for a sample with Δ φ 0 = 2π rad, set at z = 0. And different values of m: a) 1, b) 2 and c) 4.

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Fig. 8
Fig. 8 Far field intensity profiles (upper row) and cross sections (lower row) obtained for a sample with Δ φ 0 = 12π rad, set at z = 0. And different values of m: a) 1, b) 2 and c) 4.

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Fig. 9
Fig. 9 Far field intensity profiles (upper row) and cross sections (lower row) obtained for a sample with Δ φ 0 = 2π rad, set at z = z0 . And different values of m: a) 1, b) 2 and c) 4.

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Fig. 10
Fig. 10 Far field intensity profiles (upper row) and cross sections (lower row) obtained for a sample with Δ φ 0 = 12π rad, set at z = z0 . And different values of m: a) 1, b) 2 and c) 4.

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Fig. 11
Fig. 11 Far field intensity profiles (upper row) and cross sections (lower row) obtained for a sample with Δ φ 0 = 2π rad, set at z = 2z0 . And different values of m: a) 1, b) 2 and c) 4.

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Fig. 12
Fig. 12 Far field intensity profiles (upper row) and cross sections (lower row) obtained for a sample with Δ φ 0 = 12π rad, set at z = 2z0 . And different values of m: a) 1, b) 2 and c) 4.

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Fig. 13
Fig. 13 Far field intensity profiles (upper row) and cross sections (lower row) obtained for a sample with Δ φ 0 = 2π rad, set at z = 4z0 . And different values of m: a) 1, b) 2 and c) 4.

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Fig. 14
Fig. 14 Far field intensity profiles (upper row) and cross sections (lower row) obtained for a sample with Δ φ 0 = 12π rad, set at z = 4z0 . And different values of m: a) 1, b) 2 and c) 4.

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Equations (8)

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E ( r , z ) = A 0 w 0 w ( z ) exp [ − r 2 w ( z ) 2 ] exp [ − i k z − i k r 2 2 R ( z ) + i ε ( z ) ] ,
w ( z ) = w 0 [ 1 + ( z z 0 ) 2 ] 1 2 ,
R ( z ) = z [ 1 + ( z 0 z ) 2 ] ,
ε ( z ) = tan − 1 ( z z 0 ) ,
E o u t = E ( r , z ) exp ( − i Δ φ ( r ) ) ,
Δ φ ( r ) ≈ Δ φ 0 exp ( − 2 r 2 w 2 ) ,
Δ φ ( r ) ≈ Δ φ 0 exp ( − m r 2 w 2 ) = Δ φ 0 exp ( − r 2 ( w / m ) 2 ) ,
N ( I ) = s ∫ R ( ξ − r ) I ( ξ , z ) d ξ ,

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