We present a thorough theoretical study of the optical properties of periodic structures built of silver and silica
nanodisks in a sandwich-like configuration, by means of full electrodynamic calculations using the extended
layer-multiple-scattering method. The strong coupling of the metallic nanoparticles and the resulting plasmon
hybridization lead to collective electric and magnetic resonant modes, which can be tuned by changing the
structural parameters, such as nanoparticle size and lattice constant. We analyze the response of single- and
multi-layer architectures of ordered arrays of such nanosandwiches on a dielectric substrate to externally incident
light and evaluate the corresponding effective permittivity and permeability functions. Our results reveal the
existence of optical magnetism, with a strong negative effective permeability over a tunable spectral range at
near-infrared and visible frequencies. We introduce the complex photonic band structure as a tool in the study
of three-dimensional metamaterials and establish additional criteria for the validity of their effective-medium
description. Our work demonstrates the efficiency of the recently developed extended layer-multiple-scattering
method in the study of metamaterials of composite metal-dielectric particles of arbitrary shape.
Periodic nanostructures for plasmonic engineering, comprising one or two types of silica core - metallic shell spherical particles, are studied by means of full electrodynamic calculations using the layer-multiple-scattering method. The complex photonic band structure of such three-dimensional crystals is analyzed in conjunction with relevant transmission spectra of corresponding finite slabs and the physical origin of the different optical modes is elucidated, providing a consistent interpretation of the underlying physics. In the case of binary structures, collective plasmonic modes originating from the two building components coexist, leading to broadband absorption and a rich structure of resonances and hybridization gaps over an extended frequency range.