Absorption spectrum of clusters of spheres from the general solution of Maxwell's equations. III. Heterogeneous spheres

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Abstract
We present the solution of Maxwell's equations for an arbitrary distribution of heterogeneous spheres taking into account cluster geometry, retardation effects, all multipolar (electric and magnetic) order interactions, and any arbitrary light incidence. The fields are expanded in terms of the usual spherical wave-vector functions. Usual boundary conditions are applied at each interface. The problem consists in obtaining the appropriate microscopic effective susceptibility for the heterogeneous spheres, and the appropriate rewriting of the interaction and field terms. In so doing the solution of the problem is similar to that for homogeneous spheres [Phys. Rev. B 25, 4204 (1982)]. We specialize the boundary-condition problem to the case of a metallic nucleus containing plasmons and of a dielectric shell. Simpler cases are also examined: the plasmonless limit, the single sphere, the hollow sphere, and the long-wavelength limit. Numerical results are presented to show various parameter effects; the field expansions are limited to, but inlcude, the octupolar terms.