Broadband directional invisibility

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 α and a continuum of unit vectors Ω, 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 α (i.e., k∈(0,α]) and the direction of the incident wave vector ranges over Ω. 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.

Can Nth order Born approximation be exact?

“…It is easy to see that the conditions of Theorems 1 and 2 require the corresponding interaction potentials and the permittivity-permeability profiles to be respectively complex-valued and complex matrix-valued functions [16]. This shows that the acoustic and optical realizations of these systems must involve carefully engineered regions of gain and loss.…”

“…Notice that sums of the potentials of the form (21) with different choices for a, ℓ y , and ℓ z also satisfy the hypothesis of Theorem 1. These potentials may, in principle, be realized in terms of a carefully engineered permittivity profile with a rectangular cross section and regions of gain and loss as discussed in [15,16].…”

“…In [15] we generalize this result to the scattering of electromagnetic (EM) waves by a general stationary linear medium. This allows for identifying optical media displaying broadband directional invisibility [16].…”