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The Maxwell-Garnett theory is generally used to describe the optical behavior of aggregated metallic films. This theory is, however, restricted to ultrafine particles whose main dimension can be considered very small compared to that of the wavelength. With particle dimensions in experiments generally larger than 10 nm, this approach is no longer valid for many metals. The purpose of the present work is, therefore, to revise the dipole approximation to include frequency-dependent terms. The theory is also extended to quadrupolar terms, in order to assess the relative importance of these latter when the aggregates are no longer very small compared to the wavelength. Applications to real metals are discussed.

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An approximate treatment, describing the influence of a dielectric substrate on the optical behavior of a granular surface, is reported. It shows that discrepancies between experimental results and predictions mainly based upon the Maxwell Garnett theory [Philos. Trans. R. Soc. London 203, 385 (1904); 205A, 237 (1906)] cannot be interpreted as substrate-related effects. The magnitudes and locations of the multiple images of the unperturbed dipole of a small metallic sphere have been carried out in an approximate, though reliable, way in the presence of polarizing fields both parallel and perpendicular to the substrate. The resulting dipole is introduced in a long-known optical model, describing a granular surface as a planar array of equal dipoles interacting with each other. Graphical results, showing the influence of substrates of various dielectric constants, are presented. A discussion of possible improvements of the available model is also reported.