Classification of quantum-spin-hall topological phase in 2D photonic continuous media using electromagnetic parameters

Refractive index is a fundamental electromagnetic (EM) parameter that can describe photonic continuous media (PCM) traditionally as either transparency or opacity. Recently, topological theory offers a new set of phases to characterize PCM as either trivial or nontrivial, by using topological invariant which are not direct to EM parameters. As all of the optical properties in PCM should be related to EM parameters, we formulate a topological index based on EM parameters and establish its phase map in this work. The map can analytically describe the deterministic condition for a topologically nontrivial phase. Our findings indicate that the topology of 2D bi-anisotropic PCM is determined by the sign of the topological index. Another EM parameter of pseudo surface impedance is also introduced for the opaque regions of PCM, showing the topological opacity has a full range of impedance values ranging from negative to positive, while the trivial case only has either negative or positive impedance. The simulation results show that an interface between two opacities with differing index signs can support robustly optical propagation of topological edge states. The proposal of EM-parameter method reveals a deep understanding on topological properties of PCM, and will enrich the topological theory in photonic systems.