Nonlinear TM modes in cylindrical liquid crystal waveguide

We consider a nonlinear cylindrical fiber with a nematic liquid crystal (LC) core having initially the escaped configuration and subject to the action of a normal mode propagating electromagnetic field of arbitrary intensity. We derive a set of coupled equations governing the nonlinear dynamics of the electromagnetic field and the confined LC. We solve numerically these coupled equations and find simultaneously the distorted textures of the nematic inside the cylinder and the Transverse Magnetic modes in the guide. We analyze the dependence of these solutions on the electromagnetic field intensity by assuming consistently soft boundary conditions. We have found a dramatic correlation in the spatial distribution of the nematic's configuration and the Transverse Magnetic modes. Thus, the director adopts configurations completely guided by the specific mode involved. We show that the cut-off frequencies and dispersion relations can be tuned by varying the intensity of the electromagnetic propagating field.