Multiband Photonic Topological Valley‐Hall Edge Modes and Second‐Order Corner States in Square Lattices

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Abstract
Robust multiband photonic topological edge states are of great importance for photonic applications, including nonlinear wavelength conversion. In particular, higher‐order photonic topological states provide the realizability of photonic nanoresonators with high robustness against structural disorder of photonic crystals. This work reveals that multiband photonic topological valley‐Hall edge states and second‐order corner states can be observed in square lattice photonic crystals consisting of triangular dielectric rods. For small sizes of the triangles, multiband gapless edge modes propagate through the photonic topological waveguide. Their transmission characteristics and robustness against the structural defects have been evaluated for linear and Z‐shaped interfaces. When the size of the triangles increases, most of edge bands become gapped and one can obtain disorder‐immune multiband second‐order topological corner states, which is the core result of this report. The results obtained in this work can find important applications for nonlinear topological frequency conversion.

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