Topological invariants and topological charges in photonic systems

Abstract

Topology in photonics comes in two distinct flavors: global and local. Global topology considers invariants that are obtained by integrating over the energy band, whereas local topology considers defects, typically vortices, in the far-field emission. These topologies are described by a wide range of models built in both real and momentum space, which are connected only by computationally expensive numerical methods that lack physical intuition. Here we propose a general framework based on a real-space Hamiltonian capable of describing electric field as a vector in both near- and far fields, allowing us to bridge between topological defects in the far-field and global topological invariants. The proposed Hamiltonian is constructed from the symmetry-representations of the lattice, is deformable to both atomic localized-mode (tight-binding) and photonic delocalized-mode (long-range) limits, and allows for independent control over the energies of eigenmodes of different symmetries at high-symmetry points of the Brillouin zone. This symmetry-based approach enables the design of structures with almost arbitrary topological properties and is not limited to photonic systems, but could apply to any system with engineered real-space couplings.

28 pages, 9 figures

References in corpus (20)

• Scheme to Achieve Silicon Topological Photonics
• Analogs of quantum Hall effect edge states in photonic crystals
• Bulk Topological Invariants in Noninteracting Point Group Symmetric Insulators
• Novel Topological Phase with Zero Berry Curvature
• Generation and Annihilation of Topologically-Protected Bound States in the Continuum and Circularly-Polarized States by Symmetry Breaking
• Essay: Where Can Quantum Geometry Lead Us?
• Dirac-like plasmons in honeycomb lattices of metallic nanoparticles
• A perspective on topological nanophotonics: current status and future challenges
• Topological Polarization Singularities in Metaphotonics
• Bound state in the continuum in slab waveguide enables low-threshold quantum-dot lasing
• Coexistence of pseudospin- and valley-Hall-like edge states in a photonic crystal with $C_{3v}$ symmetry
• Topological Phases of Photonic Crystals under Crystalline Symmetries
• Room Temperature Exciton-Polariton Condensation in Silicon Metasurfaces Emerging from Bound States in the Continuum
• Observation of Quantum metric and non-Hermitian Berry curvature in a plasmonic lattice
• Generalized Quantum Geometric Tensor in a Non-Hermitian Exciton-Polariton System
• Flat-Band Lasing in Silicon Waveguide-Integrated Metasurfaces
• High topological charge lasing in quasicrystals
• Pseudospin-orbit coupling and non-Hermitian effects in the Quantum Geometric Tensor of a plasmonic lattice
• Transversality-Enforced Tight-Binding Models for 3D Photonic Crystals aided by Topological Quantum Chemistry
• Breakdown of Bulk-Radiation Correspondence in Radiative Photonic Lattices