Spectral singularities and Bragg scattering in complex crystals

Abstract

Spectral singularities that spoil the completeness of Bloch-Floquet states may occur in non-Hermitian Hamiltonians with complex periodic potentials. Here an equivalence is established between spectral singularities in complex crystals and secularities that arise in Bragg diffraction patterns. Signatures of spectral singularities in a scattering process with wave packets are elucidated for a PT-symmetric complex crystal.

6 pages, 5 figures, to be published in Phys. Rev. A

References in corpus (8)

• Making Sense of Non-Hermitian Hamiltonians
• Visualization of Branch Points in PT-Symmetric Waveguides
• Physical realization of $\mathcal{P}\mathcal{T}$-symmetric potential scattering in a planar slab waveguide
• Exponentially Fragile PT-Symmetry in Lattices with Localized Eigenmodes
• Exceptional Points in Atomic Spectra
• Coulomb analogy for nonhermitian degeneracies near quantum phase transitions
• Resonance Phenomenon Related to Spectral Singularities, Complex Barrier Potential, and Resonating Waveguides
• Complex Periodic Potentials with a Finite Number of Band Gaps

Cited by in corpus (131)

• Non-Hermitian Physics
• Nonlinear waves in $\mathcal{P}\mathcal{T}$-symmetric systems
• Robust light transport in non-Hermitian photonic lattices
• Invisibility in PT-symmetric complex crystals
• Nonlinear suppression of time-reversals in PT-symmetric optical couplers
• Optical solitons in $\mathcal{P}\mathcal{T}$-symmetric nonlinear couplers with gain and loss
• Information Retrieval and Criticality in Parity-Time-Symmetric Systems
• PT Metamaterials via Complex-Coordinate Transformation Optics
• Signatures of three coalescing eigenfunctions
• $\mathcal{P}\mathcal{T}$ symmetry in a fractional Schrödinger equation
• Coalescence of spectral singularities and phase diagrams for one-dimensional PT symmetric photonic crystals
• PT-Symmetric Sinusoidal Optical Lattices at the Symmetry-Breaking Threshold
• Breathers in PT-symmetric optical couplers
• Optical Spectral Singularities as Threshold Resonances
• $\mathcal{P}\mathcal{T}$-symmetry breaking in a necklace of coupled optical waveguides
• Coherent perfect absorption of nonlinear matter waves
• Stability boundaries and collisions of two-dimensional solitons in PT-symmetric couplers with the cubic-quintic nonlinearity
• Full-Counting Many-Particle Dynamics: Nonlocal and Chiral Propagation of Correlations
• Explicit definition of $\mathcal{P}\mathcal{T}$ symmetry for non-unitary quantum walks with gain and loss
• Spectral and transport properties of time-periodic PT-symmetric tight-binding lattices
• Nonlinear Spectral Singularities for Localized Nonlinearities
• Topological Wave-Guiding Near an Exceptional Point: Defect-Immune, Slow-Light, Loss-Immune Propagation
• Parity-time symmetry in optical microcavity systems
• Analytic Results for a PT-symmetric Optical Structure
• $\mathcal{P}\mathcal{T}$-symmetric wave guide system with evidence of a third-order exceptional point
• Bound states, scattering states and resonant states in PT-symmetric open quantum systems
• Non-Hermitian skin effect beyond the tight-binding models
• Spectral singularities in PT-symmetric periodic finite-gap systems
• Non-Hermitian Floquet topological phases in the double-kicked rotor
• Gegenbauer-solvable quantum chain model
• Discrete solitons and vortices on two-dimensional lattices of $\mathcal{P}\mathcal{T}$-symmetric couplers
• Half-spectral unidirectional invisibility in non-Hermitian periodic optical structures
• PT-restoration via increased loss-gain in PT-symmetric Aubry-Andre model
• A solvable model for solitons pinned to a PT-symmetric dipole
• Spectral Singularities of a Complex Spherical Barrier Potential and Their Optical Realization
• Perfect State Transfer in PT-symmetric Non-Hermitian Networks
• Scattering by finite periodic $\mathcal{P}\mathcal{T}$-symmetric structures
• Convective and absolute PT symmetry breaking in tight-binding lattices
• Reciprocal and unidirectional scattering of parity-time symmetric structures
• Solitons in $\mathcal{P}\mathcal{T}$-symmetric periodic systems with the quadratic nonlinearity
• Asymmetric transmission through a flux-controlled non-Hermitian scattering center
• Spectral Singularities and Whispering Gallery Modes of a Cylindrical Gain Medium
• Nonlinear Spectral Singularities and Lasing Threshold Condition
• Invisible defects in complex crystals
• Localization, quantum resonances and ratchet acceleration in a periodically-kicked $\mathcal{P}\mathcal{T}$-symmetric quantum rotator
• Semiclassical Analysis of Spectral Singularities and Their Applications in Optics
• Spectral Singularities of a General Point Interaction
• Nonlinear localized modes in PT-symmetric optical media with competing gain and loss
• Fingerprints of exceptional points in the survival probability of resonances in atomic spectra
• Spectral singularities for Non-Hermitian one-dimensional Hamiltonians: puzzles with resolution of identity
• Lasing Threshold Condition for Oblique TE and TM Modes, Spectral Singularities, and Coherent Perfect Absorption
• Generalized Unitarity and Reciprocity Relations for PT-symmetric Scattering Potentials
• Phase transition through the splitting of self-dual spectral singularity in optical potentials
• Spectral Singularities in the Surface Modes of a Spherical Gain Medium
• Bloch oscillations in non-Hermitian lattices with trajectories in complex plane
• Asymmetric lasing at spectral singularities
• A physical interpretation for the non-Hermitian Hamiltonian
• Reciprocity and unitarity in scattering from a non-Hermitian complex PT-symmetric potential
• Wave emission and absorption at spectral singularities
• Discrete solitons and scattering of lattice waves in guiding arrays with a nonlinear $\mathcal{P}\mathcal{T}$-symmetric defect
• PT Meets Supersymmetry and Nonlinearity: An Analytically Tractable Case Example
• Exceptional points and Bloch oscillations in non-Hermitian lattices with unidirectional hopping
• Exceptional Points in the Flatland: A Non-Hermitian Line-Wave Scenario
• Non-adiabatic transitions through exceptional points in the band structure of a PT-symmetric lattice
• Solitons in PT-symmetric ladders of optical waveguides
• Perturbative Analysis of Spectral Singularities and Their Optical Realizations
• Interaction of sine-Gordon kinks and breathers with a $\mathcal{P}\mathcal{T}$-symmetric defect
• Discrete solitons in self-defocusing systems with $\mathcal{P}\mathcal{T}$-symmetric defects
• An exactly solvable quantum-lattice model with a tunable degree of nonlocality
• Exceptional points and photonic catastrophe
• Characteristic dynamics near two coalescing eigenvalues incorporating continuum threshold effects
• Anomalous-order exceptional point and non-Markovian Purcell effect at threshold in one-dimensional continuum systems
• Crypto-unitary forms of quantum evolution operators
• Bragg-induced power oscillations in PT symmetric periodic photonic structures
• Emitter and absorber assembly for multiple self-dual operation and directional transparency
• Reservoir-assisted symmetry breaking and coalesced zero-energy modes in an open PT-symmetric Su-Schrieffer-Heeger model
• Anomalous Parity-Time Symmetry Transition away from an Exceptional Point
• Talbot self-imaging in $\mathcal{P}\mathcal{T}$-symmetric complex crystals
• Scattering cross section resonance originating from a spectral singularity
• Spectral singularity and deep multiple minima in the reflectivity in non-Hermitian (complex) Ginocchio potential
• Complex Berry phase and imperfect non-Hermitian phase transitions
• Solitary waves of a PT-symmetric Nonlinear Dirac equation
• PT-symmetric optical superlattices
• Spectral Singularity in confined PT symmetric optical potential
• Exceptional point induced lasing dynamics in a non-Hermitian system
• SUSY transformations with complex factorization constants. Application to spectral singularities
• CP symmetry in optical systems
• Fundamental transfer matrix for electromagnetic waves, scattering by a planar collection of point scatterers, and anti-PT-symmetry
• Perturbative Unidirectional Invisibility
• Staggered $\mathcal{P}\mathcal{T}$-symmetric ladders with cubic nonlinearity
• Hermitian Hamiltonian equivalent to a given non-Hermitian one. Manifestation of spectral singularity
• Non-Hermitian spectral changes in the scattering of partially coherent radiation by periodic structures
• Nonlinear Spectral Singularities and Laser Output Intensity
• Non-Hermitian Fabry-Perot Resonances in a PT-symmetric system
• A unidirectional invisible PT-symmetric complex crystal with arbitrary thickness
• Multisoliton Newton's cradles and supersolitons in regular and PT-symmetric nonlinear couplers
• PT-symmetry breaking with divergent potentials: lattice and continuum cases
• Resonant generation of $p$-wave Cooper pair in non-Hermitian Kitaev chain at exceptional point
• Real-Time Transport in Open Quantum Systems From $\mathcal{P}\mathcal{T}$-Symmetric Quantum Mechanics
• Generalized Dimers and their Stokes-variable Dynamics
• Complete particle-pair annihilation as a dynamical signature of the spectral singularity
• Exactly solvable $\mathcal{P}\mathcal{T}$-symmetric models in two dimensions
• Harnessing $\mathcal{P}\mathcal{T}$-symmetry in non-Hermitian stiffness-modulated waveguides
• Transmission phase lapse in the non-Hermitian Aharonov-Bohm interferometer near the spectral singularity
• Absence of Floquet scattering in oscillating non-Hermitian potential wells
• Emulation of lossless exciton-polariton condensates by dual-core optical waveguides: Stability, collective modes, and dark solitons
• Non-Hermitian quantum rings
• Quantum mold casting for topological insulating and edge states
• Variational Approach to studying solitary waves in the nonlinear Schrodinger equation with Complex Potentials
• Scattering states of a particle, with position-dependent mass, in a $\mathcal{P}\mathcal{T}$ symmetric heterojunction
• Non-Hermitian invisibility in tight-binding lattices
• High-Directional Wave Propagation in Periodic Gain/Loss Modulated Materials
• Solitons in a chain of charge-parity-symmetric dimers
• Simple models of three coupled $\mathcal{P}\mathcal{T}$-symmetric wave guides allowing for third-order exceptional points
• Stability of new exact solutions of the nonlinear Schrodinger equation in a Poschl-Teller external potential
• Non-Hermitian Floquet-Free Analytically Solvable Time Dependant Systems
• Stability and response of trapped solitary wave solutions of coupled nonlinear Schrödinger equations in an external, $\mathcal{P}\mathcal{T}$- and supersymmetric potential
• Non-Local Elastic Lattices with $\mathcal{P}\mathcal{T}$-Symmetry and Time Modulation: From Perfect Trapping to the Wave Boomerang Effect
• Stability of exact solutions of the nonlinear Schroedinger equation in an external potential having supersymmetry and parity-time symmetry
• Classical Trajectories of the Continuum States of the $\mathcal{P}\mathcal{T}$ symmetric Scarf II potential
• Response of exact solutions of the nonlinear Schrodinger equation to small perturbations in a class of complex external potentials having supersymmetry and parity-time symmetry
• Scattering in a varying mass PT symmetric double heterojunction
• Bloch oscillations in a Bose-Hubbard chain with single-particle losses
• An update on coherent scattering from complex non-PT-symmetric Scarf II potential with new analytic forms
• PT -symmetry breaking and universal spectral statistics in quantum kicked rotors
• Dissipation-Induced Super Scattering and Lasing PT-Spaser
• Mini-review: Spatial solitons supported by localized gain
• Quasiclassical analysis of Bloch oscillations in non-Hermitian tight-binding lattices
• Introducing a general method for solving electromagnetic radiation problem in an arbitrary linear medium
• Singular Mapping for a $PT$-Symmetric Sinusoidal Optical Lattice at the Symmetry-Breaking Threshold
• Mathieu-Bragg photonic lattices