An operator-based approach to topological photonics

Abstract

Recently, the study of topological structures in photonics has garnered significant interest, as these systems can realize robust, non-reciprocal chiral edge states and cavity-like confined states that have applications in both linear and non-linear devices. However, current band theoretic approaches to understanding topology in photonic systems yield fundamental limitations on the classes of structures that can be studied. Here, we develop a theoretical framework for assessing a photonic structure's topology directly from its effective Hamiltonian and position operators, as expressed in real space, and without the need to calculate the system's Bloch eigenstates or band structure. Using this framework, we show that non-trivial topology, and associated boundary-localized chiral resonances, can manifest in photonic crystals with broken time-reversal symmetry that lack a complete band gap, a result which may have implications for new topological laser designs. Finally, we use our operator-based framework to develop a novel class of invariants for topology stemming from a system's crystalline symmetries, which allows for the prediction of robust localized states for creating waveguides and cavities.

12 pages, 3 figures, 2 pages of supplemental material

References in corpus (22)

• Topological Photonics
• Classification of topological insulators and superconductors in three spatial dimensions
• Photonic Analogue of Two-dimensional Topological Insulators and Helical One-Way Edge Transport in Bi-Anisotropic Metamaterials
• Chiral Quantum Optics
• Scheme to Achieve Silicon Topological Photonics
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Analogs of quantum Hall effect edge states in photonic crystals
• Single-Photon Switching and Entanglement of Solid-State Qubits in an Integrated Nanophotonic System
• Visualization of higher-order topological insulating phases in two-dimensional dielectric photonic crystals
• Direct observation of corner states in second-order topological photonic crystal slabs
• Photonic topological pumping through the edges of a dynamical four-dimensional quantum Hall system
• Discovery of Weyl fermion semimetals and topological Fermi arc states
• Photonic crystal nanocavity based on a topological corner state
• Active topological photonics
• Building Blocks of Topological Quantum Chemistry: Elementary Band Representations
• High-Q optical nanocavities in bulk single-crystal diamond
• Quantized Nonlinear Thouless Pumping
• Optical isolation with nonlinear topological photonics
• Nonlinear imaging of nanoscale topological corner states
• Quadratic pseudospectrum for identifying localized states
• Anomalous quantum Hall effect of light in Bloch-wave modulated photonic crystals
• Light-matter interactions near photonic Weyl points

Cited by in corpus (19)

• Amorphous topological matter: theory and experiment
• Classifying topology in photonic heterostructures with gapless environments
• Quadratic pseudospectrum for identifying localized states
• Spectral localizer for line-gapped non-hermitian systems
• Chiral photonic topological states in Penrose quasicrystals
• Tutorial: Classifying Photonic Topology Using the Spectral Localizer and Numerical $K$-Theory
• Probing topology in nonlinear topological materials using numerical $K$-theory
• Quasicrystalline Weyl points and dense Fermi-Bragg arcs
• Structural spillage: an efficient method to identify non-crystalline topological materials
• Real-space topological invariant for time-quasiperiodic Majoranas
• Local and energy-resolved topological invariants for Floquet systems
• Even spheres as joint spectra of matrix models
• Topological zero-modes of the spectral localizer of trivial metals
• Global and Local Topological Crystalline Markers for Rotation-Symmetric Insulators
• Emergent topological phases and coexistence of gapless and spectral-localized Floquet quantum spin Hall states via electron-phonon interaction
• Quantitative measure of topological protection in Floquet systems through the spectral localizer
• A Hermitian bypass to the non-Hermitian quantum theory
• Topological photonic crystal fibre
• Dimensional crossover of class D real-space topological invariants