We present an extension of the layer-multiple-scattering method to photonic crystals of nonspherical particles in a homogeneous host medium. The efficiency of the method is demonstrated on a specific example of a crystal of metallic spheroids. We report a thorough analysis of the optical properties of this crystal and discuss aspects of the underlying physics that relate to the nonspherical shape of the particles.

Guided and quasiguided elastic waves in a glass plate coated on one side with a periodic monolayer of polymer spheres, immersed in water, are studied by means of accurate numerical calculations using the on-shell layer-multiple-scattering method. This system supports, in addition to the modes of the bare plate, almost dispersionless, slow modes which originate from the array of spheres. We calculate and analyze in detail the dispersion diagrams of the interacting modes of the composite slab, and provide a consistent interpretation of the underlying physics.

The propagation of elastic waves in macroscopically periodic composites consisting of core-shell spherical scatterers in a homogeneous host medium is studied by means of numerical calculations using the layer-multiple-scattering method. By an appropriate choice of the constituent materials, these crystals exhibit wide absolute frequency gaps, over which no elastic wave can propagate in the composite medium, whatever the direction of its propagation. We analyze the detailed structure of transmission spectra of finite slabs of such crystals in conjunction with the corresponding complex-band-structure and density-of-states diagrams, and emphasize aspects of the underlying physics which have not been discussed previously.

We propose a different type of plasmonic waveguide which consists of identical dielectric nanocavities, periodically arranged along a line, in a metallic material. The dispersion relations for the different guiding modes are obtained by means of exact mutliple scattering calculations and also by a simple tight-binding model which allows a straightforward analysis of the underlying physics. This type of waveguide combines strong lateral localization and no radiative losses with efficient transmission of light through sharp bends. We show how one can overcome absorptive losses by introducing optical gain media into the cavities and, also, how one can design such waveguides for single-mode operation over a given frequency range by using nonspherical cavities.

Composite materials with periodic variations of density and/or sound velocities, so-called phononic crystals, can exhibit bandgaps where propagation of acoustic waves is forbidden. Phononic crystals are the elastic analogue of the well-established photonic crystals and show potential for manipulating the flow of elastic energy. So far, the experimental realization of phononic crystals has been restricted to macroscopic systems with sonic or ultrasonic bandgaps in the sub-MHz frequency range. In this work, using high-resolution Brillouin spectroscopy we report the first observation of a hypersonic bandgap in face-centred-cubic colloidal crystals formed by self-assembly of polystyrene nanoparticles with subsequent fluid infiltration. Depending on the particle size and the sound velocity in the infiltrated fluid, the frequency and the width of the gap can be tuned. Promising technological applications of hypersonic crystals, ranging from tunable filters and heat management to acousto-optical devices, are anticipated.

We discuss acoustic waveguiding through weakly coupled defects along a line in a three-dimensional phononic crystal which possesses an absolute frequency gap. A chain of appropriately chosen defect cells induces modes of the elastic field over a narrow band of frequencies within the gap. We introduce a model of this band in the manner of a tight-binding description of defect bands in semiconductors and demonstrate the applicability of this model through a specific example of phononic crystal: a bubbly liquid. This allows an exact, practically analytic solution and a deeper physical insight into the processes involved.