One-dimensional simulation of field-induced director reorientation and lateral light propagation in liquid crystals

Spatial solitons in liquid crystals can be observed with milliwatts of light power due to the nonlocal saturable nonlinear effect of field-induced director reorientation. In novel generations of all-optical switching circuits and optical networks spatial solitons show some promising possibilities. Director orientation in an LC-layer is simulated for a dc-voltage over the layer and an optical field injected lateral to the layer. Due to a torque induced by the electric field the molecules will tilt and the index of refraction in the layer will rise. The simulation of the soliton behavior is based on the Euler-Lagrange variational formula for the distortion free energy of the liquid crystal. The raise in the refractive index causes a self-focusing effect. When the self-focusing balances the diffraction, a spatial soliton can occur. A BPM-algorithm is used to simulate the light propagation in the layer. Without a dc-field, a large optical field for soliton propagation is required to reach the threshold to initiate the molecular reorientation of the liquid crystal molecules. A dc-field can be used to overcome the Freederickz-transition so that a lower optical field is required. The relations between optical field profiles, dc-voltage and layer thickness which enable soliton propagation are discussed.