2015/07/08 by Ali Mostafazadeh
Mathematics · Physics and Astronomy · #Combinatorics #Geometry #Invisibility #Mathematical physics #Mathematics #Nonlinear Photonic Systems #Optics #Physics #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Realization (probability) #Scaling #physics.optics #quant-ph
paper · pdf · doi:10.1103/physreva.92.023831
published as Phys. Rev. A 92, 023831 (2015) · 15 pages, 3 figures
arxiv created 2015/07/08 · openalex publication_date 2015/08/18 · arxiv updated 2016/04/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We outline a general perturbative method of evaluating scattering features of finite-range complex potentials and use it to examine complex perturbations of a rectangular barrier potential. In optics, these correspond to modulated refractive index profiles of the form \mathfrakn(x)=n0+f(x), where n0 is real, f(x) is complex valued, and |f(x)|\ensuremath≪1\ensuremath≤n0. We give a comprehensive description of the phenomenon of unidirectional invisibility for such media, proving five general theorems on its realization in PT-symmetric and non-PT-symmetric material. In particular, we establish the impossibility of unidirectional invisibility for PT-symmetric samples whose refractive index has a constant real part and show how a simple scaling transformation of a unidirectionally invisible PT-symmetric index profile with n0=1 may be used to generate a hierarchy of unidirectionally invisible PT-symmetric index profiles with n0>1. The results pertaining to unidirectional invisibility for n0>1 open the way for the experimental studies of this phenomenon in a variety of active materials. As an application of our general results, we show that a medium with \mathfrakn(x)=n0+\ensuremathζeiKx, \ensuremathζ and K real, and |\ensuremathζ|\ensuremath≪1 can support unidirectional invisibility only for n0=1. We then construct unidirectionally invisible index profiles of the form \mathfrakn(x)=n0+\ensuremath∑_\ensuremathℓ\mathfrakz_\ensuremathℓe^iK_\ensuremathℓx with \mathfrakz_\ensuremathℓ complex, K_\ensuremathℓ real, |\mathfrakz_\ensuremathℓ|\ensuremath≪1, and n0>1.