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The present work reports a general method for the calculation of t hepolarizability of a truncated sphere on a substrate. A multipole ex pansion isused, where the multipoles are not necessarily localized in the center of thesphere but can freely move on the revolution axis. From the weak formulation ofthe boundary conditions, an infinite set of linear equations for the multipolecoefficients is derived. To obta in this set, the interaction between theisland and the substrate is t aken into account by the technique of imagemultipoles. For numerical implementation, this set is truncated at an arbitrarymu ltipole order. The accuracy of the method is jugded through the stabil ityof the truncated sphere polarizability and the the fulfilment of t he boundaryconditions which are demonstrated to be satisfied in large regions of theparameter space. This method brings an improvement wit h respect to theBedeaux's case \cite{Wind87a,Wind87b} where the multi poles are located in thecenter of the sphere.Comment: Revtex, 24 pages including 11 figures. Submitted to Phys. Rev.

Numerical modeling of the optical response of supported metallic particles