Three-dimensional photonic Dirac points stabilized by point group symmetry

Abstract

We discover a pair of stable 3D Dirac points, 3D photonic analog of graphene, in all-dielectric photonic crystals using structures commensurate with nano-fabrication for visible-frequency photonic applications. The Dirac points carry nontrivial $Z_2$ topology and emerge for a large range of material parameters in hollow cylinder hexagonal photonic crystals. From Kramers theorem and group theory, we find that only the $C_6$ symmetry lead to point group symmetry stabilized Dirac points in 3D all-dielectric photonic crystals. {The Dirac points are characterized using $\vec{k}\cdot \vec{P}$ theory for photonic bands in combination with symmetry analysis. Breaking inversion symmetry splites the Dirac points into Weyl points. The physical properties and experimental consequences of Dirac points are also studied. The Dirac points are found to be robust against parameter tuning and weak disorders.

12 pages, 13 figures. Published version

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• A brief review of topological photonics in one, two, and three dimensions
• Three dimensional photonic Dirac points in metamaterials
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• Possible Realization of Optical Quadratic and Dirac Points in Woodpile Photonic Crystals
• Floquet-Weyl and Floquet-topological-insulator phases in a stacked two-dimensional ring-network lattice
• $Z_2$ Dirac points with topologically protected multihelicoid surface states
• Bose-Einstein condensate of Dirac magnons: Pumping and collective modes
• 3D $Z_2$ Topological Nodes in Nonsymmorphic Photonic Crystals: Ultrastrong Coupling and Anomalous Refraction
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• Manipulation of photonic topological edge and corner states via trivial claddings