介电三聚体六角阵列中的Toro序和AntiToro序：磁群方法
Toroidic and antitoroidic orders in hexagonal arrays of dielectric trimers: magnetic group approach
摘要：
本文研究了一种新型电磁超材料中的环形偶极共振及其激发条件。这些超材料是布置在电介质基板上的电介质盘的全电介质平面周期性阵列。该阵列的基本构建块是分布在六边形单位超晶胞中的三聚体。超晶胞的最高几何对称性是C6v。利用群的表示论和磁群论的应用，对这类问题进行了分析，为解决这类问题提供了一种新的途径。我们已经表明，为了获得阵列的环形超模，单位超晶胞对称性必须被破坏两次：首先，三聚体的C3v对称性，其次，单位超晶胞的C6v对称性需要被降低。定义了阵列中环形偶极矩的对称阶数和反对称阶数的选择规则。特别是，我们已经表明，与减少的单位超晶胞对称性的C2v组，阵列表现出的环形偶极共振与antitoroorbital秩序。具有较低Cs对称性的阵列可以提供具有反环面和环面两种量级的共振。它也表明，这些阵列总是偏振敏感。全波模拟和实验证实了理论预测。由于在具有非常高的品质因数的谐振系统中空间和时间受限的光，所建议的超材料可以提供增强的光-物质相互作用。
英文摘要：
Herein, we investigate the symmetry-protected toroidal dipole resonances and conditions of their excitation in a new type of electromagnetic metamaterials. These metamaterials are all-dielectric planar periodic arrays of dielectric disks disposed on a dielectric substrate. The elementary building blocks of the array are trimers which are distributed in hexagonal unit supercells. The highest geometrical symmetry of the unit supercell is C6v. The analysis is fulfilled by using the representation theory of groups with the application of the magnetic group theory, which is a new approach in solving such problems. We have shown that to get access to the toroidal supermodes of the array, the unit supercell symmetry must be broken twice: firstly, the C3v symmetry of the trimer, and secondly, the C6v symmetry of the unit supercell needs to be reduced. Selection rules for the symmetric and antisymmetric orders of the toroidal dipole moments in the arrays are defined. In particular, we have shown that with the reduction of the unit supercell symmetry to the C2v group, the array exhibits the toroidal dipole resonance with an antitoroidic order. The arrays with the lower Cs symmetry can provide the resonances with both toroidic and antitoroidic orders. It is also shown that these arrays are always polarization sensitive. Full-wave simulations and experiments confirm the theoretical predictions. The suggested metamaterials can provide an enhanced light-matter interaction due to the spatially and temporally confined light in resonant systems with very high quality factors.
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