Abstract

In this paper, the Z-scan theory for nonlocal nonlinear media has been further developed when nonlinear absorption and nonlinear refraction appear simultaneously. To this end, the nonlinear photoinduced phase shift between the impinging and outgoing Gaussian beams from a nonlocal nonlinear sample has been generalized. It is shown that this kind of phase shift will reduce correctly to its known counterpart for the case of pure refractive nonlinearity. Using this generalized form of phase shift, the basic formulas for closed- and open-aperture beam transmittances in the far field have been provided, and a simple procedure for interpreting the Z-scan results has been proposed. In this procedure, by separately performing open- and closed-aperture Z-scan experiments and using the represented relations for the far-field transmittances, one can measure the nonlinear absorption coefficient and nonlinear index of refraction as well as the order of nonlocality. Theoretically, it is shown that when the absorptive nonlinearity is present in addition to the refractive nonlinearity, the sample nonlocal response can noticeably suppress the peak and enhance the valley of the Z-scan closed-aperture transmittance curves, which is due to the nonlocal action’s ability to change the beam transverse dimensions.

© 2013 Optical Society of America

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  1. M. Sheik-Bahae, A. A. Said, and E. W. Van Stryland, “High-sensitivity single-beam n2 measurements,” Opt. Lett. 14, 955–957 (1989).
    [CrossRef]
  2. M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
    [CrossRef]
  3. T. Xia, D. J. Hagan, M. Sheik-Bahae, and E. W. Van Stryland, “Eclipsing Z-scan measurement of λ/104 wave-front distortion,” Opt. Lett. 19, 317–319 (1994).
    [CrossRef]
  4. J.-G. Tian, W.-P. Zang, and G. Zhang, “Two modified Z-scan methods for determination of nonlinear-optical index with enhanced sensitivity,” Opt. Commun. 107, 415–419 (1994).
    [CrossRef]
  5. R. E. Bridges, G. L. Fischer, and R. W. Boyd, “Z-scan measurement technique for non-Gaussian beams and arbitrary sample thicknesses,” Opt. Lett. 20, 1821–1823 (1995).
    [CrossRef]
  6. H. Ma, A. S. L. Gomes, and C. B. de Araujo, “Measurements of nondegenerate optical nonlinearity using a two-color single beam method,” Appl. Phys. Lett. 59, 2666–2668 (1991).
    [CrossRef]
  7. 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]
  8. T.-H. Wei, T.-H. Huang, and H.-D. Lin, “Lifetime determination for high-lying excited states using Z scan,” Appl. Phys. Lett. 67, 2266–2668 (1995).
    [CrossRef]
  9. L. C. Oliveira, T. Catunda, and S. C. Zilio, “Saturation effects in Z-scan measurements,” Jpn. J. Appl. Phys. 35, 2649–2652 (1996).
    [CrossRef]
  10. M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, and E. W. Van Stryland, “Nonlinear refraction and optical limiting in thick media,” Opt. Eng. 30, 1228–1235 (1991).
    [CrossRef]
  11. D. Weaire, B. S. Wherrett, D. A. B. Miller, and S. D. Smith, “Effect of low-power nonlinear refraction on laser-beam propagation in InSb,” Opt. Lett. 4, 331–333 (1979).
    [CrossRef]
  12. S. Hughes, J. M. Burzler, G. Spruce, and B. S. Wherrett, “Fast Fourier transform techniques for efficient simulation of Z-scan measurements,” J. Opt. Soc. Am. B 12, 1888–1893 (1995).
    [CrossRef]
  13. W. Nasalski, “Complex ray tracing of nonlinear propagation,” Opt. Commun. 119, 218–226 (1995).
    [CrossRef]
  14. J. A. Hermann, “Self-focusing effects and applications using thin nonlinear media,” Int. J. Nonlinear Opt. Phys. 1, 541–561 (1992).
    [CrossRef]
  15. J. A. Hermann and R. G. McDuff, “Analysis of spatial scanning with thick optically nonlinear media,” J. Opt. Soc. Am. B 10, 2056–2064 (1993).
    [CrossRef]
  16. F. Cuppo, A. M. FigueiredoNeto, S. Gomez, and P. Palffy-Muhoray, “Thermal-lens model compared with the Sheik-Bahae formalism in interpreting Z-scan experiments on lyotropic liquid crystals,” J. Opt. Soc. Am. B 19, 1342–1348 (2002).
    [CrossRef]
  17. F. W. Dabby and J. R. Whinnery, “Thermal self-focusing of laser beams in lead glasses,” Appl. Phys. Lett. 13, 284–286 (1968).
    [CrossRef]
  18. M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68, 923–926 (1992).
    [CrossRef]
  19. D. Suter and T. Blasberg, “Stabilization of transverse solitary waves by a nonlocal response of the nonlinear medium,” Phys. Rev. A 48, 4583–4587 (1993).
    [CrossRef]
  20. M. R. Rashidian Vaziri, F. Hajiesmaeilbaigi, and M. H. Maleki, “Generalizing the Z-scan theory for nonlocal nonlinear media,” J. Opt. 15, 025201 (2013).
    [CrossRef]
  21. E. V. G. Ramirez, M. L. A. Carrasco, M. M. M. Otero, S. C. Cerda, and M. D. I. Castillo, “Far field intensity distributions due to spatial self phase modulation of a Gaussian beam by a thin nonlocal nonlinear media,” Opt. Express 18, 22067–22079 (2010).
    [CrossRef]
  22. E. V. G. Ramirez, M. L. A. Carrasco, M. M. M. Otero, E. R. Lara, S. Chavez-Cerda, and M. D. I. Castillo, “Z-scan and spatial self-phase modulation of a Gaussian beam in a thin nonlocal nonlinear media,” J. Opt. 13, 085203 (2011).
    [CrossRef]
  23. M. R. R. Vaziri, F. Hajiesmaeilbaigi, and M. H. Maleki, “New ducting model for analyzing the Gaussian beam propagation in nonlinear Kerr media and its application to spatial self-phase modulations,” J. Opt. 15, 035202 (2013).
    [CrossRef]
  24. X. Liu, S. Guo, H. Wang, and L. Hou, “Theoretical study on the closed-aperture Z-scan curves in the materials with nonlinear refraction and strong nonlinear absorption,” Opt. Commun. 197, 431–437 (2001).
    [CrossRef]
  25. M. Yin, H. P. Li, S. H. Tang, and W. Ji, “Determination of nonlinear absorption and refraction by single Z-scan method,” Appl. Phys. B 70, 587–591 (2000).
    [CrossRef]

2013 (2)

M. R. Rashidian Vaziri, F. Hajiesmaeilbaigi, and M. H. Maleki, “Generalizing the Z-scan theory for nonlocal nonlinear media,” J. Opt. 15, 025201 (2013).
[CrossRef]

M. R. R. Vaziri, F. Hajiesmaeilbaigi, and M. H. Maleki, “New ducting model for analyzing the Gaussian beam propagation in nonlinear Kerr media and its application to spatial self-phase modulations,” J. Opt. 15, 035202 (2013).
[CrossRef]

2011 (1)

E. V. G. Ramirez, M. L. A. Carrasco, M. M. M. Otero, E. R. Lara, S. Chavez-Cerda, and M. D. I. Castillo, “Z-scan and spatial self-phase modulation of a Gaussian beam in a thin nonlocal nonlinear media,” J. Opt. 13, 085203 (2011).
[CrossRef]

2010 (1)

2002 (1)

2001 (1)

X. Liu, S. Guo, H. Wang, and L. Hou, “Theoretical study on the closed-aperture Z-scan curves in the materials with nonlinear refraction and strong nonlinear absorption,” Opt. Commun. 197, 431–437 (2001).
[CrossRef]

2000 (1)

M. Yin, H. P. Li, S. H. Tang, and W. Ji, “Determination of nonlinear absorption and refraction by single Z-scan method,” Appl. Phys. B 70, 587–591 (2000).
[CrossRef]

1996 (1)

L. C. Oliveira, T. Catunda, and S. C. Zilio, “Saturation effects in Z-scan measurements,” Jpn. J. Appl. Phys. 35, 2649–2652 (1996).
[CrossRef]

1995 (4)

1994 (2)

T. Xia, D. J. Hagan, M. Sheik-Bahae, and E. W. Van Stryland, “Eclipsing Z-scan measurement of λ/104 wave-front distortion,” Opt. Lett. 19, 317–319 (1994).
[CrossRef]

J.-G. Tian, W.-P. Zang, and G. Zhang, “Two modified Z-scan methods for determination of nonlinear-optical index with enhanced sensitivity,” Opt. Commun. 107, 415–419 (1994).
[CrossRef]

1993 (2)

J. A. Hermann and R. G. McDuff, “Analysis of spatial scanning with thick optically nonlinear media,” J. Opt. Soc. Am. B 10, 2056–2064 (1993).
[CrossRef]

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

1992 (3)

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

J. A. Hermann, “Self-focusing effects and applications using thin nonlinear media,” Int. J. Nonlinear Opt. Phys. 1, 541–561 (1992).
[CrossRef]

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]

1991 (2)

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

M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, and E. W. Van Stryland, “Nonlinear refraction and optical limiting in thick media,” Opt. Eng. 30, 1228–1235 (1991).
[CrossRef]

1990 (1)

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

1989 (1)

1979 (1)

1968 (1)

F. W. Dabby and J. R. Whinnery, “Thermal self-focusing of laser beams in lead glasses,” Appl. Phys. Lett. 13, 284–286 (1968).
[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, 4583–4587 (1993).
[CrossRef]

Boyd, R. W.

Bridges, R. E.

Burzler, J. M.

Carrasco, M. L. A.

E. V. G. Ramirez, M. L. A. Carrasco, M. M. M. Otero, E. R. Lara, S. Chavez-Cerda, and M. D. I. Castillo, “Z-scan and spatial self-phase modulation of a Gaussian beam in a thin nonlocal nonlinear media,” J. Opt. 13, 085203 (2011).
[CrossRef]

E. V. G. Ramirez, M. L. A. Carrasco, M. M. M. Otero, S. C. Cerda, and M. D. I. Castillo, “Far field intensity distributions due to spatial self phase modulation of a Gaussian beam by a thin nonlocal nonlinear media,” Opt. Express 18, 22067–22079 (2010).
[CrossRef]

Castillo, M. D. I.

E. V. G. Ramirez, M. L. A. Carrasco, M. M. M. Otero, E. R. Lara, S. Chavez-Cerda, and M. D. I. Castillo, “Z-scan and spatial self-phase modulation of a Gaussian beam in a thin nonlocal nonlinear media,” J. Opt. 13, 085203 (2011).
[CrossRef]

E. V. G. Ramirez, M. L. A. Carrasco, M. M. M. Otero, S. C. Cerda, and M. D. I. Castillo, “Far field intensity distributions due to spatial self phase modulation of a Gaussian beam by a thin nonlocal nonlinear media,” Opt. Express 18, 22067–22079 (2010).
[CrossRef]

Catunda, T.

L. C. Oliveira, T. Catunda, and S. C. Zilio, “Saturation effects in Z-scan measurements,” Jpn. J. Appl. Phys. 35, 2649–2652 (1996).
[CrossRef]

Cerda, S. C.

Chavez-Cerda, S.

E. V. G. Ramirez, M. L. A. Carrasco, M. M. M. Otero, E. R. Lara, S. Chavez-Cerda, and M. D. I. Castillo, “Z-scan and spatial self-phase modulation of a Gaussian beam in a thin nonlocal nonlinear media,” J. Opt. 13, 085203 (2011).
[CrossRef]

Crosignani, B.

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

Cuppo, F.

Dabby, F. W.

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

de Araujo, C. B.

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

DeSalvo, R.

FigueiredoNeto, A. M.

Fischer, B.

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

Fischer, G. L.

Gomes, A. S. L.

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

Gomez, S.

Guo, S.

X. Liu, S. Guo, H. Wang, and L. Hou, “Theoretical study on the closed-aperture Z-scan curves in the materials with nonlinear refraction and strong nonlinear absorption,” Opt. Commun. 197, 431–437 (2001).
[CrossRef]

Hagan, D. J.

T. Xia, D. J. Hagan, M. Sheik-Bahae, and E. W. Van Stryland, “Eclipsing Z-scan measurement of λ/104 wave-front distortion,” Opt. Lett. 19, 317–319 (1994).
[CrossRef]

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]

M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, and E. W. Van Stryland, “Nonlinear refraction and optical limiting in thick media,” Opt. Eng. 30, 1228–1235 (1991).
[CrossRef]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

Hajiesmaeilbaigi, F.

M. R. Rashidian Vaziri, F. Hajiesmaeilbaigi, and M. H. Maleki, “Generalizing the Z-scan theory for nonlocal nonlinear media,” J. Opt. 15, 025201 (2013).
[CrossRef]

M. R. R. Vaziri, F. Hajiesmaeilbaigi, and M. H. Maleki, “New ducting model for analyzing the Gaussian beam propagation in nonlinear Kerr media and its application to spatial self-phase modulations,” J. Opt. 15, 035202 (2013).
[CrossRef]

Hermann, J. A.

J. A. Hermann and R. G. McDuff, “Analysis of spatial scanning with thick optically nonlinear media,” J. Opt. Soc. Am. B 10, 2056–2064 (1993).
[CrossRef]

J. A. Hermann, “Self-focusing effects and applications using thin nonlinear media,” Int. J. Nonlinear Opt. Phys. 1, 541–561 (1992).
[CrossRef]

Hou, L.

X. Liu, S. Guo, H. Wang, and L. Hou, “Theoretical study on the closed-aperture Z-scan curves in the materials with nonlinear refraction and strong nonlinear absorption,” Opt. Commun. 197, 431–437 (2001).
[CrossRef]

Huang, T.-H.

T.-H. Wei, T.-H. Huang, and H.-D. Lin, “Lifetime determination for high-lying excited states using Z scan,” Appl. Phys. Lett. 67, 2266–2668 (1995).
[CrossRef]

Hughes, S.

Ji, W.

M. Yin, H. P. Li, S. H. Tang, and W. Ji, “Determination of nonlinear absorption and refraction by single Z-scan method,” Appl. Phys. B 70, 587–591 (2000).
[CrossRef]

Lara, E. R.

E. V. G. Ramirez, M. L. A. Carrasco, M. M. M. Otero, E. R. Lara, S. Chavez-Cerda, and M. D. I. Castillo, “Z-scan and spatial self-phase modulation of a Gaussian beam in a thin nonlocal nonlinear media,” J. Opt. 13, 085203 (2011).
[CrossRef]

Li, H. P.

M. Yin, H. P. Li, S. H. Tang, and W. Ji, “Determination of nonlinear absorption and refraction by single Z-scan method,” Appl. Phys. B 70, 587–591 (2000).
[CrossRef]

Lin, H.-D.

T.-H. Wei, T.-H. Huang, and H.-D. Lin, “Lifetime determination for high-lying excited states using Z scan,” Appl. Phys. Lett. 67, 2266–2668 (1995).
[CrossRef]

Liu, X.

X. Liu, S. Guo, H. Wang, and L. Hou, “Theoretical study on the closed-aperture Z-scan curves in the materials with nonlinear refraction and strong nonlinear absorption,” Opt. Commun. 197, 431–437 (2001).
[CrossRef]

Ma, H.

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

Maleki, M. H.

M. R. Rashidian Vaziri, F. Hajiesmaeilbaigi, and M. H. Maleki, “Generalizing the Z-scan theory for nonlocal nonlinear media,” J. Opt. 15, 025201 (2013).
[CrossRef]

M. R. R. Vaziri, F. Hajiesmaeilbaigi, and M. H. Maleki, “New ducting model for analyzing the Gaussian beam propagation in nonlinear Kerr media and its application to spatial self-phase modulations,” J. Opt. 15, 035202 (2013).
[CrossRef]

McDuff, R. G.

Miller, D. A. B.

Nasalski, W.

W. Nasalski, “Complex ray tracing of nonlinear propagation,” Opt. Commun. 119, 218–226 (1995).
[CrossRef]

Oliveira, L. C.

L. C. Oliveira, T. Catunda, and S. C. Zilio, “Saturation effects in Z-scan measurements,” Jpn. J. Appl. Phys. 35, 2649–2652 (1996).
[CrossRef]

Otero, M. M. M.

E. V. G. Ramirez, M. L. A. Carrasco, M. M. M. Otero, E. R. Lara, S. Chavez-Cerda, and M. D. I. Castillo, “Z-scan and spatial self-phase modulation of a Gaussian beam in a thin nonlocal nonlinear media,” J. Opt. 13, 085203 (2011).
[CrossRef]

E. V. G. Ramirez, M. L. A. Carrasco, M. M. M. Otero, S. C. Cerda, and M. D. I. Castillo, “Far field intensity distributions due to spatial self phase modulation of a Gaussian beam by a thin nonlocal nonlinear media,” Opt. Express 18, 22067–22079 (2010).
[CrossRef]

Palffy-Muhoray, P.

Ramirez, E. V. G.

E. V. G. Ramirez, M. L. A. Carrasco, M. M. M. Otero, E. R. Lara, S. Chavez-Cerda, and M. D. I. Castillo, “Z-scan and spatial self-phase modulation of a Gaussian beam in a thin nonlocal nonlinear media,” J. Opt. 13, 085203 (2011).
[CrossRef]

E. V. G. Ramirez, M. L. A. Carrasco, M. M. M. Otero, S. C. Cerda, and M. D. I. Castillo, “Far field intensity distributions due to spatial self phase modulation of a Gaussian beam by a thin nonlocal nonlinear media,” Opt. Express 18, 22067–22079 (2010).
[CrossRef]

Rashidian Vaziri, M. R.

M. R. Rashidian Vaziri, F. Hajiesmaeilbaigi, and M. H. Maleki, “Generalizing the Z-scan theory for nonlocal nonlinear media,” J. Opt. 15, 025201 (2013).
[CrossRef]

Said, A. A.

M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, and E. W. Van Stryland, “Nonlinear refraction and optical limiting in thick media,” Opt. Eng. 30, 1228–1235 (1991).
[CrossRef]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

M. Sheik-Bahae, A. A. Said, and E. W. Van Stryland, “High-sensitivity single-beam n2 measurements,” Opt. Lett. 14, 955–957 (1989).
[CrossRef]

Segev, M.

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

Sheik-Bahae, M.

T. Xia, D. J. Hagan, M. Sheik-Bahae, and E. W. Van Stryland, “Eclipsing Z-scan measurement of λ/104 wave-front distortion,” Opt. Lett. 19, 317–319 (1994).
[CrossRef]

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]

M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, and E. W. Van Stryland, “Nonlinear refraction and optical limiting in thick media,” Opt. Eng. 30, 1228–1235 (1991).
[CrossRef]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

M. Sheik-Bahae, A. A. Said, and E. W. Van Stryland, “High-sensitivity single-beam n2 measurements,” Opt. Lett. 14, 955–957 (1989).
[CrossRef]

Smith, S. D.

Soileau, M. J.

M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, and E. W. Van Stryland, “Nonlinear refraction and optical limiting in thick media,” Opt. Eng. 30, 1228–1235 (1991).
[CrossRef]

Spruce, G.

Suter, D.

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

Tang, S. H.

M. Yin, H. P. Li, S. H. Tang, and W. Ji, “Determination of nonlinear absorption and refraction by single Z-scan method,” Appl. Phys. B 70, 587–591 (2000).
[CrossRef]

Tian, J.-G.

J.-G. Tian, W.-P. Zang, and G. Zhang, “Two modified Z-scan methods for determination of nonlinear-optical index with enhanced sensitivity,” Opt. Commun. 107, 415–419 (1994).
[CrossRef]

Van Stryland, E. W.

T. Xia, D. J. Hagan, M. Sheik-Bahae, and E. W. Van Stryland, “Eclipsing Z-scan measurement of λ/104 wave-front distortion,” Opt. Lett. 19, 317–319 (1994).
[CrossRef]

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]

M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, and E. W. Van Stryland, “Nonlinear refraction and optical limiting in thick media,” Opt. Eng. 30, 1228–1235 (1991).
[CrossRef]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

M. Sheik-Bahae, A. A. Said, and E. W. Van Stryland, “High-sensitivity single-beam n2 measurements,” Opt. Lett. 14, 955–957 (1989).
[CrossRef]

Vaziri, M. R. R.

M. R. R. Vaziri, F. Hajiesmaeilbaigi, and M. H. Maleki, “New ducting model for analyzing the Gaussian beam propagation in nonlinear Kerr media and its application to spatial self-phase modulations,” J. Opt. 15, 035202 (2013).
[CrossRef]

Wang, H.

X. Liu, S. Guo, H. Wang, and L. Hou, “Theoretical study on the closed-aperture Z-scan curves in the materials with nonlinear refraction and strong nonlinear absorption,” Opt. Commun. 197, 431–437 (2001).
[CrossRef]

Wang, J.

Weaire, D.

Wei, T. H.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

Wei, T.-H.

T.-H. Wei, T.-H. Huang, and H.-D. Lin, “Lifetime determination for high-lying excited states using Z scan,” Appl. Phys. Lett. 67, 2266–2668 (1995).
[CrossRef]

Wherrett, B. S.

Whinnery, J. R.

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

Xia, T.

Yariv, A.

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

Yin, M.

M. Yin, H. P. Li, S. H. Tang, and W. Ji, “Determination of nonlinear absorption and refraction by single Z-scan method,” Appl. Phys. B 70, 587–591 (2000).
[CrossRef]

Zang, W.-P.

J.-G. Tian, W.-P. Zang, and G. Zhang, “Two modified Z-scan methods for determination of nonlinear-optical index with enhanced sensitivity,” Opt. Commun. 107, 415–419 (1994).
[CrossRef]

Zhang, G.

J.-G. Tian, W.-P. Zang, and G. Zhang, “Two modified Z-scan methods for determination of nonlinear-optical index with enhanced sensitivity,” Opt. Commun. 107, 415–419 (1994).
[CrossRef]

Zilio, S. C.

L. C. Oliveira, T. Catunda, and S. C. Zilio, “Saturation effects in Z-scan measurements,” Jpn. J. Appl. Phys. 35, 2649–2652 (1996).
[CrossRef]

Appl. Phys. B (1)

M. Yin, H. P. Li, S. H. Tang, and W. Ji, “Determination of nonlinear absorption and refraction by single Z-scan method,” Appl. Phys. B 70, 587–591 (2000).
[CrossRef]

Appl. Phys. Lett. (3)

T.-H. Wei, T.-H. Huang, and H.-D. Lin, “Lifetime determination for high-lying excited states using Z scan,” Appl. Phys. Lett. 67, 2266–2668 (1995).
[CrossRef]

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

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

IEEE J. Quantum Electron. (1)

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

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

J. A. Hermann, “Self-focusing effects and applications using thin nonlinear media,” Int. J. Nonlinear Opt. Phys. 1, 541–561 (1992).
[CrossRef]

J. Opt. (3)

E. V. G. Ramirez, M. L. A. Carrasco, M. M. M. Otero, E. R. Lara, S. Chavez-Cerda, and M. D. I. Castillo, “Z-scan and spatial self-phase modulation of a Gaussian beam in a thin nonlocal nonlinear media,” J. Opt. 13, 085203 (2011).
[CrossRef]

M. R. R. Vaziri, F. Hajiesmaeilbaigi, and M. H. Maleki, “New ducting model for analyzing the Gaussian beam propagation in nonlinear Kerr media and its application to spatial self-phase modulations,” J. Opt. 15, 035202 (2013).
[CrossRef]

M. R. Rashidian Vaziri, F. Hajiesmaeilbaigi, and M. H. Maleki, “Generalizing the Z-scan theory for nonlocal nonlinear media,” J. Opt. 15, 025201 (2013).
[CrossRef]

J. Opt. Soc. Am. B (3)

Jpn. J. Appl. Phys. (1)

L. C. Oliveira, T. Catunda, and S. C. Zilio, “Saturation effects in Z-scan measurements,” Jpn. J. Appl. Phys. 35, 2649–2652 (1996).
[CrossRef]

Opt. Commun. (3)

J.-G. Tian, W.-P. Zang, and G. Zhang, “Two modified Z-scan methods for determination of nonlinear-optical index with enhanced sensitivity,” Opt. Commun. 107, 415–419 (1994).
[CrossRef]

W. Nasalski, “Complex ray tracing of nonlinear propagation,” Opt. Commun. 119, 218–226 (1995).
[CrossRef]

X. Liu, S. Guo, H. Wang, and L. Hou, “Theoretical study on the closed-aperture Z-scan curves in the materials with nonlinear refraction and strong nonlinear absorption,” Opt. Commun. 197, 431–437 (2001).
[CrossRef]

Opt. Eng. (1)

M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, and E. W. Van Stryland, “Nonlinear refraction and optical limiting in thick media,” Opt. Eng. 30, 1228–1235 (1991).
[CrossRef]

Opt. Express (1)

Opt. Lett. (5)

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, 4583–4587 (1993).
[CrossRef]

Phys. Rev. Lett. (1)

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

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Figures (4)

Fig. 1.
Fig. 1.

Closed-aperture Z-scan curves obtained for the on-axis nonlinear phase shift of 0.1 rad and different values of the m parameter m=0.5 (dashed line), m=1 (solid line), m=2 (dashed–dotted line), and m=3 (dotted line). This figure has been obtained by plotting Eq. (11).

Fig. 2.
Fig. 2.

Gaussian beam intensity distribution after exiting from the nonlocal nonlinear sample when both nonlinear refraction and nonlinear absorption are present. This figure has been obtained by plotting Eq. (6) at z=z0.

Fig. 3.
Fig. 3.

Closed-aperture peak-to-valley transmittance difference versus the parameter m. For the used physical constants in the simulations, the peak will be removed from the Z-scan curves (Fig. 1) below m=0.23, and hence ΔTpv has not been continued in this range.

Fig. 4.
Fig. 4.

Peak-to-valley separation distance as a function of the parameter m. The curve has not been continued below m=0.23.

Equations (28)

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n=n0+n2I,
E(z,r)=E0w0w(z)exp(r2w2(z))exp(ikr22R(z))exp(iφ(z)),
dIdz=(α0+βI)I,
d(Δφ)dz=kn2I,
I(z,r)=α0I(z,r)eα0zα0+βI(z,r)βI(z,r)eα0z,
Ie(z,r)=I(z,r)eα0L1+q(z,r),
q(z,r)=βI(z,r)Leff,
Δφ(z,r)=kn2βln[1+q(z,r)].
q(z,r)=βI(z,r)Leff=q01+(zz0)2exp(2mr2w2(z)),
Δφ(z,r)kn2βq(z,r)=Δφ0(z)exp(2mr2w2(z)),
Δφ0(z)=ΔΦ01+(zz0)2,
Ee(r,z)=|Ee(r,z)|exp(iΔφ(z,r)),
|Ee(r,z)|=2Ie(r,z)cnε0.
Ee(r,z)=E(z,r)e12α0L(1+q(z,r))ikn2β12.
(1+q(z,r))ikn2β12,
Ee(r,z)=E(z,r)e12α0Ln=0[(iΔφ0(z))nn!×n=0n(1i(2n1)β2kn2)]exp(2mnr2w2(z)).
fn=(iΔφ0(z))nn!n=0n(1i(2n1)β2kn2),
Ea(r)=E(z,r=0)e12α0Ln=0[iΔφ0(z)]nn!n=0n(1i(2n1)β2kn2)wn0wnexp(r2wn2ikr22Rn+iθn).
wn02=w2(z)2mn+1,
dn=kwn022,
wn2=wn02[g2+d2dn2],
Rn=d[1gg2+d2/dn2]1,
θn=tan1[d/dng].
T(z,ΔΦ0,q0)=|Ea(z,r=0,Δφ0)|2|Ea(z,r=0,Δφ0=0)|2.
T(z,ΔΦ0,q0)=1Δφ0(z)4mgdd0βkn2(g2+(2m+1)d2d02)g2+(2m+1)2d2d02.
T(z,ΔΦ0,q0)=14mΔΦ0x+q0(x2+(2m+1))(x2+(2m+1)2)(x2+1),
P(z)=Pieα0Lmln(1+q0(z))q0(z),
T(z,q0)=ln(1+q0(z))q0(z)[112q0(1+x2)].

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