An interaction theory between an arbitrary electromagnetic shaped beam and
assemblies of spheres (and/or aggregates) is presented. This theory is buil
t by the synthesis of two already available theories: (i) the generalized L
orenz-Mie theory (GLMT) for a homogeneous sphere, illuminated by an arbitra
ry shaped beam and (ii) the interaction theory between a plane wave and ass
emblies of spheres (and/or aggregates). An appealing application of this GL
MT concerns the study of chaotic scattering within the framework of a rigor
ous electromagnetic theory.