We review the mathematical modelling of propagation and specific interactions of solitary beams in nematic liquid crystals — so-called nematicons. The theory is first developed for the evolution of a single nematicon; then it is extended to the interaction of two nematicons of different wavelengths, employing linear momentum conservation equations to predict that two colour nematicons can form a vector bound state. Considering optical vortices, we show that the nonlocal response of liquid crystals stabilises a single vortex, unstable in local media. Moreover, the interaction with a nematicon in another colour can stabilise a vortex for nonlocalities far below those at which an isolated vortex remains unstable. When multiple nematicons of the same wavelength interact, the radiation they shed can join them together, still resulting in a vortex. Finally, we discuss the escape of a nematicon from a nonlinear waveguide, using simple modulation theory based on momentum conservation to model the effect and get excellent agreement with the experimental results.
Modulation theory and resonant regimes for dispersive shock waves in nematic liquid crystals
