Bloch oscillations in nematic liquid crystalline waveguide arrays

We discuss Bloch oscillations in waveguide arrays created in a nematic liquid crystalline layer. Bloch oscillations can originate from the specific distribution of refractive index, where a linear gradient is added to the transverse periodicity. Light can oscillate periodically in the transverse direction as it propagates, returning to its initial spatial position and profile after each full cycle. To introduce a spatially periodic refractive index modulation in nematic liquid crystalline waveguides a set of comb-shaped transparent ITO electrodes is placed on one of the glass surfaces. The applied bias allows tuning the structure from light confinement in one dimension, i.e. planar waveguiding, to bi-dimensional confinement. In the proposed geometry, the thickness of the liquid crystal layer changes linearly as a function of the transverse coordinate. In this way, both linear and nonlinear effective index changes are introduced in each waveguide.