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.

arXiv comment12 pages, 3 figures, 2 pages of supplemental material

References in corpus (83)

• Weyl and Dirac Semimetals in Three Dimensional Solids
• Topological Photonics
• Topological Photonics
• Classification of topological insulators and superconductors in three spatial dimensions
• Photonic Floquet Topological Insulators
• Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Quantized Electric Multipole Insulators
• Photonic Analogue of Two-dimensional Topological Insulators and Helical One-Way Edge Transport in Bi-Anisotropic Metamaterials
• Periodic table for topological insulators and superconductors
• Imaging topological edge states in silicon photonics
• Chiral Quantum Optics
• Scheme to Achieve Silicon Topological Photonics
• Topological quantum chemistry
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Analogs of quantum Hall effect edge states in photonic crystals
• Lasing in topological edge states of a 1D lattice
• Single-Photon Switching and Entanglement of Solid-State Qubits in an Integrated Nanophotonic System
• Demonstration of a quantized microwave quadrupole insulator with topologically protected corner states
• A topological quantum optics interface
• Symmetry-based Indicators of Band Topology in the 230 Space Groups
• Quantization of fractional corner charge in $C_n$-symmetric higher-order topological crystalline insulators
• All-Si Valley-Hall Photonic Topological Insulator
• Topological classification of crystalline insulators through band structure combinatorics
• A Silicon-on-Insulator Slab for Topological Valley Transport
• 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
• Topological protection of photonic mid-gap cavity modes
• Exciton-polariton topological insulator
• Classical higher-order topological insulators
• Photonic quadrupole topological phases
• Photonic topological pumping through the edges of a dynamical four-dimensional quantum Hall system
• Direct Observation of Valley-polarized Topological Edge States in Designer Surface Plasmon Crystals
• Observation of Photonic Topological Valley-Hall Edge States
• Discovery of Weyl fermion semimetals and topological Fermi arc states
• Photonic Topological Insulator in Synthetic Dimensions
• Photonic crystal nanocavity based on a topological corner state
• Edge Solitons in Nonlinear Photonic Topological Insulators
• Observation of Topological Band Gap Solitons
• A topological source of quantum light
• Experimental discovery of bulk-disclination correspondence
• A single photonic cavity with two independent physical synthetic dimensions
• Active topological photonics
• Building Blocks of Topological Quantum Chemistry: Elementary Band Representations
• High-Q optical nanocavities in bulk single-crystal diamond
• Nonlinearity-induced photonic topological insulator
• Lasing from multipole topological corner states
• Experimental Measurement of the Berry Curvature from Anomalous Transport
• Observation of a higher-order topological bound state in the continuum
• Third-harmonic generation in photonic topological metasurfaces
• Quantized Nonlinear Thouless Pumping
• Chiral quantum optics using a topological resonator
• Topological light-trapping on a dislocation
• K-Theory and Pseudospectra for Topological Insulators
• Chiral-Symmetric Higher-Order Topological Phases of Matter
• Optical isolation with nonlinear topological photonics
• Observation of Protected Photonic Edge States Induced By Real-Space Topological Lattice Defects
• Nonlinear Thouless pumping: solitons and transport breakdown
• Topological Frequency Combs and Nested Temporal Solitons
• Larger-area single-mode photonic crystal surface-emitting lasers enabled by an accidental Dirac point
• Nonlinear imaging of nanoscale topological corner states
• Nonlinear imaging of nanoscale topological corner states
• Local invariants identify topology in metals and gapless systems
• The Chern Number Governs Soliton Motion in Nonlinear Thouless Pumps
• Theory of the coherence of topological lasers
• Tunable and robust long-range coherent interactions between quantum emitters mediated by Weyl bound states
• Space-group theory of photonic bands
• Bulk metals with helical surface states
• Quadratic pseudospectrum for identifying localized states
• Extended range of dipole-dipole interactions in periodically structured photonic media
• Invariants of disordered semimetals via the spectral localizer
• Probing band topology using modulational instability
• Anomalous quantum Hall effect of light in Bloch-wave modulated photonic crystals
• Location and topology of the fundamental gap in photonic crystals
• Finite volume calculation of $K$-theory invariants
• K-Theory for Real C*-algebras via Unitary Elements with Symmetries
• Light-matter interactions near photonic Weyl points
• Why the laser linewidth is so narrow: A modern perspective
• Long-lived elementary excitations and light coherence in topological lasers
• Transport through a disordered topological-metal strip
• Nonlinear signatures of Floquet band topology
• Computing Floquet Hamiltonians with Symmetries

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• 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