关于复合薄层有效介电常数和有效磁导率的定义
On the Definition of Effective Permittivity and Permeability For Thin Composite Layers
摘要：
讨论了仅含一、二平行排列复杂形状夹杂物的复合材料层的有效材料参数（介电常数和磁导率）的定义问题。这种结构对于新型超材料的设计非常重要，其中可实现的层通常只有一层或两层粒子穿过样品厚度。引入了描述平均激发极化的有效参数。作为一个明确的例子，我们开发了一个分析模型，适用于计算的有效材料参数$ε_{\rm{eff}}$和$μ_{\rm{eff}}$的双阵列的电小的可极化散射体。电和磁的结构中诱导的偶极矩和相应的反射和透射系数的计算使用本地场法的正常平面波入射，并通过平均场和极化引入有效的参数。在没有损失的情况下，两个材料参数都是纯实的，并且满足Kramers-Kronig关系和热力学第二定律。我们比较分析结果的模拟和实验结果在文献中。详细讨论了引入参数的物理意义。
英文摘要：
The problem of definition of effective material parameters (permittivity and permeability) for composite layers containing only one-two parallel arrays of complex-shaped inclusions is discussed. Such structures are of high importance for the design of novel metamaterials, where the realizable layers quite often have only one or two layers of particles across the sample thickness. Effective parameters which describe the averaged induced polarizations are introduced. As an explicit example, we develop an analytical model suitable for calculation of the effective material parameters $ε_{\rm{eff}}$ and $μ_{\rm{eff}}$ for double arrays of electrically small electrically polarizable scatterers. Electric and magnetic dipole moments induced in the structure and the corresponding reflection and transmission coefficients are calculated using the local field approach for the normal plane-wave incidence, and effective parameters are introduced through the averaged fields and polarizations. In the absence of losses both material parameters are purely real and satisfy the Kramers-Kronig relations and the second law of thermodynamics. We compare the analytical results to the simulated and experimental results available in the literature. The physical meaning of the introduced parameters is discussed in detail.
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