The effects of gain and loss on the band structures of a bulk topological dielectric photonic crystal (PC) with C6v symmetry and the PC-air-PC interface are studied based on first-principal calculation. To illustrate the importance of parity-time (PT) symmetry, three systems are considered, namely the PT-symmetric, PT-asymmetric, and lossy systems. We find that the system with gain and loss distributed in a PT symmetric manner exhibits a phase transition from a PT exact phase to a PT broken phase as the strength of the gain and loss increases, while for the PT-asymmetric and lossy systems, no such phase transition occurs. Furthermore, based on the Wilson loop calculation, the topology of the PT-symmetric system in the PT exact phase is demonstrated to keep unchanged as the Hermitian system. At last, different kinds of edge states in Hermitian systems under the influences of gain and loss are studied and we find that while the eigenfrequencies of nontrivial edge states become complex conjugate pairs, they keep real for the trivial defect states.


Electrical and Computer Engineering


National Natural Science Foundation of China, Grant FA2386-17-1-0010

International Standard Serial Number (ISSN)

2469-9934; 2469-9926

Document Type

Article - Journal

Document Version

Final Version

File Type





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Publication Date

01 Sep 2021