On optimal cloaking-by-mapping transformations
Abstract
A central ingredient of cloaking-by-mapping is the diffeomorphisn which transforms an annulus with a small hole into an annulus with a finite size hole, while being the identity on the outer boundary of the annulus. The resulting meta-material is anisotropic, which makes it difficult to manufacture. The problem of minimizing anisotropy among radial transformations has been studied in [4]. In this work, as in [4], we formulate the problem of minimizing anisotropy as an energy minimization problem. Our main goal is to provide strong evidence for the conjecture that for cloaks with circular boundaries, non-radial transformations do not lead to lower degree of anisotropy. In the final section, we consider cloaks with non-circular boundaries and show that in this case, non-radial cloaks may be advantageous, when it comes to minimizing anisotropy.
Cite
@article{arxiv.2109.02397,
title = {On optimal cloaking-by-mapping transformations},
author = {Yves Capdeboscq and Michael Vogelius},
journal= {arXiv preprint arXiv:2109.02397},
year = {2021}
}