  Topological Quantum Chemistry (TQC) has recently emerged as a instrumental
tool to characterize the topological nature of both fermionic and bosonic band
structures. TQC is based on the study of band representations and the
localization of maximally localized Wannier functions. In this article, we
study various two-dimensional photonic crystal structures analyzing their
topological character through a combined study of TQC, their Wilson-loop
spectra and the electromagnetic energy density. Our study demonstrates that the
analysis of the spatial localization of the energy density complements the
study of the topological properties in terms of the spectrum of the Wilson-loop
operator and TQC.
