Abstract

In this work we present numerical results of the far field intensity distributions obtained for a Gaussian beam after crossing a thin nonlinear nonlocal material that exhibit nonlinear refraction and absorption. The distributions are obtained for different positions along the Z axis and different signs of the nonlinear absorption. The results demonstrate that the far field intensity patterns obtained for strong nonlocal media are more affected by the presence of the nonlinear absorption than weak nonlocal media.

© 2015 Optical Society of America

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Z-scan for thin media with more than one nonlocal nonlinear response

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Analytical expressions for z-scan with arbitrary phase change in thin nonlocal nonlinear media

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References

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  1. F. Simoni, Nonlinear Optical Properties of Liquid Crystals (World Scientific, 1997), Chap. 3.
  2. 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]
  3. 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]
  4. 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]
  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 selfphase 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(12), 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. 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]
  10. 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]
  11. J. Robertson, P. Milsom, J. Duignan, and G. Bourhill, “Spatial redistribution of energy in a nanosecond laser pulse by an organic optical limiter,” Opt. Lett. 25(17), 1258–1260 (2000).
    [Crossref] [PubMed]
  12. J. Robertson, A. Smith, J. Duignan, P. Milsom, and G. Bourchill, “Nonlinear refractive beam shaping by an organic nonlinear absorber,” Appl. Phys. Lett. 78(9), 1183 (2001).
    [Crossref]
  13. 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]
  14. 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]
  15. L. Pálfalvi, B. C. Tóth, G. Almási, J. A. Fülöp, and J. Hebling, “A general Z-scan theory,” Appl. Phys. B 97(3), 679–685 (2009).
    [Crossref]
  16. E. V. Garcia Ramirez, M. L. Arroyo Carrasco, M. M. Mendez Otero, S. Chavez Cerda, and M. D. Iturbe Castillo, “Far field distributions due to spatial self phase modulation of a Gaussian beam by a thin nonlocal nonlinear media,” Opt. Express 18(21), 22067–22079 (2010).
  17. E. V. Garcia Ramirez, M. L. Arroyo Carrasco, M. M. Mendez Otero, E. Reynoso Lara, S. Chavez-Cerda, and M. D. Iturbe Castillo, “Z-scan and spatial self-phase modulation of a Gaussian beam in a thin nonlocal nonlinear media,” J. Opt. 13(8), 085203 (2011).
    [Crossref]
  18. A. B. Ortega, M. L. Carrasco, M. M. Otero, E. R. Lara, E. V. Ramírez, and M. D. Castillo, “Analytical expressions for Z-scan with arbitrary phase change in thin nonlocal nonlinear media,” Opt. Express 22(23), 27932–27941 (2014).
    [Crossref] [PubMed]
  19. G. Tsigaridas, M. Fakis, I. Polyzos, P. Persephonis, and V. Giannetas, “Z-scan technique through beam radius measurements,” Appl. Phys. B 76(1), 83–86 (2003).
    [Crossref]

2014 (1)

2011 (1)

E. V. Garcia Ramirez, M. L. Arroyo Carrasco, M. M. Mendez Otero, E. Reynoso Lara, S. Chavez-Cerda, and M. D. Iturbe Castillo, “Z-scan and spatial self-phase modulation of a Gaussian beam in a thin nonlocal nonlinear media,” J. Opt. 13(8), 085203 (2011).
[Crossref]

2010 (1)

2009 (2)

L. Pálfalvi, B. C. Tóth, G. Almási, J. A. Fülöp, and J. Hebling, “A general Z-scan theory,” Appl. Phys. B 97(3), 679–685 (2009).
[Crossref]

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 (1)

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

2003 (1)

G. Tsigaridas, M. Fakis, I. Polyzos, P. Persephonis, and V. Giannetas, “Z-scan technique through beam radius measurements,” Appl. Phys. B 76(1), 83–86 (2003).
[Crossref]

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]

2001 (1)

J. Robertson, A. Smith, J. Duignan, P. Milsom, and G. Bourchill, “Nonlinear refractive beam shaping by an organic nonlinear absorber,” Appl. Phys. Lett. 78(9), 1183 (2001).
[Crossref]

2000 (1)

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(12), 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]

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]

1967 (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]

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]

Almási, G.

L. Pálfalvi, B. C. Tóth, G. Almási, J. A. Fülöp, and J. Hebling, “A general Z-scan theory,” Appl. Phys. B 97(3), 679–685 (2009).
[Crossref]

Arakelian, S. M.

Arroyo Carrasco, M. L.

E. V. Garcia Ramirez, M. L. Arroyo Carrasco, M. M. Mendez Otero, E. Reynoso Lara, S. Chavez-Cerda, and M. D. Iturbe Castillo, “Z-scan and spatial self-phase modulation of a Gaussian beam in a thin nonlocal nonlinear media,” J. Opt. 13(8), 085203 (2011).
[Crossref]

E. V. Garcia Ramirez, M. L. Arroyo Carrasco, M. M. Mendez Otero, S. Chavez Cerda, and M. D. Iturbe Castillo, “Far field distributions due to spatial self phase modulation of a Gaussian beam by a thin nonlocal nonlinear media,” Opt. Express 18(21), 22067–22079 (2010).

Bourchill, G.

J. Robertson, A. Smith, J. Duignan, P. Milsom, and G. Bourchill, “Nonlinear refractive beam shaping by an organic nonlinear absorber,” Appl. Phys. Lett. 78(9), 1183 (2001).
[Crossref]

Bourhill, G.

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 selfphase 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]

Carrasco, M. L.

Castillo, M. D.

Chavez Cerda, S.

Chavez-Cerda, S.

E. V. Garcia Ramirez, M. L. Arroyo Carrasco, M. M. Mendez Otero, E. Reynoso Lara, S. Chavez-Cerda, and M. D. Iturbe Castillo, “Z-scan and spatial self-phase modulation of a Gaussian beam in a thin nonlocal nonlinear media,” J. Opt. 13(8), 085203 (2011).
[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]

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]

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]

Duignan, J.

J. Robertson, A. Smith, J. Duignan, P. Milsom, and G. Bourchill, “Nonlinear refractive beam shaping by an organic nonlinear absorber,” Appl. Phys. Lett. 78(9), 1183 (2001).
[Crossref]

J. Robertson, P. Milsom, J. Duignan, and G. Bourhill, “Spatial redistribution of energy in a nanosecond laser pulse by an organic optical limiter,” Opt. Lett. 25(17), 1258–1260 (2000).
[Crossref] [PubMed]

Durbin, S. D.

Fakis, M.

G. Tsigaridas, M. Fakis, I. Polyzos, P. Persephonis, and V. Giannetas, “Z-scan technique through beam radius measurements,” Appl. Phys. B 76(1), 83–86 (2003).
[Crossref]

Fülöp, J. A.

L. Pálfalvi, B. C. Tóth, G. Almási, J. A. Fülöp, and J. Hebling, “A general Z-scan theory,” Appl. Phys. B 97(3), 679–685 (2009).
[Crossref]

Garcia Ramirez, E. V.

E. V. Garcia Ramirez, M. L. Arroyo Carrasco, M. M. Mendez Otero, E. Reynoso Lara, S. Chavez-Cerda, and M. D. Iturbe Castillo, “Z-scan and spatial self-phase modulation of a Gaussian beam in a thin nonlocal nonlinear media,” J. Opt. 13(8), 085203 (2011).
[Crossref]

E. V. Garcia Ramirez, M. L. Arroyo Carrasco, M. M. Mendez Otero, S. Chavez Cerda, and M. D. Iturbe Castillo, “Far field distributions due to spatial self phase modulation of a Gaussian beam by a thin nonlocal nonlinear media,” Opt. Express 18(21), 22067–22079 (2010).

Giannetas, V.

G. Tsigaridas, M. Fakis, I. Polyzos, P. Persephonis, and V. Giannetas, “Z-scan technique through beam radius measurements,” Appl. Phys. B 76(1), 83–86 (2003).
[Crossref]

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(12), 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]

Hebling, J.

L. Pálfalvi, B. C. Tóth, G. Almási, J. A. Fülöp, and J. Hebling, “A general Z-scan theory,” Appl. Phys. B 97(3), 679–685 (2009).
[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]

Iturbe Castillo, M. D.

E. V. Garcia Ramirez, M. L. Arroyo Carrasco, M. M. Mendez Otero, E. Reynoso Lara, S. Chavez-Cerda, and M. D. Iturbe Castillo, “Z-scan and spatial self-phase modulation of a Gaussian beam in a thin nonlocal nonlinear media,” J. Opt. 13(8), 085203 (2011).
[Crossref]

E. V. Garcia Ramirez, M. L. Arroyo Carrasco, M. M. Mendez Otero, S. Chavez Cerda, and M. D. Iturbe Castillo, “Far field distributions due to spatial self phase modulation of a Gaussian beam by a thin nonlocal nonlinear media,” Opt. Express 18(21), 22067–22079 (2010).

Kaivola, M.

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

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]

Lara, E. R.

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(12), 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]

Mendez Otero, M. M.

E. V. Garcia Ramirez, M. L. Arroyo Carrasco, M. M. Mendez Otero, E. Reynoso Lara, S. Chavez-Cerda, and M. D. Iturbe Castillo, “Z-scan and spatial self-phase modulation of a Gaussian beam in a thin nonlocal nonlinear media,” J. Opt. 13(8), 085203 (2011).
[Crossref]

E. V. Garcia Ramirez, M. L. Arroyo Carrasco, M. M. Mendez Otero, S. Chavez Cerda, and M. D. Iturbe Castillo, “Far field distributions due to spatial self phase modulation of a Gaussian beam by a thin nonlocal nonlinear media,” Opt. Express 18(21), 22067–22079 (2010).

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]

Milsom, P.

J. Robertson, A. Smith, J. Duignan, P. Milsom, and G. Bourchill, “Nonlinear refractive beam shaping by an organic nonlinear absorber,” Appl. Phys. Lett. 78(9), 1183 (2001).
[Crossref]

J. Robertson, P. Milsom, J. Duignan, and G. Bourhill, “Spatial redistribution of energy in a nanosecond laser pulse by an organic optical limiter,” Opt. Lett. 25(17), 1258–1260 (2000).
[Crossref] [PubMed]

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]

Ortega, A. B.

Otero, M. M.

Pálfalvi, L.

L. Pálfalvi, B. C. Tóth, G. Almási, J. A. Fülöp, and J. Hebling, “A general Z-scan theory,” Appl. Phys. B 97(3), 679–685 (2009).
[Crossref]

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]

Persephonis, P.

G. Tsigaridas, M. Fakis, I. Polyzos, P. Persephonis, and V. Giannetas, “Z-scan technique through beam radius measurements,” Appl. Phys. B 76(1), 83–86 (2003).
[Crossref]

Polyzos, I.

G. Tsigaridas, M. Fakis, I. Polyzos, P. Persephonis, and V. Giannetas, “Z-scan technique through beam radius measurements,” Appl. Phys. B 76(1), 83–86 (2003).
[Crossref]

Ramírez, E. V.

Reynoso Lara, E.

E. V. Garcia Ramirez, M. L. Arroyo Carrasco, M. M. Mendez Otero, E. Reynoso Lara, S. Chavez-Cerda, and M. D. Iturbe Castillo, “Z-scan and spatial self-phase modulation of a Gaussian beam in a thin nonlocal nonlinear media,” J. Opt. 13(8), 085203 (2011).
[Crossref]

Robertson, J.

J. Robertson, A. Smith, J. Duignan, P. Milsom, and G. Bourchill, “Nonlinear refractive beam shaping by an organic nonlinear absorber,” Appl. Phys. Lett. 78(9), 1183 (2001).
[Crossref]

J. Robertson, P. Milsom, J. Duignan, and G. Bourhill, “Spatial redistribution of energy in a nanosecond laser pulse by an organic optical limiter,” Opt. Lett. 25(17), 1258–1260 (2000).
[Crossref] [PubMed]

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(12), 2597–2606 (1998).
[Crossref]

Santamato, E.

Shen, Y. R.

Shevchenko, A.

A. Shevchenko, S. C. Buchter, N. V. Tabiryan, and M. Kaivola, “Creation of a hollow laser beam using selfphase 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]

Smith, A.

J. Robertson, A. Smith, J. Duignan, P. Milsom, and G. Bourchill, “Nonlinear refractive beam shaping by an organic nonlinear absorber,” Appl. Phys. Lett. 78(9), 1183 (2001).
[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]

Tabiryan, N. V.

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

Tóth, B. C.

L. Pálfalvi, B. C. Tóth, G. Almási, J. A. Fülöp, and J. Hebling, “A general Z-scan theory,” Appl. Phys. B 97(3), 679–685 (2009).
[Crossref]

Tsigaridas, G.

G. Tsigaridas, M. Fakis, I. Polyzos, P. Persephonis, and V. Giannetas, “Z-scan technique through beam radius measurements,” Appl. Phys. B 76(1), 83–86 (2003).
[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]

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(12), 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. B (2)

L. Pálfalvi, B. C. Tóth, G. Almási, J. A. Fülöp, and J. Hebling, “A general Z-scan theory,” Appl. Phys. B 97(3), 679–685 (2009).
[Crossref]

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Figures (10)

Fig. 1
Fig. 1 Far field intensity cross sections obtained for a sample set at z = - z0 with ΔΦ0 = 4π rad, ΔΨ0 = 0 and m of: a) 1, b) 2 and c) 4.
Fig. 2
Fig. 2 Far field intensity profiles obtained for a sample set at z = - z0 with ΔΦ0 = 4π rad, ΔΨ0 = 0.5 (red), ΔΨ0 = −0.5 (blue) and m of: a) 1, b) 2 and c) 4. As reference the intensity profiles for ΔΨ0 = 0 are plotted in black.
Fig. 3
Fig. 3 Far field intensity cross sections obtained for a sample set at z = 0 with ΔΦ0 = 4π rad, ΔΨ0 = 0, and m of: a) 1, b) 2 and c) 4.
Fig. 4
Fig. 4 Far field intensity profiles obtained for a sample set at z = 0 with ΔΦ0 = 4π rad, ΔΨ0 = 0.5 (red), ΔΨ0 = −0.5 (blue) and m of: a) 1, b) 2 and c) 4. As reference the intensity profiles for ΔΨ0 = 0 are plotted in black.
Fig. 5
Fig. 5 Far field intensity cross sections obtained for a sample set at z = z0 with ΔΦ0 = 4 π rad, ΔΨ0 = 0, and m of: a) 1, b) 2 y c) 4.
Fig. 6
Fig. 6 Far field intensity profiles obtained for a sample set at z = z0 with ΔΦ0 = 4π rad, ΔΨ0 = 0.5 (red), ΔΨ0 = −0.5 (blue) and m of: a) 1, b) 2 and c) 4. As reference the intensity profiles for ΔΨ0 = 0 in black.
Fig. 7
Fig. 7 Far field intensity cross sections for a nonlocal media, m = 1, with ΔΦ0 = 4π rad and ΔΨ0 = - 0.5 rad, for sample positions of: a) −3z0, b) −2z0, c) -z0, d) 0, e) z0 and f) 2z0.
Fig. 8
Fig. 8 Far field intensity cross sections for a nonlocal media, m = 1, with ΔΦ0 = 4π rad and ΔΨ0 = 0.5 rad, for sample positions of: a) −3z0, b) −2z0, c) -z0, d) 0, e) z0 and f) 2z0.
Fig. 9
Fig. 9 Far field intensity cross sections for the local case, m = 2, with ΔΦ0 = 4π rad and ΔΨ0 = - 0.5 rad. Sample positions of: a) −3z0, b) −2z0, c) -z0, d) 0, e) z0 and f) 2z0.
Fig. 10
Fig. 10 Far field intensity cross sections with ΔΦ0 = 4π rad, ΔΨ0 = - 0.5 rad, m = 4 for sample positions of: a) −3z0, b) −2z0, c) -z0, d) 0, e) z0 and f) 2z0.

Equations (4)

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n( I )= n 0 +γI,
α( I )= α 0 +βI,
E out ( r,z )=E( r,z ) exp( α 0 L/2 ) [ 1+  q m ] ( i( ΔΦ 0 / ΔΨ 0 ) 1/2 ) ,
G loc = exp( 2 r 2 w 2 ( z ) ) 1+ ( z/ z 0 ) 2 .

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