We present a computer program to calculate the frequency band structure of an infinite phononic crystal, and the transmission, reflection and absorption of elastic waves by a slab of this crystal. The crystal consists of a stack of identical slices parallel to a given surface; the slice may consist of multilayers of non-overlapping spheres of given periodicity parallel to the surface and homogeneous plates. The elastic coefficients of the various components of the crystal may be complex functions of the frequency.

The optical properties of a dielectric waveguide coated on one side with a periodic monolayer of metallic nanospheres are studied by means of transmission and density-of-states calculations using the on-shell layer-multiple-scattering method. In particular, the strong coupling mechanism between the waveguide and collective particle–plasmon modes is analysed and its influence on the optical response of the system is elucidated.

We demonstrate the existence of strong Anderson localization in certain disordered phononic systems. As a result, the transmission coefficient of elastic waves through a slab of the material practically vanishes, whatever the angle of incidence, over a region of frequency much wider than the absolute frequency gap of the corresponding ordered system. The phenomenon can be of use in the design of phononic systems with very wide absolute transmission gaps.

The optical properties of three-dimensional photonic crystals consisting of polaritonic spheres in a dielectric host medium are studied by means of accurate numerical calculations using the on-shell layer-multiple-scattering method. The transmission characteristics of finite slabs of these materials are related to the complex band structure of the corresponding infinite crystals and the effect of dissipative losses is examined.

The optical response of a two-dimensional periodic array of metallic nanoparticles on a dielectric waveguide is investigated by means of numerical calculations using the on-shell layer-multiple-scattering method. We find that the strong interaction between particle-plasmon and waveguide modes influences drastically the extinction spectrum of the system. Our results explain successfully available experimental data and provide a transparent physical picture of the underlying processes.

Photonic crystals are inhomogeneous materials whose dielectric properties vary periodically in space on a macroscopic scale. These materials have novel and interesting properties concerning both basic physics and technological applications. After a brief description of the main properties of photonic crystals, we present some specific applications related to wave guiding and Anderson localization of light due to stacking faults in these crystals.

After a brief description of the layer multiple scattering method as applied to phononic crystals, we present some results obtained by this method, relating to: crystals of polystyrene spheres in water; crystals of silica spheres in air; and crystals of steel spheres in polyester. We relate the transmission characteristics of slabs of these ma terials to the complex band structure of the corresponding infinite crystals. We emphasize aspects of the underlying physics which have not been discussed previously.