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Periodic Structures: Mode-Matching Approach and Applications in Electromagnetic Engineering by Ruey-Bing Hwang

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Chapter 7

Exotic Dielectrics Made of Periodic Structures

Investigation on the electromagnetic properties for artificial dielectrics is absolutely not a new topic. To mention a few, metallic rods or strips immersed in a host dielectric medium to mimic a natural dielectric material were implemented by Kock (1948), Cohn (1949), and Morita and Cohn (1949); the static approach, such as conformal mapping, had been developed to evaluate the effective dielectric constant of 2D periodic structures consisting of conducting-strip with negligible thickness (Collin, 1991). In this chapter we will focus our attention on an artificial dielectric exhibiting a periodic nature; the theoretical framework developed in the previous chapters will be employed. Additionally, the macroscopic viewpoint of an effective medium in connection with the eigenwave properties in a periodic medium will be elucidated. Finally, the effective refraction index of the eigenwave in an exotic1 dielectric made of a periodic structure will be demonstrated.

7.1 Synthetic Dielectrics Using a 2D Dielectric Columns Array

Figure 7.1 presents a synthetic dielectric composed of a 2D dielectric columns array immersed in a uniform dielectric medium. Here, we assume that the length of each dielectric rod is infinite in extent; the propagation constant along that direction, say the z-axis, is not zero, however. From the theoretical background illustrated in the previous chapters, we know that for kz ≠ 0 the 3D boundary-value problem ...

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