Photonic band structure of diamond colloidal crystals in a cholesteric liquid crystal

In this paper, we demonstrate the presence of a photonic band gap for a diamond lattice structure made of particles with normal anchoring inside a cholesteric liquid crystal. As is typical for liquid crystals (LCs), there is considerable contrast between the dielectric constant parallel ε_{∥} and perpendicular ε_{⊥} to the director, with ε_{∥}/ε_{⊥}∼4 here. It is shown that the size of the photonic band gap is directly related to the size of colloidal particles and the contrast between the dielectric constant in the particles and the extreme values of ε in the LC medium (one needs either ε in the particle much smaller than ε_{⊥} or much bigger than ε_{∥}). No opening is seen in the band diagrams for small particles. For larger particles a partial gap opens when the particles are composed of very low dielectric material but never a complete gap. On the other hand, a complete gap starts to be revealed when the size of the colloidal particles is increased and when a high dielectric constant is used for filling inside the particles. The maximum size of the gap is observed when the particles are large enough so that their surfaces overlap.