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.

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• Topological Photonics
• Making Sense of Non-Hermitian Hamiltonians
• Topological Crystalline Insulators
• The physics of exceptional points
• Topological Origin of Non-Hermitian Skin Effects
• Coherent Perfect Absorbers: Time-reversed Lasers
• Visualization of Branch Points in PT-Symmetric Waveguides
• Efficient Light Funneling based on the non-Hermitian Skin Effect
• Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems
• Topological nodal line semimetals
• Selective enhancement of topologically induced interface states in a dielectric resonator chain
• Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas
• Reversing the Pump-Dependence of a Laser at an Exceptional Point
• Topological Transition in a Non-Hermitian Quantum Walk
• Topological acoustics
• New topological invariants in non-Hermitian systems
• 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
• Non-Hermitian Ring Laser Gyroscopes with Enhanced Sagnac Sensitivity
• Geometric phase from Aharonov-Bohm to Pancharatnam-Berry and beyond
• Nonlinear control of PT-symmetry and non-Hermitian topological states
• PT-Symmetry in Non-Hermitian Su-Schrieffer-Heeger model with complex boundary potentials
• Topological invariance and global Berry phase in non-Hermitian systems
• A non-Hermitian $PT-$symmetric Bose-Hubbard model: eigenvalue rings from unfolding higher-order exceptional points
• Detecting topological invariants in nonunitary discrete-time quantum walks
• Invisibility and PT-symmetry
• Observation of Bloch oscillations in complex PT-symmetric photonic lattices
• Phase transitions in a non-Hermitian Aubry-André-Harper model
• Observation of Chiral State Transfer Without Encircling an Exceptional Point
• Quantum limits on phase-preserving linear amplifiers
• Theory of Coupled Resonator Optical Waveguides (CROW) Exhibiting High Order Exceptional Points of Degeneracy
• 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
• Symmetry-protected zero-mode laser with a tunable spatial profile
• Complex Skin Modes in Non-Hermitian Coupled Laser Arrays
• Dislocation Non-Hermitian Skin Effect
• Vector exceptional points with strong superchiral fields
• Interaction-induced non-Hermitian topological phases from a dynamical gauge field
• Complex modes in unstable quadratic bosonic forms
• Anisotropic exceptional points of arbitrary order
• Photonic topological insulators a beginner's introduction
• Disorder-driven Phase Transitions of Second-order Non-Hermitian Skin Effects
• Revisiting the hierarchical construction of higher-order exceptional points
• Non-Hermitian Weyl semimetal and its Floquet engineering
• Exceptional Cones in 4D Parameter Space
• Non-Hermitian Higher-Order Weyl Semimetals
• Self-healing of non-Hermitian topological skin modes
• Scalable higher-order exceptional surface with passive resonators

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