Exact high-order GPT cancellation in noncircular multilayers
Abstract
This paper is concerned with exact high-order generalized polarization tensor (GPT) cancellation in two-dimensional noncircular multilayers with finite positive isotropic coating conductivities. We first prove that, for every admissible cyclically symmetric core--shell geometry, there exists a unique positive coating conductivity for which the structure is weakly neutral to every uniform incident field. For higher orders, we establish locally unique coating conductivities that cancel the complete K-contracted GPTs (K-CGPTs) block on a broad class of fixed noncircular multilayers with cyclic symmetry. This includes homothetic multilayers generated by strictly star-shaped symmetric domains, without assuming that the geometry is close to concentric disks. We also replace the near-background condition by a small-core condition covering finite, insulating, and perfectly conducting cores. By varying selected interface modes together with the coating conductivities near a radial GPT-vanishing structure, we further construct exact families with neither rotational nor reflection symmetry. For three coatings, the relevant nondegeneracy conditions and an explicit chiral example are rigorously certified. Finally, we show that the resulting cancellation yields enhanced near-cloaking for every entire harmonic incident field. A set of certified numerical examples fully corroborates the theoretical predictions established in this work.
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BibTeX
@misc{deng2026exact,
title = {{Exact high-order GPT cancellation in noncircular multilayers}},
author = {Youjun Deng and Hongyu Liu and Longyue Tao},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.08924},
eprint = {2609.08924},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08924},
}
RIS
TY - UNPB
TI - Exact high-order GPT cancellation in noncircular multilayers
AU - Youjun Deng
AU - Hongyu Liu
AU - Longyue Tao
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.08924
UR - https://arxiv.org/abs/2609.08924
AB - This paper is concerned with exact high-order generalized polarization tensor (GPT) cancellation in two-dimensional noncircular multilayers with finite positive isotropic coating conductivities. We first prove that, for every admissible cyclically symmetric core--shell geometry, there exists a unique positive coating conductivity for which the structure is weakly neutral to every uniform incident field. For higher orders, we establish locally unique coating conductivities that cancel the complete K-contracted GPTs (K-CGPTs) block on a broad class of fixed noncircular multilayers with cyclic symmetry. This includes homothetic multilayers generated by strictly star-shaped symmetric domains, without assuming that the geometry is close to concentric disks. We also replace the near-background condition by a small-core condition covering finite, insulating, and perfectly conducting cores. By varying selected interface modes together with the coating conductivities near a radial GPT-vanishing structure, we further construct exact families with neither rotational nor reflection symmetry. For three coatings, the relevant nondegeneracy conditions and an explicit chiral example are rigorously certified. Finally, we show that the resulting cancellation yields enhanced near-cloaking for every entire harmonic incident field. A set of certified numerical examples fully corroborates the theoretical predictions established in this work.
ER -