Two-colour soliton interactions in nematic liquid crystals with temperature-dependent reorientational response

The propagation and interaction of two optical spatial solitons, termed Nematicons, at different wavelengths in (2+1) dimensions is investigated in nematic liquid crystals exhibiting competing nonlinearities. In such soft matter the all-optical refractive index nonlocal response to extraordinarily polarized beams can be self-focusing via induced rotation of the constituent molecules and self-defocusing due to temperature increase mediated by photon absorption. We consider wave-packets with initially straight trajectories either converging towards or diverging away from each other. The beams can converge or diverge depending on their transverse velocities at the input and other system parameters. We derive approximate variational solutions, finding that nematicons attract within a V-shaped region in the parameter space defined by their initial velocity and the defocusing coefficient. Comparisons between the approximate and full numerical solutions show an excellent agreement for initially diverging nematicons.