Three-dimensional photonic crystals by holographic lithography using the umbrella configuration: Symmetries and complete photonic band gaps

We present a detailed study of the crystallographic symmetries and band structures of three-dimensional photonic crystals that are amenable to nanofabrication through holographic lithography. For the experimentally preferable umbrella geometry, we identify realistic parameters that lead to structures with complete three-dimensional photonic band gaps. We find a solution, for which the photonic crystals have rhombohedral point symmetry. This solution is a member of the same space group as the celebrated Yablonovite structure and has a similar crystallographic motif. We find a complete photonic band gap with a gap/midgap ratio of 5.8% between the second and third band after silicon inversion at 38% silicon filling fraction. In addition, we identify parameter combinations for which the optimized interference contrast is as large as a factor of 10, rendering the fabrication of this structure possible.