Bending reorientational solitons with modulated alignment

While curved waveguides are fundamental elements in photonics, those induced all-optically in nonlinear uniform dielectrics tend to be straight. In uniaxial soft matter with a reorientational response, such as nematic liquid crystals, light beams in the extraordinary polarization undergo self-focusing via an increase in refractive index and eventually form spatial solitons, i.e., self-induced waveguides. Hereby we investigate the bending of such waveguides by analyzing the trajectory of solitons in nematic liquid crystals— nematicons— in the presence of a linearly varying transverse orientation of the optic axis. To
this extent we use and compare two approaches: i) a slowly varying (adiabatic) approximation based on momentum conservation of the nematicon in a Hamiltonian sense; ii) the Frank-Oseen elastic theory coupled with a fully vectorial and nonlinear beam propagation method. The models provide comparable results in such a non-homogeneously oriented uniaxial medium and predict bent soliton paths with either monotonic or non-monotonic curvatures, enabling the design of curved channel waveguides induced by light beams.