Abstract
''Investigating the topological characteristics of a given photonic crystal requires the precise knowledge of a photonic band structure. Band gaps and band crossing has to be identified, since topological calculations are performed on a group of bands that are touching, crossing, or in other words, are not separated by a photonic gap or false gap.
Furthermore, a specific class o topological insulators, Z(2) insulators, require the identification of a band inversion [6]. The band inversion is defined as a change of the ordering of eigenvectors of individual bands.
The band structure is nothing more than a set of eigenvalues in the k-space, each eigenvalue having its own eigenvector. Those eigenvectors has a symmetry group, which can be identified with atomic orbital symmetries s, p, d, f,...
Properly identifying those symmetries and the order in the band structure, especially around a photonic band gap, is crucial for further research.''