Effective medium theory for two-dimensional non-magnetic metamaterial lattices up to quadrupole expansions
Effective medium theory for two-dimensional non-magnetic metamaterial lattices up to quadrupole expansions
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DOI：
10.1088/2040-8978/17/7/075102
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发表时间：
2015-07-01
影响因子：
2.1
通讯作者：
Paspalakis, Emmanuel
中科院分区：
文献类型：
--
作者：
Chremmos, Ioannis;Kallos, Efthymios;Paspalakis, Emmanuel
我们提出了一种公式，用于推导超出传统静态和准静态限制的无限周期二维超材料晶格结构的有效介质属性。我们利用多极展开式，其中与所支持的布洛赫模式相关的极化电流通过每单位长度的电偶极子、磁偶极子和电四极矩来表示。然后，我们提出了一种基于晶格几何和单个单元单元结构计算布洛赫模式的方法。结果恢复到传统准静态极限下的众所周知的公式，并且对于光学应用中经常使用的纳米棒型超材料的均匀化很有用。
We present a formulation for deriving effective medium properties of infinitely periodic two-dimensional metamaterial lattice structures beyond the conventional static and quasi-static limits. We utilize the multipole expansions, where the polarization currents associated with the supported Bloch modes are expressed via the electric dipole, magnetic dipole, and electric quadrupole moments per unit length. We then propose a method to calculate the Bloch modes based on the lattice geometry and individual unit element structure. The results revert to well-known formulas in the traditional quasistatic limit and are useful for the homogenization of nanorod-type metamaterials which are frequently used in optical applications.