Invisibility andPTsymmetry

2012/06/30 by Ali Mostafazadeh · 10 citations
Mathematics · Physics and Astronomy · #Combinatorics #Computer science #Invariant (physics) #Invisibility #Mathematical physics #Mathematics #Nonlinear Photonic Systems #Optics #Physics #Planar #Quantum Mechanics and Non-Hermitian Physics #Quantum mechanics #Scattering #Topological Materials and Phenomena #math-ph #math.MP #physics.optics #quant-ph

paper · pdf · doi:10.1103/physreva.87.012103

published as Phys. Rev. A 87, 012103 (2013) · 11 pages, 3 figures, revised version, accepted for publication in Phys.Rev. A

arxiv created 2012/12/18 · openalex publication_date 2013/01/03 · arxiv updated 2013/03/12 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

For a general complex scattering potential defined on a real line, we show that the equations governing invisibility of the potential are invariant under the combined action of parity and time-reversal (PT) transformation. We determine the PT-symmetric as well as non-PT-symmetric invisible configurations of an easily realizable exactly solvable model that consists of a two-layer planar slab consisting of optically active material. Our analysis shows that although PT symmetry is neither necessary nor sufficient for the invisibility of a scattering potential, it plays an important role in the characterization of the invisible configurations. A byproduct of our investigation is the discovery of certain configurations of our model that are effectively reflectionless in a spectral range as wide as several hundred nanometers.

Citations

• Reflectionless potentials and symmetry
• Spectral singularities, biorthonormal systems and a two-parameter family of complex point interactions
• Geometric phase for non-Hermitian Hamiltonians and its holonomy interpretation

Cited by

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• Scattering by Finite PeriodicPT-Symmetric Structures
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• Laser-mode bifurcations induced by PT-breaking exceptional points
• Various scattering properties of a new PT-symmetric non-Hermitian potential
• Reciprocal and unidirectional scattering of parity-time symmetric structures
• Unidirectional reflection and invisibility in nonlinear media with an incoherent nonlinearity
• PT-symmetric coherent perfect absorber with graphene
• Regularization of the spectral singularity inPT-symmetric systems by all-order nonlinearities: Nonreciprocity and optical isolation