Non-Hermitian Photonic Lattices: tutorial

Abstract

Non-Hermitian photonic lattices combine the peculiar consequences of energy non-conservation with the physics of bandstructures, giving rise to a variety of exotic properties not found in conventional materials or photonic metamaterials. In this tutorial, we introduce the key concepts in the design and implementation of non-Hermitian photonic lattices, including the general features of non-Hermitian lattice Hamiltonians and their bandstructures, the role of non-Hermitian lattice symmetries, and the topological chracterization of non-Hermitian bandstructures. We survey several important non-Hermitian lattice designs, as well as the photonic platforms on which they can be realized. Finally, we discuss the possibilities for future developments in the field.

References in corpus (210)

• Topological Insulators
• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Topological Photonics
• Topological Photonics
• Photonic Floquet Topological Insulators
• Making Sense of Non-Hermitian Hamiltonians
• Classification of topological quantum matter with symmetries
• Nonreciprocal light transmission in parity-time-symmetric whispering-gallery microcavities
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Edge states and topological invariants of non-Hermitian systems
• Topological Crystalline Insulators
• Introduction to Quantum Noise, Measurement and Amplification
• Unidirectional Invisibility induced by PT-Symmetric Periodic Structures
• Exceptional Topology of Non-Hermitian Systems
• Non-Hermitian Physics
• Topological Materials: Weyl Semimetals
• Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
• Colloquium: Topological Band Theory
• Localization transitions in non-Hermitian quantum mechanics
• The physics of exceptional points
• Symmetry and Topology in Non-Hermitian Physics
• Topological Origin of Non-Hermitian Skin Effects
• Topological Band Theory for Non-Hermitian Hamiltonians
• Coherent Perfect Absorbers: Time-reversed Lasers
• Dynamically encircling exceptional points in a waveguide: asymmetric mode switching from the breakdown of adiabaticity
• Experimental observation of Weyl points
• Anomalous edge state in a non-Hermitian lattice
• Non-Bloch Band Theory of Non-Hermitian Systems
• Topolectrical circuit realization of topological corner modes
• Topological energy transfer in an optomechanical system with exceptional points
• Correspondence between winding numbers and skin modes in non-hermitian systems
• PT-symmetric laser-absorber
• Visualization of Branch Points in PT-Symmetric Waveguides
• Non-Hermitian Boundary Modes
• Spawning rings of exceptional points out of Dirac cones
• Observation of non-Hermitian bulk-boundary correspondence in quantum dynamics
• Efficient Light Funneling based on the non-Hermitian Skin Effect
• Pseudo-Hermiticity versus PT-Symmetry II: A complete characterizatio n of non-Hermitian Hamiltonians with a real spectrum
• Anatomy of skin modes and topology in non-Hermitian systems
• Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems
• Topological nodal line semimetals
• Probing topological invariants in the bulk of a non-Hermitian optical system
• Vortex Pinning and Non-Hermitian Quantum Mechanics
• Observation of Bulk Fermi Arc and Polarization Half Charge from Paired Exceptional Points
• Non-Hermitian skin effect and chiral damping in open quantum systems
• Observation of non-Hermitian degeneracies in a chaotic exciton-polariton billiard
• Non-Hermitian Topology and Exceptional-Point Geometries
• Selective enhancement of topologically induced interface states in a dielectric resonator chain
• Observation of parity-time symmetry breaking transitions in a dissipative Floquet system of ultracold atoms
• Complex Edge-State Phase Transitions in 1D Topological Laser Arrays
• Non-Hermitian bulk-boundary correspondence and auxiliary generalized Brillouin zone theory
• Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas
• Reversing the Pump-Dependence of a Laser at an Exceptional Point
• Biorthogonal Quantum Mechanics
• Edge states and topological phases in non-Hermitian systems
• Hybrid higher-order skin-topological modes in non-reciprocal systems
• Second-Order Topological Phases in Non-Hermitian Systems
• Topological Transition in a Non-Hermitian Quantum Walk
• Critical non-Hermitian Skin Effect
• Enhanced sensitivity operation of an optical gyroscope near an exceptional point
• Topological acoustics
• Conservation relations and anisotropic transmission resonances in one-dimensional PT-symmetric photonic heterostructures
• Coherent perfect absorbers: linear control of light with light
• Universal non-Hermitian skin effect in two and higher dimensions
• Topological Hybrid Silicon Microlasers
• Synthetic gauge fields and Weyl point in Time-Reversal Invariant Acoustic Systems
• Classification of Exceptional Points and Non-Hermitian Topological Semimetals
• Reciprocal skin effect and its realization in a topolectrical circuit
• Topologically protected midgap states in complex photonic lattices
• Non-Hermitian Quantum Sensing: Fundamental Limits and Non-Reciprocal Approaches
• Bulk-Boundary Correspondence in a Non-Hermitian System in One Dimension with Chiral-Inversion Symmetry
• The emergence, coalescence and topological properties of multiple exceptional points and their experimental realization
• Geometrical meaning of winding number and its characterization of topological phases in one-dimensional chiral non-Hermitian systems
• Observation of hybrid higher-order skin-topological effect in non-Hermitian topolectrical circuits
• Probing non-Hermitian Skin Effect and non-Bloch Phase Transitions
• Interplay of non-Hermitian skin effects and Anderson localization in non-reciprocal quasiperiodic lattices
• Higher-order non-Hermitian skin effect
• New topological invariants in non-Hermitian systems
• Bosonic Condensation and Disorder-Induced Localization in a Flat Band
• Experimental realization of a Weyl exceptional ring
• Observation of Parity-Time Symmetry in Optically Induced Atomic Lattices
• Observation of higher-order non-Hermitian skin effect
• Dynamically encircling exceptional points: Exact evolution and polarization state conversion
• Probing 10 μK stability and residual drifts in the cross-polarized dual-mode stabilization of single-crystal ultrahigh-Q optical resonators
• Observation of arbitrary topological windings of a non-Hermitian band
• Non-Hermitian Ring Laser Gyroscopes with Enhanced Sagnac Sensitivity
• Non-Hermitian skin modes induced by on-site dissipations and chiral tunneling effect
• Experimental observation of optical Weyl points
• Physical Aspects of Pseudo-Hermitian and $PT$-Symmetric Quantum Mechanics
• Topology-Induced Spontaneous Non-reciprocal Pumping in Cold-Atom Systems with Loss
• Photonic Topological Insulating Phase Induced Solely by Gain and Loss
• Geometric phase from Aharonov-Bohm to Pancharatnam-Berry and beyond
• Observation of an exceptional point in a chaotic optical microcavity
• Nonlinear control of PT-symmetry and non-Hermitian topological states
• Higher-order topological corner states induced by gain and loss
• Quantum Noise Theory of Exceptional Point Sensors
• Electromagnetically induced transparency at a chiral exceptional point
• PT-symmetry in honeycomb photonic lattices
• Topological unification of time-reversal and particle-hole symmetries in non-Hermitian physics
• Sensing with exceptional surfaces: combining sensitivity with robustness
• PT-Symmetry in Non-Hermitian Su-Schrieffer-Heeger model with complex boundary potentials
• Non-Hermitian extensions of higher-order topological phases and their biorthogonal bulk-boundary correspondence
• No exceptional precision of exceptional point sensors
• Topological invariance and global Berry phase in non-Hermitian systems
• Symmetry-protected nodal phases in non-Hermitian systems
• Observation of Defect States in PT-Symmetric Optical Lattices
• Petermann-factor limited sensing near an exceptional point
• Topological exceptional surfaces in non-Hermitian systems with parity-time and parity-particle-hole symmetries
• A non-Hermitian $PT-$symmetric Bose-Hubbard model: eigenvalue rings from unfolding higher-order exceptional points
• Exact solution of non-Hermitian systems with generalized boundary conditions: size-dependent boundary effect and fragility of skin effect
• Observation of non-Bloch parity-time symmetry and exceptional points
• General description of quasi-adiabatic dynamical phenomena near exceptional points
• The Chirality of Exceptional Points
• Detecting topological invariants in nonunitary discrete-time quantum walks
• Phase-dependent chiral transport and effective non-Hermitian dynamics in a bosonic Kitaev-Majorana chain
• Signatures of three coalescing eigenfunctions
• Knots and Non-Hermitian Bloch Bands
• Second-order topological non-Hermitian skin effects
• Observation of critical phenomena in parity-time-symmetric quantum dynamics
• Experimental observation of exceptional surface in synthetic dimensions with magnon polaritons
• Geometric phase around exceptional points
• Exceptional Surfaces in PT-Symmetric Photonic Systems
• Non-Hermitian Hopf-Link Exceptional Line Semimetals
• Invisibility and PT-symmetry
• Synthetic parity-time symmetry breaking in a single microcavity
• Non-Hermitian higher-order topological states in nonreciprocal and reciprocal systems with their electric-circuit realization
• Perspective on topological states of non-Hermitian lattices
• Symmetry-protected multifold exceptional points and their topological characterization
• Sensitivity of parameter estimation near the exceptional point of a non-Hermitian system
• Exceptional Links and Twisted Fermi Ribbons in non-Hermitian Systems
• Observation of non-Hermitian topological Anderson insulator in quantum dynamics
• Non-Hermitian nodal-line semimetals with an anomalous bulk-boundary correspondence
• Effects of non-Hermitian perturbations on Weyl Hamiltonians with arbitrary topological charges
• Non-Hermitian Edge Burst
• Arbitrary order exceptional point induced by photonic spin-orbit interaction in coupled resonators
• Knotted Non-Hermitian Metals
• Fluctuations and noise-limited sensing near the exceptional point of $\mathcal{P}\mathcal{T}$-symmetric resonator systems
• Observation of Bloch oscillations in complex PT-symmetric photonic lattices
• Topological quantum fluctuations and travelling wave amplifiers
• Generalized bulk-edge correspondence for non-hermitian topological systems
• Experimental demonstration of an anisotropic exceptional point
• Non-Hermitian Dirac Cones
• Non-Hermitian second-order skin and topological modes
• Phase transitions in a non-Hermitian Aubry-André-Harper model
• Observation of Chiral State Transfer Without Encircling an Exceptional Point
• Defect states emerging from a non-Hermitian flat band of photonic zero modes
• Topology of anti-parity-time-symmetric non-Hermitian Su-Schrieffer-Heeger model
• Reconfigurable topological phases in next-nearest-neighbor coupled resonator lattices
• Non-Hermitian engineering of terahertz light using exceptional points in electrically tuneable collective light-matter interactions
• Quantum limits on phase-preserving linear amplifiers
• Exceptional Points in a Non-Hermitian Topological Pump
• Observation of anti-parity-time-symmetry, phase transitions and exceptional points in an optical fibre
• Anomalous single-mode lasing induced by nonlinearity and the non-Hermitian skin effect
• Theory of Coupled Resonator Optical Waveguides (CROW) Exhibiting High Order Exceptional Points of Degeneracy
• Non-equilibrium stationary states of quantum non-Hermitian lattice models
• Geometric Response and Disclination-Induced Skin Effects in Non-Hermitian Systems
• Unraveling the Non-Hermitian Skin Effect in Dissipative Systems
• Parity anomaly and Landau-level lasing in strained photonic honeycomb lattices
• Topological Modes in a Laser Cavity through Exceptional State Transfer
• Non-trivial point-gap topology and non-Hermitian skin effect in photonic crystals
• Chiral modes at exceptional points in exciton-polariton quantum fluids
• Complex Skin Modes in Non-Hermitian Coupled Laser Arrays
• Symmetry-protected zero-mode laser with a tunable spatial profile
• Hierarchical construction of higher-order exceptional points
• Non-reciprocal transport of Exciton-Polaritons in a non-Hermitian chain
• Anomalous Floquet non-Hermitian skin effect in a ring resonator lattice
• Topological protection from exceptional points in Weyl and nodal line semimetals
• Dislocation Non-Hermitian Skin Effect
• Simulating Exceptional Non-Hermitian Metals with Single-Photon Interferometry
• Higher-Order Weyl-Exceptional-Ring Semimetals
• Topology by Dissipation: Majorana Bosons in Metastable Quadratic Markovian Dynamics
• Edge-state instabilities of bosons in a topological band
• Floquet second-order topological insulators in non-Hermitian systems
• Vector exceptional points with strong superchiral fields
• Eigenvalue topology of non-Hermitian band structures in two and three dimensions
• $\mathcal{P}\mathcal{T}$-symmetric non-Hermitian Dirac semimetals
• Non-Hermitian band topology with generalized inversion symmetry
• Non-Hermitian skin effect of dislocations and its topological origin
• Complex modes in unstable quadratic bosonic forms
• Interaction-induced non-Hermitian topological phases from a dynamical gauge field
• Anisotropic exceptional points of arbitrary order
• Curving the space by non-Hermiticity
• Selective Population of Edge States in a 2D Topological Band System
• Photonic topological insulators a beginner's introduction
• Topological instabilities in ac-driven bosonic systems
• Probing bulk topological invariants using leaky photonic lattices
• Disorder-driven Phase Transitions of Second-order Non-Hermitian Skin Effects
• Anyonic-parity-time symmetry in complex-coupled lasers
• Connections between the Open-boundary Spectrum and Generalized Brillouin Zone in Non-Hermitian Systems
• Inversion symmetric non-Hermitian Chern insulator
• Topology in non-Hermitian Chern insulators with skin effect
• PT-symmetry entails pseudo-Hermiticity regardless of diagonalizability
• Giant Enhancement of Unconventional Photon Blockade in a Dimer Chain
• Statistical PT-symmetric lasing in an optical fiber network
• Nodal Manifolds Bounded by Exceptional Points on Non-Hermitian Honeycomb Lattices and Electrical-Circuit Realizations
• Amplification of quantum signals by the non-Hermitian skin effect
• On the time evolution at a fluctuating exceptional point
• Revisiting the hierarchical construction of higher-order exceptional points
• Non-Hermitian Weyl semimetal and its Floquet engineering
• Non-Hermitian dynamics of slowly-varying Hamiltonians
• Exceptional Cones in 4D Parameter Space
• Non-Hermitian CT-Symmetric Spectral Protection of Nonlinear Defect Modes
• Pseudo-Hermitian Hamiltonians Generating Waveguide Mode Evolution
• Edge states in a non-Hermitian topological crystalline insulator
• Weyl points and exceptional rings with polaritons in bulk semiconductors
• Anyonic $\mathcal{P}\mathcal{T}$ symmetry, drifting potentials and non-Hermitian delocalization
• Symmetry-protected topological exceptional chains in non-Hermitian crystals
• Scalable higher-order exceptional surface with passive resonators
• Self-healing of non-Hermitian topological skin modes
• Non-Hermitian Higher-Order Weyl Semimetals

Cited by in corpus (26)

• Observation of Quantum metric and non-Hermitian Berry curvature in a plasmonic lattice
• Skin modes in a nonlinear Hatano-Nelson model
• Observation of non-Hermitian antichiral edge currents
• Phase transitions and bunching of correlated particles in a non-Hermitian quasicrystal
• Pseudo-Hermiticity protects the energy-difference conservation in the scattering
• Topological properties of a non-Hermitian quasi-1D chain with a flat band
• Localized states and skin effect around non-Hermitian impurities in tight-binding models
• Pseudospin-orbit coupling and non-Hermitian effects in the Quantum Geometric Tensor of a plasmonic lattice
• Giant non-reciprocity and gyration through modulation-induced Hatano-Nelson coupling in integrated photonics
• Versatile Braiding of Non-Hermitian Topological Edge States
• Waveguide QED with dissipative light-matter couplings
• Switchable Non-Hermitian Skin Effect in Bogoliubov Modes
• Unconventional and robust light-matter interactions based on the non-Hermitian skin effect
• Harnessing Nonlinearity to Tame Wave Dynamics in Nonreciprocal Active Systems
• $\mathcal{P}\mathcal{T}$-symmetric photonic lattices with type-II Dirac cones
• Nonlinear skin breathing modes in one-dimensional nonreciprocal mechanical lattices
• Reconfigurable Non-Hermitian Soliton Combs using Dissipative Couplings and Topological Windings
• Programmable non-Hermitian photonic quantum walks via dichroic metasurfaces
• An unusual phase transition in a non-Hermitian Su-Schrieffer-Heeger model
• Topological photonics in nanoscaled systems with far field radiation and polarization singularities
• Solution of Wave Acceleration and Non-Hermitian Jump in Nonreciprocal Lattices
• Continuum Landau surface states in a non-Hermitian Weyl semimetal
• Chiral lasing via broken parity-time symmetry in bound-state-in-the-continuum metasurfaces
• Phase fields in momentum space of photonic crystal slabs
• Insensitive nonreciprocal edge breathers
• Topology of the generalized Brillouin zone of one-dimensional models