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The motivation of this research stems from the need to detect and identify small particles deposited on a plane surface that is assumed to be otherwise clean. Such detection and identification is, in fact, relevant to all researches in which the cleaness of the surfaces is a fundamental prerequisite and to all the applications whose purpose is the deposition on a surface of particles of a given kind. In the preceding years we addressed our research toward the study of the resonances from particles on account that the resonance spectra are widely known to give useful information both for free particles and for particles on a surface. Nevertheless, our methods were restricted to the case of metallic surfaces because the latter are a good approximation to perfectly reflecting surfaces. In this case, in fact, the image method proved to be very efficient to yield useful information both on the presence and of the shape of the particles of interest. In the last year our interest has been directed toward the properties of particles deposited on non-perfectly reflecting surfaces, i.e. on surfaces that separate two different dielectric media. Of course this new purpose of our research did not stop our study of the shape resonances from particles on metallic surfaces, but our main aim has been toward the formulation of a theory applicable to particles on a surface of general dielectric properties.
