非圆形多层结构中的精确高阶GPT消隐
Exact high-order GPT cancellation in noncircular multilayers
- Central South University（中南大学）
- City University of Hong Kong（香港城市大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文证明非圆形循环对称多层结构存在唯一或局部唯一的涂层电导率，实现精确高阶GPT消隐，并构造无对称性的精确族，实现增强近隐身，数值验证理论。
AI中文摘要：
本文研究二维非圆形多层结构中，在有限正各向同性涂层电导率下，精确高阶广义极化张量（GPT）消隐问题。首先证明，对于每个允许的循环对称核-壳几何结构，存在唯一的正涂层电导率，使得该结构对每个均匀入射场呈弱中性。对于更高阶，我们在具有循环对称性的广泛固定非圆形多层结构类别上，建立了局部唯一的涂层电导率，以消隐完整的K-收缩GPT（K-CGPT）块。这包括由严格星形对称域生成的位似多层结构，且不假设几何形状接近同心圆。我们还将近背景条件替换为小核条件，该条件涵盖有限、绝缘和完美导电核。通过改变选定的界面模式以及径向GPT消隐结构附近的涂层电导率，我们进一步构造了既无旋转对称性也无反射对称性的精确族。对于三个涂层，相关非退化条件和显式手性示例得到严格验证。最后，我们证明所得消隐对每个整个调和入射场产生增强的近隐身效果。一组经过验证的数值示例完全证实了本工作中建立的理论预测。
英文摘要：
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.
