Abstract

We study light propagation in nematic liquid crystals in the context of spatial optical solitons formation. We propose a simple analytical model with multiplicative nonlinearity, which represents (qualitatively) the liquid crystal response by comprising the competition between focusing (reorientational) and defocusing (thermal) nonlocal nonlinearities. We show that at sufficiently high input power the interplay between both nonlinearities leads to the formations of two-peak solitons, which represent supermodes of the self-induced extended waveguide structure. We explain the beam splitting mechanism, discuss threshold effects and conclude that similar phenomena might be present in other media with competing nonlocal nonlinearities.

© 2017 Optical Society of America

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References

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  1. G. Assanto and M. Peccianti, “Spatial solitons in nematic liquid crystals,” IEEE J. Quantum Electron. 39, 13 (2003).
    [Crossref]
  2. G. Assanto, ed. Nematicons: Spatial Optical Solitons in Nematic Liquid Crystals (Wiley, 2012).
    [Crossref]
  3. M. Warenghem, J. F. Blach, and J. F. Henninot, “Thermo-nematicon: an unnatural coexistence of solitons in liquid crystals?” J. Opt. Soc. Am. B 25, 1882 (2008).
    [Crossref]
  4. O. Bang, W. Krolikowski, J. Wyller, and J.J. Rasmussen, “Collapse arrest and soliton stabilization in nonlocal nonlinear media,” Phys. Rev. E 66, 046619 (2002).
    [Crossref]
  5. X. Hutsebaut, C. Cambournac, M. Haelterman, A. Adamski, and K. Neyts, “Single-component higher-order mode solitons in liquid crystals,” Opt. Commun. 333, 211 (2004).
    [Crossref]
  6. C. Conti, M. Peccianti, and G. Assanto, “Route to nonlocality and observation of accessible solitons,” Phys. Rev. Lett. 91, 073901 (2003).
    [Crossref] [PubMed]
  7. U. A. Laudyn, P. S. Jung, M.A. Karpierz, and G. Assanto, “Quasi two-dimensional astigmatic solitons in soft chiral metastructures,” Sci. Rep. 6, 22923 (2016).
    [Crossref] [PubMed]
  8. U. A. Laudyn, P. S. Jung, M. A. Karpierz, and G. Assanto, “Power-induced evolution and increased dimensionality of nonlinear modes in reorientational soft matter,” Opt. Lett. 39(22), 6399–6402 (2014).
    [Crossref] [PubMed]
  9. U. A. Laudyn, M. Kwasny, A. Piccardi, M. A. Karpierz, R. Dabrowski, O. Chojnowska, A. Alberucci, and G. Assanto, “Nonlinear competition in nematicon propagation,” Opt. Lett. 40(22), 5235–5238 (2015).
    [Crossref] [PubMed]
  10. M. Warenghem, J. F. Blach, and J. F. Henninot, “Thermo-nematicon: an unnatural coexistence of solitons in liquid crystals,” J. Opt. Soc. Am. B 11, 1882 (2008).
    [Crossref]
  11. P. S. Jung, W. Krolikowski, U. A. Laudyn, M. Trippenbach, and M. A. Karpierz, “Supermode spatial optical solitons in liquid crystals with competing nonlinearities,” Phys. Rev. A 95, 023820 (2017).
    [Crossref]
  12. I. Khoo, Liquid Crystals: Physical Properties and Nonlinear Optical Phenomena (Wiley, 2007), Vol. 64.
    [Crossref]
  13. R. Dabrowski, J. Dziaduszek, and T. Szczucinski, “Mecomorphic characteristics of some new homologous series with the isothiocyanato terminal group,” Mol. Cryst. Liq. Cryst. 124, 241 (1985).
    [Crossref]
  14. J. Li, S. Gauza, and S. T. Wu, “Temperature effect on liquid crystal refractive indices,” J. Appl. Phys. 96, 20 (2004).
  15. A.A. Hardy and W. Streifer, “Coupled mode theory of parallel waveguides,” IEEE J. Lightwave Techn. LT-3, 1135 (1985).
    [Crossref]
  16. M. Matuszewski, B.A. Malomed, and M. Trippenbach, “Spontaneous symmetry breaking of solitons trapped in a double channel potential,” Phys. Rev. A 75, 063621 (2007).
    [Crossref]
  17. F. Derrien, J.F. Henninot, M. Warenghem, and G. Abbate, “A thermal (2D+1) spatial optical soliton in a dye doped liquid crystal,” J. Optics A 2, 332 (2000).
    [Crossref]
  18. A. Alberucci, U. A. Laudyn, A. Piccardi, M. Kwasny, B. Klus, M.A. Karpierz, and G. Assanto, “Nonlinear continuous-wave optical propagation in nematic liquid crystals: Interplay between reorientational and thermal effects,”’ Phys. Rev. E 96, 012703 (2017).
    [Crossref]

2017 (2)

P. S. Jung, W. Krolikowski, U. A. Laudyn, M. Trippenbach, and M. A. Karpierz, “Supermode spatial optical solitons in liquid crystals with competing nonlinearities,” Phys. Rev. A 95, 023820 (2017).
[Crossref]

A. Alberucci, U. A. Laudyn, A. Piccardi, M. Kwasny, B. Klus, M.A. Karpierz, and G. Assanto, “Nonlinear continuous-wave optical propagation in nematic liquid crystals: Interplay between reorientational and thermal effects,”’ Phys. Rev. E 96, 012703 (2017).
[Crossref]

2016 (1)

U. A. Laudyn, P. S. Jung, M.A. Karpierz, and G. Assanto, “Quasi two-dimensional astigmatic solitons in soft chiral metastructures,” Sci. Rep. 6, 22923 (2016).
[Crossref] [PubMed]

2015 (1)

2014 (1)

2008 (2)

M. Warenghem, J. F. Blach, and J. F. Henninot, “Thermo-nematicon: an unnatural coexistence of solitons in liquid crystals,” J. Opt. Soc. Am. B 11, 1882 (2008).
[Crossref]

M. Warenghem, J. F. Blach, and J. F. Henninot, “Thermo-nematicon: an unnatural coexistence of solitons in liquid crystals?” J. Opt. Soc. Am. B 25, 1882 (2008).
[Crossref]

2007 (1)

M. Matuszewski, B.A. Malomed, and M. Trippenbach, “Spontaneous symmetry breaking of solitons trapped in a double channel potential,” Phys. Rev. A 75, 063621 (2007).
[Crossref]

2004 (2)

J. Li, S. Gauza, and S. T. Wu, “Temperature effect on liquid crystal refractive indices,” J. Appl. Phys. 96, 20 (2004).

X. Hutsebaut, C. Cambournac, M. Haelterman, A. Adamski, and K. Neyts, “Single-component higher-order mode solitons in liquid crystals,” Opt. Commun. 333, 211 (2004).
[Crossref]

2003 (2)

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

G. Assanto and M. Peccianti, “Spatial solitons in nematic liquid crystals,” IEEE J. Quantum Electron. 39, 13 (2003).
[Crossref]

2002 (1)

O. Bang, W. Krolikowski, J. Wyller, and J.J. Rasmussen, “Collapse arrest and soliton stabilization in nonlocal nonlinear media,” Phys. Rev. E 66, 046619 (2002).
[Crossref]

2000 (1)

F. Derrien, J.F. Henninot, M. Warenghem, and G. Abbate, “A thermal (2D+1) spatial optical soliton in a dye doped liquid crystal,” J. Optics A 2, 332 (2000).
[Crossref]

1985 (2)

A.A. Hardy and W. Streifer, “Coupled mode theory of parallel waveguides,” IEEE J. Lightwave Techn. LT-3, 1135 (1985).
[Crossref]

R. Dabrowski, J. Dziaduszek, and T. Szczucinski, “Mecomorphic characteristics of some new homologous series with the isothiocyanato terminal group,” Mol. Cryst. Liq. Cryst. 124, 241 (1985).
[Crossref]

Abbate, G.

F. Derrien, J.F. Henninot, M. Warenghem, and G. Abbate, “A thermal (2D+1) spatial optical soliton in a dye doped liquid crystal,” J. Optics A 2, 332 (2000).
[Crossref]

Adamski, A.

X. Hutsebaut, C. Cambournac, M. Haelterman, A. Adamski, and K. Neyts, “Single-component higher-order mode solitons in liquid crystals,” Opt. Commun. 333, 211 (2004).
[Crossref]

Alberucci, A.

A. Alberucci, U. A. Laudyn, A. Piccardi, M. Kwasny, B. Klus, M.A. Karpierz, and G. Assanto, “Nonlinear continuous-wave optical propagation in nematic liquid crystals: Interplay between reorientational and thermal effects,”’ Phys. Rev. E 96, 012703 (2017).
[Crossref]

U. A. Laudyn, M. Kwasny, A. Piccardi, M. A. Karpierz, R. Dabrowski, O. Chojnowska, A. Alberucci, and G. Assanto, “Nonlinear competition in nematicon propagation,” Opt. Lett. 40(22), 5235–5238 (2015).
[Crossref] [PubMed]

Assanto, G.

A. Alberucci, U. A. Laudyn, A. Piccardi, M. Kwasny, B. Klus, M.A. Karpierz, and G. Assanto, “Nonlinear continuous-wave optical propagation in nematic liquid crystals: Interplay between reorientational and thermal effects,”’ Phys. Rev. E 96, 012703 (2017).
[Crossref]

U. A. Laudyn, P. S. Jung, M.A. Karpierz, and G. Assanto, “Quasi two-dimensional astigmatic solitons in soft chiral metastructures,” Sci. Rep. 6, 22923 (2016).
[Crossref] [PubMed]

U. A. Laudyn, M. Kwasny, A. Piccardi, M. A. Karpierz, R. Dabrowski, O. Chojnowska, A. Alberucci, and G. Assanto, “Nonlinear competition in nematicon propagation,” Opt. Lett. 40(22), 5235–5238 (2015).
[Crossref] [PubMed]

U. A. Laudyn, P. S. Jung, M. A. Karpierz, and G. Assanto, “Power-induced evolution and increased dimensionality of nonlinear modes in reorientational soft matter,” Opt. Lett. 39(22), 6399–6402 (2014).
[Crossref] [PubMed]

G. Assanto and M. Peccianti, “Spatial solitons in nematic liquid crystals,” IEEE J. Quantum Electron. 39, 13 (2003).
[Crossref]

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

Bang, O.

O. Bang, W. Krolikowski, J. Wyller, and J.J. Rasmussen, “Collapse arrest and soliton stabilization in nonlocal nonlinear media,” Phys. Rev. E 66, 046619 (2002).
[Crossref]

Blach, J. F.

M. Warenghem, J. F. Blach, and J. F. Henninot, “Thermo-nematicon: an unnatural coexistence of solitons in liquid crystals,” J. Opt. Soc. Am. B 11, 1882 (2008).
[Crossref]

M. Warenghem, J. F. Blach, and J. F. Henninot, “Thermo-nematicon: an unnatural coexistence of solitons in liquid crystals?” J. Opt. Soc. Am. B 25, 1882 (2008).
[Crossref]

Cambournac, C.

X. Hutsebaut, C. Cambournac, M. Haelterman, A. Adamski, and K. Neyts, “Single-component higher-order mode solitons in liquid crystals,” Opt. Commun. 333, 211 (2004).
[Crossref]

Chojnowska, O.

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]

Dabrowski, R.

U. A. Laudyn, M. Kwasny, A. Piccardi, M. A. Karpierz, R. Dabrowski, O. Chojnowska, A. Alberucci, and G. Assanto, “Nonlinear competition in nematicon propagation,” Opt. Lett. 40(22), 5235–5238 (2015).
[Crossref] [PubMed]

R. Dabrowski, J. Dziaduszek, and T. Szczucinski, “Mecomorphic characteristics of some new homologous series with the isothiocyanato terminal group,” Mol. Cryst. Liq. Cryst. 124, 241 (1985).
[Crossref]

Derrien, F.

F. Derrien, J.F. Henninot, M. Warenghem, and G. Abbate, “A thermal (2D+1) spatial optical soliton in a dye doped liquid crystal,” J. Optics A 2, 332 (2000).
[Crossref]

Dziaduszek, J.

R. Dabrowski, J. Dziaduszek, and T. Szczucinski, “Mecomorphic characteristics of some new homologous series with the isothiocyanato terminal group,” Mol. Cryst. Liq. Cryst. 124, 241 (1985).
[Crossref]

Gauza, S.

J. Li, S. Gauza, and S. T. Wu, “Temperature effect on liquid crystal refractive indices,” J. Appl. Phys. 96, 20 (2004).

Haelterman, M.

X. Hutsebaut, C. Cambournac, M. Haelterman, A. Adamski, and K. Neyts, “Single-component higher-order mode solitons in liquid crystals,” Opt. Commun. 333, 211 (2004).
[Crossref]

Hardy, A.A.

A.A. Hardy and W. Streifer, “Coupled mode theory of parallel waveguides,” IEEE J. Lightwave Techn. LT-3, 1135 (1985).
[Crossref]

Henninot, J. F.

M. Warenghem, J. F. Blach, and J. F. Henninot, “Thermo-nematicon: an unnatural coexistence of solitons in liquid crystals,” J. Opt. Soc. Am. B 11, 1882 (2008).
[Crossref]

M. Warenghem, J. F. Blach, and J. F. Henninot, “Thermo-nematicon: an unnatural coexistence of solitons in liquid crystals?” J. Opt. Soc. Am. B 25, 1882 (2008).
[Crossref]

Henninot, J.F.

F. Derrien, J.F. Henninot, M. Warenghem, and G. Abbate, “A thermal (2D+1) spatial optical soliton in a dye doped liquid crystal,” J. Optics A 2, 332 (2000).
[Crossref]

Hutsebaut, X.

X. Hutsebaut, C. Cambournac, M. Haelterman, A. Adamski, and K. Neyts, “Single-component higher-order mode solitons in liquid crystals,” Opt. Commun. 333, 211 (2004).
[Crossref]

Jung, P. S.

P. S. Jung, W. Krolikowski, U. A. Laudyn, M. Trippenbach, and M. A. Karpierz, “Supermode spatial optical solitons in liquid crystals with competing nonlinearities,” Phys. Rev. A 95, 023820 (2017).
[Crossref]

U. A. Laudyn, P. S. Jung, M.A. Karpierz, and G. Assanto, “Quasi two-dimensional astigmatic solitons in soft chiral metastructures,” Sci. Rep. 6, 22923 (2016).
[Crossref] [PubMed]

U. A. Laudyn, P. S. Jung, M. A. Karpierz, and G. Assanto, “Power-induced evolution and increased dimensionality of nonlinear modes in reorientational soft matter,” Opt. Lett. 39(22), 6399–6402 (2014).
[Crossref] [PubMed]

Karpierz, M. A.

Karpierz, M.A.

A. Alberucci, U. A. Laudyn, A. Piccardi, M. Kwasny, B. Klus, M.A. Karpierz, and G. Assanto, “Nonlinear continuous-wave optical propagation in nematic liquid crystals: Interplay between reorientational and thermal effects,”’ Phys. Rev. E 96, 012703 (2017).
[Crossref]

U. A. Laudyn, P. S. Jung, M.A. Karpierz, and G. Assanto, “Quasi two-dimensional astigmatic solitons in soft chiral metastructures,” Sci. Rep. 6, 22923 (2016).
[Crossref] [PubMed]

Khoo, I.

I. Khoo, Liquid Crystals: Physical Properties and Nonlinear Optical Phenomena (Wiley, 2007), Vol. 64.
[Crossref]

Klus, B.

A. Alberucci, U. A. Laudyn, A. Piccardi, M. Kwasny, B. Klus, M.A. Karpierz, and G. Assanto, “Nonlinear continuous-wave optical propagation in nematic liquid crystals: Interplay between reorientational and thermal effects,”’ Phys. Rev. E 96, 012703 (2017).
[Crossref]

Krolikowski, W.

P. S. Jung, W. Krolikowski, U. A. Laudyn, M. Trippenbach, and M. A. Karpierz, “Supermode spatial optical solitons in liquid crystals with competing nonlinearities,” Phys. Rev. A 95, 023820 (2017).
[Crossref]

O. Bang, W. Krolikowski, J. Wyller, and J.J. Rasmussen, “Collapse arrest and soliton stabilization in nonlocal nonlinear media,” Phys. Rev. E 66, 046619 (2002).
[Crossref]

Kwasny, M.

A. Alberucci, U. A. Laudyn, A. Piccardi, M. Kwasny, B. Klus, M.A. Karpierz, and G. Assanto, “Nonlinear continuous-wave optical propagation in nematic liquid crystals: Interplay between reorientational and thermal effects,”’ Phys. Rev. E 96, 012703 (2017).
[Crossref]

U. A. Laudyn, M. Kwasny, A. Piccardi, M. A. Karpierz, R. Dabrowski, O. Chojnowska, A. Alberucci, and G. Assanto, “Nonlinear competition in nematicon propagation,” Opt. Lett. 40(22), 5235–5238 (2015).
[Crossref] [PubMed]

Laudyn, U. A.

A. Alberucci, U. A. Laudyn, A. Piccardi, M. Kwasny, B. Klus, M.A. Karpierz, and G. Assanto, “Nonlinear continuous-wave optical propagation in nematic liquid crystals: Interplay between reorientational and thermal effects,”’ Phys. Rev. E 96, 012703 (2017).
[Crossref]

P. S. Jung, W. Krolikowski, U. A. Laudyn, M. Trippenbach, and M. A. Karpierz, “Supermode spatial optical solitons in liquid crystals with competing nonlinearities,” Phys. Rev. A 95, 023820 (2017).
[Crossref]

U. A. Laudyn, P. S. Jung, M.A. Karpierz, and G. Assanto, “Quasi two-dimensional astigmatic solitons in soft chiral metastructures,” Sci. Rep. 6, 22923 (2016).
[Crossref] [PubMed]

U. A. Laudyn, M. Kwasny, A. Piccardi, M. A. Karpierz, R. Dabrowski, O. Chojnowska, A. Alberucci, and G. Assanto, “Nonlinear competition in nematicon propagation,” Opt. Lett. 40(22), 5235–5238 (2015).
[Crossref] [PubMed]

U. A. Laudyn, P. S. Jung, M. A. Karpierz, and G. Assanto, “Power-induced evolution and increased dimensionality of nonlinear modes in reorientational soft matter,” Opt. Lett. 39(22), 6399–6402 (2014).
[Crossref] [PubMed]

Li, J.

J. Li, S. Gauza, and S. T. Wu, “Temperature effect on liquid crystal refractive indices,” J. Appl. Phys. 96, 20 (2004).

Malomed, B.A.

M. Matuszewski, B.A. Malomed, and M. Trippenbach, “Spontaneous symmetry breaking of solitons trapped in a double channel potential,” Phys. Rev. A 75, 063621 (2007).
[Crossref]

Matuszewski, M.

M. Matuszewski, B.A. Malomed, and M. Trippenbach, “Spontaneous symmetry breaking of solitons trapped in a double channel potential,” Phys. Rev. A 75, 063621 (2007).
[Crossref]

Neyts, K.

X. Hutsebaut, C. Cambournac, M. Haelterman, A. Adamski, and K. Neyts, “Single-component higher-order mode solitons in liquid crystals,” Opt. Commun. 333, 211 (2004).
[Crossref]

Peccianti, M.

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

G. Assanto and M. Peccianti, “Spatial solitons in nematic liquid crystals,” IEEE J. Quantum Electron. 39, 13 (2003).
[Crossref]

Piccardi, A.

A. Alberucci, U. A. Laudyn, A. Piccardi, M. Kwasny, B. Klus, M.A. Karpierz, and G. Assanto, “Nonlinear continuous-wave optical propagation in nematic liquid crystals: Interplay between reorientational and thermal effects,”’ Phys. Rev. E 96, 012703 (2017).
[Crossref]

U. A. Laudyn, M. Kwasny, A. Piccardi, M. A. Karpierz, R. Dabrowski, O. Chojnowska, A. Alberucci, and G. Assanto, “Nonlinear competition in nematicon propagation,” Opt. Lett. 40(22), 5235–5238 (2015).
[Crossref] [PubMed]

Rasmussen, J.J.

O. Bang, W. Krolikowski, J. Wyller, and J.J. Rasmussen, “Collapse arrest and soliton stabilization in nonlocal nonlinear media,” Phys. Rev. E 66, 046619 (2002).
[Crossref]

Streifer, W.

A.A. Hardy and W. Streifer, “Coupled mode theory of parallel waveguides,” IEEE J. Lightwave Techn. LT-3, 1135 (1985).
[Crossref]

Szczucinski, T.

R. Dabrowski, J. Dziaduszek, and T. Szczucinski, “Mecomorphic characteristics of some new homologous series with the isothiocyanato terminal group,” Mol. Cryst. Liq. Cryst. 124, 241 (1985).
[Crossref]

Trippenbach, M.

P. S. Jung, W. Krolikowski, U. A. Laudyn, M. Trippenbach, and M. A. Karpierz, “Supermode spatial optical solitons in liquid crystals with competing nonlinearities,” Phys. Rev. A 95, 023820 (2017).
[Crossref]

M. Matuszewski, B.A. Malomed, and M. Trippenbach, “Spontaneous symmetry breaking of solitons trapped in a double channel potential,” Phys. Rev. A 75, 063621 (2007).
[Crossref]

Warenghem, M.

M. Warenghem, J. F. Blach, and J. F. Henninot, “Thermo-nematicon: an unnatural coexistence of solitons in liquid crystals,” J. Opt. Soc. Am. B 11, 1882 (2008).
[Crossref]

M. Warenghem, J. F. Blach, and J. F. Henninot, “Thermo-nematicon: an unnatural coexistence of solitons in liquid crystals?” J. Opt. Soc. Am. B 25, 1882 (2008).
[Crossref]

F. Derrien, J.F. Henninot, M. Warenghem, and G. Abbate, “A thermal (2D+1) spatial optical soliton in a dye doped liquid crystal,” J. Optics A 2, 332 (2000).
[Crossref]

Wu, S. T.

J. Li, S. Gauza, and S. T. Wu, “Temperature effect on liquid crystal refractive indices,” J. Appl. Phys. 96, 20 (2004).

Wyller, J.

O. Bang, W. Krolikowski, J. Wyller, and J.J. Rasmussen, “Collapse arrest and soliton stabilization in nonlocal nonlinear media,” Phys. Rev. E 66, 046619 (2002).
[Crossref]

IEEE J. Lightwave Techn. (1)

A.A. Hardy and W. Streifer, “Coupled mode theory of parallel waveguides,” IEEE J. Lightwave Techn. LT-3, 1135 (1985).
[Crossref]

IEEE J. Quantum Electron. (1)

G. Assanto and M. Peccianti, “Spatial solitons in nematic liquid crystals,” IEEE J. Quantum Electron. 39, 13 (2003).
[Crossref]

J. Appl. Phys. (1)

J. Li, S. Gauza, and S. T. Wu, “Temperature effect on liquid crystal refractive indices,” J. Appl. Phys. 96, 20 (2004).

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

M. Warenghem, J. F. Blach, and J. F. Henninot, “Thermo-nematicon: an unnatural coexistence of solitons in liquid crystals,” J. Opt. Soc. Am. B 11, 1882 (2008).
[Crossref]

M. Warenghem, J. F. Blach, and J. F. Henninot, “Thermo-nematicon: an unnatural coexistence of solitons in liquid crystals?” J. Opt. Soc. Am. B 25, 1882 (2008).
[Crossref]

J. Optics A (1)

F. Derrien, J.F. Henninot, M. Warenghem, and G. Abbate, “A thermal (2D+1) spatial optical soliton in a dye doped liquid crystal,” J. Optics A 2, 332 (2000).
[Crossref]

Mol. Cryst. Liq. Cryst. (1)

R. Dabrowski, J. Dziaduszek, and T. Szczucinski, “Mecomorphic characteristics of some new homologous series with the isothiocyanato terminal group,” Mol. Cryst. Liq. Cryst. 124, 241 (1985).
[Crossref]

Opt. Commun. (1)

X. Hutsebaut, C. Cambournac, M. Haelterman, A. Adamski, and K. Neyts, “Single-component higher-order mode solitons in liquid crystals,” Opt. Commun. 333, 211 (2004).
[Crossref]

Opt. Lett. (2)

Phys. Rev. A (2)

P. S. Jung, W. Krolikowski, U. A. Laudyn, M. Trippenbach, and M. A. Karpierz, “Supermode spatial optical solitons in liquid crystals with competing nonlinearities,” Phys. Rev. A 95, 023820 (2017).
[Crossref]

M. Matuszewski, B.A. Malomed, and M. Trippenbach, “Spontaneous symmetry breaking of solitons trapped in a double channel potential,” Phys. Rev. A 75, 063621 (2007).
[Crossref]

Phys. Rev. E (2)

A. Alberucci, U. A. Laudyn, A. Piccardi, M. Kwasny, B. Klus, M.A. Karpierz, and G. Assanto, “Nonlinear continuous-wave optical propagation in nematic liquid crystals: Interplay between reorientational and thermal effects,”’ Phys. Rev. E 96, 012703 (2017).
[Crossref]

O. Bang, W. Krolikowski, J. Wyller, and J.J. Rasmussen, “Collapse arrest and soliton stabilization in nonlocal nonlinear media,” Phys. Rev. E 66, 046619 (2002).
[Crossref]

Phys. Rev. Lett. (1)

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

Sci. Rep. (1)

U. A. Laudyn, P. S. Jung, M.A. Karpierz, and G. Assanto, “Quasi two-dimensional astigmatic solitons in soft chiral metastructures,” Sci. Rep. 6, 22923 (2016).
[Crossref] [PubMed]

Other (2)

G. Assanto, ed. Nematicons: Spatial Optical Solitons in Nematic Liquid Crystals (Wiley, 2012).
[Crossref]

I. Khoo, Liquid Crystals: Physical Properties and Nonlinear Optical Phenomena (Wiley, 2007), Vol. 64.
[Crossref]

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Figures (4)

Fig. 1
Fig. 1 Planar configuration of the nematic liquid crystal cell considered in this work. Beam propagation direction is represented by red arrow.
Fig. 2
Fig. 2 (a) Ordinary no (solid line) and extraordinary ne (dashed line) indices versus temperature T for two types of NLC’s. Red corresponds to “6CHBT” crystal and black to “1110”. (b) Analogous plot presenting temperature dependence of elastic constant K (solid line) and Δε/K (dashed line) [18]. (c) Quality of our approximation for 6CHBT and (d) 1110 described by n 2 ( θ , T ) n 2 ( θ 0 , T ) Γ ( T ) Θ ( θ , θ 0 ) vs θ and T for θo = 0o, where the numerator is calculated from the exact model of NLC.
Fig. 3
Fig. 3 (a) An example of nonlinear response of α (black line) and β (red line) for spatial intensity (|ψ|2) profile (blue dashes line). (b) Soliton solutions for multiplicative model with competing focusing and defocusing nonlocal nonlinearities as a function of beam power (system parameters σ = 40 and γ = 0.1). Spatial intensity |ψ|2 (solid black line) and nonlinear response α (|ψ|2) β (|ψ|2) (solid red line) profiles are shown [total power (b) P=350 (c) P=380 (d) P=390 (e) P=420].
Fig. 4
Fig. 4 (a) Illustrating the threshold power Pth (left axis) of supermode soliton formation as a function of the degree of nonlocality σ, for different values of the relative strength of defocusing, γ = 0.1 (red lines) and γ = 0.2 (blue lines). The right axis refers to the ratio κ = P t h ( n u m ) / P t h. (b) Comparison of the threshold power Pth calculated using three different models: Eq. (2) (exact), Eq. (6) (simplified) and Eq. (7) (phenomenological). In the phenomenological model (Eq. (7)) we used: σ = no (θo) kod, γ = a/θo + b and d = 50μm for the width of the liquid crystal cell. Here a = 0.29(0.09), b = 0.09(0.04) for “1110” (“6CHBT”) crystal.

Equations (9)

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n ( θ , T ) = n o ( T ) n e ( T ) n o 2 ( T ) + Δ ϵ cos 2 θ
2 i k o n ( θ 0 , T ) E z = 2 E x 2 + k o 2 ( n 2 ( θ , T ) n 2 ( θ 0 , T ) ) E ,
2 θ x 2 Δ ε ( T ) ε o 2 K ( T ) sin 2 θ | E | 2 = 0 .
κ 2 T x 2 + c ε 0 α 2 | E | 2 = 0 .
n 2 ( θ , T ) n 2 ( θ 0 , T ) ( n e 2 ( T ) n o 2 ( T ) ) ( cos 2 θ cos 2 θ 0 ) = Γ ( T ) Θ ( θ , θ 0 ) ,
2 i k o n ( θ 0 ) E z = 2 E x 2 + k o 2 Γ ( T ) Θ ( θ , θ 0 ) E ,
i ψ ζ = 1 2 2 ψ ξ 2 + N ( | ψ | 2 ) ψ ,
α ( | ψ | 2 ) = R 1 ( ξ ξ ) | ψ | 2 d ξ , β ( | ψ | 2 ) = 1 γ R 2 ( ξ ξ ) | ψ | 2 d ξ ,
P π 0.5 w 2 + σ 2 2 γ .

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