Unidirectional Invisibility and Nonreciprocal Transmission in Two and Three Dimensions

TL;DR

This paper investigates unidirectional invisibility and nonreciprocal transmission in two and three-dimensional optical systems, presenting new classes of potentials and a reciprocity theorem to explain these phenomena.

Contribution

It constructs an infinite class of unidirectionally invisible optical potentials and proves a general reciprocity theorem for quantum scattering in multiple dimensions.

Findings

Demonstration of unidirectional invisibility in 2D optical potentials

Observation of nonreciprocal transmission in two dimensions

Establishment of a reciprocity theorem for complex potentials

Abstract

We explore the phenomenon of unidirectional invisibility in two dimensions, examine its optical realizations, and discuss its three-dimensional generalization. In particular we construct an infinite class of unidirectionally invisible optical potentials that describe the scattering of normally incident transverse electric waves by an infinite planar slab with refractive-index modulations along both the normal directions to the electric field. A by-product of this investigation is a demonstration of nonreciprocal transmission in two dimensions. To elucidate this phenomenon we state and prove a general reciprocity theorem that applies to quantum scattering theory of real and complex potentials in two and three dimensions.