Surface States in Topologically Trivial and Non-Trivial Photonic Crystals.

Topological insulators exhibit topologically non-trivial electronic band structure, which features an electronic band gap that causes insulating behaviour in the bulk while simultaneously supporting protected, unidirectional transport of electrons along their surface without any back-scattering, mostly unperturbed by local defects and impurities. In 2005 this unique electronic feature was transferred to the realm of photonics with the discovery of the quantum Hall effect analogue in photonic crystals. Topological photonics attracts such great scientific attention mainly due to the fundamental feature coming from the topological protection the unidirectional, back-scattering-free propagation of electromagnetic energy, immune to any perturbations. To achieve a photonic band gap, photonic crystals usually need to have a specific band structure on both sides of the interface or an outer layer with engineered material properties. This is important for suppressing surface states and evanescent waves that could interfere with the desired optical properties of the crystal. Here we discuss the process of introducing topological surface states at the interfaces of a photonic crystal and the free space and compare with the case of a non-topological photonic crystal.