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Refractive index is a fundamental electromagnetic (EM) parameter that candescribe photonic continuous media (PCM) traditionally as either transparencyor opacity. Recently, topological theory offers a new set of phases tocharacterize PCM as either trivial or nontrivial, by using topologicalinvariant which are not direct to EM parameters. As all of optical propertiesin PCM should be related to EM parameters, we formulate a topological indexbased on EM parameters and establish its phase map in this work. The map cananalytically describe the deterministic condition for a topologicallynontrivial phase. Our findings indicate that the topology of 2D bi-anisotropicPCM is determined by the sign of the topological index. Another EM parameter ofpseudo surface impedance is also introduced for the opaque regions of PCM,showing that the topological opacity has a full range of impedance valuesranging from negative to positive, while the trivial case only has eithernegative or positive impedance. The simulation results show that an interfacebetween two opacities with differing index signs can support robustly opticalpropagation of topological edge states. As the index only depends on EMparameters, it will pave an insightful way to further understand the intrinsicproperties of photonic topology.

Classification of Topological Phase in 2D Photonic Continuous Media Using Electromagnetic Parameters