Omnidirectional two-dimensional photonic crystal band gap structures

Omnidirectional (3D) band gaps can evolve in $2\frac{1}{2}$ honeycomb and squared photonic crystal lattices and also in hexagonal crystals [Li and Xia, Phys. Rev. B 64, 153 (2001)]. This study presents a study of the according full parameter space. The calculation of omnidirectional photonic bands is based on the plane wave method for a two-dimensional photonic crystal with an off-plane wave vector ${k}_{z}={k}_{0}\phantom{\rule{0.2em}{0ex}}\mathrm{sin}(\ensuremath{\theta})$. The results are fully respecting the parameters index of refraction, the angle of incidence, as well as the structure radii. Omnidirectional band gaps are found for radii between $R=0.34$ and $R=0.5$, starting with index values from $3.0$ and show maximum relative band gap sizes ranging from $2.7%$ up to $10%$.