Conservation relations and anisotropic transmission resonances in one-dimensional PT-symmetric photonic heterostructures

Abstract

We analyze the optical properties of one-dimensional (1D) PT-symmetric structures of arbitrary complexity. These structures violate normal unitarity (photon flux conservation) but are shown to satisfy generalized unitarity relations, which relate the elements of the scattering matrix and lead to a conservation relation in terms of the transmittance and (left and right) reflectances. One implication of this relation is that there exist anisotropic transmission resonances in PT-symmetric systems, frequencies at which there is unit transmission and zero reflection, but only for waves incident from a single side. The spatial profile of these transmission resonances is symmetric, and they can occur even at PT-symmetry breaking points. The general conservation relations can be utilized as an experimental signature of the presence of PT-symmetry and of PT-symmetry breaking transitions. The uniqueness of PT-symmetry breaking transitions of the scattering matrix is briefly discussed by comparing to the corresponding non-Hermitian Hamiltonians.

10 pages, 10 figures

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• Unidirectional Invisibility induced by PT-Symmetric Periodic Structures
• Coherent Perfect Absorbers: Time-reversed Lasers
• PT-symmetry breaking and laser-absorber modes in optical scattering systems
• Unidirectional Nonlinear PT-symmetric Optical Structures
• Invisibility in PT-symmetric complex crystals
• Quantum noise and mode nonorthogonality in nonhermitian PT-symmetric optical resonators
• Time-reversed optical parametric oscillation

Cited by in corpus (145)

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• Antisymmetric PT-photonic structures with balanced positive and negative index materials
• PT Metamaterials via Complex-Coordinate Transformation Optics
• Perfectly absorbing exceptional points and chiral absorbers
• Synthetic parity-time symmetry breaking in a single microcavity
• Coalescence of spectral singularities and phase diagrams for one-dimensional PT symmetric photonic crystals
• PT-Symmetric Plasmonic Metamaterials
• PT-symmetric scattering in flow duct acoustics
• Experimental observation of the dual behavior of $\mathcal{P}\mathcal{T}$-symmetric scattering
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• Non-Hermitian disorder in two-dimensional optical lattices
• Nonlinear modes in the harmonic PT-symmetric potential
• Defect states emerging from a non-Hermitian flat band of photonic zero modes
• Virtual Parity-Time Symmetry
• Theory of reflectionless scattering modes
• Parametric amplification and bidirectional invisibility in PT-symmetric time-Floquet systems
• Nonlinear modal interactions in parity-time ($\mathcal{P}\mathcal{T}$) symmetric lasers
• Tunneling of Obliquely-Incident Waves through PT-Symmetric Epsilon-Near-Zero Bi-Layers
• Unidirectional zero sonic reflection in passive $\mathcal{P}\mathcal{T}$ symmetric Willis media
• Controlling photonic spin Hall effect via exceptional points
• Symmetry-protected zero-mode laser with a tunable spatial profile
• Breaking of PT-symmetry in bounded and unbounded scattering systems
• $\mathcal{P}\mathcal{T}$-Symmetry-Induced Wave Confinement and Guiding in Epsilon-Near-Zero Metamaterials
• Parity-time symmetry in a flat band system
• Parity-time symmetry in optical microcavity systems
• Unambiguous scattering matrix for non-Hermitian systems
• PT-symmetry breaking in multilayers with resonant loss and gain locks light propagation direction
• Nonlocal homogenization of PT-symmetric multilayered structures
• Quasi-bound states in the continuum induced by $\mathcal{P}\mathcal{T}$-symmetry breaking
• Achieving arbitrary polarization control using complex birefringent meta-materials
• Simultaneous Realization of Coherent Perfect Absorber and Laser by Zero-Index Media with both Gain and Loss
• Transport and spectral features in non-Hermitian open systems
• Bound states, scattering states and resonant states in PT-symmetric open quantum systems
• Non-Hermitian Photonic Lattices: tutorial
• Self-dual Spectral Singularities and Coherent Perfect Absorbing Lasers without PT-symmetry
• Tunable elastic Parity-Time symmetric structure based on the shunted piezoelectric materials
• Non-Hermitian lattices with a flat band and polynomial power increase
• Chiral metamaterials with PT symmetry and beyond
• Transfer matrix study of the Anderson transition in non-Hermitian systems
• Coherent optical control of polarization with a critical metasurface
• Transfer Matrices as Non-Unitary S-Matrices, Multimode Unidirectional Invisibility, and Perturbative Inverse Scattering
• Symmetry-Protected Scattering in Non-Hermitian Linear Systems
• Supersymmetry generated one-way invisible PT-symmetric optical crystals
• Unveiling the Enhancement of Spontaneous Emission at Exceptional Points
• Scattering in $\mathcal{P}\mathcal{T}$ and $\mathcal{R}\mathcal{T}$ Symmetric Multimode Waveguides: Generalized Conservation Laws and Spontaneous Symmetry Breaking beyond One Dimension
• Scattering by finite periodic $\mathcal{P}\mathcal{T}$-symmetric structures
• Contrasting Spectral Signatures and Sensitivities of CPA-Lasing in a $\mathcal{P}\mathcal{T}$-Symmetric Periodic Structure
• From scattering theory to complex wave dynamics in non-hermitian PT-symmetric resonators
• Optical Lattices with Higher-order Exceptional Points by Non-Hermitian Coupling
• Gain/loss induced localization in one-dimensional PT-symmetric tight-binding models
• Invisibility on demand based on a generalized Hilbert transform
• Scattering properties of PT-symmetric layered periodic structures
• Generalized Unitarity and Reciprocity Relations for PT-symmetric Scattering Potentials
• Reflectionless excitation of arbitrary photonic structures: A general theory
• Angular-asymmetric transmitting metasurface and splitter for acoustic wave: a combining of the Coherent Perfect Absorber and Laser
• Exceptional Points in the Flatland: A Non-Hermitian Line-Wave Scenario
• PT-symmetric chiral metamaterials: Asymmetric effects and PT-phase control
• Transmission enhancement in loss-gain multilayers by resonant suppression of reflection
• Unidirectional Reflectionless Transmission for Two-Dimensional $\mathcal{P}\mathcal{T}$-symmetric Periodic Structures
• Optical Reciprocity Induced Symmetry of the Scattering Eigenstates in Non-$\mathcal{P}\mathcal{T}$-Symmetric Heterostructures
• Acoustic Multifunctional Logic Gates and Amplifier based on Passive Parity-Time Symmetry
• Imaginary gauge transformation in momentum space and Dirac exceptional point
• $\mathcal{P}\mathcal{T}$ symmetry breaking in waveguide arrays with competing loss/gain pairs
• Shape-preserving beam transmission through non-Hermitian disordered lattices
• Pseudo-chirality: a manifestation of Noether's theorem in non-Hermitian systems
• Exceptional Cones in 4D Parameter Space
• Localized Single Frequency Lasing States in a Finite Parity-Time Symmetric Resonator Chain
• Pseudo-Hermiticity protects the energy-difference conservation in the scattering
• Magnified imaging based on non-Hermitian nonlocal cylindrical metasurfaces
• Tailoring inhomogeneous $\mathcal{P}\mathcal{T}$-symmetric fiber Bragg grating spectra
• Anomalous Parity-Time Symmetry Transition away from an Exceptional Point
• Nonreciprocal surface magnetoelastic dynamics
• CPA-laser effect and exceptional points in PT-symmetric multilayer structures
• Nonlocal discrete continuity and invariant currents in locally symmetric effective Schrödinger arrays
• Eigenvalue dynamics in the presence of non-uniform gain and loss
• Systematic pathway to $\mathcal{P}\mathcal{T}$ symmetry breaking in scattering systems
• Extension of Noether's theorem in PT-symmetric systems and its experimental demonstration in an optical setup
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• Gain-Loss Coupled Systems
• Floquet control of global $PT$ symmetry in 2D arrays of quadrimer waveguides
• Coherent perfect absorption with and without lasing in complex potentials
• Accessible phases via wave impedance engineering with PT-symmetric metamaterials
• Quasi-Exactly Solvable Scattering Problems, Exactness of the Born Approximation, and Broadband Unidirectional Invisibility in Two Dimensions
• Real-Time Transport in Open Quantum Systems From $\mathcal{P}\mathcal{T}$-Symmetric Quantum Mechanics
• Generalized Parametric Space, Parity Symmetry of Reflection, and Systematic Design Approach for Parity-Time Symmetric Photonic Systems
• Unitary Scattering Protected by Pseudo-Hermiticity
• Amplified and directional spontaneous emission from arbitrary composite bodies: self-consistent treatment of Purcell effect below threshold
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• Anomalous Faraday effect in a $\mathcal{P}\mathcal{T}$-symmetric dielectric slab
• Characterization of Parity-Time Symmetry in Photonic Lattices Using Heesh-Shubnikov Group Theory
• Exceptional points and scattering of discrete mechanical metamaterials
• Parity-Time Symmetry Breaking beyond One Dimension: The Role of Degeneracy
• Theory and Numerical Modelling of Parity-Time Symmetric Structures in Photonics: Introduction and Grating Structures in One Dimension
• Asymmetric light transmission through a photonic crystal with relaxing Kerr nonlinearity
• Constructing the scattering matrix for optical microcavities as a nonlocal boundary value problem
• Tachyonic Dispersion in Coherent Networks
• Optical fluxes in coupled $\mathcal{P}\mathcal{T}$-symmetric photonic structures
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• Comprehensive understanding of parity-time transitions in $\mathcal{P}\mathcal{T}$ symmetric photonic crystals with an antiunitary group theory
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• Scattering of Spin-$\frac{1}{2}$ Particles from a $\mathcal{P}\mathcal{T}$-symmetric Complex Potential
• Double-sided unidirectional reflectivity
• PT-symmetric transport in non-PT-symmetric bi-layer optical arrays
• Chiral-reversing vortex radiation from a single emitter by eigenstates phase locking
• Oblique scattering from non-Hermitian optical waveguides
• Electromagnetic Eigenvalue Problems and Nonhermitian Effects in Linear and Saturable Scattering
• Temporal Parity-Time Symmetry for Extreme Energy Transformations
• Non-Hermitian physics and engineering in silicon photonics
• Apodized photonic crystals: A non-dissipative system hosting multiple exceptional points
• Reciprocity Theorem and Fundamental Transfer Matrix
• In-Plane Linear Stress Waves in Layered Media: I. Non-Hermitian Degeneracies and Modal Chirality
• Single-photon scattering controlled by an imperfect cavity
• Superdirective Leaky Radiation from a PT-Synthetic Metachannel
• Nonreciprocal Scattering by PT-symmetric stack of the layers
• Resonant Combinatorial Frequency Generation Induced by a PT-symmetric Periodic Layered Stack
• Optical symmetric pushing, uni-/bi-directional null, and pulling-pushing flipped forces in one dimensional PT-symmetric photonics
• Characteristic determinant approach to the spectrum of one-dimensional $\mathcal{P}\mathcal{T}$-symmetric systems
• Local perfect chirality at reflection-zeros away from exceptional points in optical whispering gallery microcavity
• Physical relevance of time-independent scattering calculations in non-Hermitian systems: The role of time-growing bound states
• $\mathcal{P}\mathcal{T}$-symmetric tight-binding model with asymmetric couplings
• CPA-lasing associated with the quasibound states in the continuum in asymmetric non-Hermitian structures
• Unidirectional weak visibility in band gap and singular scattering in conduction band of one-dimensional parity-time symmetric photonic crystal