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Chapter 14:
Homogenization of Linear and Nonlinear Complex Composite Materials
A composite medium may be characterized as an effectively homogeneous medium, provided electromagnetic wavelengths are sufficiently long as compared with length scales of the component phase inhomogeneities. The estimation of the constitutive parameters of homogenized composite mediums is a matter of considerable scientific and technological significance. A survey of recent developments in the homogenization of complex composite mediums is presented. Specifically, the implementations of the Maxwell Garnett formalism and the Bruggeman formalism—both well established for simple composites—are presented for bianisotropic composite mediums. Recent incremental and differential refinements to the Maxwell Garnett formalism are discussed. The strong-property-fluctuation theory (SPFT) provides an approach to homogenization that—in contrast to the conventional approaches of Maxwell Garnett and Bruggeman—takes more detailed account of the distributional statistics of the component phases. The SPFT for linear bianisotropic mediums and weakly nonlinear isotropic chiral mediums is presented. The issues of SPFT convergence and nonlinearity enhancement are discussed.
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