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Discrete light propagation and self-trapping in liquid crystals

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We investigate light propagation and self-localization in a voltage-controlled array of channel waveguides realized in undoped nematic liquid crystals. We report on discrete diffraction and solitons, as well as all-optical angular steering and the formation of multiband vector breathers. The results and are in excellent agreement with both coupled mode theory and full numerical simulations.

©2005 Optical Society of America

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Supplementary Material (2)

Media 1: MOV (1123 KB)     
Media 2: MOV (222 KB)     

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Figures (8)

Fig. 1 .
Fig. 1 . eft) Sketch of the NLC waveguide array. Right) Typical transverse index distribution for a bias of 1V.
Fig. 2.
Fig. 2. (1123 KB) Eigenvalue spectrum of the array (left), width of first and second gaps (center) and corresponding refractive index (cross sections at the center of the cell, x=0) for different biases. (Right) Gap 1 and gap 2 are between bands 0–1 and bands 1–2, respectively.
Fig. 3.
Fig. 3. Experimental response of the NLC array with Λ=8µm: (a) discrete diffraction in (y,z) for P=1mW; (b) assembled photographs of light propagation in z 0<z<z 1 versus bias and (c) versus input power; (d) photograph of a discrete soliton excited by P=10mW and propagating along the input channel.
Fig. 4.
Fig. 4. (222 KB) Animation showing light propagation in the plane (y,z), evolving from diffraction to discrete soliton generation as the power injected in a single channel ramps from 0.1.to 1.0mW. Here V=0.74V (z-and y-axes units are in µm).
Fig. 5.
Fig. 5. BPM simulations of discrete beam steering: (a) linear (P L =0.1mW) and (b) nonlinear (P H =2.0mW) light propagation in (y,z); (c) corresponding cross-section of the output intensity distribution in z=2mm.
Fig. 6.
Fig. 6. Experimental observations of angular beam steering: (a) discrete diffraction of a tilted beam for P L =1mW; (b) observation of nonlinear steering for P H =7mW; (c) profiles of the output intensity in z=2mm.
Fig. 7.
Fig. 7. Numerical (BPM) experiments on vectors breather in NLC: (a) Floquet-Bloch profiles (density plots) with corresponding refractive index distributions for V=1V (contour lines) and ky=1 in band 0 (top) and band 1 (bottom); (b) light propagation of FB modes belonging to band 0 (top) and band 1 (bottom) for P=0.2mW; (c) a vector breather generated by superimposing band 0 and band 1 excitations (b) with a total P=0.4mW.
Fig. 8.
Fig. 8. (a) Low power P=0.2mW and (b) high power P=7mW light propagation in the NLC array excited by a Gaussian beam with w y =5µm launched between waveguides. (c) Breather period (blue dots and error bars) and calculated width of gap 1 (red solid line) versus applied bias.

Equations (4)

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K 2 θ + Δ ε RF E x 2 2 sin 2 θ = 0
x [ ( ε cos 2 θ + ε sin 2 θ ) x V ] + ε 2 y 2 V = 0
E FB = Π k ( x , y ) exp j ( k y y k z z )
[ 2 + 2 j k y y + k 0 2 n 2 ( x , y ) k y 2 ] Π k ( x , y ) = k z 2 Π k ( x , y )
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