Abstract

The interaction of intense laser with matter gives rise to a variety of novel nonlinear optical effects, reflects the nonlinear optical property of a material, and modulates the light propagation behavior. Herein, we investigate anisotropic Kerr nonlinearities induced by both scalar and vectorial optical fields. Firstly, we present the anisotropic third-order nonlinear refraction indexes related to left-hand and right-hand components, which depend on the ellipticity, the dichroism coefficient, the anisotropy coefficient, as well as the crystal orientation angle. Secondly, we develop the elliptically polarized light Z-scan technique for characterizing third-order nonlinear susceptibility tensor in anisotropic nonlinear Kerr media, which is demonstrated experimentally. Lastly, with the known nonlinear optical parameters, we numerically study both the vectorial self-diffraction behaviors and spin angular momentum (SAM) characteristics of hybridly polarized beams induced by an anisotropic Kerr nonlinearity. It is shown that the anisotropic Kerr nonlinearity offers a new approach to manipulate the polarization-structured light field, which has potential applications in SAM manipulation, three-dimensional crystal orientation, and polarization-sensitive detection and sensing.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref] [PubMed]
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2018 (3)

T. Yang, I. Abdelwahab, H. Lin, Y. Bao, S. J. Rong Tan, S. Fraser, K. P. Loh, and B. Jia, “Anisotropic third-order nonlinearity in pristine and lithium hydride intercalated black phosphorus,” ACS Photonics 5(12), 4969–4977 (2018).
[Crossref]

Y. Xue, Y. Wan, and B. Gu, “Femtosecond-pulsed Z-scan study on third- and fifth-order refractive nonlinearities in a side-chain azobenzene copolymer film,” J. Nonlinear Opt. Phys. Mater. 27(01), 1850007 (2018).
[Crossref]

D. Wang, G. G. Liu, J. Q. Lü, P. P. Li, M. Q. Cai, G. L. Zhang, Y. Li, C. Tu, and H. T. Wang, “Femtosecond polarization-structured optical field meets an anisotropic nonlinear medium,” Opt. Express 26(21), 27726–27747 (2018).
[Crossref] [PubMed]

2017 (1)

2016 (4)

B. Gu, B. Wen, G. Rui, Y. Xue, Q. Zhan, and Y. Cui, “Varying polarization and spin angular momentum flux of radially polarized beams by anisotropic Kerr media,” Opt. Lett. 41(7), 1566–1569 (2016).
[Crossref] [PubMed]

B. Gu, B. Wen, G. Rui, Y. Xue, J. He, Q. Zhan, and Y. Cui, “Nonlinear polarization evolution of hybridly polarized vector beams through isotropic Kerr nonlinearities,” Opt. Express 24(22), 25867–25875 (2016).
[Crossref] [PubMed]

F. Bouchard, H. Larocque, A. M. Yao, C. Travis, I. De Leon, A. Rubano, E. Karimi, G. L. Oppo, and R. W. Boyd, “Polarization shaping for control of nonlinear propagation,” Phys. Rev. Lett. 117(23), 233903 (2016).
[Crossref] [PubMed]

B. Gu, C. Zhao, A. Baev, K. T. Yong, S. Wen, and P. N. Prasad, “Molecular nonlinear optics: recent advances and applications,” Adv. Opt. Photonics 8(2), 328–369 (2016).
[Crossref]

2015 (1)

Y. Fang, F. Zhou, J. Yang, X. Wu, Z. Xiao, Z. Li, and Y. Song, “Anisotropy of two-photon absorption and free-carrier effect in nonpolar GaN,” Appl. Phys. Lett. 106(13), 131903 (2015).
[Crossref]

2013 (1)

2012 (4)

B. Gu, F. Ye, K. Lou, Y. Li, J. Chen, and H. T. Wang, “Vectorial self-diffraction effect in optically Kerr medium,” Opt. Express 20(1), 149–157 (2012).
[Crossref] [PubMed]

S. M. Li, Y. Li, X. L. Wang, L. J. Kong, K. Lou, C. Tu, Y. Tian, and H. T. Wang, “Taming the collapse of optical fields,” Sci. Rep. 2(1), 1007 (2012).
[Crossref] [PubMed]

K. Wang, J. Zhou, L. Yuan, Y. Tao, J. Chen, P. Lu, and Z. L. Wang, “Anisotropic third-order optical nonlinearity of a single ZnO micro/nanowire,” Nano Lett. 12(2), 833–838 (2012).
[Crossref] [PubMed]

G. Bautista, M. J. Huttunen, J. Mäkitalo, J. M. Kontio, J. Simonen, and M. Kauranen, “Second-harmonic generation imaging of metal nano-objects with cylindrical vector beams,” Nano Lett. 12(6), 3207–3212 (2012).
[Crossref] [PubMed]

2011 (1)

C. Hnatovsky, V. Shvedov, W. Krolikowski, and A. Rode, “Revealing local field structure of focused ultrashort pulses,” Phys. Rev. Lett. 106(12), 123901 (2011).
[Crossref] [PubMed]

2010 (1)

2008 (2)

A. A. Ishaaya, L. T. Vuong, T. D. Grow, and A. L. Gaeta, “Self-focusing dynamics of polarization vortices in Kerr media,” Opt. Lett. 33(1), 13–15 (2008).
[Crossref] [PubMed]

S. Yang and Q. Zhan, “Third-harmonic generation microscopy with tightly focused radial polarization,” J. Opt. A, Pure Appl. Opt. 10(12), 125103 (2008).
[Crossref]

2007 (1)

2005 (1)

A. Ciattoni, B. Crosignani, P. Di Porto, and A. Yariv, “Azimuthally polarized spatial dark solitons: exact solutions of Maxwell’s equations in a Kerr medium,” Phys. Rev. Lett. 94(7), 073902 (2005).
[Crossref] [PubMed]

2004 (1)

1998 (1)

M. V. Berry, “Paraxial beams of spinning light,” Proc. SPIE 3487, 6–11 (1998).
[Crossref]

1995 (1)

1994 (2)

D. C. Hutchings and B. S. Wherrett, “Theory of anisotropy of two-photon absorption in zinc-blende semiconductors,” Phys. Rev. B Condens. Matter 49(4), 2418–2426 (1994).
[Crossref] [PubMed]

M. D. Dvorak, W. A. Schroeder, D. R. Andersen, A. L. Smirl, and B. S. Wherrett, “Measurement of the anisotropy of two-photon absorption coefficients in zincblende semiconductors,” IEEE J. Quantum Electron. 30(2), 256–268 (1994).
[Crossref]

1993 (1)

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]

1979 (1)

1965 (1)

P. D. Maker and R. W. Terhune, “Study of optical effects due to an induced polarization third order in the electric field strength,” Phys. Rev. 137(3A), A801–A818 (1965).
[Crossref]

Abdelwahab, I.

T. Yang, I. Abdelwahab, H. Lin, Y. Bao, S. J. Rong Tan, S. Fraser, K. P. Loh, and B. Jia, “Anisotropic third-order nonlinearity in pristine and lithium hydride intercalated black phosphorus,” ACS Photonics 5(12), 4969–4977 (2018).
[Crossref]

Andersen, D. R.

M. D. Dvorak, W. A. Schroeder, D. R. Andersen, A. L. Smirl, and B. S. Wherrett, “Measurement of the anisotropy of two-photon absorption coefficients in zincblende semiconductors,” IEEE J. Quantum Electron. 30(2), 256–268 (1994).
[Crossref]

Baev, A.

B. Gu, C. Zhao, A. Baev, K. T. Yong, S. Wen, and P. N. Prasad, “Molecular nonlinear optics: recent advances and applications,” Adv. Opt. Photonics 8(2), 328–369 (2016).
[Crossref]

Bao, Y.

T. Yang, I. Abdelwahab, H. Lin, Y. Bao, S. J. Rong Tan, S. Fraser, K. P. Loh, and B. Jia, “Anisotropic third-order nonlinearity in pristine and lithium hydride intercalated black phosphorus,” ACS Photonics 5(12), 4969–4977 (2018).
[Crossref]

Bautista, G.

G. Bautista, M. J. Huttunen, J. Mäkitalo, J. M. Kontio, J. Simonen, and M. Kauranen, “Second-harmonic generation imaging of metal nano-objects with cylindrical vector beams,” Nano Lett. 12(6), 3207–3212 (2012).
[Crossref] [PubMed]

Berry, M. V.

M. V. Berry, “Paraxial beams of spinning light,” Proc. SPIE 3487, 6–11 (1998).
[Crossref]

Bouchard, F.

F. Bouchard, H. Larocque, A. M. Yao, C. Travis, I. De Leon, A. Rubano, E. Karimi, G. L. Oppo, and R. W. Boyd, “Polarization shaping for control of nonlinear propagation,” Phys. Rev. Lett. 117(23), 233903 (2016).
[Crossref] [PubMed]

Boyd, R. W.

F. Bouchard, H. Larocque, A. M. Yao, C. Travis, I. De Leon, A. Rubano, E. Karimi, G. L. Oppo, and R. W. Boyd, “Polarization shaping for control of nonlinear propagation,” Phys. Rev. Lett. 117(23), 233903 (2016).
[Crossref] [PubMed]

Cai, M. Q.

Chen, J.

B. Gu, F. Ye, K. Lou, Y. Li, J. Chen, and H. T. Wang, “Vectorial self-diffraction effect in optically Kerr medium,” Opt. Express 20(1), 149–157 (2012).
[Crossref] [PubMed]

K. Wang, J. Zhou, L. Yuan, Y. Tao, J. Chen, P. Lu, and Z. L. Wang, “Anisotropic third-order optical nonlinearity of a single ZnO micro/nanowire,” Nano Lett. 12(2), 833–838 (2012).
[Crossref] [PubMed]

Ciattoni, A.

A. Ciattoni, B. Crosignani, P. Di Porto, and A. Yariv, “Azimuthally polarized spatial dark solitons: exact solutions of Maxwell’s equations in a Kerr medium,” Phys. Rev. Lett. 94(7), 073902 (2005).
[Crossref] [PubMed]

Crosignani, B.

A. Ciattoni, B. Crosignani, P. Di Porto, and A. Yariv, “Azimuthally polarized spatial dark solitons: exact solutions of Maxwell’s equations in a Kerr medium,” Phys. Rev. Lett. 94(7), 073902 (2005).
[Crossref] [PubMed]

Cui, Y.

De Leon, I.

F. Bouchard, H. Larocque, A. M. Yao, C. Travis, I. De Leon, A. Rubano, E. Karimi, G. L. Oppo, and R. W. Boyd, “Polarization shaping for control of nonlinear propagation,” Phys. Rev. Lett. 117(23), 233903 (2016).
[Crossref] [PubMed]

DeSalvo, R.

Di Porto, P.

A. Ciattoni, B. Crosignani, P. Di Porto, and A. Yariv, “Azimuthally polarized spatial dark solitons: exact solutions of Maxwell’s equations in a Kerr medium,” Phys. Rev. Lett. 94(7), 073902 (2005).
[Crossref] [PubMed]

Dvorak, M. D.

M. D. Dvorak, W. A. Schroeder, D. R. Andersen, A. L. Smirl, and B. S. Wherrett, “Measurement of the anisotropy of two-photon absorption coefficients in zincblende semiconductors,” IEEE J. Quantum Electron. 30(2), 256–268 (1994).
[Crossref]

Fang, Y.

Y. Fang, F. Zhou, J. Yang, X. Wu, Z. Xiao, Z. Li, and Y. Song, “Anisotropy of two-photon absorption and free-carrier effect in nonpolar GaN,” Appl. Phys. Lett. 106(13), 131903 (2015).
[Crossref]

Fraser, S.

T. Yang, I. Abdelwahab, H. Lin, Y. Bao, S. J. Rong Tan, S. Fraser, K. P. Loh, and B. Jia, “Anisotropic third-order nonlinearity in pristine and lithium hydride intercalated black phosphorus,” ACS Photonics 5(12), 4969–4977 (2018).
[Crossref]

Gaeta, A. L.

Grow, T. D.

Gu, B.

Hagan, D. J.

R. DeSalvo, M. Sheik-Bahae, A. A. Said, D. J. Hagan, and E. W. Van Stryland, “Z-scan measurements of the anisotropy of nonlinear refraction and absorption in crystals,” Opt. Lett. 18(3), 194–196 (1993).
[Crossref] [PubMed]

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]

He, J.

Hnatovsky, C.

C. Hnatovsky, V. Shvedov, W. Krolikowski, and A. Rode, “Revealing local field structure of focused ultrashort pulses,” Phys. Rev. Lett. 106(12), 123901 (2011).
[Crossref] [PubMed]

Hutchings, D. C.

D. C. Hutchings and B. S. Wherrett, “Theory of anisotropy of two-photon absorption in zinc-blende semiconductors,” Phys. Rev. B Condens. Matter 49(4), 2418–2426 (1994).
[Crossref] [PubMed]

Huttunen, M. J.

G. Bautista, M. J. Huttunen, J. Mäkitalo, J. M. Kontio, J. Simonen, and M. Kauranen, “Second-harmonic generation imaging of metal nano-objects with cylindrical vector beams,” Nano Lett. 12(6), 3207–3212 (2012).
[Crossref] [PubMed]

Ishaaya, A. A.

Jia, B.

T. Yang, I. Abdelwahab, H. Lin, Y. Bao, S. J. Rong Tan, S. Fraser, K. P. Loh, and B. Jia, “Anisotropic third-order nonlinearity in pristine and lithium hydride intercalated black phosphorus,” ACS Photonics 5(12), 4969–4977 (2018).
[Crossref]

Karimi, E.

F. Bouchard, H. Larocque, A. M. Yao, C. Travis, I. De Leon, A. Rubano, E. Karimi, G. L. Oppo, and R. W. Boyd, “Polarization shaping for control of nonlinear propagation,” Phys. Rev. Lett. 117(23), 233903 (2016).
[Crossref] [PubMed]

Kauranen, M.

G. Bautista, M. J. Huttunen, J. Mäkitalo, J. M. Kontio, J. Simonen, and M. Kauranen, “Second-harmonic generation imaging of metal nano-objects with cylindrical vector beams,” Nano Lett. 12(6), 3207–3212 (2012).
[Crossref] [PubMed]

Kong, L. J.

S. M. Li, Y. Li, X. L. Wang, L. J. Kong, K. Lou, C. Tu, Y. Tian, and H. T. Wang, “Taming the collapse of optical fields,” Sci. Rep. 2(1), 1007 (2012).
[Crossref] [PubMed]

Kontio, J. M.

G. Bautista, M. J. Huttunen, J. Mäkitalo, J. M. Kontio, J. Simonen, and M. Kauranen, “Second-harmonic generation imaging of metal nano-objects with cylindrical vector beams,” Nano Lett. 12(6), 3207–3212 (2012).
[Crossref] [PubMed]

Krauss, T. D.

Krolikowski, W.

C. Hnatovsky, V. Shvedov, W. Krolikowski, and A. Rode, “Revealing local field structure of focused ultrashort pulses,” Phys. Rev. Lett. 106(12), 123901 (2011).
[Crossref] [PubMed]

Larocque, H.

F. Bouchard, H. Larocque, A. M. Yao, C. Travis, I. De Leon, A. Rubano, E. Karimi, G. L. Oppo, and R. W. Boyd, “Polarization shaping for control of nonlinear propagation,” Phys. Rev. Lett. 117(23), 233903 (2016).
[Crossref] [PubMed]

Li, P. P.

Li, S. M.

S. M. Li, Y. Li, X. L. Wang, L. J. Kong, K. Lou, C. Tu, Y. Tian, and H. T. Wang, “Taming the collapse of optical fields,” Sci. Rep. 2(1), 1007 (2012).
[Crossref] [PubMed]

Li, Y.

Li, Z.

Y. Fang, F. Zhou, J. Yang, X. Wu, Z. Xiao, Z. Li, and Y. Song, “Anisotropy of two-photon absorption and free-carrier effect in nonpolar GaN,” Appl. Phys. Lett. 106(13), 131903 (2015).
[Crossref]

Lin, H.

T. Yang, I. Abdelwahab, H. Lin, Y. Bao, S. J. Rong Tan, S. Fraser, K. P. Loh, and B. Jia, “Anisotropic third-order nonlinearity in pristine and lithium hydride intercalated black phosphorus,” ACS Photonics 5(12), 4969–4977 (2018).
[Crossref]

Liu, G. G.

Liu, Z. B.

Loh, K. P.

T. Yang, I. Abdelwahab, H. Lin, Y. Bao, S. J. Rong Tan, S. Fraser, K. P. Loh, and B. Jia, “Anisotropic third-order nonlinearity in pristine and lithium hydride intercalated black phosphorus,” ACS Photonics 5(12), 4969–4977 (2018).
[Crossref]

Lou, K.

S. M. Li, Y. Li, X. L. Wang, L. J. Kong, K. Lou, C. Tu, Y. Tian, and H. T. Wang, “Taming the collapse of optical fields,” Sci. Rep. 2(1), 1007 (2012).
[Crossref] [PubMed]

B. Gu, F. Ye, K. Lou, Y. Li, J. Chen, and H. T. Wang, “Vectorial self-diffraction effect in optically Kerr medium,” Opt. Express 20(1), 149–157 (2012).
[Crossref] [PubMed]

Lu, P.

K. Wang, J. Zhou, L. Yuan, Y. Tao, J. Chen, P. Lu, and Z. L. Wang, “Anisotropic third-order optical nonlinearity of a single ZnO micro/nanowire,” Nano Lett. 12(2), 833–838 (2012).
[Crossref] [PubMed]

Lü, J. Q.

Maker, P. D.

P. D. Maker and R. W. Terhune, “Study of optical effects due to an induced polarization third order in the electric field strength,” Phys. Rev. 137(3A), A801–A818 (1965).
[Crossref]

Mäkitalo, J.

G. Bautista, M. J. Huttunen, J. Mäkitalo, J. M. Kontio, J. Simonen, and M. Kauranen, “Second-harmonic generation imaging of metal nano-objects with cylindrical vector beams,” Nano Lett. 12(6), 3207–3212 (2012).
[Crossref] [PubMed]

Miller, D. A. B.

Oppo, G. L.

F. Bouchard, H. Larocque, A. M. Yao, C. Travis, I. De Leon, A. Rubano, E. Karimi, G. L. Oppo, and R. W. Boyd, “Polarization shaping for control of nonlinear propagation,” Phys. Rev. Lett. 117(23), 233903 (2016).
[Crossref] [PubMed]

Prasad, P. N.

B. Gu, C. Zhao, A. Baev, K. T. Yong, S. Wen, and P. N. Prasad, “Molecular nonlinear optics: recent advances and applications,” Adv. Opt. Photonics 8(2), 328–369 (2016).
[Crossref]

Ranka, J. K.

Rode, A.

C. Hnatovsky, V. Shvedov, W. Krolikowski, and A. Rode, “Revealing local field structure of focused ultrashort pulses,” Phys. Rev. Lett. 106(12), 123901 (2011).
[Crossref] [PubMed]

Rong Tan, S. J.

T. Yang, I. Abdelwahab, H. Lin, Y. Bao, S. J. Rong Tan, S. Fraser, K. P. Loh, and B. Jia, “Anisotropic third-order nonlinearity in pristine and lithium hydride intercalated black phosphorus,” ACS Photonics 5(12), 4969–4977 (2018).
[Crossref]

Rubano, A.

F. Bouchard, H. Larocque, A. M. Yao, C. Travis, I. De Leon, A. Rubano, E. Karimi, G. L. Oppo, and R. W. Boyd, “Polarization shaping for control of nonlinear propagation,” Phys. Rev. Lett. 117(23), 233903 (2016).
[Crossref] [PubMed]

Rui, G.

Said, A. A.

R. DeSalvo, M. Sheik-Bahae, A. A. Said, D. J. Hagan, and E. W. Van Stryland, “Z-scan measurements of the anisotropy of nonlinear refraction and absorption in crystals,” Opt. Lett. 18(3), 194–196 (1993).
[Crossref] [PubMed]

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]

Schroeder, W. A.

M. D. Dvorak, W. A. Schroeder, D. R. Andersen, A. L. Smirl, and B. S. Wherrett, “Measurement of the anisotropy of two-photon absorption coefficients in zincblende semiconductors,” IEEE J. Quantum Electron. 30(2), 256–268 (1994).
[Crossref]

She, W.

Sheik-Bahae, M.

R. DeSalvo, M. Sheik-Bahae, A. A. Said, D. J. Hagan, and E. W. Van Stryland, “Z-scan measurements of the anisotropy of nonlinear refraction and absorption in crystals,” Opt. Lett. 18(3), 194–196 (1993).
[Crossref] [PubMed]

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]

Shvedov, V.

C. Hnatovsky, V. Shvedov, W. Krolikowski, and A. Rode, “Revealing local field structure of focused ultrashort pulses,” Phys. Rev. Lett. 106(12), 123901 (2011).
[Crossref] [PubMed]

Simonen, J.

G. Bautista, M. J. Huttunen, J. Mäkitalo, J. M. Kontio, J. Simonen, and M. Kauranen, “Second-harmonic generation imaging of metal nano-objects with cylindrical vector beams,” Nano Lett. 12(6), 3207–3212 (2012).
[Crossref] [PubMed]

Smirl, A. L.

M. D. Dvorak, W. A. Schroeder, D. R. Andersen, A. L. Smirl, and B. S. Wherrett, “Measurement of the anisotropy of two-photon absorption coefficients in zincblende semiconductors,” IEEE J. Quantum Electron. 30(2), 256–268 (1994).
[Crossref]

Smith, S. D.

Song, Y.

Y. Fang, F. Zhou, J. Yang, X. Wu, Z. Xiao, Z. Li, and Y. Song, “Anisotropy of two-photon absorption and free-carrier effect in nonpolar GaN,” Appl. Phys. Lett. 106(13), 131903 (2015).
[Crossref]

Tao, Y.

K. Wang, J. Zhou, L. Yuan, Y. Tao, J. Chen, P. Lu, and Z. L. Wang, “Anisotropic third-order optical nonlinearity of a single ZnO micro/nanowire,” Nano Lett. 12(2), 833–838 (2012).
[Crossref] [PubMed]

Terhune, R. W.

P. D. Maker and R. W. Terhune, “Study of optical effects due to an induced polarization third order in the electric field strength,” Phys. Rev. 137(3A), A801–A818 (1965).
[Crossref]

Tian, J. G.

Tian, Y.

S. M. Li, Y. Li, X. L. Wang, L. J. Kong, K. Lou, C. Tu, Y. Tian, and H. T. Wang, “Taming the collapse of optical fields,” Sci. Rep. 2(1), 1007 (2012).
[Crossref] [PubMed]

Travis, C.

F. Bouchard, H. Larocque, A. M. Yao, C. Travis, I. De Leon, A. Rubano, E. Karimi, G. L. Oppo, and R. W. Boyd, “Polarization shaping for control of nonlinear propagation,” Phys. Rev. Lett. 117(23), 233903 (2016).
[Crossref] [PubMed]

Tu, C.

Van Stryland, E. W.

R. DeSalvo, M. Sheik-Bahae, A. A. Said, D. J. Hagan, and E. W. Van Stryland, “Z-scan measurements of the anisotropy of nonlinear refraction and absorption in crystals,” Opt. Lett. 18(3), 194–196 (1993).
[Crossref] [PubMed]

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]

Vuong, L. T.

Wan, Y.

Y. Xue, Y. Wan, and B. Gu, “Femtosecond-pulsed Z-scan study on third- and fifth-order refractive nonlinearities in a side-chain azobenzene copolymer film,” J. Nonlinear Opt. Phys. Mater. 27(01), 1850007 (2018).
[Crossref]

Wang, D.

Wang, H. T.

Wang, K.

K. Wang, J. Zhou, L. Yuan, Y. Tao, J. Chen, P. Lu, and Z. L. Wang, “Anisotropic third-order optical nonlinearity of a single ZnO micro/nanowire,” Nano Lett. 12(2), 833–838 (2012).
[Crossref] [PubMed]

Wang, X. L.

S. M. Li, Y. Li, X. L. Wang, L. J. Kong, K. Lou, C. Tu, Y. Tian, and H. T. Wang, “Taming the collapse of optical fields,” Sci. Rep. 2(1), 1007 (2012).
[Crossref] [PubMed]

Wang, Z. L.

K. Wang, J. Zhou, L. Yuan, Y. Tao, J. Chen, P. Lu, and Z. L. Wang, “Anisotropic third-order optical nonlinearity of a single ZnO micro/nanowire,” Nano Lett. 12(2), 833–838 (2012).
[Crossref] [PubMed]

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(4), 760–769 (1990).
[Crossref]

Wen, B.

Wen, S.

B. Gu, C. Zhao, A. Baev, K. T. Yong, S. Wen, and P. N. Prasad, “Molecular nonlinear optics: recent advances and applications,” Adv. Opt. Photonics 8(2), 328–369 (2016).
[Crossref]

Wherrett, B. S.

M. D. Dvorak, W. A. Schroeder, D. R. Andersen, A. L. Smirl, and B. S. Wherrett, “Measurement of the anisotropy of two-photon absorption coefficients in zincblende semiconductors,” IEEE J. Quantum Electron. 30(2), 256–268 (1994).
[Crossref]

D. C. Hutchings and B. S. Wherrett, “Theory of anisotropy of two-photon absorption in zinc-blende semiconductors,” Phys. Rev. B Condens. Matter 49(4), 2418–2426 (1994).
[Crossref] [PubMed]

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).
[Crossref] [PubMed]

Wise, F. W.

Wu, X.

Y. Fang, F. Zhou, J. Yang, X. Wu, Z. Xiao, Z. Li, and Y. Song, “Anisotropy of two-photon absorption and free-carrier effect in nonpolar GaN,” Appl. Phys. Lett. 106(13), 131903 (2015).
[Crossref]

Xiao, Z.

Y. Fang, F. Zhou, J. Yang, X. Wu, Z. Xiao, Z. Li, and Y. Song, “Anisotropy of two-photon absorption and free-carrier effect in nonpolar GaN,” Appl. Phys. Lett. 106(13), 131903 (2015).
[Crossref]

Xue, Y.

Yan, X. Q.

Yang, J.

Y. Fang, F. Zhou, J. Yang, X. Wu, Z. Xiao, Z. Li, and Y. Song, “Anisotropy of two-photon absorption and free-carrier effect in nonpolar GaN,” Appl. Phys. Lett. 106(13), 131903 (2015).
[Crossref]

Yang, S.

S. Yang and Q. Zhan, “Third-harmonic generation microscopy with tightly focused radial polarization,” J. Opt. A, Pure Appl. Opt. 10(12), 125103 (2008).
[Crossref]

Yang, T.

T. Yang, I. Abdelwahab, H. Lin, Y. Bao, S. J. Rong Tan, S. Fraser, K. P. Loh, and B. Jia, “Anisotropic third-order nonlinearity in pristine and lithium hydride intercalated black phosphorus,” ACS Photonics 5(12), 4969–4977 (2018).
[Crossref]

Yao, A. M.

F. Bouchard, H. Larocque, A. M. Yao, C. Travis, I. De Leon, A. Rubano, E. Karimi, G. L. Oppo, and R. W. Boyd, “Polarization shaping for control of nonlinear propagation,” Phys. Rev. Lett. 117(23), 233903 (2016).
[Crossref] [PubMed]

Yariv, A.

A. Ciattoni, B. Crosignani, P. Di Porto, and A. Yariv, “Azimuthally polarized spatial dark solitons: exact solutions of Maxwell’s equations in a Kerr medium,” Phys. Rev. Lett. 94(7), 073902 (2005).
[Crossref] [PubMed]

Ye, F.

Yong, K. T.

B. Gu, C. Zhao, A. Baev, K. T. Yong, S. Wen, and P. N. Prasad, “Molecular nonlinear optics: recent advances and applications,” Adv. Opt. Photonics 8(2), 328–369 (2016).
[Crossref]

Yuan, L.

K. Wang, J. Zhou, L. Yuan, Y. Tao, J. Chen, P. Lu, and Z. L. Wang, “Anisotropic third-order optical nonlinearity of a single ZnO micro/nanowire,” Nano Lett. 12(2), 833–838 (2012).
[Crossref] [PubMed]

Zang, W. P.

Zhan, Q.

Zhang, G. L.

Zhang, X. L.

Zhao, C.

B. Gu, C. Zhao, A. Baev, K. T. Yong, S. Wen, and P. N. Prasad, “Molecular nonlinear optics: recent advances and applications,” Adv. Opt. Photonics 8(2), 328–369 (2016).
[Crossref]

Zhou, F.

Y. Fang, F. Zhou, J. Yang, X. Wu, Z. Xiao, Z. Li, and Y. Song, “Anisotropy of two-photon absorption and free-carrier effect in nonpolar GaN,” Appl. Phys. Lett. 106(13), 131903 (2015).
[Crossref]

Zhou, J.

K. Wang, J. Zhou, L. Yuan, Y. Tao, J. Chen, P. Lu, and Z. L. Wang, “Anisotropic third-order optical nonlinearity of a single ZnO micro/nanowire,” Nano Lett. 12(2), 833–838 (2012).
[Crossref] [PubMed]

Zhou, W. Y.

Zhu, W.

ACS Photonics (1)

T. Yang, I. Abdelwahab, H. Lin, Y. Bao, S. J. Rong Tan, S. Fraser, K. P. Loh, and B. Jia, “Anisotropic third-order nonlinearity in pristine and lithium hydride intercalated black phosphorus,” ACS Photonics 5(12), 4969–4977 (2018).
[Crossref]

Adv. Opt. Photonics (1)

B. Gu, C. Zhao, A. Baev, K. T. Yong, S. Wen, and P. N. Prasad, “Molecular nonlinear optics: recent advances and applications,” Adv. Opt. Photonics 8(2), 328–369 (2016).
[Crossref]

Appl. Phys. Lett. (1)

Y. Fang, F. Zhou, J. Yang, X. Wu, Z. Xiao, Z. Li, and Y. Song, “Anisotropy of two-photon absorption and free-carrier effect in nonpolar GaN,” Appl. Phys. Lett. 106(13), 131903 (2015).
[Crossref]

IEEE J. Quantum Electron. (2)

M. D. Dvorak, W. A. Schroeder, D. R. Andersen, A. L. Smirl, and B. S. Wherrett, “Measurement of the anisotropy of two-photon absorption coefficients in zincblende semiconductors,” IEEE J. Quantum Electron. 30(2), 256–268 (1994).
[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]

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

Y. Xue, Y. Wan, and B. Gu, “Femtosecond-pulsed Z-scan study on third- and fifth-order refractive nonlinearities in a side-chain azobenzene copolymer film,” J. Nonlinear Opt. Phys. Mater. 27(01), 1850007 (2018).
[Crossref]

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

S. Yang and Q. Zhan, “Third-harmonic generation microscopy with tightly focused radial polarization,” J. Opt. A, Pure Appl. Opt. 10(12), 125103 (2008).
[Crossref]

Nano Lett. (2)

G. Bautista, M. J. Huttunen, J. Mäkitalo, J. M. Kontio, J. Simonen, and M. Kauranen, “Second-harmonic generation imaging of metal nano-objects with cylindrical vector beams,” Nano Lett. 12(6), 3207–3212 (2012).
[Crossref] [PubMed]

K. Wang, J. Zhou, L. Yuan, Y. Tao, J. Chen, P. Lu, and Z. L. Wang, “Anisotropic third-order optical nonlinearity of a single ZnO micro/nanowire,” Nano Lett. 12(2), 833–838 (2012).
[Crossref] [PubMed]

Opt. Express (7)

Opt. Lett. (6)

Phys. Rev. (1)

P. D. Maker and R. W. Terhune, “Study of optical effects due to an induced polarization third order in the electric field strength,” Phys. Rev. 137(3A), A801–A818 (1965).
[Crossref]

Phys. Rev. B Condens. Matter (1)

D. C. Hutchings and B. S. Wherrett, “Theory of anisotropy of two-photon absorption in zinc-blende semiconductors,” Phys. Rev. B Condens. Matter 49(4), 2418–2426 (1994).
[Crossref] [PubMed]

Phys. Rev. Lett. (3)

C. Hnatovsky, V. Shvedov, W. Krolikowski, and A. Rode, “Revealing local field structure of focused ultrashort pulses,” Phys. Rev. Lett. 106(12), 123901 (2011).
[Crossref] [PubMed]

A. Ciattoni, B. Crosignani, P. Di Porto, and A. Yariv, “Azimuthally polarized spatial dark solitons: exact solutions of Maxwell’s equations in a Kerr medium,” Phys. Rev. Lett. 94(7), 073902 (2005).
[Crossref] [PubMed]

F. Bouchard, H. Larocque, A. M. Yao, C. Travis, I. De Leon, A. Rubano, E. Karimi, G. L. Oppo, and R. W. Boyd, “Polarization shaping for control of nonlinear propagation,” Phys. Rev. Lett. 117(23), 233903 (2016).
[Crossref] [PubMed]

Proc. SPIE (1)

M. V. Berry, “Paraxial beams of spinning light,” Proc. SPIE 3487, 6–11 (1998).
[Crossref]

Sci. Rep. (1)

S. M. Li, Y. Li, X. L. Wang, L. J. Kong, K. Lou, C. Tu, Y. Tian, and H. T. Wang, “Taming the collapse of optical fields,” Sci. Rep. 2(1), 1007 (2012).
[Crossref] [PubMed]

Other (2)

R. K. Luneburg, Mathematical theory of optics (University of California, 1964).

R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, 2008).

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Figures (5)

Fig. 1
Fig. 1 The relationship between the principal axis coordinate system (XYZ) of the crystal and the laboratory coordinate system (xyz) of the elliptically polarized light E ( x , y , z ) in the analysis.
Fig. 2
Fig. 2 Examples of Z-scan traces for BaF2 crystal at I 00 = 190 GW/cm2 and θ = 45 ° under the excitation of three polarized lights.
Fig. 3
Fig. 3 The dependence of Δ T P V on the orientation angle θ for BaF2 crystal at I 00 = 190 GW/cm2 under the excitation of three polarized lights.
Fig. 4
Fig. 4 Normalized far-field intensity patterns and SAM distributions superimposed with SoPs (Deep green: LH polarization; Deep blue: RH polarization; White lines: linear polarization) of hybridly polarized beams through anisotropic Kerr nonlinearities for different crystal orientation angles θ .
Fig. 5
Fig. 5 The schematic of a hybridly polarized beam passing through an anisotropic nonlinear Kerr medium. (a) The intensity and SoPs distribution of the incident beam. (b) Additional phase shift of the light field induced by an anisotropic Kerr nonlinearity. (c) Far-field intensity pattern superimposed with SoPs distributions.

Equations (37)

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n 2 , ± aniso = n 2 0 [ 1 2 e δ 1 + e 2 σ 2 sin 2 ( 2 θ ) ( 1 e ) 2 1 + e 2 ] ,
δ = Re [ χ 1111 ( 3 ) ] + Re [ χ 1122 ( 3 ) ] 2 Re [ χ 1221 ( 3 ) ] 2 Re [ χ 1111 ( 3 ) ] ,
σ = Re [ χ 1111 ( 3 ) ] Re [ χ 1122 ( 3 ) ] 2 Re [ χ 1221 ( 3 ) ] Re [ χ 1111 ( 3 ) ] .
E ( r , z ; t ) = ( E + σ + E σ ) = E 0 ( t ) 2 ( 1 + e 2 ) ω 0 ω ( z ) exp [ r 2 ω 2 ( z ) i k r 2 2 R ( z ) ] ( ( 1 + e ) σ + ( 1 e ) σ ) ,
I ( r , z ; t ) = I 0 ( t ) 1 1 + z 2 / z 0 2 exp [ 2 r 2 ω 2 ( z ) ] ,
E ( r , φ , z ; t ) = ( E + σ + E σ ) = 2 η π E 0 ( t ) g 1 f μ 3 / 2 ω 3 ( f + z ) e i k ( f + z ) 2 η ( ( e i φ i e i φ ) σ + ( e i φ + i e i φ ) σ ) ,
I ( r , z ; t ) = 8 I 0 ( t ) g 1 2 f 2 η η π | μ | 3 ω 6 ( f + z ) 2 e 2 η 2 η .
E e = ( E + e σ + E e σ ) = e α 0 L / 2 ( E + e i Δ ϕ + σ + E e i Δ ϕ σ ) ,
E a ( ρ , z ; t ) = E + ( 0 , z ; t ) e α 0 L / 2 m = 0 [ i Δ ϕ + ( 0 , z ; t ) ] m m ! ω 0 m ω m exp ( ρ 2 ω m 2 i k ρ 2 2 R m + i θ m ) σ + + E ( 0 , z ; t ) e α 0 L / 2 m = 0 [ i Δ ϕ ( 0 , z ; t ) ] m m ! ω 0 m ω m exp ( ρ 2 ω m 2 i k ρ 2 2 R m + i θ m ) σ ,
g = 1 + d R ( z ) ,
ω 0 m 2 = ω 2 ( z ) 2 m + 1 ,
d m = 1 2 k ω 0 m 2 ,
ω m 2 = ω 0 m 2 ( g 2 + d 2 d m 2 ) ,
R m = d ( 1 g g 2 + d 2 / d m 2 ) 1 ,
θ m = tan 1 ( d / d m g ) .
E a ( ρ , ϕ , z ; t ) = ( E + a σ + E a σ ) = i k e i k D 2 π D 0 0 2 π ( E + e σ + E e σ ) exp ( i k r 2 2 D ) exp ( i k r ρ D cos ( φ ϕ ) ) r d r d φ ,
T ( z , S ) = + d t 0 R a | E a ( ρ , z ; t ) | 2 ρ d ρ + d t 0 R a | E a ( ρ , z ; t ) | Φ 0 = 0 2 ρ d ρ ,
T ( z , S ) = 1 S [ 1 m , m = 0 F m m m + m ( 1 S ) λ m m cos ψ m m m ! m ! ( m + m + 1 ) 3 / 2 ( x 2 + 1 ) m + m ] ,
F m m m + m = ( 1 + e ) 2 Φ + m + m + ( 1 e ) 2 Φ m + m 2 ( 1 + e 2 ) ,
λ m m = ( m + m + 1 ) ( x 2 + 1 ) [ x 2 + ( 2 m + 1 ) ( 2 m + 1 ) ] [ x 2 + ( 2 m + 1 ) 2 ] [ x 2 + ( 2 m + 1 ) 2 ] ,
ψ m m = ( m m ) { π 2 2 ( m + m + 1 ) x ( x 2 + 1 ) ln ( 1 S ) [ x 2 + ( 2 m + 1 ) 2 ] [ x 2 + ( 2 m + 1 ) 2 ] } .
T ( z , S ) = 1 [ ( 1 + e ) 2 Φ + + ( 1 e ) 2 Φ ] 2 2 S ( 1 + e 2 ) ( x 2 + 1 ) ( 1 S ) 2 ( x 2 + 3 ) x 2 + 9 sin [ 4 x ln ( 1 S ) x 2 + 9 ] + [ ( 1 + e ) 2 Φ + 2 + ( 1 e ) 2 Φ 2 ] 6 3 S ( 1 + e 2 ) ( x 2 + 1 ) 2 × { ( 1 S ) 3 ( x 2 + 5 ) x 2 + 25 cos [ 12 x ln ( 1 S ) x 2 + 25 ] ( 1 S ) 3 ( x 2 + 1 ) x 2 + 9 } .
ψ = 1 2 [ ( arg ( E a , ) arg ( E a , + ) ] ,
β = 1 2 arc sin ( | E a , + | 2 | E a , | 2 | E a , + | 2 + | E a , | 2 ) .
S z = ( | E + a | 2 | E a | 2 ) d x d y ( | E + a | 2 + | E a | 2 ) d x d y e z ,
E = E X e X + E Y e Y ,
E X = 1 1 + e 2 E ( cos θ i e sin θ ) ,
E Y = 1 1 + e 2 E ( sin θ + i e cos θ ) .
P N L = P X e X + P Y e Y ,
P X = 3 ε 0 χ 1111 ( 3 ) ( E X E X * ) E X + 3 ε 0 χ 1122 ( 3 ) ( E Y E Y ) E X * + 6 ε 0 χ 1221 ( 3 ) ( E Y E Y * ) E X ,
P Y = 3 ε 0 χ 1111 ( 3 ) ( E Y E Y * ) E Y + 3 ε 0 χ 1122 ( 3 ) ( E X E X ) E Y * + 6 ε 0 χ 1221 ( 3 ) ( E X E X * ) E Y .
P N L = P x e x + P y e y
P x = P X cos θ + P Y sin θ ,
P y = P X sin θ + P Y cos θ .
P N L = P + σ + + P σ ,
P ± = 3 2 ε 0 ( χ 1111 ( 3 ) χ 1122 ( 3 ) 2 χ 1221 ( 3 ) ) | E | 2 [ 1 + ( 1 e ) 2 1 + e 2 ( 1 sin 2 2 θ ) ± i sin 2 θ cos 2 θ ( 1 e ) 2 1 + e 2 ] E + 3 ε 0 χ 1122 ( 3 ) ( 1 e ) 2 1 + e 2 | E | 2 E + 6 ε 0 χ 1221 ( 3 ) | E | 2 E .
n ± = n 0 2 + Re [ χ ± N L ] n 0 + 3 2 n 0 { 1 2 ( Re [ χ 1111 ( 3 ) ] Re [ χ 1122 ( 3 ) ] 2 Re [ χ 1221 ( 3 ) ] ) [ 1 + ( 1 e ) 2 1 + e 2 ( 1 sin 2 2 θ ) ] | E | 2 + Re [ χ 1122 ( 3 ) ] ( 1 e ) 2 1 + e 2 | E | 2 + 2 Re [ χ 1221 ( 3 ) ] | E | 2 } .

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