Abstract
The all-optical control of the trajectory of a nonlinear optical beam propagating in a nematic liquid crystal cell is studied using a combination of modulation theory and full numerical solutions of the governing nematic equations. In detail, the output position of a signal beam is controlled via its interaction with a second, co-propagating control beam. The input positions of both the signal and control beams are fixed, with the output position of the signal beam determined by the input angle of the control beam. A simple modulation theory based on treating the optical beams as mechanical particles in a potential well is found to give only adequate agreement with numerical solutions. However, extending this modulation theory to include the detailed profiles of the beams, so that the beams are treated as rigid bodies moving in a potential well, leads to simple, extended equations which determine the input angle of the control beam required for a given output position of the signal beam. The predictions of this extended particle theory, or rigid body theory, are compared with full numerical solutions of the nematic equations and excellent agreement is found.
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