Edge and corner states in non-Hermitian second-order topological photonic crystals

The PT symmetric phase transition existing in the gain-loss boundary of non-Hermitian second-order topological photonic crystals is investigated. The variation of the 2D bulk polarization of the photonic bands is analyzed as the gain-loss quantity increases. By tuning the gain or loss strength, topological edge states can appear at the interface between different non-Hermitian topologically nontrivial photonic crystals. Both the edge and corner states are studied in a topological cavity composed of a square closed domain wall between gain and loss domains. Calculated results show the non-Hermitian cavity has better mode localization of the electric field than the Hermitian one. Besides, the existence of the non-Hermitian induced states does not require strict balance of the gain and loss.