Fractal topological band-gap structure induced by singularities in the one-dimensional Thue–Morse system

Yu Zhang; Langlang Xiong; Meng Zhang; Xunya Jiang

doi:10.1364/PRJ.405230

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[46] 46On the transmission map, the width, central frequency, and structure of the FGs are different at two sides of the SL, which is the track of the first-type singularity. If we choose two σ very near the SL, which correspond to the two TM systems, the reflection phase of the left (ϕl) and right (ϕr) TM systems can match well, which satisfies ϕl+ϕr=0. But, due to the slow decaying of the field magnitude, it is difficult to observe the topological edge-state between the two TM systems. However, if we choose σ a little farther away from the SL, due to the gap structure difference, it is difficult to satisfy ϕl+ϕr=0 at a certain frequency inside the two gaps.