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Chapter 4:
Composite Media and Effective Medium Approximations
The interest in manmade or engineered composite electromagnetic media goes back at least to Lord Rayleigh (1892), who determined the dielectric constants of a rectangular array of parallel cylinders. Early expressions for refractive indices based on the fill factor of inclusions date back to Wiener (1912), and a considerable amount of research was carried out after World War II in order to make impedance-matching materials, [e.g., Lewin (1947)]. Effective medium approximations are analytical models that describe the macroscopic properties of a medium based on the properties and the relative fractions of its components. Several models are shown in Fig. 4.1 as a general comparison. Among the numerous effective medium approximations, Bruggeman’s symmetrical theory is one that has been widely accepted. Effective medium approximations (EMAs) have been applied in the theory of inhomogeneous materials and were first proposed by Bruggeman and then, in a different context, by Landauer. Since its inception, EMA has been the basis for studies of macroscopically inhomogeneous media and has been generalized by many authors to treat a wide variety of problems. As more shrinking composite structures are developed, one might expect EMAs to become even more important in predicting the bulk structure’s performance. However, in EMA, composite materials are modeled in terms of their averaged percentage or fill factor of some inclusion or material having properties that differ from those of the host. Underlying these effective medium theories, of which there are many, such as Maxwell–Garnett, Bruggeman, etc., is the expectation that averaging of properties still leads to a reasonably correct description of the propagation of a wave through that medium.
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