New transform techniques applied to anomolous absorption in the dense chain of metal cylinders

The quasi-static absorption response, at optical and infrared frequencies, of an infinite chain of circular metal cylinders has been modelled in a new way for arbitrarily small separations between the particles. A number of novel features are predicted. The starting point is a solution of the Laplace equation in a conformal frame with correct chain symmetry, not a solution for an isolated cylinder, as is usual. Boundary equations based on Fourier analysis lead to a matrix equation for polarization Convergence as a function of matrix dimensions is rapid, even at almost touching separations. The absorption modal characteristics of a chain emerge naturally in this model. For the same small separations, these characteristics are very different for the pair and extremely different for the single cylinder. In the chain, most of the spectral weight is in the fundamental mode which is strongly red shifted arid intense. In contrast, weak higher-order modes combine to dominate (at shorter wavelengths) in the component pair by itself. Long-range effects are thus very important. This fundamental mode in a dense chain appears to be responsible for the well-known infrared anomaly experimentally observed in collections of fine metal particles.