Surface Impedance and Bulk Band Geometric Phases in One-Dimensional Systems

By M. Xiao, Zhao-qing Zhang, C. T. Chan. 2014

461 citations recorded by the source corpus.

Surface impedance is an important concept in classical wave systems such as photonic crystals (PCs). For example, the condition of an interface state formation in the interfacial region of two different one-dimensional PCs is simply Z_SL +Z_SR=0, where Z_SL (Z_SR)is the surface impedance of the semi-infinite PC on the left- (right-) hand side of the interface. Here, we also show a rigorous relation between the surface impedance of a one-dimensional PC and its bulk properties through the geometrical (Zak) phases of the bulk bands, which can be used to determine the existence or non-existence of interface states at the interface of the two PCs in a particular band gap. Our results hold for any PCs with inversion symmetry, independent of the frequency of the gap and the symmetry point where the gap lies in the Brillouin Zone. Our results provide new insights on the relationship between surface scattering properties, the bulk band properties and the formation of interface states, which in turn can enable the design of systems with interface states in a rational manner.

Subfields: Atomic and Molecular Physics, and Optics, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/52642eb2cc4af8f58240d6bab6523cbe387d5ad9

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In Atomic and Molecular Physics, and Optics

In Electrical and Electronic Engineering

Citations in the corpus

Topological photonics (2018, background): “Since then, the SSH model or related models have been discussed and realized in photonic crystals (Keil et al., 2013; Xiao et al., 2014), electromagnetic metamaterials (Tan et al.”
Photonic crystal nanocavity based on a topological corner state (2018, background): “Each component of the 2D Zak phase corresponds to the existence of edge polarization (px or py), or an edge mode at one of the 1D edges [31,37].”
Topological Photonic Crystals: Physics, Designs, and Applications (2022, background): “One-dimensional topological photonic crystals As one of the representative topological models in 1D systems, SSH model can be realized in photonics, and has brought many theoretical and experimental results [86-90].”
Topological photonics (2014, background): “These single-mode one-way waveguides can also be realized in coupled defect cavities [26], self-guide [27] in freestanding slabs [28] and have robust local density of states [29].”