Numerical Simulations of Electrically Induced Birefringence in Photonic Liquid Crystal Fibers

It has been recently experimentally demonstrated that propagation and polarization properties of the photonic liquid crystal fibers can be effectively tuned with the electric field. In particular, effective electric tuning of the phase birefringence has been obtained in the photonic liquid crystal fibers based on the high index glasses. Accurate numerical simulations of the impact of electric field on the guiding properties of the photonic liquid crystal fibers require complex methods, in which all important physical properties of the liquid crystal are taken into account (optical anisotropy, molecular orientation and relatively high losses). In this paper we present two different numerical approaches based on the finite element method. First one utilizes the simplified assumption of the "collective tilt" of molecules, and gives rough estimation of the phase birefringence tuning range. The second approach is much more rigorous, since electrically induced reorientation of the liquid crystal is calculated with a Q-tensor method giving the values of the inhomogeneous permittivity tensor. The value of the electrically induced birefringence calculated with the second method is in a good agreement with the experimental results.