Abstract

We made a theoretical investigation on the top-hat-beam Z scan when the nonlinear media possess third- and fifth-order nonlinearities simultaneously. A high-accuracy method was proposed to allow the determination of the nonlinear refraction coefficients related to the third- and fifth-order effects. We also reconfirmed the common procedure for dividing the contributions of the third- and fifth-order effects to the nonlinearity in the top-hat-beam Z-scan measurements; the results indicated that the common procedure can be still employed for the determination of the third-order nonlinearity, whereas it is inapplicable for the fifth-order nonlinearity. We investigated experimentally, as a test, the nonlinear refraction of a Disperse Yellow 7 thin film by using the top-hat-beam Z-scan technique, with 35-ps-duration pulses at a 1064-nm wavelength.

© 2005 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] [PubMed]
  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 lambda/10^4 wave-front distortion," Opt. Lett. 19, 317-319 (1994).
    [CrossRef] [PubMed]
  4. S. V. Kershaw, "Analysis of the EZ scan measurement technique," J. Mod. Opt. 42, L1361-L1366 (1995).
    [CrossRef]
  5. A. O. Marcano, F. E. Hernandez, and A. D. Sena, "Two-color near-field eclipsing Z-scan technique for the determination of nonlinear refraction," J. Opt. Soc. Am. B 14, 3363-3367 (1997).
    [CrossRef]
  6. S. Hughes and J. M. Burzler, "Theory of Z-scan measurement using Gaussian-Bessel beams," Phys. Rev. A 56, R1103-R1106 (1997).
    [CrossRef]
  7. G. Tsigaridas, M. Fakis, I. Polyzos, P. Persephonis, and V. Giannetas, "Z-scan technique through beam radius measurements," Appl. Phys. B 76, 83-86 (2003).
    [CrossRef]
  8. G. Tsigaridas, M. Fakis, I. Polyzos, P. Persephonis, and V. Giannetas, "Z-scan technique for elliptic Gaussian beams," Appl. Phys. B 77, 71-75 (2003).
    [CrossRef]
  9. W. Zhao and P. Palffy-Muhoray, "Z-scan technique using top-hat beams," Appl. Phys. Lett. 63, 1613-1615 (1993).
    [CrossRef]
  10. W. Zhao and P. Palffy-Muhoray, "Z-scan measurement of chi(3) using top-hat beams," Appl. Phys. Lett. 65, 673-675 (1994).
    [CrossRef]
  11. S. M. Chen, R. P. Pan, and C. L. Pan, "Identification of third and fifth order self-phase modulation effects in laser-induced diffraction rings from a nematic liquid crystal film," Opt. Commun. 79, 469-472 (1990).
    [CrossRef]
  12. K. Ekvall, C. Lundevall, and P. Van der Meulen, "Studies of the fifth-order nonlinear susceptibility of ultraviolet-grade fused silica," Opt. Lett. 26, 896-898 (2001).
    [CrossRef]
  13. A. A. Said, M. Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. Van Stryland, "Determination of bound-electronic and free-carrier nonlinearities in ZnSe, GaAs, CdTe, and ZnTe," J. Opt. Soc. Am. B 9, 405-414 (1992).
    [CrossRef]
  14. K. S. Bindra, S. M. Oak, and K. C. Rustagi, "Intensity de-pendence of Z-scan in semiconductor-doped glasses for separation of third and fifth order contributions in the below band gap region," Opt. Commun. 168, 219-225 (1999).
    [CrossRef]
  15. G. Tsigaridas, M. Fakis, I. Polyzos, P. Persephonis, and V. Giannetas, "Z-scan analysis for high order nonlinearities through Gaussian decomposition," Opt. Commun. 225, 253-268 (2003).
    [CrossRef]
  16. M. Born and E. Wolf, Principles of Optics , 6th ed. (Pergamon, Oxford, UK, 1980), Section 8.8.
  17. B. L. Lawrence, M. Cha, W. E. Torruellas, G. I. Stegenman, S. Etemad, G. Baker, and F. Kajzar, "Measurement of the complex nonlinear refractive index of single crystal p-toluene sulfonate at 1064 nm," Appl. Phys. Lett. 64, 2773-2775 (1994).
    [CrossRef]
  18. Z. B. Liu, W. P. Zang, J. G. Tian, W. Y. Zhou, C. P. Zhang, and G. Y. Zhang, "Analysis of Z-scan of thick media with high-order nonlinearity by variational approach," Opt. Commun. 219, 411-419 (2003).
    [CrossRef]
  19. C. L. Zhan, D. H. Li, D. Y. Wang, D. Q. Zhang, Y. J. Li, W. Xu, Z. Z. Lu, L. Z. Zhao, Y. X. Nie, and D. B. Zhu, "The high fifth-order nonlinearity in a new stilbazolium derivative: trans-1-[p-(p-dimethylaminobenzyl-azo)-benzyl]-2-(N-methyl-4-pyridinium)-ethene iodide," Chem. Phys. Lett. 347, 410-414 (2001).
    [CrossRef]

2003 (4)

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

G. Tsigaridas, M. Fakis, I. Polyzos, P. Persephonis, and V. Giannetas, "Z-scan technique for elliptic Gaussian beams," Appl. Phys. B 77, 71-75 (2003).
[CrossRef]

Z. B. Liu, W. P. Zang, J. G. Tian, W. Y. Zhou, C. P. Zhang, and G. Y. Zhang, "Analysis of Z-scan of thick media with high-order nonlinearity by variational approach," Opt. Commun. 219, 411-419 (2003).
[CrossRef]

G. Tsigaridas, M. Fakis, I. Polyzos, P. Persephonis, and V. Giannetas, "Z-scan analysis for high order nonlinearities through Gaussian decomposition," Opt. Commun. 225, 253-268 (2003).
[CrossRef]

2001 (2)

C. L. Zhan, D. H. Li, D. Y. Wang, D. Q. Zhang, Y. J. Li, W. Xu, Z. Z. Lu, L. Z. Zhao, Y. X. Nie, and D. B. Zhu, "The high fifth-order nonlinearity in a new stilbazolium derivative: trans-1-[p-(p-dimethylaminobenzyl-azo)-benzyl]-2-(N-methyl-4-pyridinium)-ethene iodide," Chem. Phys. Lett. 347, 410-414 (2001).
[CrossRef]

K. Ekvall, C. Lundevall, and P. Van der Meulen, "Studies of the fifth-order nonlinear susceptibility of ultraviolet-grade fused silica," Opt. Lett. 26, 896-898 (2001).
[CrossRef]

1999 (1)

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

1997 (2)

1995 (1)

S. V. Kershaw, "Analysis of the EZ scan measurement technique," J. Mod. Opt. 42, L1361-L1366 (1995).
[CrossRef]

1994 (3)

W. Zhao and P. Palffy-Muhoray, "Z-scan measurement of chi(3) using top-hat beams," Appl. Phys. Lett. 65, 673-675 (1994).
[CrossRef]

T. Xia, D. J. Hagan, M. Sheik-Bahae, and E. W. Van Stryland, "Eclipsing Z-scan measurement of lambda/10^4 wave-front distortion," Opt. Lett. 19, 317-319 (1994).
[CrossRef] [PubMed]

B. L. Lawrence, M. Cha, W. E. Torruellas, G. I. Stegenman, S. Etemad, G. Baker, and F. Kajzar, "Measurement of the complex nonlinear refractive index of single crystal p-toluene sulfonate at 1064 nm," Appl. Phys. Lett. 64, 2773-2775 (1994).
[CrossRef]

1993 (1)

W. Zhao and P. Palffy-Muhoray, "Z-scan technique using top-hat beams," Appl. Phys. Lett. 63, 1613-1615 (1993).
[CrossRef]

1992 (1)

1990 (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]

S. M. Chen, R. P. Pan, and C. L. Pan, "Identification of third and fifth order self-phase modulation effects in laser-induced diffraction rings from a nematic liquid crystal film," Opt. Commun. 79, 469-472 (1990).
[CrossRef]

1989 (1)

Bahae, M.

Baker, G.

B. L. Lawrence, M. Cha, W. E. Torruellas, G. I. Stegenman, S. Etemad, G. Baker, and F. Kajzar, "Measurement of the complex nonlinear refractive index of single crystal p-toluene sulfonate at 1064 nm," Appl. Phys. Lett. 64, 2773-2775 (1994).
[CrossRef]

Bindra, K. S.

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

Burzler, J. M.

S. Hughes and J. M. Burzler, "Theory of Z-scan measurement using Gaussian-Bessel beams," Phys. Rev. A 56, R1103-R1106 (1997).
[CrossRef]

Cha, M.

B. L. Lawrence, M. Cha, W. E. Torruellas, G. I. Stegenman, S. Etemad, G. Baker, and F. Kajzar, "Measurement of the complex nonlinear refractive index of single crystal p-toluene sulfonate at 1064 nm," Appl. Phys. Lett. 64, 2773-2775 (1994).
[CrossRef]

Chen, S. M.

S. M. Chen, R. P. Pan, and C. L. Pan, "Identification of third and fifth order self-phase modulation effects in laser-induced diffraction rings from a nematic liquid crystal film," Opt. Commun. 79, 469-472 (1990).
[CrossRef]

Ekvall, K.

Etemad, S.

B. L. Lawrence, M. Cha, W. E. Torruellas, G. I. Stegenman, S. Etemad, G. Baker, and F. Kajzar, "Measurement of the complex nonlinear refractive index of single crystal p-toluene sulfonate at 1064 nm," Appl. Phys. Lett. 64, 2773-2775 (1994).
[CrossRef]

Fakis, M.

G. Tsigaridas, M. Fakis, I. Polyzos, P. Persephonis, and V. Giannetas, "Z-scan technique for elliptic Gaussian beams," Appl. Phys. B 77, 71-75 (2003).
[CrossRef]

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

G. Tsigaridas, M. Fakis, I. Polyzos, P. Persephonis, and V. Giannetas, "Z-scan analysis for high order nonlinearities through Gaussian decomposition," Opt. Commun. 225, 253-268 (2003).
[CrossRef]

Giannetas, V.

G. Tsigaridas, M. Fakis, I. Polyzos, P. Persephonis, and V. Giannetas, "Z-scan analysis for high order nonlinearities through Gaussian decomposition," Opt. Commun. 225, 253-268 (2003).
[CrossRef]

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

G. Tsigaridas, M. Fakis, I. Polyzos, P. Persephonis, and V. Giannetas, "Z-scan technique for elliptic Gaussian beams," Appl. Phys. B 77, 71-75 (2003).
[CrossRef]

Hagan, D. J.

Hernandez, F. E.

Hughes , S.

S. Hughes and J. M. Burzler, "Theory of Z-scan measurement using Gaussian-Bessel beams," Phys. Rev. A 56, R1103-R1106 (1997).
[CrossRef]

Kajzar, F.

B. L. Lawrence, M. Cha, W. E. Torruellas, G. I. Stegenman, S. Etemad, G. Baker, and F. Kajzar, "Measurement of the complex nonlinear refractive index of single crystal p-toluene sulfonate at 1064 nm," Appl. Phys. Lett. 64, 2773-2775 (1994).
[CrossRef]

Kershaw, S. V.

S. V. Kershaw, "Analysis of the EZ scan measurement technique," J. Mod. Opt. 42, L1361-L1366 (1995).
[CrossRef]

Lawrence, B. L.

B. L. Lawrence, M. Cha, W. E. Torruellas, G. I. Stegenman, S. Etemad, G. Baker, and F. Kajzar, "Measurement of the complex nonlinear refractive index of single crystal p-toluene sulfonate at 1064 nm," Appl. Phys. Lett. 64, 2773-2775 (1994).
[CrossRef]

Li, D. H.

C. L. Zhan, D. H. Li, D. Y. Wang, D. Q. Zhang, Y. J. Li, W. Xu, Z. Z. Lu, L. Z. Zhao, Y. X. Nie, and D. B. Zhu, "The high fifth-order nonlinearity in a new stilbazolium derivative: trans-1-[p-(p-dimethylaminobenzyl-azo)-benzyl]-2-(N-methyl-4-pyridinium)-ethene iodide," Chem. Phys. Lett. 347, 410-414 (2001).
[CrossRef]

Li, Y. J.

C. L. Zhan, D. H. Li, D. Y. Wang, D. Q. Zhang, Y. J. Li, W. Xu, Z. Z. Lu, L. Z. Zhao, Y. X. Nie, and D. B. Zhu, "The high fifth-order nonlinearity in a new stilbazolium derivative: trans-1-[p-(p-dimethylaminobenzyl-azo)-benzyl]-2-(N-methyl-4-pyridinium)-ethene iodide," Chem. Phys. Lett. 347, 410-414 (2001).
[CrossRef]

Liu, Z. B.

Z. B. Liu, W. P. Zang, J. G. Tian, W. Y. Zhou, C. P. Zhang, and G. Y. Zhang, "Analysis of Z-scan of thick media with high-order nonlinearity by variational approach," Opt. Commun. 219, 411-419 (2003).
[CrossRef]

Lu, Z. Z.

C. L. Zhan, D. H. Li, D. Y. Wang, D. Q. Zhang, Y. J. Li, W. Xu, Z. Z. Lu, L. Z. Zhao, Y. X. Nie, and D. B. Zhu, "The high fifth-order nonlinearity in a new stilbazolium derivative: trans-1-[p-(p-dimethylaminobenzyl-azo)-benzyl]-2-(N-methyl-4-pyridinium)-ethene iodide," Chem. Phys. Lett. 347, 410-414 (2001).
[CrossRef]

Lundevall, C.

Marcano, A. O.

Nie, Y. X.

C. L. Zhan, D. H. Li, D. Y. Wang, D. Q. Zhang, Y. J. Li, W. Xu, Z. Z. Lu, L. Z. Zhao, Y. X. Nie, and D. B. Zhu, "The high fifth-order nonlinearity in a new stilbazolium derivative: trans-1-[p-(p-dimethylaminobenzyl-azo)-benzyl]-2-(N-methyl-4-pyridinium)-ethene iodide," Chem. Phys. Lett. 347, 410-414 (2001).
[CrossRef]

Oak, S. M.

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

Palffy-Muhoray, P.

W. Zhao and P. Palffy-Muhoray, "Z-scan measurement of chi(3) using top-hat beams," Appl. Phys. Lett. 65, 673-675 (1994).
[CrossRef]

W. Zhao and P. Palffy-Muhoray, "Z-scan technique using top-hat beams," Appl. Phys. Lett. 63, 1613-1615 (1993).
[CrossRef]

Pan, C. L.

S. M. Chen, R. P. Pan, and C. L. Pan, "Identification of third and fifth order self-phase modulation effects in laser-induced diffraction rings from a nematic liquid crystal film," Opt. Commun. 79, 469-472 (1990).
[CrossRef]

Pan, R. P.

S. M. Chen, R. P. Pan, and C. L. Pan, "Identification of third and fifth order self-phase modulation effects in laser-induced diffraction rings from a nematic liquid crystal film," Opt. Commun. 79, 469-472 (1990).
[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, 83-86 (2003).
[CrossRef]

G. Tsigaridas, M. Fakis, I. Polyzos, P. Persephonis, and V. Giannetas, "Z-scan analysis for high order nonlinearities through Gaussian decomposition," Opt. Commun. 225, 253-268 (2003).
[CrossRef]

G. Tsigaridas, M. Fakis, I. Polyzos, P. Persephonis, and V. Giannetas, "Z-scan technique for elliptic Gaussian beams," Appl. Phys. B 77, 71-75 (2003).
[CrossRef]

Polyzos, I.

G. Tsigaridas, M. Fakis, I. Polyzos, P. Persephonis, and V. Giannetas, "Z-scan technique for elliptic Gaussian beams," Appl. Phys. B 77, 71-75 (2003).
[CrossRef]

G. Tsigaridas, M. Fakis, I. Polyzos, P. Persephonis, and V. Giannetas, "Z-scan analysis for high order nonlinearities through Gaussian decomposition," Opt. Commun. 225, 253-268 (2003).
[CrossRef]

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

Rustagi, K. C.

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

Said, A. A.

Sena, A. D.

Sheik-Bahae, M.

Stegenman, G. I.

B. L. Lawrence, M. Cha, W. E. Torruellas, G. I. Stegenman, S. Etemad, G. Baker, and F. Kajzar, "Measurement of the complex nonlinear refractive index of single crystal p-toluene sulfonate at 1064 nm," Appl. Phys. Lett. 64, 2773-2775 (1994).
[CrossRef]

Tian, J. G.

Z. B. Liu, W. P. Zang, J. G. Tian, W. Y. Zhou, C. P. Zhang, and G. Y. Zhang, "Analysis of Z-scan of thick media with high-order nonlinearity by variational approach," Opt. Commun. 219, 411-419 (2003).
[CrossRef]

Torruellas, W. E.

B. L. Lawrence, M. Cha, W. E. Torruellas, G. I. Stegenman, S. Etemad, G. Baker, and F. Kajzar, "Measurement of the complex nonlinear refractive index of single crystal p-toluene sulfonate at 1064 nm," Appl. Phys. Lett. 64, 2773-2775 (1994).
[CrossRef]

Tsigaridas, G.

G. Tsigaridas, M. Fakis, I. Polyzos, P. Persephonis, and V. Giannetas, "Z-scan technique for elliptic Gaussian beams," Appl. Phys. B 77, 71-75 (2003).
[CrossRef]

G. Tsigaridas, M. Fakis, I. Polyzos, P. Persephonis, and V. Giannetas, "Z-scan analysis for high order nonlinearities through Gaussian decomposition," Opt. Commun. 225, 253-268 (2003).
[CrossRef]

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

Van der Meulen, P.

Van Stryland, E. W.

Wang, D. Y.

C. L. Zhan, D. H. Li, D. Y. Wang, D. Q. Zhang, Y. J. Li, W. Xu, Z. Z. Lu, L. Z. Zhao, Y. X. Nie, and D. B. Zhu, "The high fifth-order nonlinearity in a new stilbazolium derivative: trans-1-[p-(p-dimethylaminobenzyl-azo)-benzyl]-2-(N-methyl-4-pyridinium)-ethene iodide," Chem. Phys. Lett. 347, 410-414 (2001).
[CrossRef]

Wang, J.

Wei, T. H.

A. A. Said, M. Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. Van Stryland, "Determination of bound-electronic and free-carrier nonlinearities in ZnSe, GaAs, CdTe, and ZnTe," J. Opt. Soc. Am. B 9, 405-414 (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, 760-769 (1990).
[CrossRef]

Xia, T.

Xu, W.

C. L. Zhan, D. H. Li, D. Y. Wang, D. Q. Zhang, Y. J. Li, W. Xu, Z. Z. Lu, L. Z. Zhao, Y. X. Nie, and D. B. Zhu, "The high fifth-order nonlinearity in a new stilbazolium derivative: trans-1-[p-(p-dimethylaminobenzyl-azo)-benzyl]-2-(N-methyl-4-pyridinium)-ethene iodide," Chem. Phys. Lett. 347, 410-414 (2001).
[CrossRef]

Young, J.

Zang, W. P.

Z. B. Liu, W. P. Zang, J. G. Tian, W. Y. Zhou, C. P. Zhang, and G. Y. Zhang, "Analysis of Z-scan of thick media with high-order nonlinearity by variational approach," Opt. Commun. 219, 411-419 (2003).
[CrossRef]

Zhan, C. L.

C. L. Zhan, D. H. Li, D. Y. Wang, D. Q. Zhang, Y. J. Li, W. Xu, Z. Z. Lu, L. Z. Zhao, Y. X. Nie, and D. B. Zhu, "The high fifth-order nonlinearity in a new stilbazolium derivative: trans-1-[p-(p-dimethylaminobenzyl-azo)-benzyl]-2-(N-methyl-4-pyridinium)-ethene iodide," Chem. Phys. Lett. 347, 410-414 (2001).
[CrossRef]

Zhang, C. P.

Z. B. Liu, W. P. Zang, J. G. Tian, W. Y. Zhou, C. P. Zhang, and G. Y. Zhang, "Analysis of Z-scan of thick media with high-order nonlinearity by variational approach," Opt. Commun. 219, 411-419 (2003).
[CrossRef]

Zhang, D. Q.

C. L. Zhan, D. H. Li, D. Y. Wang, D. Q. Zhang, Y. J. Li, W. Xu, Z. Z. Lu, L. Z. Zhao, Y. X. Nie, and D. B. Zhu, "The high fifth-order nonlinearity in a new stilbazolium derivative: trans-1-[p-(p-dimethylaminobenzyl-azo)-benzyl]-2-(N-methyl-4-pyridinium)-ethene iodide," Chem. Phys. Lett. 347, 410-414 (2001).
[CrossRef]

Zhang, G. Y.

Z. B. Liu, W. P. Zang, J. G. Tian, W. Y. Zhou, C. P. Zhang, and G. Y. Zhang, "Analysis of Z-scan of thick media with high-order nonlinearity by variational approach," Opt. Commun. 219, 411-419 (2003).
[CrossRef]

Zhao, L. Z.

C. L. Zhan, D. H. Li, D. Y. Wang, D. Q. Zhang, Y. J. Li, W. Xu, Z. Z. Lu, L. Z. Zhao, Y. X. Nie, and D. B. Zhu, "The high fifth-order nonlinearity in a new stilbazolium derivative: trans-1-[p-(p-dimethylaminobenzyl-azo)-benzyl]-2-(N-methyl-4-pyridinium)-ethene iodide," Chem. Phys. Lett. 347, 410-414 (2001).
[CrossRef]

Zhao , W.

W. Zhao and P. Palffy-Muhoray, "Z-scan measurement of chi(3) using top-hat beams," Appl. Phys. Lett. 65, 673-675 (1994).
[CrossRef]

W. Zhao and P. Palffy-Muhoray, "Z-scan technique using top-hat beams," Appl. Phys. Lett. 63, 1613-1615 (1993).
[CrossRef]

Zhou, W. Y.

Z. B. Liu, W. P. Zang, J. G. Tian, W. Y. Zhou, C. P. Zhang, and G. Y. Zhang, "Analysis of Z-scan of thick media with high-order nonlinearity by variational approach," Opt. Commun. 219, 411-419 (2003).
[CrossRef]

Zhu, D. B.

C. L. Zhan, D. H. Li, D. Y. Wang, D. Q. Zhang, Y. J. Li, W. Xu, Z. Z. Lu, L. Z. Zhao, Y. X. Nie, and D. B. Zhu, "The high fifth-order nonlinearity in a new stilbazolium derivative: trans-1-[p-(p-dimethylaminobenzyl-azo)-benzyl]-2-(N-methyl-4-pyridinium)-ethene iodide," Chem. Phys. Lett. 347, 410-414 (2001).
[CrossRef]

Appl. Phys. B (2)

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

G. Tsigaridas, M. Fakis, I. Polyzos, P. Persephonis, and V. Giannetas, "Z-scan technique for elliptic Gaussian beams," Appl. Phys. B 77, 71-75 (2003).
[CrossRef]

Appl. Phys. Lett. (3)

W. Zhao and P. Palffy-Muhoray, "Z-scan technique using top-hat beams," Appl. Phys. Lett. 63, 1613-1615 (1993).
[CrossRef]

W. Zhao and P. Palffy-Muhoray, "Z-scan measurement of chi(3) using top-hat beams," Appl. Phys. Lett. 65, 673-675 (1994).
[CrossRef]

B. L. Lawrence, M. Cha, W. E. Torruellas, G. I. Stegenman, S. Etemad, G. Baker, and F. Kajzar, "Measurement of the complex nonlinear refractive index of single crystal p-toluene sulfonate at 1064 nm," Appl. Phys. Lett. 64, 2773-2775 (1994).
[CrossRef]

Chem. Phys. Lett. (1)

C. L. Zhan, D. H. Li, D. Y. Wang, D. Q. Zhang, Y. J. Li, W. Xu, Z. Z. Lu, L. Z. Zhao, Y. X. Nie, and D. B. Zhu, "The high fifth-order nonlinearity in a new stilbazolium derivative: trans-1-[p-(p-dimethylaminobenzyl-azo)-benzyl]-2-(N-methyl-4-pyridinium)-ethene iodide," Chem. Phys. Lett. 347, 410-414 (2001).
[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]

J. Mod. Opt. (1)

S. V. Kershaw, "Analysis of the EZ scan measurement technique," J. Mod. Opt. 42, L1361-L1366 (1995).
[CrossRef]

J. Opt. Soc. Am. B (2)

Opt. Commun. (4)

Z. B. Liu, W. P. Zang, J. G. Tian, W. Y. Zhou, C. P. Zhang, and G. Y. Zhang, "Analysis of Z-scan of thick media with high-order nonlinearity by variational approach," Opt. Commun. 219, 411-419 (2003).
[CrossRef]

S. M. Chen, R. P. Pan, and C. L. Pan, "Identification of third and fifth order self-phase modulation effects in laser-induced diffraction rings from a nematic liquid crystal film," Opt. Commun. 79, 469-472 (1990).
[CrossRef]

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

G. Tsigaridas, M. Fakis, I. Polyzos, P. Persephonis, and V. Giannetas, "Z-scan analysis for high order nonlinearities through Gaussian decomposition," Opt. Commun. 225, 253-268 (2003).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. A (1)

S. Hughes and J. M. Burzler, "Theory of Z-scan measurement using Gaussian-Bessel beams," Phys. Rev. A 56, R1103-R1106 (1997).
[CrossRef]

Other (1)

M. Born and E. Wolf, Principles of Optics , 6th ed. (Pergamon, Oxford, UK, 1980), Section 8.8.

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Figures (7)

Fig. 1
Fig. 1

Top-hat-beam Z-scan traces with S=0.007, and γ and γ (i.e., ϕ0 and ϕ0) have the same signs for |ϕ0|=0.2π. (a) The case of (ϕ0>0 and ϕ0>0) and (b) the case of (ϕ0<0 and ϕ0<0). The thick solid, the dashed, the dotted, the dashed–dotted, and the dashed–dotted–dotted curves represent the situations of |ϕ0|=0, 0.2π, 0.4π, 0.6π, and 0.8π, respectively.

Fig. 2
Fig. 2

Top-hat-beam Z-scan traces with S=0.007 when γ and γ (i.e., ϕ0 and ϕ0) have opposite signs. (a) The case of (ϕ0=0.2π and ϕ0<0) and (b) the case of (ϕ0=-0.2π and ϕ0>0). The thick solid, the dashed, the dashed–dotted, the dotted, and the thin solid curves correspond to the situations of |ϕ0|=0, 0.2π, 0.292π, 0.413π, and 0.9π, respectively.

Fig. 3
Fig. 3

Sensitivities TPV versus I0 for S=0.007 and γ=5.0×10-5 cm2/GW. Squares, triangles, and circles are the cases of γ=0, 5.0×10-6, and -5.0×10-6 cm4/GW, respectively.

Fig. 4
Fig. 4

Dependences of the nominal third-order nonlinear refraction coefficient γnom on I0 for different methods. (a) The case of the same signs of γ(=5.0×10-5 cm2/GW) and γ(=5.0×10-6 cm4/GW2), and (b) the case of opposite signs of γ(=5.0×10-5 cm2/GW) and γ(=-5.0×10-6 cm4/GW2). Squares, circles, and triangles are the results given by the theory, the common method, and our method, respectively.

Fig. 5
Fig. 5

Comparison of top-hat-beam Z-scan traces between without TPA (solid curves) and with TPA (dashed curves) for S=0.007. (a) γ and γ (i.e., ϕ0 and ϕ0) have the same signs (ϕ0=0.2π, ϕ0=0.4π, and ψ0=0.15π). (b) γ and γ (i.e., ϕ0 and ϕ0) have opposite signs (ϕ0=0.2π, ϕ0=-0.4π, and ψ0=0.15π).

Fig. 6
Fig. 6

Examples of the top-hat-beam Z-scan traces measured at different values of I0 in the DY7 thin film for S=0.22. Squares, circles, and triangles are the experimental data obtained by I0=0.56, 0.90, and 1.28 GW/cm2, respectively; the corresponding solid curves are their theoretical fittings.

Fig. 7
Fig. 7

Estimated values of γnom as a function of I0 in the DY7 thin film. Circles are the experimental results, and the solid line is the linear fitting by γnom=γ+γI0.

Equations (12)

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E(r, z)2J1(πr/ω0)πr/ω0exp(iπr2/λz)λz,
E(r, z=0)2J1(πr/ω0)πr/ω0.
Δn(I)=γI+γI2,
Ee(r, z)=E(r, z)exp[ikrLeffI(r, z)+ikγLeffI2(r, z)],
Ee(r, z)=E(r, z)exp[iϕ0I¯(r, z)+iϕ0I¯2(r, z)],
ϕ0=kLeffγI0,
ϕ0=kLeffγI02.
EA2(r, z)F{Ee(r, z)},
P(z)=2π0D/2IA2(r, z)rdr,
T(z)=P(z)/P().
ϕ0=2.7 tanh-1TPV2.8(1-S)1.14.
ϕ0=[1.35+1.97 cosh(3.6S)]tan{[0.5-0.05 sin(-7.6S)]TPV}.

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