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The Polarizability of Chains of Touching Cylinder Pairs
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By solving the Laplace equation in an appropriate coordinate frame, simple expressions have been derived for the polarizability per unit area of infinitely long chains of touching pairs of cylinders. The method used presupposes no restrictions on the value of the dielectric constant of the cylindrical particles and yields an exact analytic solution incorporating all multipoles. The results offer an insight into the effect of long range interactions between particle pairs. Moreover the technique can be extended to the study of arrays generally. Comparisons are made between the induced dipole moment on pairs within a chain and the moment on an isolated touching pair in the case of aluminum columns in air. A quasistatic assumption is used at optical frequencies. It is found that while the general behaviours for the wavelength-dependent polarizability is the same in both models, there are significant differences in the average degree of absorption and polarization.
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