Active Invisibility Cloaks in One Dimension

TL;DR

This paper presents a general method for constructing finite-range cloaking potentials that can make a given potential unidirectionally reflectionless or invisible at a chosen wavenumber, with explicit formulas and practical examples.

Contribution

It introduces a novel, explicit analytic approach to design cloaking potentials that preserve scattering properties and can achieve bidirectional invisibility, applicable to various optical structures.

Findings

Explicit formulas for three classes of cloaking potentials

Construction of cloaks that preserve scattering properties

Application to anti-reflection and invisibility cloaks for Bragg reflectors

Abstract

We outline a general method of constructing finite-range cloaking potentials which render a given finite-range real or complex potential $v(x)$ unidirectionally reflectionless or invisible at a wavenumber $k_0$ of our choice. We give explicit analytic expressions for three classes of cloaking potentials which achieve this goal while preserving some or all of the other scattering properties of $v(x)$. The cloaking potentials we construct are the sum of up to three constituent unidirectionally invisible potentials. We also discuss their application in making $v(x)$ bidirectionally invisible at $k_0$, and demonstrate the application of our method to obtain anti-reflection and invisibility cloaks for a Bragg reflector.