Abstract

We investigate, both theoretically and experimentally, self-trapping of light beams in nematic liquid crystals arranged so as to exhibit the optical Fréedericksz transition in planar cells. The resulting threshold in the nonlinear reorientational response supports a bistable behavior between diffracting and self-localized beam states, leading to the appearance of a hysteretic loop versus input excitation. Our results confirm the role of nematic liquid crystals in the study of non-perturbative nonlinear photonics.

© 2014 Optical Society of America

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  1. R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett. 13, 479–482 (1964).
    [Crossref]
  2. R. W. Boyd, S. G. Lukishova, and Y. R. Shen, eds., Self-focusing: Past and Present (Springer, 2009).
    [Crossref]
  3. B. Shim, S. E. Schrauth, A. L. Gaeta, M. Klein, and G. Fibich, “Loss of phase of collapsing beams,” Phys. Rev. Lett. 108, 043902 (2012).
    [Crossref] [PubMed]
  4. A. Barthelemy, S. Maneuf, and C. Froehly, “Propagation soliton et auto-confinement de faisceaux laser par non linearite optique de Kerr,” Opt. Commun. 55, 201–206 (1985).
    [Crossref]
  5. E. L. Falcão Filho, C. B. de Araújo, G. Boudebs, H. Leblond, and V. Skarka, “Robust two-dimensional spatial solitons in liquid carbon disulfide,” Phys. Rev. Lett. 110, 013901 (2013).
    [Crossref] [PubMed]
  6. J. E. Bjorkholm and A. A. Ashkin, “CW self-focusing and self-trapping of light in sodium vapor,” Phys. Rev. Lett. 32, 129–132 (1974).
    [Crossref]
  7. W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
    [Crossref] [PubMed]
  8. D. Suter and T. Blasberg, “Stabilization of transverse solitary waves by a nonlocal response of the nonlinear medium,” Phys. Rev. A 48, 4583–4587 (1993).
    [Crossref] [PubMed]
  9. C. Conti, M. Peccianti, and G. Assanto, “Route to nonlocality and observation of accessible solitons,” Phys. Rev. Lett. 91, 073901 (2003).
    [Crossref] [PubMed]
  10. A. E. Kaplan, “Bistable solitons,” Phys. Rev. Lett. 55, 1291–1294 (1985).
    [Crossref] [PubMed]
  11. J. M. Christian, G. S. McDonald, and P. Chamorro-Posada, “Bistable Helmholtz solitons in cubic-quintic materials,” Phys. Rev. A 76, 033833 (2007).
    [Crossref]
  12. M. Matuszewski, W. Krolikowski, and Y. S. Kivshar, “Spatial solitons and light-induced instabilities in colloidal media,” Opt. Express 16, 1371–1376 (2008).
    [Crossref] [PubMed]
  13. M. Matuszewski, “Engineering optical soliton bistability in colloidal media,” Phys. Rev. A 81, 013820 (2010).
    [Crossref]
  14. I. C. Khoo, “Nonlinear optics of liquid crystalline materials,” Phys. Rep. 471, 221–267 (2009).
    [Crossref]
  15. G. Assanto, ed., Nematicons: Spatial Optical Solitons in Nematic Liquid Crystals (Wiley, 2012).
    [Crossref]
  16. M. Peccianti and G. Assanto, “Nematicons,” Phys. Rep. 516, 147–208 (2012).
    [Crossref]
  17. S. D. Durbin, S. M. Arakelian, and Y. R. Shen, “Optical-field-induced birefringence and Fréedericksz transition in a nematic liquid crystal,” Phys. Rev. Lett. 47, 1411–1414 (1981).
    [Crossref]
  18. H. L. Ong, “Optically induced Fréedericksz transition and bistability in a nematic liquid crystal,” Phys. Rev. A 28, 2393–2407 (1983).
    [Crossref]
  19. I. C. Khoo, “Optical bistability in nematic films utilizing self-focusing of light,” Appl. Phys. Lett. 41, 909–911 (1982).
    [Crossref]
  20. E. Braun, L. P. Faucheux, and A. Libchaber, “Strong self-focusing in nematic liquid crystals,” Phys. Rev. A 48, 611–622 (1993).
    [Crossref] [PubMed]
  21. A. Alberucci, A. Piccardi, N. Kravets, and G. Assanto, “Beam hysteresis via reorientational self-focusing,” Opt. Lett. 39, 5830–5833 (2014).
    [Crossref] [PubMed]
  22. N. Kravets, A. Piccardi, A. Alberucci, O. Buchnev, M. Kaczmarek, and G. Assanto, “Bistability with optical beams propagating in a reorientational medium,” Phys. Rev. Lett. 113, 023901 (2014).
    [Crossref] [PubMed]
  23. A. V. Zakharov and R. Y. Dong, “Giant optical nonlinearity in the mesophase of a nematic liquid crystals (ncl),” Phys. Rev. E 64, 031701 (2001).
    [Crossref]

2014 (2)

N. Kravets, A. Piccardi, A. Alberucci, O. Buchnev, M. Kaczmarek, and G. Assanto, “Bistability with optical beams propagating in a reorientational medium,” Phys. Rev. Lett. 113, 023901 (2014).
[Crossref] [PubMed]

A. Alberucci, A. Piccardi, N. Kravets, and G. Assanto, “Beam hysteresis via reorientational self-focusing,” Opt. Lett. 39, 5830–5833 (2014).
[Crossref] [PubMed]

2013 (1)

E. L. Falcão Filho, C. B. de Araújo, G. Boudebs, H. Leblond, and V. Skarka, “Robust two-dimensional spatial solitons in liquid carbon disulfide,” Phys. Rev. Lett. 110, 013901 (2013).
[Crossref] [PubMed]

2012 (2)

B. Shim, S. E. Schrauth, A. L. Gaeta, M. Klein, and G. Fibich, “Loss of phase of collapsing beams,” Phys. Rev. Lett. 108, 043902 (2012).
[Crossref] [PubMed]

M. Peccianti and G. Assanto, “Nematicons,” Phys. Rep. 516, 147–208 (2012).
[Crossref]

2010 (1)

M. Matuszewski, “Engineering optical soliton bistability in colloidal media,” Phys. Rev. A 81, 013820 (2010).
[Crossref]

2009 (1)

I. C. Khoo, “Nonlinear optics of liquid crystalline materials,” Phys. Rep. 471, 221–267 (2009).
[Crossref]

2008 (1)

2007 (1)

J. M. Christian, G. S. McDonald, and P. Chamorro-Posada, “Bistable Helmholtz solitons in cubic-quintic materials,” Phys. Rev. A 76, 033833 (2007).
[Crossref]

2003 (1)

C. Conti, M. Peccianti, and G. Assanto, “Route to nonlocality and observation of accessible solitons,” Phys. Rev. Lett. 91, 073901 (2003).
[Crossref] [PubMed]

2001 (1)

A. V. Zakharov and R. Y. Dong, “Giant optical nonlinearity in the mesophase of a nematic liquid crystals (ncl),” Phys. Rev. E 64, 031701 (2001).
[Crossref]

1995 (1)

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[Crossref] [PubMed]

1993 (2)

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

E. Braun, L. P. Faucheux, and A. Libchaber, “Strong self-focusing in nematic liquid crystals,” Phys. Rev. A 48, 611–622 (1993).
[Crossref] [PubMed]

1985 (2)

A. E. Kaplan, “Bistable solitons,” Phys. Rev. Lett. 55, 1291–1294 (1985).
[Crossref] [PubMed]

A. Barthelemy, S. Maneuf, and C. Froehly, “Propagation soliton et auto-confinement de faisceaux laser par non linearite optique de Kerr,” Opt. Commun. 55, 201–206 (1985).
[Crossref]

1983 (1)

H. L. Ong, “Optically induced Fréedericksz transition and bistability in a nematic liquid crystal,” Phys. Rev. A 28, 2393–2407 (1983).
[Crossref]

1982 (1)

I. C. Khoo, “Optical bistability in nematic films utilizing self-focusing of light,” Appl. Phys. Lett. 41, 909–911 (1982).
[Crossref]

1981 (1)

S. D. Durbin, S. M. Arakelian, and Y. R. Shen, “Optical-field-induced birefringence and Fréedericksz transition in a nematic liquid crystal,” Phys. Rev. Lett. 47, 1411–1414 (1981).
[Crossref]

1974 (1)

J. E. Bjorkholm and A. A. Ashkin, “CW self-focusing and self-trapping of light in sodium vapor,” Phys. Rev. Lett. 32, 129–132 (1974).
[Crossref]

1964 (1)

R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett. 13, 479–482 (1964).
[Crossref]

Alberucci, A.

N. Kravets, A. Piccardi, A. Alberucci, O. Buchnev, M. Kaczmarek, and G. Assanto, “Bistability with optical beams propagating in a reorientational medium,” Phys. Rev. Lett. 113, 023901 (2014).
[Crossref] [PubMed]

A. Alberucci, A. Piccardi, N. Kravets, and G. Assanto, “Beam hysteresis via reorientational self-focusing,” Opt. Lett. 39, 5830–5833 (2014).
[Crossref] [PubMed]

Arakelian, S. M.

S. D. Durbin, S. M. Arakelian, and Y. R. Shen, “Optical-field-induced birefringence and Fréedericksz transition in a nematic liquid crystal,” Phys. Rev. Lett. 47, 1411–1414 (1981).
[Crossref]

Ashkin, A. A.

J. E. Bjorkholm and A. A. Ashkin, “CW self-focusing and self-trapping of light in sodium vapor,” Phys. Rev. Lett. 32, 129–132 (1974).
[Crossref]

Assanto, G.

N. Kravets, A. Piccardi, A. Alberucci, O. Buchnev, M. Kaczmarek, and G. Assanto, “Bistability with optical beams propagating in a reorientational medium,” Phys. Rev. Lett. 113, 023901 (2014).
[Crossref] [PubMed]

A. Alberucci, A. Piccardi, N. Kravets, and G. Assanto, “Beam hysteresis via reorientational self-focusing,” Opt. Lett. 39, 5830–5833 (2014).
[Crossref] [PubMed]

M. Peccianti and G. Assanto, “Nematicons,” Phys. Rep. 516, 147–208 (2012).
[Crossref]

C. Conti, M. Peccianti, and G. Assanto, “Route to nonlocality and observation of accessible solitons,” Phys. Rev. Lett. 91, 073901 (2003).
[Crossref] [PubMed]

Barthelemy, A.

A. Barthelemy, S. Maneuf, and C. Froehly, “Propagation soliton et auto-confinement de faisceaux laser par non linearite optique de Kerr,” Opt. Commun. 55, 201–206 (1985).
[Crossref]

Bjorkholm, J. E.

J. E. Bjorkholm and A. A. Ashkin, “CW self-focusing and self-trapping of light in sodium vapor,” Phys. Rev. Lett. 32, 129–132 (1974).
[Crossref]

Blasberg, T.

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

Boudebs, G.

E. L. Falcão Filho, C. B. de Araújo, G. Boudebs, H. Leblond, and V. Skarka, “Robust two-dimensional spatial solitons in liquid carbon disulfide,” Phys. Rev. Lett. 110, 013901 (2013).
[Crossref] [PubMed]

Braun, E.

E. Braun, L. P. Faucheux, and A. Libchaber, “Strong self-focusing in nematic liquid crystals,” Phys. Rev. A 48, 611–622 (1993).
[Crossref] [PubMed]

Buchnev, O.

N. Kravets, A. Piccardi, A. Alberucci, O. Buchnev, M. Kaczmarek, and G. Assanto, “Bistability with optical beams propagating in a reorientational medium,” Phys. Rev. Lett. 113, 023901 (2014).
[Crossref] [PubMed]

Chamorro-Posada, P.

J. M. Christian, G. S. McDonald, and P. Chamorro-Posada, “Bistable Helmholtz solitons in cubic-quintic materials,” Phys. Rev. A 76, 033833 (2007).
[Crossref]

Chiao, R. Y.

R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett. 13, 479–482 (1964).
[Crossref]

Christian, J. M.

J. M. Christian, G. S. McDonald, and P. Chamorro-Posada, “Bistable Helmholtz solitons in cubic-quintic materials,” Phys. Rev. A 76, 033833 (2007).
[Crossref]

Conti, C.

C. Conti, M. Peccianti, and G. Assanto, “Route to nonlocality and observation of accessible solitons,” Phys. Rev. Lett. 91, 073901 (2003).
[Crossref] [PubMed]

de Araújo, C. B.

E. L. Falcão Filho, C. B. de Araújo, G. Boudebs, H. Leblond, and V. Skarka, “Robust two-dimensional spatial solitons in liquid carbon disulfide,” Phys. Rev. Lett. 110, 013901 (2013).
[Crossref] [PubMed]

Dong, R. Y.

A. V. Zakharov and R. Y. Dong, “Giant optical nonlinearity in the mesophase of a nematic liquid crystals (ncl),” Phys. Rev. E 64, 031701 (2001).
[Crossref]

Durbin, S. D.

S. D. Durbin, S. M. Arakelian, and Y. R. Shen, “Optical-field-induced birefringence and Fréedericksz transition in a nematic liquid crystal,” Phys. Rev. Lett. 47, 1411–1414 (1981).
[Crossref]

Falcão Filho, E. L.

E. L. Falcão Filho, C. B. de Araújo, G. Boudebs, H. Leblond, and V. Skarka, “Robust two-dimensional spatial solitons in liquid carbon disulfide,” Phys. Rev. Lett. 110, 013901 (2013).
[Crossref] [PubMed]

Faucheux, L. P.

E. Braun, L. P. Faucheux, and A. Libchaber, “Strong self-focusing in nematic liquid crystals,” Phys. Rev. A 48, 611–622 (1993).
[Crossref] [PubMed]

Fibich, G.

B. Shim, S. E. Schrauth, A. L. Gaeta, M. Klein, and G. Fibich, “Loss of phase of collapsing beams,” Phys. Rev. Lett. 108, 043902 (2012).
[Crossref] [PubMed]

Froehly, C.

A. Barthelemy, S. Maneuf, and C. Froehly, “Propagation soliton et auto-confinement de faisceaux laser par non linearite optique de Kerr,” Opt. Commun. 55, 201–206 (1985).
[Crossref]

Gaeta, A. L.

B. Shim, S. E. Schrauth, A. L. Gaeta, M. Klein, and G. Fibich, “Loss of phase of collapsing beams,” Phys. Rev. Lett. 108, 043902 (2012).
[Crossref] [PubMed]

Garmire, E.

R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett. 13, 479–482 (1964).
[Crossref]

Hagan, D. J.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[Crossref] [PubMed]

Kaczmarek, M.

N. Kravets, A. Piccardi, A. Alberucci, O. Buchnev, M. Kaczmarek, and G. Assanto, “Bistability with optical beams propagating in a reorientational medium,” Phys. Rev. Lett. 113, 023901 (2014).
[Crossref] [PubMed]

Kaplan, A. E.

A. E. Kaplan, “Bistable solitons,” Phys. Rev. Lett. 55, 1291–1294 (1985).
[Crossref] [PubMed]

Khoo, I. C.

I. C. Khoo, “Nonlinear optics of liquid crystalline materials,” Phys. Rep. 471, 221–267 (2009).
[Crossref]

I. C. Khoo, “Optical bistability in nematic films utilizing self-focusing of light,” Appl. Phys. Lett. 41, 909–911 (1982).
[Crossref]

Kivshar, Y. S.

Klein, M.

B. Shim, S. E. Schrauth, A. L. Gaeta, M. Klein, and G. Fibich, “Loss of phase of collapsing beams,” Phys. Rev. Lett. 108, 043902 (2012).
[Crossref] [PubMed]

Kravets, N.

A. Alberucci, A. Piccardi, N. Kravets, and G. Assanto, “Beam hysteresis via reorientational self-focusing,” Opt. Lett. 39, 5830–5833 (2014).
[Crossref] [PubMed]

N. Kravets, A. Piccardi, A. Alberucci, O. Buchnev, M. Kaczmarek, and G. Assanto, “Bistability with optical beams propagating in a reorientational medium,” Phys. Rev. Lett. 113, 023901 (2014).
[Crossref] [PubMed]

Krolikowski, W.

Leblond, H.

E. L. Falcão Filho, C. B. de Araújo, G. Boudebs, H. Leblond, and V. Skarka, “Robust two-dimensional spatial solitons in liquid carbon disulfide,” Phys. Rev. Lett. 110, 013901 (2013).
[Crossref] [PubMed]

Libchaber, A.

E. Braun, L. P. Faucheux, and A. Libchaber, “Strong self-focusing in nematic liquid crystals,” Phys. Rev. A 48, 611–622 (1993).
[Crossref] [PubMed]

Maneuf, S.

A. Barthelemy, S. Maneuf, and C. Froehly, “Propagation soliton et auto-confinement de faisceaux laser par non linearite optique de Kerr,” Opt. Commun. 55, 201–206 (1985).
[Crossref]

Matuszewski, M.

McDonald, G. S.

J. M. Christian, G. S. McDonald, and P. Chamorro-Posada, “Bistable Helmholtz solitons in cubic-quintic materials,” Phys. Rev. A 76, 033833 (2007).
[Crossref]

Menyuk, C. R.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[Crossref] [PubMed]

Ong, H. L.

H. L. Ong, “Optically induced Fréedericksz transition and bistability in a nematic liquid crystal,” Phys. Rev. A 28, 2393–2407 (1983).
[Crossref]

Peccianti, M.

M. Peccianti and G. Assanto, “Nematicons,” Phys. Rep. 516, 147–208 (2012).
[Crossref]

C. Conti, M. Peccianti, and G. Assanto, “Route to nonlocality and observation of accessible solitons,” Phys. Rev. Lett. 91, 073901 (2003).
[Crossref] [PubMed]

Piccardi, A.

N. Kravets, A. Piccardi, A. Alberucci, O. Buchnev, M. Kaczmarek, and G. Assanto, “Bistability with optical beams propagating in a reorientational medium,” Phys. Rev. Lett. 113, 023901 (2014).
[Crossref] [PubMed]

A. Alberucci, A. Piccardi, N. Kravets, and G. Assanto, “Beam hysteresis via reorientational self-focusing,” Opt. Lett. 39, 5830–5833 (2014).
[Crossref] [PubMed]

Schrauth, S. E.

B. Shim, S. E. Schrauth, A. L. Gaeta, M. Klein, and G. Fibich, “Loss of phase of collapsing beams,” Phys. Rev. Lett. 108, 043902 (2012).
[Crossref] [PubMed]

Shen, Y. R.

S. D. Durbin, S. M. Arakelian, and Y. R. Shen, “Optical-field-induced birefringence and Fréedericksz transition in a nematic liquid crystal,” Phys. Rev. Lett. 47, 1411–1414 (1981).
[Crossref]

Shim, B.

B. Shim, S. E. Schrauth, A. L. Gaeta, M. Klein, and G. Fibich, “Loss of phase of collapsing beams,” Phys. Rev. Lett. 108, 043902 (2012).
[Crossref] [PubMed]

Skarka, V.

E. L. Falcão Filho, C. B. de Araújo, G. Boudebs, H. Leblond, and V. Skarka, “Robust two-dimensional spatial solitons in liquid carbon disulfide,” Phys. Rev. Lett. 110, 013901 (2013).
[Crossref] [PubMed]

Stegeman, G. I.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[Crossref] [PubMed]

Suter, D.

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

Torner, L.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[Crossref] [PubMed]

Torruellas, W. E.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[Crossref] [PubMed]

Townes, C. H.

R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett. 13, 479–482 (1964).
[Crossref]

VanStryland, E. W.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[Crossref] [PubMed]

Wang, Z.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[Crossref] [PubMed]

Zakharov, A. V.

A. V. Zakharov and R. Y. Dong, “Giant optical nonlinearity in the mesophase of a nematic liquid crystals (ncl),” Phys. Rev. E 64, 031701 (2001).
[Crossref]

Appl. Phys. Lett. (1)

I. C. Khoo, “Optical bistability in nematic films utilizing self-focusing of light,” Appl. Phys. Lett. 41, 909–911 (1982).
[Crossref]

Opt. Commun. (1)

A. Barthelemy, S. Maneuf, and C. Froehly, “Propagation soliton et auto-confinement de faisceaux laser par non linearite optique de Kerr,” Opt. Commun. 55, 201–206 (1985).
[Crossref]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rep. (2)

I. C. Khoo, “Nonlinear optics of liquid crystalline materials,” Phys. Rep. 471, 221–267 (2009).
[Crossref]

M. Peccianti and G. Assanto, “Nematicons,” Phys. Rep. 516, 147–208 (2012).
[Crossref]

Phys. Rev. A (5)

M. Matuszewski, “Engineering optical soliton bistability in colloidal media,” Phys. Rev. A 81, 013820 (2010).
[Crossref]

J. M. Christian, G. S. McDonald, and P. Chamorro-Posada, “Bistable Helmholtz solitons in cubic-quintic materials,” Phys. Rev. A 76, 033833 (2007).
[Crossref]

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

E. Braun, L. P. Faucheux, and A. Libchaber, “Strong self-focusing in nematic liquid crystals,” Phys. Rev. A 48, 611–622 (1993).
[Crossref] [PubMed]

H. L. Ong, “Optically induced Fréedericksz transition and bistability in a nematic liquid crystal,” Phys. Rev. A 28, 2393–2407 (1983).
[Crossref]

Phys. Rev. E (1)

A. V. Zakharov and R. Y. Dong, “Giant optical nonlinearity in the mesophase of a nematic liquid crystals (ncl),” Phys. Rev. E 64, 031701 (2001).
[Crossref]

Phys. Rev. Lett. (9)

N. Kravets, A. Piccardi, A. Alberucci, O. Buchnev, M. Kaczmarek, and G. Assanto, “Bistability with optical beams propagating in a reorientational medium,” Phys. Rev. Lett. 113, 023901 (2014).
[Crossref] [PubMed]

C. Conti, M. Peccianti, and G. Assanto, “Route to nonlocality and observation of accessible solitons,” Phys. Rev. Lett. 91, 073901 (2003).
[Crossref] [PubMed]

A. E. Kaplan, “Bistable solitons,” Phys. Rev. Lett. 55, 1291–1294 (1985).
[Crossref] [PubMed]

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[Crossref]

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Other (2)

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[Crossref]

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[Crossref]

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Figures (3)

Fig. 1
Fig. 1 (a) Side and (b) top view of NLC planar cell; the blue arrows indicate the director distribution at rest. (c) Free energy F versus θm when K = 12×10−12N and the temperature is 18°C. (d) Soliton width versus input power P corresponding to (c). (e) Sketch of the hysteresis loop in the plane (P, θm). (f) Power threshold for a fixed Gaussian beam of waist 3.5μm versus applied bias V (blue line with crosses, left axis); the dotted lines with squares graph the loop width versus V between win = 5, 11, 35μm (from bottom to top, right axis) and a soliton with an average width of 3.5μm.

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Fig. 2
Fig. 2 Observation of the hysteresis loop by imaging beam propagation in the plane yz. (a) The input power is 2mW, corresponding to standard diffraction; the power is increased (b and c) until OFT occurs above 16.5mW; then (d) a stable nematicon is formed. Starting from a stable nematicon, the power is ramped down (b’ and c’): the beam remains self-trapped for P > 14.5mW. Further decreases in power lead to linear diffraction (a) as in first half of the cycle. The beam width w normalized to the apparent input width w0 [22] is plotted versus z for (e) P = 15.5mW and (f) P = 16.5mW; blue and red lines correspond to ramp-up (b–c) and ramp-down (b’–c’) halves of the cycle. Dashed and dotted-dashed lines are the beam widths for P = 2mW and 20mW, respectively. The observed states were stable over time intervals of the order of 30 minutes.

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Fig. 3
Fig. 3 Hysteresis of normalized beam width versus power in z = 930μm, at temperatures of (a) 16°, (b) 18° and (c) 23°C. Panel (b) corresponds to the experiment in Fig. 2. (d) Both the experimental (red stars) and the theoretical (black squares) data show that the loop shrinks at higher temperatures. The theoretical results are found with the z-invariant model [22] and effective widths 3.5 and 11μm for self-trapped and diffracting states, respectively.

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Equations (3)

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2 i k 0 n e ( θ m ) ∂ A ∂ z + D x ( θ m ) ∂ 2 A ∂ x 2 + ∂ 2 A ∂ y 2 + k 0 2 Δ n e 2 ( θ ) A = 0 ,
∇ 2 θ + ε 0 2 K ( ε a | A | 2 2 + Δ ε LF E LF 2 ) sin ( 2 θ ) = 0 .
F ≈ α κ 2 θ m 2 2 + 2 γ Z 0 P π n S w 2 ∫ − L x 2 L x 2 d x ∫ − ∞ ∞ cos ( 2 θ ) e − 2 x 2 + y 2 w 2 d y + { ε 0 Z 0 n S k 0 2 K 1 w 2 + ε 0 Z 0 n S K − γ Z 0 cos ( 2 θ m ) n S } P ,

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