Virtual reshaping and invisibility in obstacle scattering

TL;DR

This paper explores how transformation optics can virtually reshape obstacles in acoustic and electromagnetic scattering, achieving effects like cloaking and invisibility through minification and magnification, with stability estimates supporting these phenomena.

Contribution

It introduces a mathematical framework for virtual obstacle reshaping using transformation optics, including stability estimates and conditions for perfect cloaking.

Findings

Virtual minification leads to near-invisibility of obstacles.

Stability estimates relate scattering amplitude to obstacle size.

Perfect cloaking is theoretically achievable in the limiting case.

Abstract

We consider reshaping a scattering obstacle virtually by using transformation optics in acoustic and electromagnetic scattering. Among the general virtual reshaping results, the virtual minification and virtual magnification are particularly studied. Stability estimates are derived for scattering amplitude in terms of the diameter of a small obstacle, which implies that the limiting case for minification corresponds to a perfect cloaking, i.e., the obstacle is invisible to detection.