Active propagation and cut-off for low TM modes in a nonlinear nematic waveguide

Liquid crystals are optically active media whose properties may strongly vary when they are subjected to magnetic or electric fields. This high susceptibility can have a profound influence on the propagation of light through the fluid and gives rise to highly nonlinear coupling between the optical field and the reorientation. In the present work, the influence of the reorientation of the crystal on the propagation of the TM optical modes when this reorientation is due to the propagating optical field is studied. Furthermore, only the TM optical modes which couple to the reorientation are considered. The orientation of the nematic in the waveguide is taken to be such that the frequency of impinging light of low amplitude is below the cut-off frequency. However, when the impinging light wave is of sufficiently high amplitude, reorientation occurs, so that the cut-off frequency is lowered and the mode propagates through the crystal. A front of reorientation then propagates into the waveguide, which in turn makes the crystal transparent. Simplified equations governing this process are derived from the full equations for the optical field and the reorientation by noting the different time and space scales involved. These simplified equations are studied qualitatively and the induced transparency phenomenon is thus explained in terms of the bistable behaviour of the reorientation equation, this bistability being induced by the incident wave. The simplified equations are also solved numerically for a range of parameter values susceptible to experimental verification. The paper is concluded by a discussion of the advantages and limitations of the model and its possible application to other situations.