Abstract

In this work we present a study of the far-field diffraction intensity patterns in the Rb atomic medium. It is found that the far-field diffraction intensity patterns are intimately related to the incident frequency, power, the atomic number density and the position of the sample. The results demonstrate that the far-field diffraction intensity patterns can sensitively reflect the nonlinear optical properties of the medium. The information obtained is of meaning in the application fields, such as the nonlinearity of the medium measuring, optical limiting.

© 2015 Optical Society of America

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References

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    [Crossref]
  9. F. Z. Henari and A. Al-Saie, “Nonlinear refractive index measurements and self-action effects in roselle-hibiscus sabdariffa solutions,” Laser Phys. 16(12), 1664–1667 (2006).
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  10. B. Hussain, M. Ahmed, M. Nawaz, and F. Gul, “Self-focusing in transformer oil with external electric field,” Laser Phys. 22(12), 1815–1818 (2012).
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  11. 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), 70 (1997).
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  12. R. Wu, Y. Zhang, S. Yan, F. Bian, W. Wang, X. Bai, X. Lu, J. Zhao, and E. Wang, “Purely coherent nonlinear optical response in solution dispersions of graphene sheets,” Nano Lett. 11(12), 5159–5164 (2011).
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
  22. Y. Zhang, C. Zuo, H. Zheng, C. Li, Z. Nie, J. Song, H. Chang, and M. Xiao, “Controlled spatial beam splitter using four-wave-mixing images,” Phys. Rev. A 80(5), 055804 (2009).
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    [Crossref]
  26. X. Cheng, Y. Du, Y. Zhang, Z. Wang, Y. Miao, Z. Ren, and J. Bai, “Polarization of four-wave mixing with electromagnetically induced transparency,” Opt. Commun. 285(21-22), 4507–4514 (2012).
    [Crossref]
  27. B. Yao, L. Ren, X. Hou, W. Yi, and M. Wang, “Diffraction behavior of polypyrrylarylenemethine/polyvinyl film to Gaussian beam,” Acta Opt. Sin. 21(9), 1142 (2001) (in Chinese).

2014 (2)

M. D. Zidan, A. W. Allaf, M. B. Alsous, and A. Allahham, “Investigation of optical nonlinearity and diffraction ring patterns of carbon nanotubes,” Opt. Laser Technol. 58, 128–134 (2014).
[Crossref]

M. D. Zidan, A. W. Allaf, M. B. Alsous, and A. Allahham, “Investigation of optical nonlinearity and diffraction ring patterns of carbon nanotubes,” Opt. Laser Technol. 58, 128–134 (2014).
[Crossref]

2013 (1)

J. Sahota and D. F. V. James, “Quantum-enhanced phase estimation with an amplified Bell state,” Phys. Rev. A 88(6), 063828 (2013).
[Crossref]

2012 (2)

B. Hussain, M. Ahmed, M. Nawaz, and F. Gul, “Self-focusing in transformer oil with external electric field,” Laser Phys. 22(12), 1815–1818 (2012).
[Crossref]

X. Cheng, Y. Du, Y. Zhang, Z. Wang, Y. Miao, Z. Ren, and J. Bai, “Polarization of four-wave mixing with electromagnetically induced transparency,” Opt. Commun. 285(21-22), 4507–4514 (2012).
[Crossref]

2011 (2)

Y. Zhang, Z. Wang, Z. Nie, C. Li, H. Chen, K. Lu, and M. Xiao, “Four-wave mixing dipole soliton in laser-induced atomic gratings,” Phys. Rev. Lett. 106(9), 093904 (2011).
[Crossref] [PubMed]

R. Wu, Y. Zhang, S. Yan, F. Bian, W. Wang, X. Bai, X. Lu, J. Zhao, and E. Wang, “Purely coherent nonlinear optical response in solution dispersions of graphene sheets,” Nano Lett. 11(12), 5159–5164 (2011).
[Crossref] [PubMed]

2010 (1)

2009 (4)

Y. Zhang, Z. Nie, H. Zheng, C. Li, J. Song, and M. Xiao, “Electromagnetically induced spatial nonlinear dispersion of four-wave mixing,” Phys. Rev. A 80(1), 013835 (2009).
[Crossref]

Y. Zhang, C. Zuo, H. Zheng, C. Li, Z. Nie, J. Song, H. Chang, and M. Xiao, “Controlled spatial beam splitter using four-wave-mixing images,” Phys. Rev. A 80(5), 055804 (2009).
[Crossref]

Y. Zhang, U. Khadka, B. Anderson, and M. Xiao, “Temporal and spatial interference between four-wave mixing and six-wave mixing channels,” Phys. Rev. Lett. 102(1), 013601 (2009).
[Crossref] [PubMed]

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]

2008 (1)

L. Guo, D. Wei, H. Chen, D. Xiong, P. Wang, and J. Zhang, “Experimental study on laser pattern formation by strong nonlinear effects in rubidium atomic hot vapor,” Chin. Phys. Soc. 57(7), 4227 (2008) (in Chinese).

2006 (1)

F. Z. Henari and A. Al-Saie, “Nonlinear refractive index measurements and self-action effects in roselle-hibiscus sabdariffa solutions,” Laser Phys. 16(12), 1664–1667 (2006).
[Crossref]

2002 (1)

R. S. Bennink, V. Wong, A. M. Marino, D. L. Aronstein, R. W. Boyd, C. R. Stroud, S. Lukishova, and D. J. Gauthier, “Honeycomb pattern formation by laser-beam filamentation in atomic sodium vapor,” Phys. Rev. Lett. 88(11), 113901 (2002).
[Crossref] [PubMed]

2001 (1)

B. Yao, L. Ren, X. Hou, W. Yi, and M. Wang, “Diffraction behavior of polypyrrylarylenemethine/polyvinyl film to Gaussian beam,” Acta Opt. Sin. 21(9), 1142 (2001) (in Chinese).

1997 (2)

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]

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), 70 (1997).
[Crossref]

1990 (2)

1986 (1)

1984 (1)

1981 (1)

1972 (1)

D. Grischkowsky and J. A. Armstrong, “Self-defocusing of light by adiabatic following in rubidium vapor,” Phys. Rev. A 6(4), 1566 (1972).
[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 (1967).
[Crossref]

Ahmed, M.

B. Hussain, M. Ahmed, M. Nawaz, and F. Gul, “Self-focusing in transformer oil with external electric field,” Laser Phys. 22(12), 1815–1818 (2012).
[Crossref]

Allaf, A. W.

M. D. Zidan, A. W. Allaf, M. B. Alsous, and A. Allahham, “Investigation of optical nonlinearity and diffraction ring patterns of carbon nanotubes,” Opt. Laser Technol. 58, 128–134 (2014).
[Crossref]

M. D. Zidan, A. W. Allaf, M. B. Alsous, and A. Allahham, “Investigation of optical nonlinearity and diffraction ring patterns of carbon nanotubes,” Opt. Laser Technol. 58, 128–134 (2014).
[Crossref]

Allahham, A.

M. D. Zidan, A. W. Allaf, M. B. Alsous, and A. Allahham, “Investigation of optical nonlinearity and diffraction ring patterns of carbon nanotubes,” Opt. Laser Technol. 58, 128–134 (2014).
[Crossref]

M. D. Zidan, A. W. Allaf, M. B. Alsous, and A. Allahham, “Investigation of optical nonlinearity and diffraction ring patterns of carbon nanotubes,” Opt. Laser Technol. 58, 128–134 (2014).
[Crossref]

Al-Saie, A.

F. Z. Henari and A. Al-Saie, “Nonlinear refractive index measurements and self-action effects in roselle-hibiscus sabdariffa solutions,” Laser Phys. 16(12), 1664–1667 (2006).
[Crossref]

Alsous, M. B.

M. D. Zidan, A. W. Allaf, M. B. Alsous, and A. Allahham, “Investigation of optical nonlinearity and diffraction ring patterns of carbon nanotubes,” Opt. Laser Technol. 58, 128–134 (2014).
[Crossref]

M. D. Zidan, A. W. Allaf, M. B. Alsous, and A. Allahham, “Investigation of optical nonlinearity and diffraction ring patterns of carbon nanotubes,” Opt. Laser Technol. 58, 128–134 (2014).
[Crossref]

Anderson, B.

Y. Zhang, U. Khadka, B. Anderson, and M. Xiao, “Temporal and spatial interference between four-wave mixing and six-wave mixing channels,” Phys. Rev. Lett. 102(1), 013601 (2009).
[Crossref] [PubMed]

Arakelian, S. M.

Armstrong, J. A.

D. Grischkowsky and J. A. Armstrong, “Self-defocusing of light by adiabatic following in rubidium vapor,” Phys. Rev. A 6(4), 1566 (1972).
[Crossref]

Aronstein, D. L.

R. S. Bennink, V. Wong, A. M. Marino, D. L. Aronstein, R. W. Boyd, C. R. Stroud, S. Lukishova, and D. J. Gauthier, “Honeycomb pattern formation by laser-beam filamentation in atomic sodium vapor,” Phys. Rev. Lett. 88(11), 113901 (2002).
[Crossref] [PubMed]

Bai, J.

X. Cheng, Y. Du, Y. Zhang, Z. Wang, Y. Miao, Z. Ren, and J. Bai, “Polarization of four-wave mixing with electromagnetically induced transparency,” Opt. Commun. 285(21-22), 4507–4514 (2012).
[Crossref]

Bai, X.

R. Wu, Y. Zhang, S. Yan, F. Bian, W. Wang, X. Bai, X. Lu, J. Zhao, and E. Wang, “Purely coherent nonlinear optical response in solution dispersions of graphene sheets,” Nano Lett. 11(12), 5159–5164 (2011).
[Crossref] [PubMed]

Bennink, R. S.

R. S. Bennink, V. Wong, A. M. Marino, D. L. Aronstein, R. W. Boyd, C. R. Stroud, S. Lukishova, and D. J. Gauthier, “Honeycomb pattern formation by laser-beam filamentation in atomic sodium vapor,” Phys. Rev. Lett. 88(11), 113901 (2002).
[Crossref] [PubMed]

Bian, F.

R. Wu, Y. Zhang, S. Yan, F. Bian, W. Wang, X. Bai, X. Lu, J. Zhao, and E. Wang, “Purely coherent nonlinear optical response in solution dispersions of graphene sheets,” Nano Lett. 11(12), 5159–5164 (2011).
[Crossref] [PubMed]

Boyd, R. W.

R. S. Bennink, V. Wong, A. M. Marino, D. L. Aronstein, R. W. Boyd, C. R. Stroud, S. Lukishova, and D. J. Gauthier, “Honeycomb pattern formation by laser-beam filamentation in atomic sodium vapor,” Phys. Rev. Lett. 88(11), 113901 (2002).
[Crossref] [PubMed]

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 (1967).
[Crossref]

Carrasco, M. L.

Castillo, M. D.

Cerda, S. C.

Chang, H.

Y. Zhang, C. Zuo, H. Zheng, C. Li, Z. Nie, J. Song, H. Chang, and M. Xiao, “Controlled spatial beam splitter using four-wave-mixing images,” Phys. Rev. A 80(5), 055804 (2009).
[Crossref]

Chen, H.

Y. Zhang, Z. Wang, Z. Nie, C. Li, H. Chen, K. Lu, and M. Xiao, “Four-wave mixing dipole soliton in laser-induced atomic gratings,” Phys. Rev. Lett. 106(9), 093904 (2011).
[Crossref] [PubMed]

L. Guo, D. Wei, H. Chen, D. Xiong, P. Wang, and J. Zhang, “Experimental study on laser pattern formation by strong nonlinear effects in rubidium atomic hot vapor,” Chin. Phys. Soc. 57(7), 4227 (2008) (in Chinese).

Cheng, X.

X. Cheng, Y. Du, Y. Zhang, Z. Wang, Y. Miao, Z. Ren, and J. Bai, “Polarization of four-wave mixing with electromagnetically induced transparency,” Opt. Commun. 285(21-22), 4507–4514 (2012).
[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]

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), 70 (1997).
[Crossref]

Du, Y.

X. Cheng, Y. Du, Y. Zhang, Z. Wang, Y. Miao, Z. Ren, and J. Bai, “Polarization of four-wave mixing with electromagnetically induced transparency,” Opt. Commun. 285(21-22), 4507–4514 (2012).
[Crossref]

Durbin, S. D.

Fattinger, C.

Finn, G. M.

Fischer, B.

M. Segev, Y. Ophir, and B. Fischer, “Photorefractive self-defocusing,” Appl. Phys. Lett. 56(12), 1086 (1990).
[Crossref]

Gauthier, D. J.

R. S. Bennink, V. Wong, A. M. Marino, D. L. Aronstein, R. W. Boyd, C. R. Stroud, S. Lukishova, and D. J. Gauthier, “Honeycomb pattern formation by laser-beam filamentation in atomic sodium vapor,” Phys. Rev. Lett. 88(11), 113901 (2002).
[Crossref] [PubMed]

Grischkowsky, D.

Gul, F.

B. Hussain, M. Ahmed, M. Nawaz, and F. Gul, “Self-focusing in transformer oil with external electric field,” Laser Phys. 22(12), 1815–1818 (2012).
[Crossref]

Guo, L.

L. Guo, D. Wei, H. Chen, D. Xiong, P. Wang, and J. Zhang, “Experimental study on laser pattern formation by strong nonlinear effects in rubidium atomic hot vapor,” Chin. Phys. Soc. 57(7), 4227 (2008) (in Chinese).

Harrison, R. G.

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), 70 (1997).
[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]

Henari, F. Z.

F. Z. Henari and A. Al-Saie, “Nonlinear refractive index measurements and self-action effects in roselle-hibiscus sabdariffa solutions,” Laser Phys. 16(12), 1664–1667 (2006).
[Crossref]

Hou, X.

B. Yao, L. Ren, X. Hou, W. Yi, and M. Wang, “Diffraction behavior of polypyrrylarylenemethine/polyvinyl film to Gaussian beam,” Acta Opt. Sin. 21(9), 1142 (2001) (in Chinese).

Hussain, B.

B. Hussain, M. Ahmed, M. Nawaz, and F. Gul, “Self-focusing in transformer oil with external electric field,” Laser Phys. 22(12), 1815–1818 (2012).
[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 (1967).
[Crossref]

James, D. F. V.

J. Sahota and D. F. V. James, “Quantum-enhanced phase estimation with an amplified Bell state,” Phys. Rev. A 88(6), 063828 (2013).
[Crossref]

Keiding, S.

Khadka, U.

Y. Zhang, U. Khadka, B. Anderson, and M. Xiao, “Temporal and spatial interference between four-wave mixing and six-wave mixing channels,” Phys. Rev. Lett. 102(1), 013601 (2009).
[Crossref] [PubMed]

Khoo, I. C.

Li, C.

Y. Zhang, Z. Wang, Z. Nie, C. Li, H. Chen, K. Lu, and M. Xiao, “Four-wave mixing dipole soliton in laser-induced atomic gratings,” Phys. Rev. Lett. 106(9), 093904 (2011).
[Crossref] [PubMed]

Y. Zhang, Z. Nie, H. Zheng, C. Li, J. Song, and M. Xiao, “Electromagnetically induced spatial nonlinear dispersion of four-wave mixing,” Phys. Rev. A 80(1), 013835 (2009).
[Crossref]

Y. Zhang, C. Zuo, H. Zheng, C. Li, Z. Nie, J. Song, H. Chang, and M. Xiao, “Controlled spatial beam splitter using four-wave-mixing images,” Phys. Rev. A 80(5), 055804 (2009).
[Crossref]

Liu, T. H.

Lu, K.

Y. Zhang, Z. Wang, Z. Nie, C. Li, H. Chen, K. Lu, and M. Xiao, “Four-wave mixing dipole soliton in laser-induced atomic gratings,” Phys. Rev. Lett. 106(9), 093904 (2011).
[Crossref] [PubMed]

Lu, W.

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), 70 (1997).
[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]

Lu, X.

R. Wu, Y. Zhang, S. Yan, F. Bian, W. Wang, X. Bai, X. Lu, J. Zhao, and E. Wang, “Purely coherent nonlinear optical response in solution dispersions of graphene sheets,” Nano Lett. 11(12), 5159–5164 (2011).
[Crossref] [PubMed]

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]

Lukishova, S.

R. S. Bennink, V. Wong, A. M. Marino, D. L. Aronstein, R. W. Boyd, C. R. Stroud, S. Lukishova, and D. J. Gauthier, “Honeycomb pattern formation by laser-beam filamentation in atomic sodium vapor,” Phys. Rev. Lett. 88(11), 113901 (2002).
[Crossref] [PubMed]

Marino, A. M.

R. S. Bennink, V. Wong, A. M. Marino, D. L. Aronstein, R. W. Boyd, C. R. Stroud, S. Lukishova, and D. J. Gauthier, “Honeycomb pattern formation by laser-beam filamentation in atomic sodium vapor,” Phys. Rev. Lett. 88(11), 113901 (2002).
[Crossref] [PubMed]

Miao, Y.

X. Cheng, Y. Du, Y. Zhang, Z. Wang, Y. Miao, Z. Ren, and J. Bai, “Polarization of four-wave mixing with electromagnetically induced transparency,” Opt. Commun. 285(21-22), 4507–4514 (2012).
[Crossref]

Michael, R. R.

Nawaz, M.

B. Hussain, M. Ahmed, M. Nawaz, and F. Gul, “Self-focusing in transformer oil with external electric field,” Laser Phys. 22(12), 1815–1818 (2012).
[Crossref]

Nie, Z.

Y. Zhang, Z. Wang, Z. Nie, C. Li, H. Chen, K. Lu, and M. Xiao, “Four-wave mixing dipole soliton in laser-induced atomic gratings,” Phys. Rev. Lett. 106(9), 093904 (2011).
[Crossref] [PubMed]

Y. Zhang, Z. Nie, H. Zheng, C. Li, J. Song, and M. Xiao, “Electromagnetically induced spatial nonlinear dispersion of four-wave mixing,” Phys. Rev. A 80(1), 013835 (2009).
[Crossref]

Y. Zhang, C. Zuo, H. Zheng, C. Li, Z. Nie, J. Song, H. Chang, and M. Xiao, “Controlled spatial beam splitter using four-wave-mixing images,” Phys. Rev. A 80(5), 055804 (2009).
[Crossref]

Ophir, Y.

M. Segev, Y. Ophir, and B. Fischer, “Photorefractive self-defocusing,” Appl. Phys. Lett. 56(12), 1086 (1990).
[Crossref]

Otero, M. M.

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 (1967).
[Crossref]

Ramirez, E. V.

Ren, L.

B. Yao, L. Ren, X. Hou, W. Yi, and M. Wang, “Diffraction behavior of polypyrrylarylenemethine/polyvinyl film to Gaussian beam,” Acta Opt. Sin. 21(9), 1142 (2001) (in Chinese).

Ren, Z.

X. Cheng, Y. Du, Y. Zhang, Z. Wang, Y. Miao, Z. Ren, and J. Bai, “Polarization of four-wave mixing with electromagnetically induced transparency,” Opt. Commun. 285(21-22), 4507–4514 (2012).
[Crossref]

Sahota, J.

J. Sahota and D. F. V. James, “Quantum-enhanced phase estimation with an amplified Bell state,” Phys. Rev. A 88(6), 063828 (2013).
[Crossref]

Santamato, E.

Segev, M.

M. Segev, Y. Ophir, and B. Fischer, “Photorefractive self-defocusing,” Appl. Phys. Lett. 56(12), 1086 (1990).
[Crossref]

Shen, Y. R.

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]

Song, J.

Y. Zhang, Z. Nie, H. Zheng, C. Li, J. Song, and M. Xiao, “Electromagnetically induced spatial nonlinear dispersion of four-wave mixing,” Phys. Rev. A 80(1), 013835 (2009).
[Crossref]

Y. Zhang, C. Zuo, H. Zheng, C. Li, Z. Nie, J. Song, H. Chang, and M. Xiao, “Controlled spatial beam splitter using four-wave-mixing images,” Phys. Rev. A 80(5), 055804 (2009).
[Crossref]

Stroud, C. R.

R. S. Bennink, V. Wong, A. M. Marino, D. L. Aronstein, R. W. Boyd, C. R. Stroud, S. Lukishova, and D. J. Gauthier, “Honeycomb pattern formation by laser-beam filamentation in atomic sodium vapor,” Phys. Rev. Lett. 88(11), 113901 (2002).
[Crossref] [PubMed]

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]

van Exter, M.

Wang, E.

R. Wu, Y. Zhang, S. Yan, F. Bian, W. Wang, X. Bai, X. Lu, J. Zhao, and E. Wang, “Purely coherent nonlinear optical response in solution dispersions of graphene sheets,” Nano Lett. 11(12), 5159–5164 (2011).
[Crossref] [PubMed]

Wang, M.

B. Yao, L. Ren, X. Hou, W. Yi, and M. Wang, “Diffraction behavior of polypyrrylarylenemethine/polyvinyl film to Gaussian beam,” Acta Opt. Sin. 21(9), 1142 (2001) (in Chinese).

Wang, P.

L. Guo, D. Wei, H. Chen, D. Xiong, P. Wang, and J. Zhang, “Experimental study on laser pattern formation by strong nonlinear effects in rubidium atomic hot vapor,” Chin. Phys. Soc. 57(7), 4227 (2008) (in Chinese).

Wang, W.

R. Wu, Y. Zhang, S. Yan, F. Bian, W. Wang, X. Bai, X. Lu, J. Zhao, and E. Wang, “Purely coherent nonlinear optical response in solution dispersions of graphene sheets,” Nano Lett. 11(12), 5159–5164 (2011).
[Crossref] [PubMed]

Wang, Z.

X. Cheng, Y. Du, Y. Zhang, Z. Wang, Y. Miao, Z. Ren, and J. Bai, “Polarization of four-wave mixing with electromagnetically induced transparency,” Opt. Commun. 285(21-22), 4507–4514 (2012).
[Crossref]

Y. Zhang, Z. Wang, Z. Nie, C. Li, H. Chen, K. Lu, and M. Xiao, “Four-wave mixing dipole soliton in laser-induced atomic gratings,” Phys. Rev. Lett. 106(9), 093904 (2011).
[Crossref] [PubMed]

Wei, D.

L. Guo, D. Wei, H. Chen, D. Xiong, P. Wang, and J. Zhang, “Experimental study on laser pattern formation by strong nonlinear effects in rubidium atomic hot vapor,” Chin. Phys. Soc. 57(7), 4227 (2008) (in Chinese).

Wong, V.

R. S. Bennink, V. Wong, A. M. Marino, D. L. Aronstein, R. W. Boyd, C. R. Stroud, S. Lukishova, and D. J. Gauthier, “Honeycomb pattern formation by laser-beam filamentation in atomic sodium vapor,” Phys. Rev. Lett. 88(11), 113901 (2002).
[Crossref] [PubMed]

Wu, R.

R. Wu, Y. Zhang, S. Yan, F. Bian, W. Wang, X. Bai, X. Lu, J. Zhao, and E. Wang, “Purely coherent nonlinear optical response in solution dispersions of graphene sheets,” Nano Lett. 11(12), 5159–5164 (2011).
[Crossref] [PubMed]

Xiao, M.

Y. Zhang, Z. Wang, Z. Nie, C. Li, H. Chen, K. Lu, and M. Xiao, “Four-wave mixing dipole soliton in laser-induced atomic gratings,” Phys. Rev. Lett. 106(9), 093904 (2011).
[Crossref] [PubMed]

Y. Zhang, U. Khadka, B. Anderson, and M. Xiao, “Temporal and spatial interference between four-wave mixing and six-wave mixing channels,” Phys. Rev. Lett. 102(1), 013601 (2009).
[Crossref] [PubMed]

Y. Zhang, Z. Nie, H. Zheng, C. Li, J. Song, and M. Xiao, “Electromagnetically induced spatial nonlinear dispersion of four-wave mixing,” Phys. Rev. A 80(1), 013835 (2009).
[Crossref]

Y. Zhang, C. Zuo, H. Zheng, C. Li, Z. Nie, J. Song, H. Chang, and M. Xiao, “Controlled spatial beam splitter using four-wave-mixing images,” Phys. Rev. A 80(5), 055804 (2009).
[Crossref]

Xiong, D.

L. Guo, D. Wei, H. Chen, D. Xiong, P. Wang, and J. Zhang, “Experimental study on laser pattern formation by strong nonlinear effects in rubidium atomic hot vapor,” Chin. Phys. Soc. 57(7), 4227 (2008) (in Chinese).

Yan, S.

R. Wu, Y. Zhang, S. Yan, F. Bian, W. Wang, X. Bai, X. Lu, J. Zhao, and E. Wang, “Purely coherent nonlinear optical response in solution dispersions of graphene sheets,” Nano Lett. 11(12), 5159–5164 (2011).
[Crossref] [PubMed]

Yao, B.

B. Yao, L. Ren, X. Hou, W. Yi, and M. Wang, “Diffraction behavior of polypyrrylarylenemethine/polyvinyl film to Gaussian beam,” Acta Opt. Sin. 21(9), 1142 (2001) (in Chinese).

Yi, W.

B. Yao, L. Ren, X. Hou, W. Yi, and M. Wang, “Diffraction behavior of polypyrrylarylenemethine/polyvinyl film to Gaussian beam,” Acta Opt. Sin. 21(9), 1142 (2001) (in Chinese).

Yu, D.

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]

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), 70 (1997).
[Crossref]

Zhang, J.

L. Guo, D. Wei, H. Chen, D. Xiong, P. Wang, and J. Zhang, “Experimental study on laser pattern formation by strong nonlinear effects in rubidium atomic hot vapor,” Chin. Phys. Soc. 57(7), 4227 (2008) (in Chinese).

Zhang, Y.

X. Cheng, Y. Du, Y. Zhang, Z. Wang, Y. Miao, Z. Ren, and J. Bai, “Polarization of four-wave mixing with electromagnetically induced transparency,” Opt. Commun. 285(21-22), 4507–4514 (2012).
[Crossref]

Y. Zhang, Z. Wang, Z. Nie, C. Li, H. Chen, K. Lu, and M. Xiao, “Four-wave mixing dipole soliton in laser-induced atomic gratings,” Phys. Rev. Lett. 106(9), 093904 (2011).
[Crossref] [PubMed]

R. Wu, Y. Zhang, S. Yan, F. Bian, W. Wang, X. Bai, X. Lu, J. Zhao, and E. Wang, “Purely coherent nonlinear optical response in solution dispersions of graphene sheets,” Nano Lett. 11(12), 5159–5164 (2011).
[Crossref] [PubMed]

Y. Zhang, U. Khadka, B. Anderson, and M. Xiao, “Temporal and spatial interference between four-wave mixing and six-wave mixing channels,” Phys. Rev. Lett. 102(1), 013601 (2009).
[Crossref] [PubMed]

Y. Zhang, Z. Nie, H. Zheng, C. Li, J. Song, and M. Xiao, “Electromagnetically induced spatial nonlinear dispersion of four-wave mixing,” Phys. Rev. A 80(1), 013835 (2009).
[Crossref]

Y. Zhang, C. Zuo, H. Zheng, C. Li, Z. Nie, J. Song, H. Chang, and M. Xiao, “Controlled spatial beam splitter using four-wave-mixing images,” Phys. Rev. A 80(5), 055804 (2009).
[Crossref]

Zhao, J.

R. Wu, Y. Zhang, S. Yan, F. Bian, W. Wang, X. Bai, X. Lu, J. Zhao, and E. Wang, “Purely coherent nonlinear optical response in solution dispersions of graphene sheets,” Nano Lett. 11(12), 5159–5164 (2011).
[Crossref] [PubMed]

Zheng, H.

Y. Zhang, Z. Nie, H. Zheng, C. Li, J. Song, and M. Xiao, “Electromagnetically induced spatial nonlinear dispersion of four-wave mixing,” Phys. Rev. A 80(1), 013835 (2009).
[Crossref]

Y. Zhang, C. Zuo, H. Zheng, C. Li, Z. Nie, J. Song, H. Chang, and M. Xiao, “Controlled spatial beam splitter using four-wave-mixing images,” Phys. Rev. A 80(5), 055804 (2009).
[Crossref]

Zidan, M. D.

M. D. Zidan, A. W. Allaf, M. B. Alsous, and A. Allahham, “Investigation of optical nonlinearity and diffraction ring patterns of carbon nanotubes,” Opt. Laser Technol. 58, 128–134 (2014).
[Crossref]

M. D. Zidan, A. W. Allaf, M. B. Alsous, and A. Allahham, “Investigation of optical nonlinearity and diffraction ring patterns of carbon nanotubes,” Opt. Laser Technol. 58, 128–134 (2014).
[Crossref]

Zuo, C.

Y. Zhang, C. Zuo, H. Zheng, C. Li, Z. Nie, J. Song, H. Chang, and M. Xiao, “Controlled spatial beam splitter using four-wave-mixing images,” Phys. Rev. A 80(5), 055804 (2009).
[Crossref]

Acta Opt. Sin. (1)

B. Yao, L. Ren, X. Hou, W. Yi, and M. Wang, “Diffraction behavior of polypyrrylarylenemethine/polyvinyl film to Gaussian beam,” Acta Opt. Sin. 21(9), 1142 (2001) (in Chinese).

Appl. Phys. Lett. (2)

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

M. Segev, Y. Ophir, and B. Fischer, “Photorefractive self-defocusing,” Appl. Phys. Lett. 56(12), 1086 (1990).
[Crossref]

Chin. Phys. Soc. (1)

L. Guo, D. Wei, H. Chen, D. Xiong, P. Wang, and J. Zhang, “Experimental study on laser pattern formation by strong nonlinear effects in rubidium atomic hot vapor,” Chin. Phys. Soc. 57(7), 4227 (2008) (in Chinese).

J. Opt. A, Pure Appl. Opt. (1)

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

J. Opt. Soc. Am. B (1)

Laser Phys. (2)

F. Z. Henari and A. Al-Saie, “Nonlinear refractive index measurements and self-action effects in roselle-hibiscus sabdariffa solutions,” Laser Phys. 16(12), 1664–1667 (2006).
[Crossref]

B. Hussain, M. Ahmed, M. Nawaz, and F. Gul, “Self-focusing in transformer oil with external electric field,” Laser Phys. 22(12), 1815–1818 (2012).
[Crossref]

Nano Lett. (1)

R. Wu, Y. Zhang, S. Yan, F. Bian, W. Wang, X. Bai, X. Lu, J. Zhao, and E. Wang, “Purely coherent nonlinear optical response in solution dispersions of graphene sheets,” Nano Lett. 11(12), 5159–5164 (2011).
[Crossref] [PubMed]

Opt. Commun. (3)

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), 70 (1997).
[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]

X. Cheng, Y. Du, Y. Zhang, Z. Wang, Y. Miao, Z. Ren, and J. Bai, “Polarization of four-wave mixing with electromagnetically induced transparency,” Opt. Commun. 285(21-22), 4507–4514 (2012).
[Crossref]

Opt. Express (1)

Opt. Laser Technol. (2)

M. D. Zidan, A. W. Allaf, M. B. Alsous, and A. Allahham, “Investigation of optical nonlinearity and diffraction ring patterns of carbon nanotubes,” Opt. Laser Technol. 58, 128–134 (2014).
[Crossref]

M. D. Zidan, A. W. Allaf, M. B. Alsous, and A. Allahham, “Investigation of optical nonlinearity and diffraction ring patterns of carbon nanotubes,” Opt. Laser Technol. 58, 128–134 (2014).
[Crossref]

Opt. Lett. (3)

Phys. Rev. A (4)

D. Grischkowsky and J. A. Armstrong, “Self-defocusing of light by adiabatic following in rubidium vapor,” Phys. Rev. A 6(4), 1566 (1972).
[Crossref]

J. Sahota and D. F. V. James, “Quantum-enhanced phase estimation with an amplified Bell state,” Phys. Rev. A 88(6), 063828 (2013).
[Crossref]

Y. Zhang, Z. Nie, H. Zheng, C. Li, J. Song, and M. Xiao, “Electromagnetically induced spatial nonlinear dispersion of four-wave mixing,” Phys. Rev. A 80(1), 013835 (2009).
[Crossref]

Y. Zhang, C. Zuo, H. Zheng, C. Li, Z. Nie, J. Song, H. Chang, and M. Xiao, “Controlled spatial beam splitter using four-wave-mixing images,” Phys. Rev. A 80(5), 055804 (2009).
[Crossref]

Phys. Rev. Lett. (3)

Y. Zhang, Z. Wang, Z. Nie, C. Li, H. Chen, K. Lu, and M. Xiao, “Four-wave mixing dipole soliton in laser-induced atomic gratings,” Phys. Rev. Lett. 106(9), 093904 (2011).
[Crossref] [PubMed]

Y. Zhang, U. Khadka, B. Anderson, and M. Xiao, “Temporal and spatial interference between four-wave mixing and six-wave mixing channels,” Phys. Rev. Lett. 102(1), 013601 (2009).
[Crossref] [PubMed]

R. S. Bennink, V. Wong, A. M. Marino, D. L. Aronstein, R. W. Boyd, C. R. Stroud, S. Lukishova, and D. J. Gauthier, “Honeycomb pattern formation by laser-beam filamentation in atomic sodium vapor,” Phys. Rev. Lett. 88(11), 113901 (2002).
[Crossref] [PubMed]

Other (2)

R. W. Boyd, Nonlinear Optics (Academic, 2003).

M. Born and E. Wolf, Principles of Optics (Pergamon, 1980).

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Figures (6)

Fig. 1
Fig. 1 (a) Scheme of the key part of the experimental setup. (b) (Experiment) and (c) (Simulation) The absorption spectrum of Rb D2 and the corresponding diffraction patterns.
Fig. 2
Fig. 2 (a) The experimental graphs of the far-field diffraction ring patterns with three different incident power. (b) The simulation graphs of x-y plane diffraction patterns and the radial direction normalized intensity with three different incident power.
Fig. 3
Fig. 3 (a) The experimental graphs of the far-field diffraction ring patterns with the cell temperature at 90 ° C , 100 ° C and 105 ° C respectively. (b) The simulation graphs of x-y plane diffraction patterns and the radial direction normalized intensity with the cell temperature at 90 ° C , 100 ° C and 105 ° C respectively.
Fig. 4
Fig. 4 The experimental and simulation graphs of the far-field diffraction ring patterns with the front side to the sample cell set at the positions of f-240 and f, where f, is the focusing length of the lens.
Fig. 5
Fig. 5 The real part of the third-order nonlinear susceptibility χ (3) versus Δ T 2 .
Fig. 6
Fig. 6 The simulations of the far-field diffraction intensity patterns for (a) Δφ(0)=π , (b) R( z 0 ) , and (c) Δφ(0)=3π .

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

a: R 87 b|5 S 1/2 ,F=1>|5 P 3/2 >780.2006nm b: R 85 b|5 S 1/2 ,F=2>|5 P 3/2 >780.2055nm c: R 85 b|5 S 1/2 ,F=3>|5 P 3/2 >780.2114nm d: R 87 b|5 S 1/2 ,F=2>|5 P 3/2 >780.2138nm
n 2 = 12 π 2 n 0 2 c Re χ (3) = 12 π 2 n 0 2 c ×(- 4 3 N ( ρ bb - ρ aa ) eq | μ ba | 4 T 1 T 2 2 ε 0 3 Δ T 2 (1+ Δ 2 T 2 2 ) 2 )
Δϕ(r)=k z 0 z 0 +L Δn(r,z)dz =k z 0 z 0 +L n 2 I(r,z)dz
Δϕ(r)=k z 0 z 0 +L n 2 I(0,0) r 0 2 r p 2 (z) exp(α(z- z 0 ))exp(2 r 2 / r p 2 (z)) dz
I= | 1 iλD | 2 | 0 0 2π E(r, z 0 +L)exp(ikrθcosϕ)exp[i( k r 2 2R( z 0 ) +Δϕ(r)]rdrdϕ | 2

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