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Simulations and experiments on self-focusing conditions in nematic liquid-crystal planar cells

Jeroen Beeckman, Kristiaan Neyts, Xavier Hutsebaut, Cyril Cambournac, and Marc Haelterman

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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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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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