Nonlinear switching and solitons in PT-symmetric photonic systems

Abstract

One of the challenges of the modern photonics is to develop all-optical devices enabling increased speed and energy efficiency for transmitting and processing information on an optical chip. It is believed that the recently suggested Parity-Time (PT) symmetric photonic systems with alternating regions of gain and loss can bring novel functionalities. In such systems, losses are as important as gain and, depending on the structural parameters, gain compensates losses. Generally, PT systems demonstrate nontrivial non-conservative wave interactions and phase transitions, which can be employed for signal filtering and switching, opening new prospects for active control of light. In this review, we discuss a broad range of problems involving nonlinear PT-symmetric photonic systems with an intensity-dependent refractive index. Nonlinearity in such PT symmetric systems provides a basis for many effects such as the formation of localized modes, nonlinearly-induced PT-symmetry breaking, and all-optical switching. Nonlinear PT-symmetric systems can serve as powerful building blocks for the development of novel photonic devices targeting an active light control.

33 pages, 33 figures

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• Unidirectional Nonlinear PT-symmetric Optical Structures
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• Physical realization of $\mathcal{P}\mathcal{T}$-symmetric potential scattering in a planar slab waveguide
• Solitons in PT-symmetric nonlinear lattices
• Exponentially Fragile PT-Symmetry in Lattices with Localized Eigenmodes
• Robust light transport in non-Hermitian photonic lattices
• Visualization of Coherent Destruction of Tunneling in an Optical Double Well System
• Invisibility and PT-symmetry
• Experimental observation of the dual behavior of $\mathcal{P}\mathcal{T}$-symmetric scattering
• Constant-intensity waves and their modulation instability in non-Hermitian potentials
• Breathers in PT-symmetric optical couplers
• Stable dark solitons in PT-symmetric dual-core waveguides
• Optical mesh lattices with PT-symmetry
• Bragg solitons in nonlinear PT-symmetric periodic potentials
• Quantum control and entanglement using periodic driving fields
• $\mathcal{P}\mathcal{T}$-symmetric microring laser-absorber
• Symmetry breaking of solitons in one-dimensional parity-time-symmetric optical potentials
• SUSY-inspired one-dimensional transformation optics
• Nonlocal gap solitons in PT-symmetric periodic potentials with defocusing nonlinearity
• PT spectroscopy of the Rabi problem
• Stable localized modes in asymmetric waveguides with gain and loss
• Stabilizing Non-Hermitian Systems by Periodic Driving
• Parity-Time Anti-Symmetric Parametric Amplifier
• Families of stationary modes in complex potentials
• Nonlinear Schrödinger equation for a PT symmetric delta-functions double well
• Discrete solitons in PT-symmetric lattices
• Impact of loss on the wave dynamics in photonic waveguide lattices
• Unbreakable PT-symmetry of solitons supported by inhomogeneous defocusing nonlinearity
• Symmetry breaking of solitons in two-dimensional complex potentials
• Discrete solitons and vortices on two-dimensional lattices of $\mathcal{P}\mathcal{T}$-symmetric couplers
• Hamiltonian formulation of the standard $\mathcal{P}\mathcal{T}$-symmetric nonlinear Schrödinger dimer
• Nonlinear PT-symmetric plaquettes
• Dimer with gain and loss: Integrability and $\mathcal{P}\mathcal{T}$-symmetry restoration
• PT-symmetry in optics beyond the paraxial approximation
• From scattering theory to complex wave dynamics in non-hermitian PT-symmetric resonators
• 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
• Nonlinear multi-core waveguiding structures with balanced gain and loss
• Interaction of sine-Gordon kinks and breathers with a $\mathcal{P}\mathcal{T}$-symmetric defect
• Interplay between Fano resonance and $\mathcal{P}\mathcal{T}$ symmetry in non-Hermitian discrete systems
• Exactly solvable Wadati potentials in the PT-symmetric Gross-Pitaevskii equation
• PT-symmetric Double Well Potentials Revisited: Bifurcations, Stability and Dynamics
• Light propagation in periodically modulated complex waveguides
• Spectral Singularities and CPA-Laser Action in a Weakly Nonlinear PT-Symmetric Bilayer Slab
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• Pseudo PT symmetric lattice
• Localised nonlinear modes in the PT-symmetric double-delta well Gross-Pitaevskii equation

Cited by in corpus (132)

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• Time-periodic stiffness modulation in elastic metamaterials for selective wave filtering: theory and experimental investigations
• Vortex solitons: Old results and new perspectives
• Optical isolation with nonlinear topological photonics
• Parity-Time Symmetry in Non-Hermitian Complex Optical Media
• Observation of anti-parity-time-symmetry, phase transitions and exceptional points in an optical fibre
• Dark Solitons in Waveguide Polariton Fluids Shed Light on Interaction Constants
• Chirality of topological gap solitons in bosonic dimer chains
• One-dimensional gap solitons in quintic and cubic-quintic Fractional nonlinear Schrödinger equations with a periodically modulated linear potential
• Solving forward and inverse problems of the logarithmic nonlinear Schrodinger equation with PT-symmetric harmonic potential via deep learning
• Parity-time symmetry in optical microcavity systems
• PT-symmetry breaking in multilayers with resonant loss and gain locks light propagation direction
• Multidimensional dissipative solitons and solitary vortices
• An Adiabatic Invariant Approach to Transverse Instability: Landau Dynamics of Soliton Filaments
• Integrable nonlocal Hirota equations
• Parity-time-symmetric optical lattice with alternating gain and loss atomic configurations
• Metastable soliton necklaces supported by fractional diffraction and competing nonlinearities
• Non-Hermitian Floquet Topological Matter -- A Review
• Two (2 + 1)-dimensional integrable nonlocal nonlinear Schrodinger equations: Breather, rational and semi-rational solutions
• Enhanced stability, bistability, and exceptional points in saturable active photonic couplers
• Field Patterns: A New Mathematical Object
• Symmetry-Protected Scattering in Non-Hermitian Linear Systems
• 2D Solitons in PT-symmetric photonic lattices
• High energy density in the collision of $N$ kinks in the ${\varphi }^4$ model
• Inversion symmetric non-Hermitian Chern insulator
• Jamming anomaly in $\mathcal{P}\mathcal{T}$-symmetric systems
• Stable and oscillating solitons of $\mathcal{P}\mathcal{T}$-symmetric couplers with gain and loss in fractional dimension
• Localization, quantum resonances and ratchet acceleration in a periodically-kicked $\mathcal{P}\mathcal{T}$-symmetric quantum rotator
• One- and two-dimensional solitons in PT-symmetric systems emulating the spin-orbit coupling
• Tailoring $\mathcal{P}\mathcal{T}$-symmetric soliton switch
• Stability of soliton families in nonlinear Schroedinger equations with non-parity-time-symmetric complex potentials
• Extreme values of elastic strain and energy in sine-Gordon multi-kink collisions
• $\mathcal{P}\mathcal{T}$-symmetric mode-locking
• Dissipative Kerr solitons in a photonic dimer on both sides of exceptional point
• Skin modes in a nonlinear Hatano-Nelson model
• Optical solitons in media with focusing and defocusing saturable nonlinearity and a parity-time-symmetric external potential
• $\mathcal{P}\mathcal{T}$ symmetry and anti-symmetry by anti-Hermitian wave coupling and nonlinear optical interactions
• Families of exact solutions of a new extended (2+1)-dimensional Boussinesq equation
• New classes of non-parity-time-symmetric optical potentials with all-real spectra and exceptional-point-free phase transition
• Chiral current circulation and $\mathcal{P}\mathcal{T}$ symmetry in a trimer of oscillators
• Radiative topological biphoton states in modulated qubit arrays
• Spontaneous symmetry breaking of fundamental states, vortices, and dipoles in two- and one-dimensional linearly coupled traps with cubic self-attraction
• Multiple quantum wells for PT-symmetric phononic crystals
• Solitons in PT-symmetric ladders of optical waveguides
• PT-symmetry in nonlinear twisted multi-core fibers
• Transmission enhancement in loss-gain multilayers by resonant suppression of reflection
• Gaussian-like and flat-top solitons of atoms with spatially modulated repulsive interactions
• Nonlinear Topological Edge States in a non-Hermitian Array of Optical Waveguides Embedded in an Atomic Gas
• Bound states in the continuum in a two-dimensional PT-symmetric system
• Attraction centers and PT-symmetric delta-functional dipoles in critical and supercritical self-focusing media
• Impact of near-PT symmetry on exciting solitons and interactions based on a complex Ginzburg-Landau model
• Pseudo-Hermiticity protects the energy-difference conservation in the scattering
• Designing lasing and perfectly absorbing potentials
• Spinor solitons and their $\mathcal{P}\mathcal{T}$-symmetric offspring
• $\mathcal{P}\mathcal{T}$ symmetric phase transition and single-photon transmission in an optical trimmer system
• Snakes and ghosts in a parity-time-symmetric chain of dimers
• Light dynamics in nonlinear trimers and twisted multicore fibers
• Asymmetric Acoustic Energy Transport in Non-Hermitian Metamaterials
• Super-exponential diffusion in nonlinear non-Hermitian systems
• Symmetry breaking with opposite stability between bifurcated asymmetric solitons in parity-time-symmetric potentials
• Exceptional points in oligomer chains
• Continuous families of solitary waves in non-symmetric complex potentials: A Melnikov theory approach
• Nonlinear wave dynamics near phase transition in $\mathcal{P}\mathcal{T}$-symmetric localized potentials
• Nonlinear anti-directional couplers with gain and loss
• Cavity solitons in a microring dimer with gain and loss
• Floquet control of global $PT$ symmetry in 2D arrays of quadrimer waveguides
• Laser Mode Bifurcations Induced by $\mathcal{P}\mathcal{T}$-Breaking Exceptional Points
• Effective protection of quantum coherence by non-Hermitian driving
• PT-symmetric quantum oscillator in an optical cavity
• Signature of exceptional point phase transition in Hermitian systems
• On the spontaneous time-reversal symmetry breaking in synchronously-pumped passive Kerr resonators
• Edge and bulk dissipative solitons in modulated PT-symmetric waveguide arrays
• Cross-symmetric dipolar-matter-wave solitons in double-well chains
• Self-stabilization of light sails by damped internal degrees of freedom
• Unitary Scattering Protected by Pseudo-Hermiticity
• Phase space representation of non-Hermitian system with $\mathcal{P}\mathcal{T}$-symmetry
• Bistable soliton switching dynamics in a $\mathcal{P}\mathcal{T}$-symmetric coupler with saturable nonlinearity
• Pseudo-invariant approach for a particle in a complex time-dependent linear potential
• Resonant interaction of ${\varphi }^4$ kink with spatially periodic $\mathcal{P}\mathcal{T}$-symmetric perturbation
• Solitons in $\mathcal{P}\mathcal{T}$-symmetric systems with spin-orbit coupling and critical nonlinearity
• Switching dynamics of femtosecond solitons in parity-time-symmetric coupled optical waveguides
• Dynamical control of solitons in a parity-time-symmetric coupler by periodic management
• Metastable two-component solitons near an exceptional point
• Modulational instability in $\mathcal{P}\mathcal{T}$-symmetric Bragg grating structures with saturable nonlinearity
• Exceptional point in a coupled Swanson system
• Controllable high-speed polariton waves in a PT-symmetric lattice
• Variational approximations of soliton dynamics in the Ablowitz-Musslimani nonlinear Schrödinger equation
• Solitons in a chain of charge-parity-symmetric dimers
• Asymmetric soliton mobility in competing linear-nonlinear PT-symmetric lattices
• Nonlocal gauge equivalence: Hirota versus extended continuous Heisenberg and Landau-Lifschitz equation
• Excitation Transmission through a non-Hermitian traversable wormhole
• Solitons and nonlinear dynamics in dual-core optical fibers
• Pseudo-conservative dynamics of coupled polariton condensates
• Tunable nonlinear spectra of anti-directional couplers
• Non-Hermiticity in quantum nonlinear optics through symplectic transformations
• Non-Hermitian matter wave mixing in Bose Einstein condensates: dissipation induced amplification
• Two-way enhancement of sensitivity by tailoring higher-order exceptional points
• Nonlinear transition between PT-symmetric and PT-broken modes in coupled fiber lasers
• Nonlinear plasmonic amplification via dissipative soliplasmons
• Effects of correlated noise on the excitation of robust breathers in an ac-driven, lossy sine-Gordon system
• New families of non-parity-time-symmetric complex potentials with all-real spectra
• Parity-Time Symmetry and Exceptional points: A Tutorial
• Integrability and trajectory confinement in $\mathcal{P}\mathcal{T}$-symmetric waveguide arrays
• Symmetry breaking bifurcations and excitations of solitons in linearly coupled NLS equations with PT-symmetric potentials
• A PT-symmetric dual-core system with the sine-Gordon nonlinearity and derivative coupling
• Intensity Correlation Measurement to Simulate Two-body BICs and Probe Nonlinear Discrete Breathers
• Non-reciprocal population dynamics in a quantum trimer
• Optical solitons in periodically managed PT-symmetric media
• Krein signature for instability of $\mathcal{P}\mathcal{T}$-symmetric states
• Hybrid patterns and solitonic frequency combs in non-Hermitian Kerr Cavities
• Robust PT symmetry of two-dimensional fundamental and vortex solitons supported by spatially modulated nonlinearity
• Making the PT symmetry unbreakable
• Nonlinear behaviors of parity-time-symmetric lasers
• Exact States in Waveguides With Periodically Modulated Nonlinearity
• PT-symmetric and antisymmetric nonlinear states in a split potential box
• Non-adiabatic transitions in parabolic and super-parabolic $\mathcal{P}\mathcal{T}$-symmetric non-Hermitian systems
• Stability restoration by asymmetric nonlinear states in non-Hermitian double-well potentials
• Dual opposing quadrature-PT symmetry
• Degenerate soliton solutions and their dynamics in the nonlocal Manakov system: I Symmetry preserving and symmetry breaking solutions
• Extraction of power transmission parameters from PT-symmetric waveguides
• Electrically Pumped Single Transverse-Mode Coupled Waveguide Lasers by Parity-time (PT) Symmetry
• Spontaneous symmetry emergence in a Hermitian system of coupled oscillators without symmetry
• Higher-dimensional soliton generation, stability and excitations of the PT-symmetric nonlinear Schrödinger equations
• Existence and stability of PT-symmetric vortices in nonlinear two-dimensional square lattices
• Pursuing complex optical energy through Exceptional Points of Degeneracy (EPDs)
• State Diagram of the Non-Reciprocal Cahn-Hilliard Model and the Effects of Symmetry
• Analytical construction of soliton families in one- and two-dimensional nonlinear Schrödinger equations with non-parity-time-symmetric complex potentials
• On non-existence of continuous families of stationary nonlinear modes for a class of complex potentials
• Superexponential amplification, power blowup, and solitons sustained by non-Hermitian gauge potentials
• Kinks scattering in deformed ${\phi }^6$ model
• Construction of non-PT-symmetric complex potentials with all-real spectra
• Stability band structure for periodic states in periodic potentials