Broadband directional invisibility

TL;DR

This paper characterizes conditions for broadband directional invisibility in higher-dimensional scalar and electromagnetic wave scattering, enabling the design of media with perfect invisibility over finite frequency ranges.

Contribution

It provides explicit conditions for achieving perfect directional invisibility in 2D and 3D scalar and electromagnetic scattering media, extending the concept to higher dimensions and finite frequency domains.

Findings

Conditions for perfect invisibility in 2D and 3D scattering

Construction of media with finite-frequency broadband invisibility

Explicit criteria based on interaction potentials and material tensors

Abstract

The discovery of unidirectional invisibility and its broadband realization in optical media satisfying spatial Kramers-Kronig relations are important landmarks of non-Hermitian photonics. We offer a precise characterization of a higher-dimensional generalization of this effect and find sufficient conditions for its realization in the scattering of scalar waves in two and three dimensions and electromagnetic waves in three dimensions. More specifically, given a positive real number $\alpha$ and a continuum of unit vectors $\Omega$, we provide explicit conditions on the interaction potential (or the permittivity and permeability tensors of the scattering medium in the case of electromagnetic scattering) under which it displays perfect (non-approximate) invisibility whenever the incident wavenumber $k$ does not exceed $\alpha$ (i.e., $k\in(0,\alpha]$) and the direction of the incident wave vector ranges over $\Omega$. A distinctive feature of our approach is that it allows for the construction of potentials and linear dielectric media that display perfect directional invisibility in a finite frequency domain.