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Discrete light propagation and self-trapping in liquid crystals

Andrea Fratalocchi, Gaetano Assanto, Kasia A. Brzdąkiewicz, and Mirek A. Karpierz

Open Access Open Access

Abstract

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.

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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.

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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.

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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).

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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.

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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.

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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.

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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.

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Equations (4)

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

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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