Abstract

Owing to the nonlinear effect of optical field-induced director reorientation, self-focusing of an optical beam can occur in nematic liquid crystals and an almost diffraction-compensated propagation can be observed with milliwatts of light power and propagation lengths of several millimeters. This opens the way for applications in all-optical signal handling and reconfigurable optical interconnections. Self-focusing of an optical beam in nematic liquid-crystal cells has been studied experimentally and by means of numerical simulation. The relationships between bias voltage, cell thickness and required optical power have been examined, thus allowing the determination of the most favorable conditions for soliton-like beam propagation.

©2004 Optical Society of America

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References

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  1. G.I. Stegeman and M. Segev, “Optical spatial solitons and their interactions: universality and diversity,” Science 286, 1518–1523 (1999).
    [Crossref] [PubMed]
  2. M. Peccianti and G. Assanto, “Signal readdressing by steering of spatial solitons in bulk nematic liquid crystals,” Opt. Lett. 26, 1690–1692 (2001).
    [Crossref]
  3. I.C. Khoo, Liquid Crystals: Physical Properties and Nonlinear Optical Phenomena (John Wiley & Sons, New York, 1992).
  4. X. Hutsebaut, C. Cambournac, M. Haelterman, A. Adamski, and K. Neyts, “Single-component higher-order mode solitons in liquid crystals,” Opt. Commun. (in press).
  5. 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]
  6. P. Yeh and C. Gu, Optics of Liquid Crystal Displays (John Wiley & Sons, New York, 1999).
  7. J. Beeckman, K. Neyts, X. Hutsebaut, and M. Haelterman, “One-dimensional simulation of field-induced director reorientation and lateral light propagation in liquid crystals,” in Optical Design and Engineering — Optical Systems Design 2003, L. Mazuray, P.J. Rogers, and R. Wartmann, eds., Proc. SPIE5249, 577–585 (2003).
  8. P.G. de Gennes and J. Prost, The Physics of Liquid Crystals (Clarendon Press, Oxford, 1993).
  9. W.H. Press, S.A. Teukolsky, W.T. Vetterling, and B.P. Flannery, Numerical Recipes in C (Cambridge University Press, Cambridge, 1992).
  10. J. Van Roey, J. Van der Donk, and P.E. Lagasse, “Beam propagation method: analysis and assessment,” J. Opt. Soc. Am. 71, 803–810 (1981).
    [Crossref]
  11. C. Conti, M. Peccianti, and G. Assanto, “Route to nonlocality and observation of accessible solitons,” Phys. Rev. Lett. 91, 073901 (2003).
    [Crossref] [PubMed]
  12. X. Hutsebaut, C. Cambournac, M. Haelterman, J. Beeckman, and K. Neyts, “Measurement of the self-consistent waveguide of an accessible soliton,” to be presented at the Nonlinear Guided Waves and their Applications conference, Toronto (Canada), 28–31 March 2004 (presentation TuC20).
  13. K. Iizuka, Elements of Photonicsvol. 1 (John Wiley & Sons, New York, 2002).

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)

2000 (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]

1999 (1)

G.I. Stegeman and M. Segev, “Optical spatial solitons and their interactions: universality and diversity,” Science 286, 1518–1523 (1999).
[Crossref] [PubMed]

1981 (1)

Adamski, A.

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

Assanto, G.

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

M. Peccianti and G. Assanto, “Signal readdressing by steering of spatial solitons in bulk nematic liquid crystals,” Opt. Lett. 26, 1690–1692 (2001).
[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]

Beeckman, J.

J. Beeckman, K. Neyts, X. Hutsebaut, and M. Haelterman, “One-dimensional simulation of field-induced director reorientation and lateral light propagation in liquid crystals,” in Optical Design and Engineering — Optical Systems Design 2003, L. Mazuray, P.J. Rogers, and R. Wartmann, eds., Proc. SPIE5249, 577–585 (2003).

X. Hutsebaut, C. Cambournac, M. Haelterman, J. Beeckman, and K. Neyts, “Measurement of the self-consistent waveguide of an accessible soliton,” to be presented at the Nonlinear Guided Waves and their Applications conference, Toronto (Canada), 28–31 March 2004 (presentation TuC20).

Cambournac, C.

X. Hutsebaut, C. Cambournac, M. Haelterman, J. Beeckman, and K. Neyts, “Measurement of the self-consistent waveguide of an accessible soliton,” to be presented at the Nonlinear Guided Waves and their Applications conference, Toronto (Canada), 28–31 March 2004 (presentation TuC20).

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

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 Gennes, P.G.

P.G. de Gennes and J. Prost, The Physics of Liquid Crystals (Clarendon Press, Oxford, 1993).

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]

Flannery, B.P.

W.H. Press, S.A. Teukolsky, W.T. Vetterling, and B.P. Flannery, Numerical Recipes in C (Cambridge University Press, Cambridge, 1992).

Gu, C.

P. Yeh and C. Gu, Optics of Liquid Crystal Displays (John Wiley & Sons, New York, 1999).

Haelterman, M.

J. Beeckman, K. Neyts, X. Hutsebaut, and M. Haelterman, “One-dimensional simulation of field-induced director reorientation and lateral light propagation in liquid crystals,” in Optical Design and Engineering — Optical Systems Design 2003, L. Mazuray, P.J. Rogers, and R. Wartmann, eds., Proc. SPIE5249, 577–585 (2003).

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

X. Hutsebaut, C. Cambournac, M. Haelterman, J. Beeckman, and K. Neyts, “Measurement of the self-consistent waveguide of an accessible soliton,” to be presented at the Nonlinear Guided Waves and their Applications conference, Toronto (Canada), 28–31 March 2004 (presentation TuC20).

Hutsebaut, X.

X. Hutsebaut, C. Cambournac, M. Haelterman, J. Beeckman, and K. Neyts, “Measurement of the self-consistent waveguide of an accessible soliton,” to be presented at the Nonlinear Guided Waves and their Applications conference, Toronto (Canada), 28–31 March 2004 (presentation TuC20).

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

J. Beeckman, K. Neyts, X. Hutsebaut, and M. Haelterman, “One-dimensional simulation of field-induced director reorientation and lateral light propagation in liquid crystals,” in Optical Design and Engineering — Optical Systems Design 2003, L. Mazuray, P.J. Rogers, and R. Wartmann, eds., Proc. SPIE5249, 577–585 (2003).

Iizuka, K.

K. Iizuka, Elements of Photonicsvol. 1 (John Wiley & Sons, New York, 2002).

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]

I.C. Khoo, Liquid Crystals: Physical Properties and Nonlinear Optical Phenomena (John Wiley & Sons, New York, 1992).

Lagasse, P.E.

Neyts, K.

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

J. Beeckman, K. Neyts, X. Hutsebaut, and M. Haelterman, “One-dimensional simulation of field-induced director reorientation and lateral light propagation in liquid crystals,” in Optical Design and Engineering — Optical Systems Design 2003, L. Mazuray, P.J. Rogers, and R. Wartmann, eds., Proc. SPIE5249, 577–585 (2003).

X. Hutsebaut, C. Cambournac, M. Haelterman, J. Beeckman, and K. Neyts, “Measurement of the self-consistent waveguide of an accessible soliton,” to be presented at the Nonlinear Guided Waves and their Applications conference, Toronto (Canada), 28–31 March 2004 (presentation TuC20).

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]

M. Peccianti and G. Assanto, “Signal readdressing by steering of spatial solitons in bulk nematic liquid crystals,” Opt. Lett. 26, 1690–1692 (2001).
[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]

Press, W.H.

W.H. Press, S.A. Teukolsky, W.T. Vetterling, and B.P. Flannery, Numerical Recipes in C (Cambridge University Press, Cambridge, 1992).

Prost, J.

P.G. de Gennes and J. Prost, The Physics of Liquid Crystals (Clarendon Press, Oxford, 1993).

Segev, M.

G.I. Stegeman and M. Segev, “Optical spatial solitons and their interactions: universality and diversity,” Science 286, 1518–1523 (1999).
[Crossref] [PubMed]

Stegeman, G.I.

G.I. Stegeman and M. Segev, “Optical spatial solitons and their interactions: universality and diversity,” Science 286, 1518–1523 (1999).
[Crossref] [PubMed]

Teukolsky, S.A.

W.H. Press, S.A. Teukolsky, W.T. Vetterling, and B.P. Flannery, Numerical Recipes in C (Cambridge University Press, Cambridge, 1992).

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]

Van der Donk, J.

Van Roey, J.

Vetterling, W.T.

W.H. Press, S.A. Teukolsky, W.T. Vetterling, and B.P. Flannery, Numerical Recipes in C (Cambridge University Press, Cambridge, 1992).

Yeh, P.

P. Yeh and C. Gu, Optics of Liquid Crystal Displays (John Wiley & Sons, New York, 1999).

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]

J. Opt. Soc. Am. (1)

Opt. Lett. (1)

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]

Science (1)

G.I. Stegeman and M. Segev, “Optical spatial solitons and their interactions: universality and diversity,” Science 286, 1518–1523 (1999).
[Crossref] [PubMed]

Other (8)

X. Hutsebaut, C. Cambournac, M. Haelterman, J. Beeckman, and K. Neyts, “Measurement of the self-consistent waveguide of an accessible soliton,” to be presented at the Nonlinear Guided Waves and their Applications conference, Toronto (Canada), 28–31 March 2004 (presentation TuC20).

K. Iizuka, Elements of Photonicsvol. 1 (John Wiley & Sons, New York, 2002).

I.C. Khoo, Liquid Crystals: Physical Properties and Nonlinear Optical Phenomena (John Wiley & Sons, New York, 1992).

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

P. Yeh and C. Gu, Optics of Liquid Crystal Displays (John Wiley & Sons, New York, 1999).

J. Beeckman, K. Neyts, X. Hutsebaut, and M. Haelterman, “One-dimensional simulation of field-induced director reorientation and lateral light propagation in liquid crystals,” in Optical Design and Engineering — Optical Systems Design 2003, L. Mazuray, P.J. Rogers, and R. Wartmann, eds., Proc. SPIE5249, 577–585 (2003).

P.G. de Gennes and J. Prost, The Physics of Liquid Crystals (Clarendon Press, Oxford, 1993).

W.H. Press, S.A. Teukolsky, W.T. Vetterling, and B.P. Flannery, Numerical Recipes in C (Cambridge University Press, Cambridge, 1992).

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Figures (8)

Fig. 1.
Fig. 1. Experimental setup and indication of axes.

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Fig. 2.
Fig. 2. Light propagation in a 75 µm-thick cell for a voltage of 1 V and different optical powers: (a) 0.8 mW and D1; (b) 1.5 mW and D2; (c) 2.3 mW and D2; (d) 6 mW and D3.

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Fig. 3.
Fig. 3. Relationship between required optical power for soliton propagation and voltage for different cell thickness d. (Experiment.)

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Fig. 4.
Fig. 4. Light propagation in a 18 µm-thick cell for a voltage of 1.6 V: (a) for 1.5 mW and D1 filter; (b) for 4.5 mW and D3 filter. The scattering on the left side of the pictures comes from the entrance window.

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Fig. 5.
Fig. 5. (a) Tilt distribution in the presence of the optical field for a 53 µm-thick cell and 1-V voltage. (b) Evolution of the optical-field peak amplitude for different input powers. (c, d) Corresponding evolution of beam width in the y- and x-direction, respectively. [The arrows indicate an increasing initial optical field A (i.e. an increasing optical power).]

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Fig. 6.
Fig. 6. Evolution of the width of a beam propagating in a 18 µm-thick cell, for a voltage of 1.6 V and an optical power of 3.66 mW.

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Fig. 7.
Fig. 7. Optimal optical power in function of voltage for different cell thickness with a maximal relative error of 5%. (Numerical simulations.)

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Fig. 8.
Fig. 8. Tilt distribution in the middle of the layer along the y-axis for a voltage of 1 V and for the same parameter A for the different cell thicknesses. The shape of the optical-field distribution is also shown as indication.

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Equations (4)

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K [ ∂ 2 θ ∂ x 2 + ∂ 2 θ ∂ y 2 ] + ε 0 2 sin ⁡ 2 θ [ Δ ε DC ∣ E DC ∣ 2 + Δ ε opt ∣ E opt ∣ 2 ] = 0 .
[ ε ⊥ DC + Δ ε DC sin 2 ⁡ θ ] ∂ 2 V ∂ x 2 + Δ ε DC sin ⁡ 2 θ ∂ V ∂ x ∂ θ ∂ x + ε ⊥ DC ∂ 2 V ∂ y 2 = 0 .
E opt = A exp [ − ( x − d ⁄ 2 ) 2 + y 2 r 0 2 ] ,
2 ik ∂ E opt ∂ z + ( ∂ 2 ∂ x 2 + ∂ 2 ∂ y 2 ) E opt + k 0 2 Δ ε opt ( sin 2 ⁡ θ − sin 2 ⁡ θ 0 ) E opt = 0 .

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