Abstract

Dynamical and steady-state behavior of beams propagating in nematic liquid crystals (NLCs) is analyzed. A well-known model for the beam propagation and the director reorientation angle in a NLC cell is treated numerically in space and time. The formation of steady-state soliton breathers in a threshold region of beam intensities is displayed. Below the region the beams diffract, above the region spatiotemporal instabilities develop, as the input intensity and the material parameters are varied. Curiously, the only kind of solitons we could demonstrate in our numerical studies was the breathers. Despite repeated efforts, we could not find the solitons with a steady profile propagating in the NLC model at hand.

© 2009 Optical Society of America

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References

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  1. I. C. Khoo, Liquid Crystals: Physical Properties and Nonlinear Optical Phenomena (Wiley, New York, 1995).
  2. Y. S. Kivshar and G. P. Agrawal, Optical solitons (Academic Press, San Diego, 2003).
  3. G. Assanto, M. Peccianti, K. Brzdakiewicz, A. De Luca, and C. Umeton, “Nonlinear wave propagation and spatial solitons in nematic liquid crystals,” J. Nonlinear Opt. Phys. Mater. 12, 123–134 (2003).
    [Crossref]
  4. X. Hutsebaut, C. Cambournac, M. Haelterman, J. Beeckman, and K. Neyts, “Measurement of the self-induced waveguide of a solitonlike optical beam in a nematic liquid crystal,” J. Opt. Soc. Am. B 22, 1424–1431 (2005).
    [Crossref]
  5. A.I. Strinić, D.V. Timotijević, D. Arsenović, M.S. Petrović, and M.R. Belic, “Spatiotemporal optical instabilities in nematic solitons,” Opt. Express 13, 493–504 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=OPEX-13-2-493.
    [Crossref] [PubMed]
  6. P. D. Rasmussen, O. Bang, and W. Krolikowski, “Theory of nonlocal soliton interaction in nematic liquid crystals,” Phys. Rev. E 72, 066611 1–7 (2005).
    [Crossref]
  7. G. D’Alessandro and A. A. Wheeler, “Bistability of liquid crystal microcavities,” Phys. Rev. A 67, 023816 1–12 (2003).
  8. J. F. Henninot, M. Debailleul, and M. Warenghem, “Tunable non-locality of thermal non-linearity in dye doped nematic liquid crystal,” Mol. Cryst. Liq. Cryst. 375, 631–640 (2002).
    [Crossref]
  9. T. M. Monro, C. Martijn de Sterke, and L. Poladian, “Investigation of waveguide growth in photosensitive germanosilicate glass,” J. Opt. Soc. Am. B. 13, 2824–2832 (1996).
    [Crossref]
  10. S. LaRochelle, V. Mizrahi, G. I. Stegeman, and J. E. Sipe, “Growth dynamics of photosensitive gratings in optical fibers,” Appl. Phys. Lett. 57, 747–749 (1990).
    [Crossref]
  11. T. M. Monro, C. Martijn de Sterke, and L. Poladian, “Catching light in its own trap,” J. Mod. Opt. 48, 191–238 (2001).
  12. A. S. Kewitsch and A. Yariv, “Nonlinear optical properties of photoresists for projection lithography,” Appl. Phys. Lett. 68, 455–457 (1996).
    [Crossref]
  13. A. A. Sukhorukov, S. Shoji, Y. S. Kivshar, and S. Kawata, “Self-written waveguides in photosensitive materials,” J. Nonlinear Opt. Phys. Mater. 11, 391–407 (2002).
    [Crossref]
  14. K. D. Dorkenoo, F. Gillot, O. Crégut, Y. Sonnefraud, A. Fort, and H. Leblond, “Control of the refractive index in photopolymerizable materials for (2+1)D solitary wave guide formation,” Phys. Rev. Lett. 93, 143905 1–4 (2004).
    [Crossref]
  15. M. Peccianti, A. De Rossi, G. Assanto, A. De Luca, C. Umeton, and I. Khoo, “Electrically assisted self-confinement and waveguiding in planar nematic liquid crystal cells,” Appl. Phys. Lett. 77, 7–9 (2000).
    [Crossref]
  16. J. Beeckman, K. Neyts, X. Hutsebaut, C. Cambournac, and M. Haelterman, “Simulations and experiments on self-focusing conditions in nematic liquid-crystal planar cells,” Opt. Express 12, 1011–1018 (2004), http://www.opticsinfobase.org/oe/abstract.cfm?URI=OPEX-12-6-1011.
    [Crossref] [PubMed]
  17. J. Beeckman, K. Neyts, X. Hutsebaut, C. Cambournac, and M. Haelterman, “Time-dependence of soliton formation in planar cells of nematic liquid crystals,” IEEE J. Quantum Electron. 41, 735–740 (2005).
    [Crossref]
  18. A. Strinić, D. Jović, M. Petrović, D. Timotijević, N. Aleksić, and M. Belić, “Counterpropagating beams in nematic liquid crystals,” Opt. Express 14, 12310–12315 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-25-12310.
    [Crossref] [PubMed]
  19. W. Krolikowski, O. Bang, N. Nikolov, D. Neshev, J. Wyller, J. Rasmussen, and D. Edmundson, “Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media,” J. Opt. B 6, S288–S294 (2004).
    [Crossref]
  20. C. Conti, M. Peccianti, and G. Assanto, “Route to nonlocality and observation of accessible solitons,” Phys. Rev. Lett. 91, 073901 1–4 (2003).
    [Crossref]
  21. C. Conti, M. Peccianti, and G. Assanto, “Observation of optical spatial solitons in a highly nonlocal medium,” Phys. Rev. Lett. 92, 113902 1–4 (2004).
    [Crossref]
  22. M. Peccianti, C. Conti, and G. Assanto, “Optical modulational instability in a nonlocal medium,” Phys. Rev. E 68, 025602(R) 1–4 (2003).
    [Crossref]
  23. G. Assanto, M. Peccianti, and C. Conti, “One dimensional transverse modulational instability in nonlocal media witha reorientational nonlinearity,” IEEE J. Sel. Top. Quantum Electron. 10, 862–869 (2004).
    [Crossref]
  24. A. I. Strinic and M. R. Belic, “Beam propagation in nematic liquid crystals,” Acta Phys. Pol. A,  Vol. 112(5), 877–883 (2007).
  25. M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, “Nonlocal optical propagation in nonlinear nematic liquid crystals,” J. Nonlinear Opt. Phys. Mater. 12, 525–538 (2003).
    [Crossref]
  26. J.F. Henninot, J.F. Blach, and M. Warenghem, “The investigation of an electrically stabilized optical spatial soliton induced in a nematic liquid crystal,” J. Opt. A: Pure Appl. Opt. 10, 085704 (2008).
    [Crossref]
  27. A. W. Snyder and D. J. Mitchell, “Accessible solitons,” Science 276, 1538–1541 (1997).
    [Crossref]

2008 (1)

J.F. Henninot, J.F. Blach, and M. Warenghem, “The investigation of an electrically stabilized optical spatial soliton induced in a nematic liquid crystal,” J. Opt. A: Pure Appl. Opt. 10, 085704 (2008).
[Crossref]

2007 (1)

A. I. Strinic and M. R. Belic, “Beam propagation in nematic liquid crystals,” Acta Phys. Pol. A,  Vol. 112(5), 877–883 (2007).

2006 (1)

2005 (4)

A.I. Strinić, D.V. Timotijević, D. Arsenović, M.S. Petrović, and M.R. Belic, “Spatiotemporal optical instabilities in nematic solitons,” Opt. Express 13, 493–504 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=OPEX-13-2-493.
[Crossref] [PubMed]

X. Hutsebaut, C. Cambournac, M. Haelterman, J. Beeckman, and K. Neyts, “Measurement of the self-induced waveguide of a solitonlike optical beam in a nematic liquid crystal,” J. Opt. Soc. Am. B 22, 1424–1431 (2005).
[Crossref]

J. Beeckman, K. Neyts, X. Hutsebaut, C. Cambournac, and M. Haelterman, “Time-dependence of soliton formation in planar cells of nematic liquid crystals,” IEEE J. Quantum Electron. 41, 735–740 (2005).
[Crossref]

P. D. Rasmussen, O. Bang, and W. Krolikowski, “Theory of nonlocal soliton interaction in nematic liquid crystals,” Phys. Rev. E 72, 066611 1–7 (2005).
[Crossref]

2004 (5)

K. D. Dorkenoo, F. Gillot, O. Crégut, Y. Sonnefraud, A. Fort, and H. Leblond, “Control of the refractive index in photopolymerizable materials for (2+1)D solitary wave guide formation,” Phys. Rev. Lett. 93, 143905 1–4 (2004).
[Crossref]

G. Assanto, M. Peccianti, and C. Conti, “One dimensional transverse modulational instability in nonlocal media witha reorientational nonlinearity,” IEEE J. Sel. Top. Quantum Electron. 10, 862–869 (2004).
[Crossref]

W. Krolikowski, O. Bang, N. Nikolov, D. Neshev, J. Wyller, J. Rasmussen, and D. Edmundson, “Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media,” J. Opt. B 6, S288–S294 (2004).
[Crossref]

C. Conti, M. Peccianti, and G. Assanto, “Observation of optical spatial solitons in a highly nonlocal medium,” Phys. Rev. Lett. 92, 113902 1–4 (2004).
[Crossref]

J. Beeckman, K. Neyts, X. Hutsebaut, C. Cambournac, and M. Haelterman, “Simulations and experiments on self-focusing conditions in nematic liquid-crystal planar cells,” Opt. Express 12, 1011–1018 (2004), http://www.opticsinfobase.org/oe/abstract.cfm?URI=OPEX-12-6-1011.
[Crossref] [PubMed]

2003 (5)

G. Assanto, M. Peccianti, K. Brzdakiewicz, A. De Luca, and C. Umeton, “Nonlinear wave propagation and spatial solitons in nematic liquid crystals,” J. Nonlinear Opt. Phys. Mater. 12, 123–134 (2003).
[Crossref]

M. Peccianti, C. Conti, and G. Assanto, “Optical modulational instability in a nonlocal medium,” Phys. Rev. E 68, 025602(R) 1–4 (2003).
[Crossref]

C. Conti, M. Peccianti, and G. Assanto, “Route to nonlocality and observation of accessible solitons,” Phys. Rev. Lett. 91, 073901 1–4 (2003).
[Crossref]

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, “Nonlocal optical propagation in nonlinear nematic liquid crystals,” J. Nonlinear Opt. Phys. Mater. 12, 525–538 (2003).
[Crossref]

G. D’Alessandro and A. A. Wheeler, “Bistability of liquid crystal microcavities,” Phys. Rev. A 67, 023816 1–12 (2003).

2002 (2)

J. F. Henninot, M. Debailleul, and M. Warenghem, “Tunable non-locality of thermal non-linearity in dye doped nematic liquid crystal,” Mol. Cryst. Liq. Cryst. 375, 631–640 (2002).
[Crossref]

A. A. Sukhorukov, S. Shoji, Y. S. Kivshar, and S. Kawata, “Self-written waveguides in photosensitive materials,” J. Nonlinear Opt. Phys. Mater. 11, 391–407 (2002).
[Crossref]

2001 (1)

T. M. Monro, C. Martijn de Sterke, and L. Poladian, “Catching light in its own trap,” J. Mod. Opt. 48, 191–238 (2001).

2000 (1)

M. Peccianti, A. De Rossi, G. Assanto, A. De Luca, C. Umeton, and I. Khoo, “Electrically assisted self-confinement and waveguiding in planar nematic liquid crystal cells,” Appl. Phys. Lett. 77, 7–9 (2000).
[Crossref]

1997 (1)

A. W. Snyder and D. J. Mitchell, “Accessible solitons,” Science 276, 1538–1541 (1997).
[Crossref]

1996 (2)

A. S. Kewitsch and A. Yariv, “Nonlinear optical properties of photoresists for projection lithography,” Appl. Phys. Lett. 68, 455–457 (1996).
[Crossref]

T. M. Monro, C. Martijn de Sterke, and L. Poladian, “Investigation of waveguide growth in photosensitive germanosilicate glass,” J. Opt. Soc. Am. B. 13, 2824–2832 (1996).
[Crossref]

1990 (1)

S. LaRochelle, V. Mizrahi, G. I. Stegeman, and J. E. Sipe, “Growth dynamics of photosensitive gratings in optical fibers,” Appl. Phys. Lett. 57, 747–749 (1990).
[Crossref]

Agrawal, G. P.

Y. S. Kivshar and G. P. Agrawal, Optical solitons (Academic Press, San Diego, 2003).

Aleksic, N.

Arsenovic, D.

Assanto, G.

C. Conti, M. Peccianti, and G. Assanto, “Observation of optical spatial solitons in a highly nonlocal medium,” Phys. Rev. Lett. 92, 113902 1–4 (2004).
[Crossref]

G. Assanto, M. Peccianti, and C. Conti, “One dimensional transverse modulational instability in nonlocal media witha reorientational nonlinearity,” IEEE J. Sel. Top. Quantum Electron. 10, 862–869 (2004).
[Crossref]

M. Peccianti, C. Conti, and G. Assanto, “Optical modulational instability in a nonlocal medium,” Phys. Rev. E 68, 025602(R) 1–4 (2003).
[Crossref]

C. Conti, M. Peccianti, and G. Assanto, “Route to nonlocality and observation of accessible solitons,” Phys. Rev. Lett. 91, 073901 1–4 (2003).
[Crossref]

G. Assanto, M. Peccianti, K. Brzdakiewicz, A. De Luca, and C. Umeton, “Nonlinear wave propagation and spatial solitons in nematic liquid crystals,” J. Nonlinear Opt. Phys. Mater. 12, 123–134 (2003).
[Crossref]

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, “Nonlocal optical propagation in nonlinear nematic liquid crystals,” J. Nonlinear Opt. Phys. Mater. 12, 525–538 (2003).
[Crossref]

M. Peccianti, A. De Rossi, G. Assanto, A. De Luca, C. Umeton, and I. Khoo, “Electrically assisted self-confinement and waveguiding in planar nematic liquid crystal cells,” Appl. Phys. Lett. 77, 7–9 (2000).
[Crossref]

Bang, O.

P. D. Rasmussen, O. Bang, and W. Krolikowski, “Theory of nonlocal soliton interaction in nematic liquid crystals,” Phys. Rev. E 72, 066611 1–7 (2005).
[Crossref]

W. Krolikowski, O. Bang, N. Nikolov, D. Neshev, J. Wyller, J. Rasmussen, and D. Edmundson, “Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media,” J. Opt. B 6, S288–S294 (2004).
[Crossref]

Beeckman, J.

Belic, M.

Belic, M. R.

A. I. Strinic and M. R. Belic, “Beam propagation in nematic liquid crystals,” Acta Phys. Pol. A,  Vol. 112(5), 877–883 (2007).

Belic, M.R.

Blach, J.F.

J.F. Henninot, J.F. Blach, and M. Warenghem, “The investigation of an electrically stabilized optical spatial soliton induced in a nematic liquid crystal,” J. Opt. A: Pure Appl. Opt. 10, 085704 (2008).
[Crossref]

Brzdakiewicz, K.

G. Assanto, M. Peccianti, K. Brzdakiewicz, A. De Luca, and C. Umeton, “Nonlinear wave propagation and spatial solitons in nematic liquid crystals,” J. Nonlinear Opt. Phys. Mater. 12, 123–134 (2003).
[Crossref]

Cambournac, C.

Conti, C.

G. Assanto, M. Peccianti, and C. Conti, “One dimensional transverse modulational instability in nonlocal media witha reorientational nonlinearity,” IEEE J. Sel. Top. Quantum Electron. 10, 862–869 (2004).
[Crossref]

C. Conti, M. Peccianti, and G. Assanto, “Observation of optical spatial solitons in a highly nonlocal medium,” Phys. Rev. Lett. 92, 113902 1–4 (2004).
[Crossref]

C. Conti, M. Peccianti, and G. Assanto, “Route to nonlocality and observation of accessible solitons,” Phys. Rev. Lett. 91, 073901 1–4 (2003).
[Crossref]

M. Peccianti, C. Conti, and G. Assanto, “Optical modulational instability in a nonlocal medium,” Phys. Rev. E 68, 025602(R) 1–4 (2003).
[Crossref]

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, “Nonlocal optical propagation in nonlinear nematic liquid crystals,” J. Nonlinear Opt. Phys. Mater. 12, 525–538 (2003).
[Crossref]

Crégut, O.

K. D. Dorkenoo, F. Gillot, O. Crégut, Y. Sonnefraud, A. Fort, and H. Leblond, “Control of the refractive index in photopolymerizable materials for (2+1)D solitary wave guide formation,” Phys. Rev. Lett. 93, 143905 1–4 (2004).
[Crossref]

D’Alessandro, G.

G. D’Alessandro and A. A. Wheeler, “Bistability of liquid crystal microcavities,” Phys. Rev. A 67, 023816 1–12 (2003).

De Luca, A.

G. Assanto, M. Peccianti, K. Brzdakiewicz, A. De Luca, and C. Umeton, “Nonlinear wave propagation and spatial solitons in nematic liquid crystals,” J. Nonlinear Opt. Phys. Mater. 12, 123–134 (2003).
[Crossref]

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, “Nonlocal optical propagation in nonlinear nematic liquid crystals,” J. Nonlinear Opt. Phys. Mater. 12, 525–538 (2003).
[Crossref]

M. Peccianti, A. De Rossi, G. Assanto, A. De Luca, C. Umeton, and I. Khoo, “Electrically assisted self-confinement and waveguiding in planar nematic liquid crystal cells,” Appl. Phys. Lett. 77, 7–9 (2000).
[Crossref]

De Rossi, A.

M. Peccianti, A. De Rossi, G. Assanto, A. De Luca, C. Umeton, and I. Khoo, “Electrically assisted self-confinement and waveguiding in planar nematic liquid crystal cells,” Appl. Phys. Lett. 77, 7–9 (2000).
[Crossref]

Debailleul, M.

J. F. Henninot, M. Debailleul, and M. Warenghem, “Tunable non-locality of thermal non-linearity in dye doped nematic liquid crystal,” Mol. Cryst. Liq. Cryst. 375, 631–640 (2002).
[Crossref]

Dorkenoo, K. D.

K. D. Dorkenoo, F. Gillot, O. Crégut, Y. Sonnefraud, A. Fort, and H. Leblond, “Control of the refractive index in photopolymerizable materials for (2+1)D solitary wave guide formation,” Phys. Rev. Lett. 93, 143905 1–4 (2004).
[Crossref]

Edmundson, D.

W. Krolikowski, O. Bang, N. Nikolov, D. Neshev, J. Wyller, J. Rasmussen, and D. Edmundson, “Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media,” J. Opt. B 6, S288–S294 (2004).
[Crossref]

Fort, A.

K. D. Dorkenoo, F. Gillot, O. Crégut, Y. Sonnefraud, A. Fort, and H. Leblond, “Control of the refractive index in photopolymerizable materials for (2+1)D solitary wave guide formation,” Phys. Rev. Lett. 93, 143905 1–4 (2004).
[Crossref]

Gillot, F.

K. D. Dorkenoo, F. Gillot, O. Crégut, Y. Sonnefraud, A. Fort, and H. Leblond, “Control of the refractive index in photopolymerizable materials for (2+1)D solitary wave guide formation,” Phys. Rev. Lett. 93, 143905 1–4 (2004).
[Crossref]

Haelterman, M.

Henninot, J. F.

J. F. Henninot, M. Debailleul, and M. Warenghem, “Tunable non-locality of thermal non-linearity in dye doped nematic liquid crystal,” Mol. Cryst. Liq. Cryst. 375, 631–640 (2002).
[Crossref]

Henninot, J.F.

J.F. Henninot, J.F. Blach, and M. Warenghem, “The investigation of an electrically stabilized optical spatial soliton induced in a nematic liquid crystal,” J. Opt. A: Pure Appl. Opt. 10, 085704 (2008).
[Crossref]

Hutsebaut, X.

Jovic, D.

Kawata, S.

A. A. Sukhorukov, S. Shoji, Y. S. Kivshar, and S. Kawata, “Self-written waveguides in photosensitive materials,” J. Nonlinear Opt. Phys. Mater. 11, 391–407 (2002).
[Crossref]

Kewitsch, A. S.

A. S. Kewitsch and A. Yariv, “Nonlinear optical properties of photoresists for projection lithography,” Appl. Phys. Lett. 68, 455–457 (1996).
[Crossref]

Khoo, I.

M. Peccianti, A. De Rossi, G. Assanto, A. De Luca, C. Umeton, and I. Khoo, “Electrically assisted self-confinement and waveguiding in planar nematic liquid crystal cells,” Appl. Phys. Lett. 77, 7–9 (2000).
[Crossref]

Khoo, I. C.

I. C. Khoo, Liquid Crystals: Physical Properties and Nonlinear Optical Phenomena (Wiley, New York, 1995).

Kivshar, Y. S.

A. A. Sukhorukov, S. Shoji, Y. S. Kivshar, and S. Kawata, “Self-written waveguides in photosensitive materials,” J. Nonlinear Opt. Phys. Mater. 11, 391–407 (2002).
[Crossref]

Y. S. Kivshar and G. P. Agrawal, Optical solitons (Academic Press, San Diego, 2003).

Krolikowski, W.

P. D. Rasmussen, O. Bang, and W. Krolikowski, “Theory of nonlocal soliton interaction in nematic liquid crystals,” Phys. Rev. E 72, 066611 1–7 (2005).
[Crossref]

W. Krolikowski, O. Bang, N. Nikolov, D. Neshev, J. Wyller, J. Rasmussen, and D. Edmundson, “Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media,” J. Opt. B 6, S288–S294 (2004).
[Crossref]

LaRochelle, S.

S. LaRochelle, V. Mizrahi, G. I. Stegeman, and J. E. Sipe, “Growth dynamics of photosensitive gratings in optical fibers,” Appl. Phys. Lett. 57, 747–749 (1990).
[Crossref]

Leblond, H.

K. D. Dorkenoo, F. Gillot, O. Crégut, Y. Sonnefraud, A. Fort, and H. Leblond, “Control of the refractive index in photopolymerizable materials for (2+1)D solitary wave guide formation,” Phys. Rev. Lett. 93, 143905 1–4 (2004).
[Crossref]

Martijn de Sterke, C.

T. M. Monro, C. Martijn de Sterke, and L. Poladian, “Catching light in its own trap,” J. Mod. Opt. 48, 191–238 (2001).

T. M. Monro, C. Martijn de Sterke, and L. Poladian, “Investigation of waveguide growth in photosensitive germanosilicate glass,” J. Opt. Soc. Am. B. 13, 2824–2832 (1996).
[Crossref]

Mitchell, D. J.

A. W. Snyder and D. J. Mitchell, “Accessible solitons,” Science 276, 1538–1541 (1997).
[Crossref]

Mizrahi, V.

S. LaRochelle, V. Mizrahi, G. I. Stegeman, and J. E. Sipe, “Growth dynamics of photosensitive gratings in optical fibers,” Appl. Phys. Lett. 57, 747–749 (1990).
[Crossref]

Monro, T. M.

T. M. Monro, C. Martijn de Sterke, and L. Poladian, “Catching light in its own trap,” J. Mod. Opt. 48, 191–238 (2001).

T. M. Monro, C. Martijn de Sterke, and L. Poladian, “Investigation of waveguide growth in photosensitive germanosilicate glass,” J. Opt. Soc. Am. B. 13, 2824–2832 (1996).
[Crossref]

Neshev, D.

W. Krolikowski, O. Bang, N. Nikolov, D. Neshev, J. Wyller, J. Rasmussen, and D. Edmundson, “Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media,” J. Opt. B 6, S288–S294 (2004).
[Crossref]

Neyts, K.

Nikolov, N.

W. Krolikowski, O. Bang, N. Nikolov, D. Neshev, J. Wyller, J. Rasmussen, and D. Edmundson, “Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media,” J. Opt. B 6, S288–S294 (2004).
[Crossref]

Peccianti, M.

C. Conti, M. Peccianti, and G. Assanto, “Observation of optical spatial solitons in a highly nonlocal medium,” Phys. Rev. Lett. 92, 113902 1–4 (2004).
[Crossref]

G. Assanto, M. Peccianti, and C. Conti, “One dimensional transverse modulational instability in nonlocal media witha reorientational nonlinearity,” IEEE J. Sel. Top. Quantum Electron. 10, 862–869 (2004).
[Crossref]

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, “Nonlocal optical propagation in nonlinear nematic liquid crystals,” J. Nonlinear Opt. Phys. Mater. 12, 525–538 (2003).
[Crossref]

C. Conti, M. Peccianti, and G. Assanto, “Route to nonlocality and observation of accessible solitons,” Phys. Rev. Lett. 91, 073901 1–4 (2003).
[Crossref]

M. Peccianti, C. Conti, and G. Assanto, “Optical modulational instability in a nonlocal medium,” Phys. Rev. E 68, 025602(R) 1–4 (2003).
[Crossref]

G. Assanto, M. Peccianti, K. Brzdakiewicz, A. De Luca, and C. Umeton, “Nonlinear wave propagation and spatial solitons in nematic liquid crystals,” J. Nonlinear Opt. Phys. Mater. 12, 123–134 (2003).
[Crossref]

M. Peccianti, A. De Rossi, G. Assanto, A. De Luca, C. Umeton, and I. Khoo, “Electrically assisted self-confinement and waveguiding in planar nematic liquid crystal cells,” Appl. Phys. Lett. 77, 7–9 (2000).
[Crossref]

Petrovic, M.

Petrovic, M.S.

Poladian, L.

T. M. Monro, C. Martijn de Sterke, and L. Poladian, “Catching light in its own trap,” J. Mod. Opt. 48, 191–238 (2001).

T. M. Monro, C. Martijn de Sterke, and L. Poladian, “Investigation of waveguide growth in photosensitive germanosilicate glass,” J. Opt. Soc. Am. B. 13, 2824–2832 (1996).
[Crossref]

Rasmussen, J.

W. Krolikowski, O. Bang, N. Nikolov, D. Neshev, J. Wyller, J. Rasmussen, and D. Edmundson, “Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media,” J. Opt. B 6, S288–S294 (2004).
[Crossref]

Rasmussen, P. D.

P. D. Rasmussen, O. Bang, and W. Krolikowski, “Theory of nonlocal soliton interaction in nematic liquid crystals,” Phys. Rev. E 72, 066611 1–7 (2005).
[Crossref]

Shoji, S.

A. A. Sukhorukov, S. Shoji, Y. S. Kivshar, and S. Kawata, “Self-written waveguides in photosensitive materials,” J. Nonlinear Opt. Phys. Mater. 11, 391–407 (2002).
[Crossref]

Sipe, J. E.

S. LaRochelle, V. Mizrahi, G. I. Stegeman, and J. E. Sipe, “Growth dynamics of photosensitive gratings in optical fibers,” Appl. Phys. Lett. 57, 747–749 (1990).
[Crossref]

Snyder, A. W.

A. W. Snyder and D. J. Mitchell, “Accessible solitons,” Science 276, 1538–1541 (1997).
[Crossref]

Sonnefraud, Y.

K. D. Dorkenoo, F. Gillot, O. Crégut, Y. Sonnefraud, A. Fort, and H. Leblond, “Control of the refractive index in photopolymerizable materials for (2+1)D solitary wave guide formation,” Phys. Rev. Lett. 93, 143905 1–4 (2004).
[Crossref]

Stegeman, G. I.

S. LaRochelle, V. Mizrahi, G. I. Stegeman, and J. E. Sipe, “Growth dynamics of photosensitive gratings in optical fibers,” Appl. Phys. Lett. 57, 747–749 (1990).
[Crossref]

Strinic, A.

Strinic, A. I.

A. I. Strinic and M. R. Belic, “Beam propagation in nematic liquid crystals,” Acta Phys. Pol. A,  Vol. 112(5), 877–883 (2007).

Strinic, A.I.

Sukhorukov, A. A.

A. A. Sukhorukov, S. Shoji, Y. S. Kivshar, and S. Kawata, “Self-written waveguides in photosensitive materials,” J. Nonlinear Opt. Phys. Mater. 11, 391–407 (2002).
[Crossref]

Timotijevic, D.

Timotijevic, D.V.

Umeton, C.

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, “Nonlocal optical propagation in nonlinear nematic liquid crystals,” J. Nonlinear Opt. Phys. Mater. 12, 525–538 (2003).
[Crossref]

G. Assanto, M. Peccianti, K. Brzdakiewicz, A. De Luca, and C. Umeton, “Nonlinear wave propagation and spatial solitons in nematic liquid crystals,” J. Nonlinear Opt. Phys. Mater. 12, 123–134 (2003).
[Crossref]

M. Peccianti, A. De Rossi, G. Assanto, A. De Luca, C. Umeton, and I. Khoo, “Electrically assisted self-confinement and waveguiding in planar nematic liquid crystal cells,” Appl. Phys. Lett. 77, 7–9 (2000).
[Crossref]

Warenghem, M.

J.F. Henninot, J.F. Blach, and M. Warenghem, “The investigation of an electrically stabilized optical spatial soliton induced in a nematic liquid crystal,” J. Opt. A: Pure Appl. Opt. 10, 085704 (2008).
[Crossref]

J. F. Henninot, M. Debailleul, and M. Warenghem, “Tunable non-locality of thermal non-linearity in dye doped nematic liquid crystal,” Mol. Cryst. Liq. Cryst. 375, 631–640 (2002).
[Crossref]

Wheeler, A. A.

G. D’Alessandro and A. A. Wheeler, “Bistability of liquid crystal microcavities,” Phys. Rev. A 67, 023816 1–12 (2003).

Wyller, J.

W. Krolikowski, O. Bang, N. Nikolov, D. Neshev, J. Wyller, J. Rasmussen, and D. Edmundson, “Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media,” J. Opt. B 6, S288–S294 (2004).
[Crossref]

Yariv, A.

A. S. Kewitsch and A. Yariv, “Nonlinear optical properties of photoresists for projection lithography,” Appl. Phys. Lett. 68, 455–457 (1996).
[Crossref]

Acta Phys. Pol. A (1)

A. I. Strinic and M. R. Belic, “Beam propagation in nematic liquid crystals,” Acta Phys. Pol. A,  Vol. 112(5), 877–883 (2007).

Appl. Phys. Lett. (3)

S. LaRochelle, V. Mizrahi, G. I. Stegeman, and J. E. Sipe, “Growth dynamics of photosensitive gratings in optical fibers,” Appl. Phys. Lett. 57, 747–749 (1990).
[Crossref]

A. S. Kewitsch and A. Yariv, “Nonlinear optical properties of photoresists for projection lithography,” Appl. Phys. Lett. 68, 455–457 (1996).
[Crossref]

M. Peccianti, A. De Rossi, G. Assanto, A. De Luca, C. Umeton, and I. Khoo, “Electrically assisted self-confinement and waveguiding in planar nematic liquid crystal cells,” Appl. Phys. Lett. 77, 7–9 (2000).
[Crossref]

IEEE J. Quantum Electron. (1)

J. Beeckman, K. Neyts, X. Hutsebaut, C. Cambournac, and M. Haelterman, “Time-dependence of soliton formation in planar cells of nematic liquid crystals,” IEEE J. Quantum Electron. 41, 735–740 (2005).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

G. Assanto, M. Peccianti, and C. Conti, “One dimensional transverse modulational instability in nonlocal media witha reorientational nonlinearity,” IEEE J. Sel. Top. Quantum Electron. 10, 862–869 (2004).
[Crossref]

J. Mod. Opt. (1)

T. M. Monro, C. Martijn de Sterke, and L. Poladian, “Catching light in its own trap,” J. Mod. Opt. 48, 191–238 (2001).

J. Nonlinear Opt. Phys. Mater. (3)

A. A. Sukhorukov, S. Shoji, Y. S. Kivshar, and S. Kawata, “Self-written waveguides in photosensitive materials,” J. Nonlinear Opt. Phys. Mater. 11, 391–407 (2002).
[Crossref]

G. Assanto, M. Peccianti, K. Brzdakiewicz, A. De Luca, and C. Umeton, “Nonlinear wave propagation and spatial solitons in nematic liquid crystals,” J. Nonlinear Opt. Phys. Mater. 12, 123–134 (2003).
[Crossref]

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, “Nonlocal optical propagation in nonlinear nematic liquid crystals,” J. Nonlinear Opt. Phys. Mater. 12, 525–538 (2003).
[Crossref]

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

J.F. Henninot, J.F. Blach, and M. Warenghem, “The investigation of an electrically stabilized optical spatial soliton induced in a nematic liquid crystal,” J. Opt. A: Pure Appl. Opt. 10, 085704 (2008).
[Crossref]

J. Opt. B (1)

W. Krolikowski, O. Bang, N. Nikolov, D. Neshev, J. Wyller, J. Rasmussen, and D. Edmundson, “Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media,” J. Opt. B 6, S288–S294 (2004).
[Crossref]

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

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

T. M. Monro, C. Martijn de Sterke, and L. Poladian, “Investigation of waveguide growth in photosensitive germanosilicate glass,” J. Opt. Soc. Am. B. 13, 2824–2832 (1996).
[Crossref]

Mol. Cryst. Liq. Cryst. (1)

J. F. Henninot, M. Debailleul, and M. Warenghem, “Tunable non-locality of thermal non-linearity in dye doped nematic liquid crystal,” Mol. Cryst. Liq. Cryst. 375, 631–640 (2002).
[Crossref]

Opt. Express (3)

Phys. Rev. A (1)

G. D’Alessandro and A. A. Wheeler, “Bistability of liquid crystal microcavities,” Phys. Rev. A 67, 023816 1–12 (2003).

Phys. Rev. E (2)

P. D. Rasmussen, O. Bang, and W. Krolikowski, “Theory of nonlocal soliton interaction in nematic liquid crystals,” Phys. Rev. E 72, 066611 1–7 (2005).
[Crossref]

M. Peccianti, C. Conti, and G. Assanto, “Optical modulational instability in a nonlocal medium,” Phys. Rev. E 68, 025602(R) 1–4 (2003).
[Crossref]

Phys. Rev. Lett. (3)

C. Conti, M. Peccianti, and G. Assanto, “Route to nonlocality and observation of accessible solitons,” Phys. Rev. Lett. 91, 073901 1–4 (2003).
[Crossref]

C. Conti, M. Peccianti, and G. Assanto, “Observation of optical spatial solitons in a highly nonlocal medium,” Phys. Rev. Lett. 92, 113902 1–4 (2004).
[Crossref]

K. D. Dorkenoo, F. Gillot, O. Crégut, Y. Sonnefraud, A. Fort, and H. Leblond, “Control of the refractive index in photopolymerizable materials for (2+1)D solitary wave guide formation,” Phys. Rev. Lett. 93, 143905 1–4 (2004).
[Crossref]

Science (1)

A. W. Snyder and D. J. Mitchell, “Accessible solitons,” Science 276, 1538–1541 (1997).
[Crossref]

Other (2)

I. C. Khoo, Liquid Crystals: Physical Properties and Nonlinear Optical Phenomena (Wiley, New York, 1995).

Y. S. Kivshar and G. P. Agrawal, Optical solitons (Academic Press, San Diego, 2003).

Supplementary Material (15)

» Media 1: MOV (1880 KB)     
» Media 2: MOV (2516 KB)     
» Media 3: MOV (1888 KB)     
» Media 4: MOV (2203 KB)     
» Media 5: MOV (2078 KB)     
» Media 6: MOV (2313 KB)     
» Media 7: MOV (902 KB)     
» Media 8: MOV (831 KB)     
» Media 9: MOV (660 KB)     
» Media 10: MOV (605 KB)     
» Media 11: MOV (992 KB)     
» Media 12: MOV (617 KB)     
» Media 13: MOV (609 KB)     
» Media 14: MOV (2751 KB)     
» Media 15: MOV (3828 KB)     

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Figures (7)

Fig. 1.
Fig. 1.

Breathing solitons. Beam propagation in z-direction, in the middle of the crystal, shown for intensities I(0,y,z) (left) and reorientation angles θ̂ (0,y,z) (right). Input intensities: (a) I=2.8×10+10 V2/m2 (Media 1) and (Media 2), (b) I=3.5×10+10 V2/m2 (Media 3) and (Media 4), and (c) I=4×10+10 V2/m2 (Media 5) and (Media 6). Parameters: ΔεOPT=0.5, ΔεDC=14.5, FWHM=4 µm and L=1.5 mm.

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Fig. 2.
Fig. 2.

(a) Soliton propagation in the z direction: the input beam intensity in the middle of the crystal is shown for different input FWHM widths (FWHM=2µm (Media 7), FWHM=2.5µm (Media 8), FWHM=3µm (Media 9), FWHM=3.5µm (Media 10), FWHM=4µm (Media 11), FWHM=4.5µm (Media 12) and FWHM=5µm (Media 13)). For each input beam width appropriate input beam intensity is found for the existence of a breathing soliton. (b) Input intensities of breathers versus input FWHM widths (blue dots). Red line is the fit y=1/x4 through the dots. Parameters: ΔεOPT=0.4, ΔεDC=14.5 and L=1.5 mm.

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Fig. 3.
Fig. 3.

(a) Beam intensity, and (b) optically induced molecular reorientation in the middle of the crystal, with the corresponding FWHMs, as functions of the propagation distance (the first row), and the corresponding transverse profiles at the exit (x, y) plane: the optical field intensity I(x, y) (Media 14) and the optically induced molecular reorientation θ̂ (x, y) (Media 15) (the second row). The example shown is for the input beam intensity I=8.6×1010 V2/m2 from Fig. 1. Parameters are as in Fig. 2.

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Fig. 4.
Fig. 4.

(A) Intensity of soliton breathing propagation versus birefringence ΔεOPT, for two values of ΔεDC, ΔεDC=10 and ΔεDC=14.5. Curves through the points are only a guide to the eyes. Inset depicts soliton propagation in the z direction, for different ΔεOPT and ΔεDC; four cases are shown: a) ΔεOPT=0.3 and ΔεDC=10, b) ΔεOPT=0.4 and ΔεDC=10, c) ΔεOPT=0.3 and ΔεDC=14.5, and d) ΔεOPT=0.4 and ΔεDC=14.5. (B) The molecular orientation induced by the electric field only θ0 (x, 0) at any z, for the two mentioned values of ΔεDC. Insets depict θ0 (x, y). Other parameters: FWHM=4 µm and L=1.5 mm.

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Fig. 5.
Fig. 5.

The first column: The molecular orientation induced by the electric field only θ0 (x,y), as a function of transverse cordinates. The second column: Soliton propagation in the z direction, the beam intensity profile is shown for different input FWHM. For each input beam width appropriate input beam intensity is found for the existence of BSs. (a): ΔεDC=10, θb =θ(x=-D/2)=θ(x=D/2)=300; (b): ΔεDC=-10, θb =θ(x=-D/2)=θ(x=D/2)=300. Parameters: ΔεOPT=0.4, L=1.5 mm.

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Fig. 6.
Fig. 6.

(a) Steady state beam propagation along the z-direction, shown for intensities in the middle of the crystal, I (0,0,z), (for different input intensities). Inset presents the lowest intensity beam on the linear scale. (b) Beam propagation along the z-direction in the middle of the crystal, for the input intensity I=3.6×10+10 V2/m2. I(0,0,z) (top) and θ̂ (0,0,z) (bottom) are shown on the linear scale. Parameters: ΔεOPT=0.5, ΔεDC=14.5, FWHM=4 µm, θ(-D/2)=θ(D/2)=2° and LD =76.57 µm.

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Fig. 7.
Fig. 7.

Comparison between the steady-state procedure (black curve) and the time-dependent procedure (red, green and blue curves): Three profiles at the noted maximum (red dot), middle (green dot), and minimum (blue dot) points on the steady-state curve are used as the input intensity profiles in the time-dependent procedure. The resulting curves after steady state is reached are represented in red, green, and blue. Parameters: The input intensity (for steady-state) I=8.6×10+10 V2/m2, ΔεOPT=0.4, ΔεDC=14.5, θ(-D/2)=θ(D/2)=2° and L=1.5 mm.

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Equations (4)

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

2i∂A∂z=+Δx,yA+α[sin2θ−sin2θ0] A=0 ,
2γx02Kτ∂θ∂t=2Δx,yθ+[β+α∣A∣2]sin(2θ),
θ(x=−D/2)=θ (x=D/2)=20.
α=k02x02ΔεOPT,β=ε0x02ΔεDC∣EDC∣2K.

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