Abstract

A model to characterize the response of a thin media that can exhibit more than one nonlocal nonlinear response when it is illuminated with a Gaussian beam in a z-scan experiment is proposed. The model considers that these nonlocal contributions can be treated as independent contributions in the refractive or absorptive nonlinear response. Numerical results for two nonlocal nonlinear contributions with different magnitudes between them are presented. Experimental results obtained from a hydrogenated amorphous silicon sample are used to corroborate this model.

© 2016 Optical Society of America

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  1. M. Sheik-Bahae, A. A. Said, E. W. Van Stryland, D. J. Hagan, and E. W. Van Stryland, “High-sensitivity, single-beam n2 measurements,” Opt. Lett. 14(17), 955–957 (1989).
    [Crossref] [PubMed]
  2. 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(10), 331–333 (1979).
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    [Crossref]
  4. S. Q. Chen, Z. B. Liu, W. P. Zang, J. G. Tian, W. J. Zhou, F. Song, and C. P. Zhang, “Study on Z-scan characteristics for a large nonlinear phase shift,” J. Opt. Soc. Am. B 22(9), 1911–1916 (2005).
    [Crossref]
  5. 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]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
  22. B. A. Martinez Irivas, M. L. Arroyo Carrasco, M. M. Mendez Otero, R. Ramos García, and M. D. Iturbe Castillo, “Far-field diffraction patterns by a thin nonlinear absorptive nonlocal media,” Opt. Express 23(11), 14036–14043 (2015).
    [Crossref] [PubMed]

2015 (1)

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]

2009 (1)

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]

2007 (1)

2005 (3)

2003 (1)

W. P. Zang, J. G. Tian, Z. B. Liu, W. Y. Zhou, C. P. Zhang, and G. Y. Zhang, “Study on Z-scan characteristics of cascaded nonlinear media,” App. Phys. 77(5), 529–533 (2003).
[Crossref]

1999 (1)

K. S. Bindra, S. M. Oak, and K. C. Rustagi, “Intensity dependence of Z-scan in semiconductor-doped glasses for separation of third and fifth order contributions in the below band gap region,” Opt. Commun. 168(1-4), 219–225 (1999).
[Crossref]

1995 (3)

1994 (3)

P. B. Chapple, J. Staromlynska, and R. G. McDuff, “Z-scan studies in the thin – and the thick –sample limits,” J. Opt. Soc. Am. B 11(6), 975–982 (1994).
[Crossref]

L. Lawrence, M. Cha, W. E. Torruellas, G. I. Stegeman, S. Eternad, G. Baker, and F. Kajzar, “Measurement of the complex nonlinear refractive index of single crystal p-toluene sulfonate at 1061 nm,” Appl. Phys. Lett. 64(21), 2773 (1994).
[Crossref]

A. A. Said, C. Wamsley, D. J. Hagan, E. W. Van Stryland, B. A. Reinhardt, P. Roderer, and A. G. Dillard, “Third- and fifth-order optical nonlineatities in organic materials,” Chem. Phys. Lett. 228(6), 646–650 (1994).
[Crossref]

1993 (1)

1992 (1)

A. A. Said, M. Shaik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. Stryland, “Determination of bound-electronic and free carrier nonlinearities in ZnSe, GaAs, CdTe and ZnTe,” J. Opt. Am. B 9(3), 405 (1992).
[Crossref]

1991 (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]

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(4), 760–769 (1990).
[Crossref]

1989 (1)

1979 (1)

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]

Araújo, G. B. D.

Arroyo Carrasco, M. L.

B. A. Martinez Irivas, M. L. Arroyo Carrasco, M. M. Mendez Otero, R. Ramos García, and M. D. Iturbe Castillo, “Far-field diffraction patterns by a thin nonlinear absorptive nonlocal media,” Opt. Express 23(11), 14036–14043 (2015).
[Crossref] [PubMed]

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]

Baker, G.

L. Lawrence, M. Cha, W. E. Torruellas, G. I. Stegeman, S. Eternad, G. Baker, and F. Kajzar, “Measurement of the complex nonlinear refractive index of single crystal p-toluene sulfonate at 1061 nm,” Appl. Phys. Lett. 64(21), 2773 (1994).
[Crossref]

Bindra, K. S.

K. S. Bindra, S. M. Oak, and K. C. Rustagi, “Intensity dependence of Z-scan in semiconductor-doped glasses for separation of third and fifth order contributions in the below band gap region,” Opt. Commun. 168(1-4), 219–225 (1999).
[Crossref]

Burzler, J. M.

Carrasco, M. L.

Castillo, M. D.

Cha, M.

L. Lawrence, M. Cha, W. E. Torruellas, G. I. Stegeman, S. Eternad, G. Baker, and F. Kajzar, “Measurement of the complex nonlinear refractive index of single crystal p-toluene sulfonate at 1061 nm,” Appl. Phys. Lett. 64(21), 2773 (1994).
[Crossref]

Chapple, P. B.

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]

Chen, J.

Chen, S. Q.

Dillard, A. G.

A. A. Said, C. Wamsley, D. J. Hagan, E. W. Van Stryland, B. A. Reinhardt, P. Roderer, and A. G. Dillard, “Third- and fifth-order optical nonlineatities in organic materials,” Chem. Phys. Lett. 228(6), 646–650 (1994).
[Crossref]

Ding, J.

Eternad, S.

L. Lawrence, M. Cha, W. E. Torruellas, G. I. Stegeman, S. Eternad, G. Baker, and F. Kajzar, “Measurement of the complex nonlinear refractive index of single crystal p-toluene sulfonate at 1061 nm,” Appl. Phys. Lett. 64(21), 2773 (1994).
[Crossref]

Falcão-Filho, E. L.

Fan, Y.

Fan, Y. X.

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]

Gu, B.

Hagan, D. J.

A. A. Said, C. Wamsley, D. J. Hagan, E. W. Van Stryland, B. A. Reinhardt, P. Roderer, and A. G. Dillard, “Third- and fifth-order optical nonlineatities in organic materials,” Chem. Phys. Lett. 228(6), 646–650 (1994).
[Crossref]

A. A. Said, M. Shaik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. Stryland, “Determination of bound-electronic and free carrier nonlinearities in ZnSe, GaAs, CdTe and ZnTe,” J. Opt. Am. B 9(3), 405 (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(4), 760–769 (1990).
[Crossref]

M. Sheik-Bahae, A. A. Said, E. W. Van Stryland, D. J. Hagan, and E. W. Van Stryland, “High-sensitivity, single-beam n2 measurements,” Opt. Lett. 14(17), 955–957 (1989).
[Crossref] [PubMed]

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]

Herman, J. A.

Hochbaum, A.

Hughes, S.

Iturbe Castillo, M. D.

B. A. Martinez Irivas, M. L. Arroyo Carrasco, M. M. Mendez Otero, R. Ramos García, and M. D. Iturbe Castillo, “Far-field diffraction patterns by a thin nonlinear absorptive nonlocal media,” Opt. Express 23(11), 14036–14043 (2015).
[Crossref] [PubMed]

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]

Kajzar, F.

L. Lawrence, M. Cha, W. E. Torruellas, G. I. Stegeman, S. Eternad, G. Baker, and F. Kajzar, “Measurement of the complex nonlinear refractive index of single crystal p-toluene sulfonate at 1061 nm,” Appl. Phys. Lett. 64(21), 2773 (1994).
[Crossref]

Lara, E. R.

Lawrence, L.

L. Lawrence, M. Cha, W. E. Torruellas, G. I. Stegeman, S. Eternad, G. Baker, and F. Kajzar, “Measurement of the complex nonlinear refractive index of single crystal p-toluene sulfonate at 1061 nm,” Appl. Phys. Lett. 64(21), 2773 (1994).
[Crossref]

Liu, Z. B.

S. Q. Chen, Z. B. Liu, W. P. Zang, J. G. Tian, W. J. Zhou, F. Song, and C. P. Zhang, “Study on Z-scan characteristics for a large nonlinear phase shift,” J. Opt. Soc. Am. B 22(9), 1911–1916 (2005).
[Crossref]

W. P. Zang, J. G. Tian, Z. B. Liu, W. Y. Zhou, C. P. Zhang, and G. Y. Zhang, “Study on Z-scan characteristics of cascaded nonlinear media,” App. Phys. 77(5), 529–533 (2003).
[Crossref]

Martinez Irivas, B. A.

McDuff, R. G.

Mendez Otero, M. M.

B. A. Martinez Irivas, M. L. Arroyo Carrasco, M. M. Mendez Otero, R. Ramos García, and M. D. Iturbe Castillo, “Far-field diffraction patterns by a thin nonlinear absorptive nonlocal media,” Opt. Express 23(11), 14036–14043 (2015).
[Crossref] [PubMed]

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]

Miller, D. A. B.

Miller, M. J.

Mott, A. G.

Oak, S. M.

K. S. Bindra, S. M. Oak, and K. C. Rustagi, “Intensity dependence of Z-scan in semiconductor-doped glasses for separation of third and fifth order contributions in the below band gap region,” Opt. Commun. 168(1-4), 219–225 (1999).
[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]

Ramírez, E. V.

Ramos García, R.

Reinhardt, B. A.

A. A. Said, C. Wamsley, D. J. Hagan, E. W. Van Stryland, B. A. Reinhardt, P. Roderer, and A. G. Dillard, “Third- and fifth-order optical nonlineatities in organic materials,” Chem. Phys. Lett. 228(6), 646–650 (1994).
[Crossref]

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]

Roderer, P.

A. A. Said, C. Wamsley, D. J. Hagan, E. W. Van Stryland, B. A. Reinhardt, P. Roderer, and A. G. Dillard, “Third- and fifth-order optical nonlineatities in organic materials,” Chem. Phys. Lett. 228(6), 646–650 (1994).
[Crossref]

Rodrigues, J. J.

Rustagi, K. C.

K. S. Bindra, S. M. Oak, and K. C. Rustagi, “Intensity dependence of Z-scan in semiconductor-doped glasses for separation of third and fifth order contributions in the below band gap region,” Opt. Commun. 168(1-4), 219–225 (1999).
[Crossref]

Said, A. A.

A. A. Said, C. Wamsley, D. J. Hagan, E. W. Van Stryland, B. A. Reinhardt, P. Roderer, and A. G. Dillard, “Third- and fifth-order optical nonlineatities in organic materials,” Chem. Phys. Lett. 228(6), 646–650 (1994).
[Crossref]

A. A. Said, M. Shaik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. Stryland, “Determination of bound-electronic and free carrier nonlinearities in ZnSe, GaAs, CdTe and ZnTe,” J. Opt. Am. B 9(3), 405 (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(4), 760–769 (1990).
[Crossref]

M. Sheik-Bahae, A. A. Said, E. W. Van Stryland, D. J. Hagan, and E. W. Van Stryland, “High-sensitivity, single-beam n2 measurements,” Opt. Lett. 14(17), 955–957 (1989).
[Crossref] [PubMed]

Shaik-Bahae, M.

A. A. Said, M. Shaik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. Stryland, “Determination of bound-electronic and free carrier nonlinearities in ZnSe, GaAs, CdTe and ZnTe,” J. Opt. Am. B 9(3), 405 (1992).
[Crossref]

Sheik-Bahae, M.

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(4), 760–769 (1990).
[Crossref]

M. Sheik-Bahae, A. A. Said, E. W. Van Stryland, D. J. Hagan, and E. W. Van Stryland, “High-sensitivity, single-beam n2 measurements,” Opt. Lett. 14(17), 955–957 (1989).
[Crossref] [PubMed]

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]

Song, F.

Spruce, G.

Staromlynska, J.

Stegeman, G. I.

L. Lawrence, M. Cha, W. E. Torruellas, G. I. Stegeman, S. Eternad, G. Baker, and F. Kajzar, “Measurement of the complex nonlinear refractive index of single crystal p-toluene sulfonate at 1061 nm,” Appl. Phys. Lett. 64(21), 2773 (1994).
[Crossref]

Stryland, E. W.

A. A. Said, M. Shaik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. Stryland, “Determination of bound-electronic and free carrier nonlinearities in ZnSe, GaAs, CdTe and ZnTe,” J. Opt. Am. B 9(3), 405 (1992).
[Crossref]

Tian, J. G.

S. Q. Chen, Z. B. Liu, W. P. Zang, J. G. Tian, W. J. Zhou, F. Song, and C. P. Zhang, “Study on Z-scan characteristics for a large nonlinear phase shift,” J. Opt. Soc. Am. B 22(9), 1911–1916 (2005).
[Crossref]

W. P. Zang, J. G. Tian, Z. B. Liu, W. Y. Zhou, C. P. Zhang, and G. Y. Zhang, “Study on Z-scan characteristics of cascaded nonlinear media,” App. Phys. 77(5), 529–533 (2003).
[Crossref]

Torruellas, W. E.

L. Lawrence, M. Cha, W. E. Torruellas, G. I. Stegeman, S. Eternad, G. Baker, and F. Kajzar, “Measurement of the complex nonlinear refractive index of single crystal p-toluene sulfonate at 1061 nm,” Appl. Phys. Lett. 64(21), 2773 (1994).
[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]

Van Stryland, E. W.

A. A. Said, C. Wamsley, D. J. Hagan, E. W. Van Stryland, B. A. Reinhardt, P. Roderer, and A. G. Dillard, “Third- and fifth-order optical nonlineatities in organic materials,” Chem. Phys. Lett. 228(6), 646–650 (1994).
[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(4), 760–769 (1990).
[Crossref]

M. Sheik-Bahae, A. A. Said, E. W. Van Stryland, D. J. Hagan, and E. W. Van Stryland, “High-sensitivity, single-beam n2 measurements,” Opt. Lett. 14(17), 955–957 (1989).
[Crossref] [PubMed]

M. Sheik-Bahae, A. A. Said, E. W. Van Stryland, D. J. Hagan, and E. W. Van Stryland, “High-sensitivity, single-beam n2 measurements,” Opt. Lett. 14(17), 955–957 (1989).
[Crossref] [PubMed]

Wamsley, C.

A. A. Said, C. Wamsley, D. J. Hagan, E. W. Van Stryland, B. A. Reinhardt, P. Roderer, and A. G. Dillard, “Third- and fifth-order optical nonlineatities in organic materials,” Chem. Phys. Lett. 228(6), 646–650 (1994).
[Crossref]

Wang, H.

Wang, H. T.

Wang, J.

B. Gu, J. Wang, J. Chen, Y. X. Fan, J. Ding, and H. T. Wang, “Z-scan theory for material with two- and three-photon absorption,” Opt. Express 13(23), 9230–9234 (2005).
[Crossref] [PubMed]

A. A. Said, M. Shaik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. Stryland, “Determination of bound-electronic and free carrier nonlinearities in ZnSe, GaAs, CdTe and ZnTe,” J. Opt. Am. B 9(3), 405 (1992).
[Crossref]

Weaire, D.

Wei, T. H.

A. A. Said, M. Shaik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. Stryland, “Determination of bound-electronic and free carrier nonlinearities in ZnSe, GaAs, CdTe and ZnTe,” J. Opt. Am. B 9(3), 405 (1992).
[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(4), 760–769 (1990).
[Crossref]

Wherret, B. S.

Wherrett, B. S.

Wood, G. L.

Young, J.

A. A. Said, M. Shaik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. Stryland, “Determination of bound-electronic and free carrier nonlinearities in ZnSe, GaAs, CdTe and ZnTe,” J. Opt. Am. B 9(3), 405 (1992).
[Crossref]

Zang, W. P.

S. Q. Chen, Z. B. Liu, W. P. Zang, J. G. Tian, W. J. Zhou, F. Song, and C. P. Zhang, “Study on Z-scan characteristics for a large nonlinear phase shift,” J. Opt. Soc. Am. B 22(9), 1911–1916 (2005).
[Crossref]

W. P. Zang, J. G. Tian, Z. B. Liu, W. Y. Zhou, C. P. Zhang, and G. Y. Zhang, “Study on Z-scan characteristics of cascaded nonlinear media,” App. Phys. 77(5), 529–533 (2003).
[Crossref]

Zhang, C. P.

S. Q. Chen, Z. B. Liu, W. P. Zang, J. G. Tian, W. J. Zhou, F. Song, and C. P. Zhang, “Study on Z-scan characteristics for a large nonlinear phase shift,” J. Opt. Soc. Am. B 22(9), 1911–1916 (2005).
[Crossref]

W. P. Zang, J. G. Tian, Z. B. Liu, W. Y. Zhou, C. P. Zhang, and G. Y. Zhang, “Study on Z-scan characteristics of cascaded nonlinear media,” App. Phys. 77(5), 529–533 (2003).
[Crossref]

Zhang, G. Y.

W. P. Zang, J. G. Tian, Z. B. Liu, W. Y. Zhou, C. P. Zhang, and G. Y. Zhang, “Study on Z-scan characteristics of cascaded nonlinear media,” App. Phys. 77(5), 529–533 (2003).
[Crossref]

Zhou, W. J.

Zhou, W. Y.

W. P. Zang, J. G. Tian, Z. B. Liu, W. Y. Zhou, C. P. Zhang, and G. Y. Zhang, “Study on Z-scan characteristics of cascaded nonlinear media,” App. Phys. 77(5), 529–533 (2003).
[Crossref]

App. Phys. (1)

W. P. Zang, J. G. Tian, Z. B. Liu, W. Y. Zhou, C. P. Zhang, and G. Y. Zhang, “Study on Z-scan characteristics of cascaded nonlinear media,” App. Phys. 77(5), 529–533 (2003).
[Crossref]

Appl. Phys. B (1)

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]

Appl. Phys. Lett. (1)

L. Lawrence, M. Cha, W. E. Torruellas, G. I. Stegeman, S. Eternad, G. Baker, and F. Kajzar, “Measurement of the complex nonlinear refractive index of single crystal p-toluene sulfonate at 1061 nm,” Appl. Phys. Lett. 64(21), 2773 (1994).
[Crossref]

Chem. Phys. Lett. (1)

A. A. Said, C. Wamsley, D. J. Hagan, E. W. Van Stryland, B. A. Reinhardt, P. Roderer, and A. G. Dillard, “Third- and fifth-order optical nonlineatities in organic materials,” Chem. Phys. Lett. 228(6), 646–650 (1994).
[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(4), 760–769 (1990).
[Crossref]

J. Opt. (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]

J. Opt. Am. B (1)

A. A. Said, M. Shaik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. Stryland, “Determination of bound-electronic and free carrier nonlinearities in ZnSe, GaAs, CdTe and ZnTe,” J. Opt. Am. B 9(3), 405 (1992).
[Crossref]

J. Opt. Soc. Am. B (6)

Opt. Commun. (1)

K. S. Bindra, S. M. Oak, and K. C. Rustagi, “Intensity dependence of Z-scan in semiconductor-doped glasses for separation of third and fifth order contributions in the below band gap region,” Opt. Commun. 168(1-4), 219–225 (1999).
[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 (3)

Opt. Lett. (4)

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Figures (7)

Fig. 1
Fig. 1 Numerical close-aperture z-scan curves without nonlinear absorption for m1 = 2 with ΔΦ01 = 0.4π rad and m2 = 4 for ΔΦ02 = 0 (black) with (a) positive and (b) negative values of: 0.4π rad (blue), 1.2π rad (red) and 2π rad (green).
Fig. 2
Fig. 2 Numerical close-aperture z-scan curves without nonlinear absorption for m1 = 2 with ΔΦ01 = 0.4π rad and m2 = 1 for ΔΦ02 = 0 (black) with (a) positive and (b) negative values of: 0.4π rad (blue), 1.2π rad (red) and 2π rad (green).
Fig. 3
Fig. 3 Numerical z-scan curves for m1 = 2, ΔΦ01 = 0.2π rad, ΔΨ01 = 0 and m2 = 4, for close aperture with a) ΔΦ02 = 0.4π rad, b) ΔΦ02 = − 0.4π rad and c) open aperture, for ΔΨ02 of: −0.6 rad (blue), −0.3 rad (cyan), 0 (black), 0.3 rad (green) and 0.6 rad (red).
Fig. 4
Fig. 4 Numerical z-scan curves for m1 = 2, ΔΦ01 = 0.2π rad, ΔΨ01 = 0 and m2 = 1, for close aperture with a) ΔΦ02 = 0.4π rad, b) ΔΦ02 = − 0.4π rad and c) open aperture, for ΔΨ02 of: −0.6 rad (blue), −0.3 rad (cyan), 0 (black), 0.3 rad (green) and 0.6 rad (red).
Fig. 5
Fig. 5 Numerical z-scan curves for m1 = 2 and m2 of: 1 (black), 2 (blue) and 4 (red), nonlinear absorption phase changes of: ΔΨ01 = ΔΨ02 = 0.2 rad. For close aperture a) large nonlinear phase changes with ΔΦ01 = 4 π rad and ΔΦ02 = − 2 π rad, b) small nonlinear phase changes with ΔΦ01 = 0.4 π rad and ΔΦ02 = − 0.2 π rad and (c) open aperture.
Fig. 6
Fig. 6 Experimental ( + ) and numerical (lines) z-scan curves for (a) close and (b) open aperture at incident powers of: 2 (black), 4 (blue), 6 (red), and 12 (green) mW.
Fig. 7
Fig. 7 Experimental ( + ) and numerical (lines) z-scan curves for (a) closed and (b) open aperture for incident power of: 2 (black), 4 (blue), 6 (red), and 12 (green) mW.

Equations (2)

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E out (r,z)=E(r,z)exp( α 0 L/2) (1+ q m ) ( i( Δ Φ 0 /Δ Ψ 0 )1/2 ) ,
E out ( r,z )=E( r,z )exp( α 0 L/2) ( 1+ q m 1 ) ( i( Δ Φ 01 /Δ Ψ 01 )1/2 ) ( 1+ q m 2 ) ( i( Δ Φ 02 /Δ Ψ 02 )1/2 ) ,

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