Analytical study of spherical cloak/anti-cloak interactions

TL;DR

This paper provides an analytical study of spherical cloak/anti-cloak interactions using a generalized Mie-series approach, extending previous cylindrical analyses to three dimensions, and explores their effects on cloaking and sensing capabilities.

Contribution

It extends the analytical framework of cloak/anti-cloak interactions from 2D cylindrical to 3D spherical geometries using a full-wave solution.

Findings

Demonstrates cloaking and field restoration in spherical configurations

Highlights differences between spherical and cylindrical cases

Provides insights for approximate implementations with positive media

Abstract

The intriguing concept of "anti-cloaking" has been recently introduced within the framework of transformation optics (TO), first as a "countermeasure" to invisibility-cloaking (i.e., to restore the scattering response of a cloaked target), and more recently in connection with "sensor invisibility" (i.e., to strongly reduce the scattering response while maintaining the field-sensing capabilities). In this paper, we extend our previous studies, which were limited to a two-dimensional cylindrical scenario, to the three-dimensional spherical case. More specifically, via a generalized (coordinate-mapped) Mie-series approach, we derive a general analytical full-wave solution pertaining to plane-wave-excited configurations featuring a spherical object surrounded by a TO-based invisibility cloak coupled via a vacuum layer to an anti-cloak, and explore the various interactions of interest. With a number of selected examples, we illustrate the cloaking and field-restoring capabilities of various configurations, highlighting similarities and differences with respect to the cylindrical case, with special emphasis on sensor-cloaking scenarios and ideas for approximate implementations that require the use of double-positive media only.