Discrete X-wave-like spatio-temporal structures in one-dimensional nonlinear liquid crystal waveguide arrays

摘要

Optical spatio-temporal X-wave-like pattern formation is investigated in a voltage-controlled array of channel waveguides in nematic liquid crystals and in generic optically dispersive nonlocal nonlinear media as well. The nonlinear response of the system is governed by the spatio-temporal diffusion equation for the medium's response to the optical field, while the respective equation for the evolving light pulse may incorporate normal temporal dispersion. The associated discrete nonlinear Schr&diaero;dinger equation which governs the evolution of the temporal profiles of a discrete set of modes is derived and is studied numerically. The results are obtained via full numerical investigation of the array with beam propagation techniques.