Using the equilibrium configuration of an imprinted cholesteric elastomer film with a twist defect, we have found the
solution of the boundary value problem for the reflection and transmission of normal incident circularly polarized light
for different values of chiral order parameter. We have found resonant modes for both polarizations in smaller values of
chiral order parameter and in parameters related with elastic energy.
Our calculation concerns two-dimensional photonic crystals (PCs) of hollow cylinders (in a dielectric matrix) that are infilled with a nematic liquid crystal (NLC). A static electric field, applied parallel to the cylinders, tunes the optical response of the PC. A crucial aspect is the calculation of the dielectric tensor of the NLC. Here we generalize a preliminary study , now considering three possible configurations: escaped radial, planar radial, and axial. Further, the anchoring of the molecules at the cylinder walls now has an arbitrary strength. Finally, we address the full problem of inhomogeniety and anisotropy of the NLC cylinders. A phase transition is found from the escaped radial to the axial configuration for sufficiently high field values, which depend on the cylinder radius. The Photonic Band (PB) structure reveals gaps for propagation in the  and  directions and also a PB gap in all directions (in the plane of periodicity) for modes that are approximately polarized parallel to the cylinders. Our results show that these gaps can be tuned by the applied field.
We have calculated the photonic band structure of a 2D photonic crystal whose empty cylinders are infiltrated by a liquid crystal; a D.C. electric field is applied in the direction parallel to the cylinders. The local dielectric constant within the cylinders is obtained by minimizing the free energy, which has elastic and electrostatic contributions. We have assumed strong anchoring of the molecules of the nematic liquid crystal at the cylinder boundaries and have averaged over the cross-sectional area of the cylinder. The resulting dielectric tensor is diagonal and depends on the applied field. Moreover, it has the same symmetry as a uniaxial material, so that the optical response of the H-modes and E-modes is given by different dielectric constants (“ordinary” and “extraordinary”). The photonic band structures exhibit a notable dependence on the applied field with shifts up to 6% of the bands. For the E-modes, with a careful choice of the filling fraction it is possible to design a complete photonic gap for a certain range of electric fields, and close the gap for other values of the field. Such behaviour could be applied to optical tuning, switching, and polarizing of light.