Optical absorption for parallel cylinder arrays

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We study the long wavelength electromagnetic resonances of interacting cylinder arrays. By using a normal modes expansion where the effects of geometry and material are separated, it is shown that two parallel cylinders with different radii have electromagnetic modes distributed symmetrically about depolarization factor 1/2. Both sets couple to longitudinal and transverse components of the external field, but amplitudes of symmetric depolarization factors become exchanged when considering longitudinal or transverse polarization. We also find that amplitudes satisfy sum rules that depend on the ratio of the cylinders radii.