Anchoring effects on the electrically controlled optical band gap in twisted photonic liquid crystals

We study a one-dimensional twisted photonic liquid crystal (TPLC), consisting of various nematic liquid crystal cells adopting a twisted configuration intercalated by isotropic dielectric layers, submitted to a dc electric field (E^dc ) aligned along the periodicity axis. We write the corresponding Euler–Lagrange equations describing the nematic layer configuration. By assuming arbitrary anchoring quasi-planar boundary conditions, we calculate the equilibrium textures for the nematic, parametrized by the two types of strength of its interaction (polar and azimuthal) with the plane walls. We write the electromagnetic equations in a 4?×?4 matrix representation and using the transfer matrix formalism, we obtain the transmittance and reflectance coefficients for normal incidence as functions of the external electric field and anchoring strengths. We have observed a remarkable dependence of the electric field on the transmission and reflection spectra in opening and closing band gaps.