Optical properties of inverted opal photonic band gap crystals with stacking disorder

We present a detailed study of the effect of planar stacking disorder on optical properties of inverted opal photonic crystals. Systems with periodic stacking sequences are first studied that include face centered cubic, hexagonal close-packed, and doubly hexagonal close-packed photonic crystals. For the structures with periodic stacking order, we evaluate the band structure followed by calculation of transmission spectrum along the direction perpendicular to the hexagonal close-packing plane of the structures. Inverted opal photonic crystals with random stacking sequences are then studied by calculating average transmittance of the photonic crystal slabs over various random stacking configurations. The position and width of the lowest stop gap along the direction normal to the hexagonal close-packing plane is found to be invariant, regardless of the stacking sequence in the photonic crystal. We show how the propagation properties at higher frequencies are affected by the stacking configurations (both periodic and disordered stacking sequences), particularly those near the edges of the absolute band gap. The obtained results are directly relevant to transmission/reflection experiments on inverted opal photonic crystals with complete band gap.