In this work, we first derive the nonradiating anapole condition with a straightforward theoretical demonstration exploiting one of the Devaney-Wolf theorems for nonradiating currents. Based on the equivalent volumetric and surface electromagnetic sources, it is possible to establish a unique compact conditions directly from Maxwell’s Equations in order to ensure nonradiating anapole state. In addition, we support our theoretical findings with a numerical investigation on a broken-symmetry dielectric particle, building block of a metamaterial structure, demonstrating through a detailed multiple expansion the nonradiating anapole condition behind these peculiar destructive interactions.

中文翻译：

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由Devaney-Wolf定理导出并在对称对称介电粒子中激发的非辐射偶极子条件

在这项工作中，我们首先通过简单的理论论证得出非辐射的偶极子条件，该论证利用了Devaney-Wolf定理之一来计算非辐射电流。基于等效的体积和表面电磁源，可以直接根据麦克斯韦方程建立唯一的紧致条件，以确保无辐射的偶极状态。此外，我们还通过对破碎对称介电粒子的数值研究（一种超材料结构的基本组成部分）进行了数值研究来支持我们的理论发现，并通过详细的多次扩展论证了这些独特的破坏性相互作用背后的非辐射偶极子条件。