Topological Phases of Photonic Crystals under Crystalline Symmetries

Abstract

Photonic crystals (PhCs) have emerged as a popular platform for realizing various topological phases due to their flexibility and potential for device applications. In this article, we present a comprehensive classification of topological bands in one- and two dimensional photonic crystals, with and without time-reversal symmetry. Our approach exploits the symmetry representations of field eigenmodes at high-symmetry points in momentum space, allowing for the efficient design of a wide range of topological PhCs. In particular, we show that the complete classification provided here is useful for diagnosing photonic crystal analogs of obstructed atomic limits, fragile phases, and stable topological phases that include bands with Dirac points and Chern numbers.

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• Topological Corner States in Bilayer and Trilayer Systems with Vertically Stacked Topological Heterostructures
• Topological invariants and topological charges in photonic systems
• Efficient algorithms for surface density of states in topological photonic and acoustic systems
• Global and Local Topological Crystalline Markers for Rotation-Symmetric Insulators
• Wilson Loop and Topological Properties in 3D Woodpile Photonic Crystal
• Higher-order Topological Knots and the classification of non-Hermitian lattices under $C_n$ symmetry
• Topological photonic crystal fibre
• Manipulation of photonic topological edge and corner states via trivial claddings
• Topological photonics in nanoscaled systems with far field radiation and polarization singularities