Location and topology of the fundamental gap in photonic crystals

Abstract

The fundamental, or first, band gap is of unmatched importance in the study of photonic crystals. Here, we address precisely where this gap can be opened in the band structure of three-dimensional photonic crystals. Although strongly constrained by symmetry, this problem cannot be addressed directly with conventional band-symmetry analysis due to the existence of a photonic polarization vortex at zero frequency. We develop an approach for overcoming the associated symmetry singularity by incorporating fictitious, auxiliary longitudinal modes. Our strategy also enables us to extend recent developments in symmetry-based topological analysis to the fundamental gap of three-dimensional photonic crystals. Exploiting this, we systematically study the topology of the minimal fundamental gaps. This reveals the existence of topological gap-obstructions that push the fundamental gap higher than what a conventional analysis would suggest. Our work demonstrates that topology can play a crucial role in the opening of the fundamental photonic gap and informs future theoretical and experimental searches for conventional and topological band gaps in three-dimensional photonic crystals.

arXiv commentMain text: 12 pages, 5 figures Supplemental material: 344 pages, 6 figures, multiple tables

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• An operator-based approach to topological photonics
• Local markers for crystalline topology
• Wannier Function Methods for Topological Modes in 1D Photonic Crystals
• Tutorial: Classifying Photonic Topology Using the Spectral Localizer and Numerical $K$-Theory
• Efficient Design of Helical Higher-Order Topological Insulators in 3D Elastic Medium
• Demonstration of non-Abelian frame charge flow in photonic crystals
• Intrinsic triple degeneracy point bounded by nodal surfaces in chiral photonic crystal
• Transversality-Enforced Tight-Binding Models for 3D Photonic Crystals aided by Topological Quantum Chemistry
• New geometric receipts for design of photonic crystals and metamaterials: optimal toric packings
• Dirac plasmon polaritons and magnetic modes in topological-insulator nanoparticles
• Wilson Loop and Topological Properties in 3D Woodpile Photonic Crystal