Spectral efficiency of engineered thermal cloaks in the frequency regime

TL;DR

This paper evaluates the spectral efficiency of various engineered thermal cloaks across frequencies, revealing that multiple layers improve cloaking performance regardless of singular conductivity issues.

Contribution

It provides a quantitative analysis of thermal cloaks' spectral efficiency and highlights the importance of multilayer homogenization for effective cloaking.

Findings

All cloaks have similar efficiency regardless of singular conductivity.

Multi-layered cloaks require at least fifty layers for significant improvement.

Homogenization algorithms critically affect approximate cloaking performance.

Abstract

We analyse basic thermal cloaks designed via different geometric transforms applied to thermal cloaking. We evaluate quantitatively the efficiency of these heterogeneous anisotropic thermal cloaks through the calculation of the standard deviation of the isotherms. The study addresses the frequency regime and we point out the cloak's spectral efficiencies. We find that all these cloaks have comparable efficiency irrespective of whether or not they have singular conductivity at their inner boundary. However, approximate cloaking with multi-layered cloak critically depends upon the homogenization algorithm and a large number of thin layers (at least fifty) is required to reduce substantially the standard deviation of the isotherms.