Liquid Crystalline Cores for Optical Fibers

We consider the problem of wave guiding by optical fibers with nematic liquid crystal cores. The dielectric properties of the core which govern wave guiding in the fiber are determined by the nematic director field. We focus on the problem of determining the configuration of the liquid crystal in a cylindrical cavity with homeotropic boundary conditions. Using the Frank free energy, we find a transition from a radial to an axial structure. The order parameter field in the radial structure is also examined. If the core radius is greater than an optical wavelength, then, away from the nematic-isotropic transition, the free energy of the axial structure is smaller than that of the radial one. The dielectric tensor corresponding to the axial configuration is both inhomogeneous and anisotropic. We derive uncoupled wave equations for the TE and TM modes, and we propose an effective numerical method to obtain solutions.