A theory of electromagnetic (EM) wave scattering by many small particles of an arbitrary shape is developed. The particles are perfectly conducting or impedance. For a small impedance particle of an arbitrary shape, an explicit analytical formula is derived for the scattering amplitude. The formula holds as a → 0, where a is a characteristic size of the small particle and the wavelength is arbitrary but fixed. The scattering amplitude for a small impedance particle is shown to be proportional to a2−κ, where κ ∈ [0,1) is a parameter which can be chosen by an experimenteras he/she wants. The boundary impedance of a small particle is assumed to be of the form ζ = ha−κ, where h = const, Reh ≥ 0. The scattering amplitude for a small perfectly conducting particle is proportional to a3, and it is much smaller than that for the small impedance particle. The many-body scattering problem is solved under the physical assumptions a ≪ d ≪ λ, where d is the minimal distance between neighboring particles and λ is the wavelength. The distribution law for the smallimpedance particles is N(∆) ∼ 1/a2−κ∆ N(x)dx as a → 0. Here, N(x) ≥ 0 is anarbitrary continuous function that can be chosen by the experimenter and N(∆)is the number of particles in an arbitrary sub-domain ∆. It is proved that the EM field in the medium where many small particles, impedance or perfectly conducting, are distributed, has a limit, as a → 0 and a differential equation is derived for the limiting field. On this basis, a recipe is given for creating materials with a desired refraction coefficient by embedding many small impedance particles into a given material. C 2015 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4929965]
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机译:建立了由任意形状的许多小颗粒散射电磁波的理论。粒子具有完美的导电性或阻抗性。对于任意形状的小阻抗颗粒,导出了散射幅度的明确解析公式。该公式为a→0,其中a是小颗粒的特征尺寸,波长是任意的,但是固定的。小阻抗粒子的散射幅度与a2-κ成正比,其中κ∈[0,1)是可以由他/她想要的实验者选择的参数。假定一个小颗粒的边界阻抗为ζ=ha-κ形式,其中h = const,Reh≥0。一个完美导电的小颗粒的散射幅度与a3成正比,比它小得多。对于小阻抗粒子。多体散射问题是在物理假设a d dλ下解决的,其中d是相邻粒子之间的最小距离,而λ是波长。小阻抗粒子的分布定律是N(Δ)〜1 /a2-κΔN(x)dx为a→0。在这里,N(x)≥0是实验者可以选择的任意连续函数,并且N(∆)是任意子域∆中的粒子数。事实证明,分布有许多小颗粒(阻抗或完全导电)的介质中的EM场有一个极限,即a→0,并为该极限场导出了一个微分方程。在此基础上,给出了通过将许多小阻抗颗粒嵌入到给定材料中来创建具有所需折射率的材料的方法。 C 2015 AIP Publishing LLC。 [http://dx.doi.org/10.1063/1.4929965]
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