Comparison of approximations for effective parameters of artificial dielectrics

Formulas available in the literature for approximating the effective permittivity and permeability of a periodic array of (possibly lossy) dielectric rods of arbitrary cross section are assessed for their accuracy by comparing them with precise numerical values for special forms of the arrays. The literature on effective properties of arrays of dielectric rods is reviewed, covering what is known about general bounds, as well as the numerical results that are available for two specific arrays of square rods. It is found that while no single formula is capable of very high precision in every case, it is possible to construct good approximate formulas in individual cases as a result of this comparison.<
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