A diameter--bandwidth product limitation of isolated-object cloaking

TL;DR

This paper establishes a fundamental limit on cloaking large isolated objects, showing that as object size increases, the cloaking bandwidth must decrease inversely, due to causality constraints, even with perfect materials.

Contribution

It generalizes previous causality-based limitations on cloaking, deriving a diameter-bandwidth product constraint applicable to all cloaking scenarios using complex analysis.

Findings

Cloaking bandwidth decreases inversely with object diameter.

Causality constraints impose fundamental limits on cloaking performance.

Broader scaling limitations are derived for bandwidth-averaged cloaking cross-sections.

Abstract

We show that cloaking of isolated objects is subject to a diameter-bandwidth product limitation: as the size of the object increases, the bandwidth of good (small cross-section) cloaking decreases inversely with the diameter, as a consequence of causality constraints even for perfect fabrication and materials with negligible absorption. This generalizes a previous result that perfect cloaking of isolated objects over a nonzero bandwidth violates causality. Furthermore, we demonstrate broader causality-based scaling limitations on any bandwidth-averaged cloaking cross-section, using complex analysis and the optical theorem to transform the frequency-averaged problem into a single scattering problem with transformed materials.