Biased liquid crystal infiltrated photonic bandgap fiber

A simulation scheme for the transmission spectrum of a photonic crystal fiber infiltrated with a nematic liquid crystal and subject to an external bias is presented. The alignment of the biased liquid crystal is simulated using the finite element method to solve the relevant system of coupled partial differential equations. From the liquid crystal alignment the full tensorial dielectric permittivity in the capillaries is derived. The transmission spectrum for the photonic crystal fiber is obtained by solving the generalized eigenvalue problem deriving from Maxwell's equations using a vector element based finite element method. We demonstrate results for a splay aligned liquid crystal infiltrated into the capillaries of a four-ring photonic crystal fiber and compare them to corresponding experiments.