Abstract

Spatial solitons can be excited in liquid crystal, with the required self-focusing being achieved by setting either a thermal gradient or an orientational one. Although the thermal gradient yields to ordinary wave self-focusing, it also yields to extraordinary wave defocusing, thereby killing the reorientational focusing effect. Thus, coexistence of both solitons looks unlikely. However, by analyzing the optical properties of the used mixture, it is shown that the focusing orientational contribution to the index gradient is two orders of magnitude larger than the thermal defocusing one. Then, by properly choosing the materials and geometry, it becomes possible to excite simultaneously the thermal soliton and the nematicon. This can be done in a large range of optical axis tilt angle.

© 2008 Optical Society of America

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References

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  1. S. Trillo and W. Torruellas, Spatial Solitons (Springer-Verlag, 2001).
  2. Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, 2003).
  3. F. Simoni, Nonlinear Optical Properties of Liquid Crystals and PDLC, Vol. 2 (World Scientific, 1997).
  4. N. V. Tabiryan, A. V. Sukhov, and B. Ya Zel'dovich, “The orientational optical nonlinearity of liquid crystals,” Mol. Cryst. Liq. Cryst. 136, 1-139 (1986).
    [CrossRef]
  5. E. Braun, L. Faucheux, A. Libchaber, D. W. McLaughlin, D. J. Muraki, and M. J. Shelley, “Filamentation and undulation of self-focused laser beams in liquid crystals,” Europhys. Lett. 23, 239-244 (1993).
    [CrossRef]
  6. M. Warenghem, J. F. Henninot, and G. Abbate, “Non linearly induced self waveguiding structure in dye doped nematics liquid crystals confined in capillaries,” Opt. Express 2, 483-490 (1998).
    [CrossRef] [PubMed]
  7. M. Peccianti, A. de Rossi, G. Assanto, A. de Luca, C. Umeton, and I. C. Khoo, “Electrically assisted self-confinement and waveguiding in planar nematic liquid crystal cells,” Appl. Phys. Lett. 77, 7-9 (2000).
    [CrossRef]
  8. M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, “Nonlinear shift of spatial solitons at a graded dielectric interface,” Opt. Lett. 32, 271-273 (2007).
    [CrossRef] [PubMed]
  9. M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, “Nonspecular total internal reflection of spatial solitons at the interface between highly birefringent media,” Phys. Rev. Lett. 98, 113902 (2007).
    [CrossRef] [PubMed]
  10. G. Assanto and M. Peccianti, “Nematicons across interfaces: anomalous refraction of solitons in liquid crystals,” Opt. Express 15, 8021-8028 (2007).
    [CrossRef] [PubMed]
  11. A. Alberucci, M. Peccianti, and G. Assanto, “Nonlinear bouncing of nonlocal spatial solitons at the boundaries,” Opt. Lett. 32, 2795-2597 (2007).
    [CrossRef] [PubMed]
  12. M. Warenghem and G. Joly, “Liquid crystal refractive indices behavior versus wavelength and temperature,” Mol. Cryst. Liq. Cryst. 220, 39-51 (1992).
    [CrossRef]
  13. F. Derrien, J. F. Henninot, M. Warenghem, and G. Abbate, “A thermal (2D+1) spatial optical soliton in a dye doped liquid crystal,” J. Opt. A, Pure Appl. Opt. 2, 332-337 (2000).
    [CrossRef]
  14. J. F. Henninot, M. Debailleul, F. Derrien, and M. Warenghem, “In situ intensity profile measurements of spatial quasi-solitons in thick dye-doped liquid crystal samples,” J. Opt. A, Pure Appl. Opt. 5, 250-255 (2003).
    [CrossRef]
  15. J. Beeckman, K. Neyts, X. Hutsebaut, C. Combournac, and M. Haelterman, “Simulations and experiments on self-focusing conditions in nematic liquid-crystal planar cells,” Opt. Express 12, 1011-1018 (2004).
    [CrossRef] [PubMed]

2007 (4)

2004 (1)

2003 (1)

J. F. Henninot, M. Debailleul, F. Derrien, and M. Warenghem, “In situ intensity profile measurements of spatial quasi-solitons in thick dye-doped liquid crystal samples,” J. Opt. A, Pure Appl. Opt. 5, 250-255 (2003).
[CrossRef]

2000 (2)

F. Derrien, J. F. Henninot, M. Warenghem, and G. Abbate, “A thermal (2D+1) spatial optical soliton in a dye doped liquid crystal,” J. Opt. A, Pure Appl. Opt. 2, 332-337 (2000).
[CrossRef]

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

1998 (1)

1993 (1)

E. Braun, L. Faucheux, A. Libchaber, D. W. McLaughlin, D. J. Muraki, and M. J. Shelley, “Filamentation and undulation of self-focused laser beams in liquid crystals,” Europhys. Lett. 23, 239-244 (1993).
[CrossRef]

1992 (1)

M. Warenghem and G. Joly, “Liquid crystal refractive indices behavior versus wavelength and temperature,” Mol. Cryst. Liq. Cryst. 220, 39-51 (1992).
[CrossRef]

1986 (1)

N. V. Tabiryan, A. V. Sukhov, and B. Ya Zel'dovich, “The orientational optical nonlinearity of liquid crystals,” Mol. Cryst. Liq. Cryst. 136, 1-139 (1986).
[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. Opt. A, Pure Appl. Opt. 2, 332-337 (2000).
[CrossRef]

M. Warenghem, J. F. Henninot, and G. Abbate, “Non linearly induced self waveguiding structure in dye doped nematics liquid crystals confined in capillaries,” Opt. Express 2, 483-490 (1998).
[CrossRef] [PubMed]

Agrawal, G. P.

Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, 2003).

Alberucci, A.

Assanto, G.

A. Alberucci, M. Peccianti, and G. Assanto, “Nonlinear bouncing of nonlocal spatial solitons at the boundaries,” Opt. Lett. 32, 2795-2597 (2007).
[CrossRef] [PubMed]

M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, “Nonlinear shift of spatial solitons at a graded dielectric interface,” Opt. Lett. 32, 271-273 (2007).
[CrossRef] [PubMed]

G. Assanto and M. Peccianti, “Nematicons across interfaces: anomalous refraction of solitons in liquid crystals,” Opt. Express 15, 8021-8028 (2007).
[CrossRef] [PubMed]

M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, “Nonspecular total internal reflection of spatial solitons at the interface between highly birefringent media,” Phys. Rev. Lett. 98, 113902 (2007).
[CrossRef] [PubMed]

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

Beeckman, J.

Braun, E.

E. Braun, L. Faucheux, A. Libchaber, D. W. McLaughlin, D. J. Muraki, and M. J. Shelley, “Filamentation and undulation of self-focused laser beams in liquid crystals,” Europhys. Lett. 23, 239-244 (1993).
[CrossRef]

Combournac, C.

de Luca, A.

M. Peccianti, A. de Rossi, G. Assanto, A. de Luca, C. Umeton, and I. C. 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. C. 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, F. Derrien, and M. Warenghem, “In situ intensity profile measurements of spatial quasi-solitons in thick dye-doped liquid crystal samples,” J. Opt. A, Pure Appl. Opt. 5, 250-255 (2003).
[CrossRef]

Derrien, F.

J. F. Henninot, M. Debailleul, F. Derrien, and M. Warenghem, “In situ intensity profile measurements of spatial quasi-solitons in thick dye-doped liquid crystal samples,” J. Opt. A, Pure Appl. Opt. 5, 250-255 (2003).
[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. Opt. A, Pure Appl. Opt. 2, 332-337 (2000).
[CrossRef]

Dyadyusha, A.

M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, “Nonspecular total internal reflection of spatial solitons at the interface between highly birefringent media,” Phys. Rev. Lett. 98, 113902 (2007).
[CrossRef] [PubMed]

M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, “Nonlinear shift of spatial solitons at a graded dielectric interface,” Opt. Lett. 32, 271-273 (2007).
[CrossRef] [PubMed]

Faucheux, L.

E. Braun, L. Faucheux, A. Libchaber, D. W. McLaughlin, D. J. Muraki, and M. J. Shelley, “Filamentation and undulation of self-focused laser beams in liquid crystals,” Europhys. Lett. 23, 239-244 (1993).
[CrossRef]

Haelterman, M.

Henninot, J. F.

J. F. Henninot, M. Debailleul, F. Derrien, and M. Warenghem, “In situ intensity profile measurements of spatial quasi-solitons in thick dye-doped liquid crystal samples,” J. Opt. A, Pure Appl. Opt. 5, 250-255 (2003).
[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. Opt. A, Pure Appl. Opt. 2, 332-337 (2000).
[CrossRef]

M. Warenghem, J. F. Henninot, and G. Abbate, “Non linearly induced self waveguiding structure in dye doped nematics liquid crystals confined in capillaries,” Opt. Express 2, 483-490 (1998).
[CrossRef] [PubMed]

Hutsebaut, X.

Joly, G.

M. Warenghem and G. Joly, “Liquid crystal refractive indices behavior versus wavelength and temperature,” Mol. Cryst. Liq. Cryst. 220, 39-51 (1992).
[CrossRef]

Kaczmarek, M.

M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, “Nonspecular total internal reflection of spatial solitons at the interface between highly birefringent media,” Phys. Rev. Lett. 98, 113902 (2007).
[CrossRef] [PubMed]

M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, “Nonlinear shift of spatial solitons at a graded dielectric interface,” Opt. Lett. 32, 271-273 (2007).
[CrossRef] [PubMed]

Khoo, I. C.

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

Kivshar, Y. S.

Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, 2003).

Libchaber, A.

E. Braun, L. Faucheux, A. Libchaber, D. W. McLaughlin, D. J. Muraki, and M. J. Shelley, “Filamentation and undulation of self-focused laser beams in liquid crystals,” Europhys. Lett. 23, 239-244 (1993).
[CrossRef]

McLaughlin, D. W.

E. Braun, L. Faucheux, A. Libchaber, D. W. McLaughlin, D. J. Muraki, and M. J. Shelley, “Filamentation and undulation of self-focused laser beams in liquid crystals,” Europhys. Lett. 23, 239-244 (1993).
[CrossRef]

Muraki, D. J.

E. Braun, L. Faucheux, A. Libchaber, D. W. McLaughlin, D. J. Muraki, and M. J. Shelley, “Filamentation and undulation of self-focused laser beams in liquid crystals,” Europhys. Lett. 23, 239-244 (1993).
[CrossRef]

Neyts, K.

Peccianti, M.

M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, “Nonspecular total internal reflection of spatial solitons at the interface between highly birefringent media,” Phys. Rev. Lett. 98, 113902 (2007).
[CrossRef] [PubMed]

G. Assanto and M. Peccianti, “Nematicons across interfaces: anomalous refraction of solitons in liquid crystals,” Opt. Express 15, 8021-8028 (2007).
[CrossRef] [PubMed]

M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, “Nonlinear shift of spatial solitons at a graded dielectric interface,” Opt. Lett. 32, 271-273 (2007).
[CrossRef] [PubMed]

A. Alberucci, M. Peccianti, and G. Assanto, “Nonlinear bouncing of nonlocal spatial solitons at the boundaries,” Opt. Lett. 32, 2795-2597 (2007).
[CrossRef] [PubMed]

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

Shelley, M. J.

E. Braun, L. Faucheux, A. Libchaber, D. W. McLaughlin, D. J. Muraki, and M. J. Shelley, “Filamentation and undulation of self-focused laser beams in liquid crystals,” Europhys. Lett. 23, 239-244 (1993).
[CrossRef]

Simoni, F.

F. Simoni, Nonlinear Optical Properties of Liquid Crystals and PDLC, Vol. 2 (World Scientific, 1997).

Sukhov, A. V.

N. V. Tabiryan, A. V. Sukhov, and B. Ya Zel'dovich, “The orientational optical nonlinearity of liquid crystals,” Mol. Cryst. Liq. Cryst. 136, 1-139 (1986).
[CrossRef]

Tabiryan, N. V.

N. V. Tabiryan, A. V. Sukhov, and B. Ya Zel'dovich, “The orientational optical nonlinearity of liquid crystals,” Mol. Cryst. Liq. Cryst. 136, 1-139 (1986).
[CrossRef]

Torruellas, W.

S. Trillo and W. Torruellas, Spatial Solitons (Springer-Verlag, 2001).

Trillo, S.

S. Trillo and W. Torruellas, Spatial Solitons (Springer-Verlag, 2001).

Umeton, C.

M. Peccianti, A. de Rossi, G. Assanto, A. de Luca, C. Umeton, and I. C. 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, M. Debailleul, F. Derrien, and M. Warenghem, “In situ intensity profile measurements of spatial quasi-solitons in thick dye-doped liquid crystal samples,” J. Opt. A, Pure Appl. Opt. 5, 250-255 (2003).
[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. Opt. A, Pure Appl. Opt. 2, 332-337 (2000).
[CrossRef]

M. Warenghem, J. F. Henninot, and G. Abbate, “Non linearly induced self waveguiding structure in dye doped nematics liquid crystals confined in capillaries,” Opt. Express 2, 483-490 (1998).
[CrossRef] [PubMed]

M. Warenghem and G. Joly, “Liquid crystal refractive indices behavior versus wavelength and temperature,” Mol. Cryst. Liq. Cryst. 220, 39-51 (1992).
[CrossRef]

Ya Zel'dovich, B.

N. V. Tabiryan, A. V. Sukhov, and B. Ya Zel'dovich, “The orientational optical nonlinearity of liquid crystals,” Mol. Cryst. Liq. Cryst. 136, 1-139 (1986).
[CrossRef]

Appl. Phys. Lett. (1)

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

Europhys. Lett. (1)

E. Braun, L. Faucheux, A. Libchaber, D. W. McLaughlin, D. J. Muraki, and M. J. Shelley, “Filamentation and undulation of self-focused laser beams in liquid crystals,” Europhys. Lett. 23, 239-244 (1993).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (2)

F. Derrien, J. F. Henninot, M. Warenghem, and G. Abbate, “A thermal (2D+1) spatial optical soliton in a dye doped liquid crystal,” J. Opt. A, Pure Appl. Opt. 2, 332-337 (2000).
[CrossRef]

J. F. Henninot, M. Debailleul, F. Derrien, and M. Warenghem, “In situ intensity profile measurements of spatial quasi-solitons in thick dye-doped liquid crystal samples,” J. Opt. A, Pure Appl. Opt. 5, 250-255 (2003).
[CrossRef]

Mol. Cryst. Liq. Cryst. (2)

N. V. Tabiryan, A. V. Sukhov, and B. Ya Zel'dovich, “The orientational optical nonlinearity of liquid crystals,” Mol. Cryst. Liq. Cryst. 136, 1-139 (1986).
[CrossRef]

M. Warenghem and G. Joly, “Liquid crystal refractive indices behavior versus wavelength and temperature,” Mol. Cryst. Liq. Cryst. 220, 39-51 (1992).
[CrossRef]

Opt. Express (3)

Opt. Lett. (2)

Phys. Rev. Lett. (1)

M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, “Nonspecular total internal reflection of spatial solitons at the interface between highly birefringent media,” Phys. Rev. Lett. 98, 113902 (2007).
[CrossRef] [PubMed]

Other (3)

S. Trillo and W. Torruellas, Spatial Solitons (Springer-Verlag, 2001).

Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, 2003).

F. Simoni, Nonlinear Optical Properties of Liquid Crystals and PDLC, Vol. 2 (World Scientific, 1997).

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Figures (10)

Fig. 1
Fig. 1

Thermal nonlinearity. Direction of propagation: k; z and r are the on-axis and transverse coordinates, respectively. (a) optical intensity, (b) temperature distribution induced by adsorption, (c) corresponding index distribution; ordinary, focusing; extraordinary, defocusing.

Fig. 2
Fig. 2

Geometries to excite “thermal” soliton. (a) In capillary, independent from input polarization. (b) In planar cell, independent from the beam tilt angle θ, input polarization o z .

Fig. 3
Fig. 3

Orientational nonlinearity: direction of propagation: k; optical field: E opt . z and r are the on-axis and transverse coordinates respectively. (a) optical intensity, (b) tilt angle distribution induced by OFE, (c) corresponding extraordinary index distribution.

Fig. 4
Fig. 4

Geometries to excite orientational soliton. (a) side view, (b) top view. Similar to the geometry depicted on Fig. 2b, the polarization is nevertheless in the plane ( x , y ) of the cell.

Fig. 5
Fig. 5

Extraordinary index of refraction for 5CB versus temperature and tilt angle. The top and bottom curves correspond to n e and n o , respectively. The extraordinary index slightly depends on temperature for θ = 32 ° (solid intermediate line).

Fig. 6
Fig. 6

Sign of the transverse gradient factor f ( θ , T ) for different thermal/orientational gradients ratio. White areas: positive (focusing). Top left: pure thermal ( A = 0 ) ; top right: thermal 200, orientational 1 ( A = 0.005 ) ; bottom right: thermal 100, orientational 1 ( A = 0.01 ) ; bottom left: thermal 10, orientational 1 ( A = 0.1 ) .

Fig. 7
Fig. 7

Geometry of Fig. 4. The beam emerges out of a fiber from the left of the photo. The polarization is such as to split the beam in both ordinary and extraordinary rays. The power is low, and no collimation occurs. The arrow on the left shows the scale (identical for both directions) and the other arrow shows the optical axis direction.

Fig. 8
Fig. 8

Coexistence of “thermal” (horizontal) and “orientational” (down) solitons. Same sample as in Fig. 7, with an input power of 2.4 mW .

Fig. 9
Fig. 9

Geometry of the second series of experiments. The beam is launched within the cell via a microscope objective. The sample can be rotated to adjust the angle of incidence θ 0 . The optical axis is set to 45° with respect to the sample o x axis.

Fig. 10
Fig. 10

Geometry of Fig. 9. Coexistence of “thermal” (horizontal) and “orientational” (up) solitons. The input beam impinges the cell under normal incidence (left) or 6° (right); the white line marks the input face; the input beam arrives from the left, horizontally.

Tables (1)

Tables Icon

Table 1 Values of the Parameters for Temperature Index Dependence

Equations (8)

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

n = n e n o ( n e 2 cos 2 ( θ ) + n o 2 sin 2 ( θ ) ) 1 2 ,
n o , e ( T ) = a o , e + b o , e T 1 + c o , e T + d o , e T 2 .
d n d r = n θ d θ d r + n T d T d r .
n = n e [ 1 + K cos 2 ( θ ) ] 1 2 ,
K = n e 2 n o 2 n o 2 = n e 2 n o 2 1 .
n T = n e [ 1 + K cos 2 ( θ ) ] 3 2 [ sin 2 ( θ ) 1 n e d n e d T + cos 2 ( θ ) ( K + 1 ) 1 n o d n o d T ] ,
n θ = n e [ 1 + K cos 2 ( θ ) ] 3 2 K cos ( θ ) sin ( θ ) .
d n d r = [ A n θ + n T ] d T d r = f ( θ , T ) d T d r .

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