Abstract
The solutions of the electrostatic potential problem for the square and hexagonal arrays of circular cylinders with zero applied field (homogeneous or resonant solutions) are studied. We show that for non-touching cylinders, the set of resonances is discrete except in the neighbourhood of one point, at which the dielectric constant of the array has an essential singularity. For arrays of touching cylinders, the set is well represented by a continuous distribution. This representation enables the derivation of the asymptotic form of the expansion for the dielectric constant of the array when the dielectric constant of the cylinders is large. The known value of the first term in the expansion enables us to derive the second term. The physical characteristics of the resonant solutions are studied. Metals achieve values of dielectric constant which are close to the resonant values (real and negative) for certain wavelengths. Curves are given which enable the prediction of those wavelengths at which the optical resonances of both arrays occur, for any area fraction and composition of a columnar cerment film.
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