Breaking of PT-symmetry in bounded and unbounded scattering systems

Abstract

PT-symmetric scattering systems with balanced gain and loss can undergo a symmetry-breaking transition in which the eigenvalues of the non-unitary scattering matrix change their phase shifts from real to complex values. We relate the PT-symmetry breaking points of such an unbounded scattering system to those of underlying bounded systems. In particular, we show how the PT-thresholds in the scattering matrix of the unbounded system translate into analogous transitions in the Robin boundary conditions of the corresponding bounded systems. Based on this relation, we argue and then confirm that the PT-transitions in the scattering matrix are, under very general conditions, entirely insensitive to a variable coupling strength between the bounded region and the unbounded asymptotic region, a result that can be tested experimentally and visualized using the concept of Smith charts.

9 pages, 6 figures (final version, including newly added connection to the concept of "Smith charts")

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• The physics of exceptional points
• PT-symmetry breaking and laser-absorber modes in optical scattering systems
• Visualization of Branch Points in PT-Symmetric Waveguides
• Faster than Hermitian Quantum Mechanics
• Gain-Driven Discrete Breathers in PT-Symmetric Nonlinear Metamaterials
• PT-Symmetric Talbot Effects
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• Stationary states of a PT-symmetric two-mode Bose-Einstein condensate
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• Coalescence of spectral singularities and phase diagrams for one-dimensional PT symmetric photonic crystals
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• Experimental demonstration of an anisotropic exceptional point
• Defect states emerging from a non-Hermitian flat band of photonic zero modes
• Virtual Parity-Time Symmetry
• Theory of reflectionless scattering modes
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• Symmetry-protected zero-mode laser with a tunable spatial profile
• Wave propagation through disordered media without backscattering and intensity variations
• Topological Wave-Guiding Near an Exceptional Point: Defect-Immune, Slow-Light, Loss-Immune Propagation
• Parity-time symmetry in a flat band system
• Parity-time symmetry in optical microcavity systems
• 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
• Parity-time symmetry from stacking purely dielectric and magnetic slabs
• Anisotropic exceptional points of arbitrary order
• Symmetry-Protected Scattering in Non-Hermitian Linear Systems
• Scattering in $\mathcal{P}\mathcal{T}$ and $\mathcal{R}\mathcal{T}$ Symmetric Multimode Waveguides: Generalized Conservation Laws and Spontaneous Symmetry Breaking beyond One Dimension
• Bulk and edge-state arcs in non-hermitian coupled-resonator arrays
• Contrasting Spectral Signatures and Sensitivities of CPA-Lasing in a $\mathcal{P}\mathcal{T}$-Symmetric Periodic Structure
• Gain/loss induced localization in one-dimensional PT-symmetric tight-binding models
• Unified theory of resonances and bound states in the continuum in Hermitian tight-binding models
• Scattering Experiments with Microwave Billiards at an Exceptional Point under Broken Time Reversal Invariance
• Optical Reciprocity Induced Symmetry of the Scattering Eigenstates in Non-$\mathcal{P}\mathcal{T}$-Symmetric Heterostructures
• Nonreciprocal transmission of electromagnetic waves with nonlinear active plasmonic metasurfaces
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• Unidirectional zero reflection as gauged parity-time symmetry
• Emitter and absorber assembly for multiple self-dual operation and directional transparency
• Systematic pathway to $\mathcal{P}\mathcal{T}$ symmetry breaking in scattering systems
• $\mathcal{P}\mathcal{T}$ symmetry breaking for the scattering problem in a one-dimensional non-Hermitian lattice model
• $\mathcal{P}\mathcal{T}$ symmetry of the Su-Schrieffer-Heeger model with imaginary boundary potentials and next-nearest-neighboring coupling
• Quasinormal mode analysis of chiral power flow from linearly polarized dipole emitters coupled to index-modulated microring resonators close to an exceptional point
• Unitary Scattering Protected by Pseudo-Hermiticity
• Confluences of exceptional points and a systematic classification of quantum catastrophes
• Optical fluxes in coupled $\mathcal{P}\mathcal{T}$-symmetric photonic structures
• Bound states emerging from below the continuum in a solvable PT-symmetric discrete Schroedinger equation
• Born-Padé approach to electromagnetic scattering in complex one-dimensional inhomogeneous slabs
• An Algebraic PT-Symmetric Quantum Theory with a Maximal Mass
• Non-hermitian time evolution: from static to parametric instability
• Oblique scattering from non-Hermitian optical waveguides
• Duality of bounded and scattering wave systems with local symmetries