介电复合材料均匀化的Bergman-Milton边界
On the Bergman-Milton bounds for the homogenization of dielectric composite materials
摘要：
Bergman-Milton边界提供了对包括两种各向同性介电材料的复合材料的有效介电常数的限制。这些为由许多常规材料产生的复合材料提供了严格的界限。我们重新考虑伯格曼-米尔顿边界的光最近出现的超材料，在非常规的参数范围内遇到的相对折射率。具体地说，它表明：（a）对于非耗散材料的边界可能是无限的，如果组成材料具有相反的符号的相对电阻率;（b）弱耗散材料的特征在于相对电阻率与相反的符号的实部，边界可能是非常大的。
英文摘要：
The Bergman-Milton bounds provide limits on the effective permittivity of a composite material comprising two isotropic dielectric materials. These provide tight bounds for composites arising from many conventional materials. We reconsider the Bergman-Milton bounds in light of the recent emergence of metamaterials, in which unconventional parameter ranges for relative permittivities are encountered. Specifically, it is demonstrated that: (a) for nondissipative materials the bounds may be unlimited if the constituent materials have relative permittivities of opposite signs; (b) for weakly dissipative materials characterized by relative permittivities with real parts of opposite signs, the bounds may be exceedingly large.
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