Rhombohedral photonic crystals by triple-exposure interference lithography: Complete photonic band gap

The band structure of 3D photonic crystal that could be synthesized by means of interference lithography with triple-exposure two-beam interference technique has been investigated. As a result of the geometry optimization the optimal conditions for maximal band gaps with different refractive index contrast have been obtained. The refractive index threshold for gap opening equaled to 2.14 has been predicted for this method of photonic crystals synthesis. This value is close to the refractive index thresholds of the best known structures. The continuous transition between simple cubic, face centered cubic and bulk centered cubic symmetries has been considered.