We developed a Green’s function formalism to investigate the localized and resonant acoustic modes of shear horizontal polarization associated with the surface of a substrate supporting a periodic array of wires. Each material is assumed to be an isotropic elastic medium. The calculation can be applied to an arbitrary choice of the shape and elastic parameters of the wires. The surface modes are obtained as well-defined peaks of the densities of states (DOS). In this paper, we calculate the dispersion curves of the surface modes for wires of parabolic section, and discuss their behaviour as a function of the elastic parameters, the height and the periodicity of the wires.

We investigate both the photonic and electronic band structure of a comb-like waveguide geometry in which dangling side branches are grafted along an infinite one-dimensional waveguide. In a periodic (superlattice like) waveguide, we report the opening-up of stop bands which originate both from the periodicity of the system and the resonant states of the grafted branches (which play the role of resonators). Wide gaps (narrow bands) can be obtained by grafting several dangling side branches at every node. The stop bands still remain even for identical constituent materials. We also propose a tandem structure composed of two or several successive combs which differ by their physical characteristics that allows an ultrawideband filter. This behavior results from the superposition of the bandgaps in the successive structures. The presence of a defect branch in the comb can give rise to localized modes inside gaps. These states appear as very narrow peaks in the transmission spectrum and therefore may have useful applications in the frame of photonic bandgap materials or electronic band engineering of nanostructures.

We present the application of a general Green function formalism to the study of near- and far-field scattering of an incident acoustic plane wave by a perturbation (an inhomogeneity) existing at the planar surface of a substrate. The perturbing element will be a supported wire which, in principle, can have an arbitrary shape and composition. Considering the case of shear horizontal vibrations, we discuss for a wire of parabolic section the behavior of the scattered field as a function of frequencyω, of material parameters, and of incidence angle. At normal incidence, typical behaviors depend on the relative impedance and sound velocity of both materials. For an oblique incidence, there are a large variety of cases depending on ω and on material parameters; one typical behavior will be the predominance of a scattered wave towards the specular reflection direction.

An exact numerical method has been developed to calculate the Green's function and the dynamical properties of a wire of arbitrary shape near a planar surface. In this paper, we present the first applications of this formalism to the scattering of an incident acoustic plane wave by such a surface perturbation, considering the case of shear horizontal vibrations for an adsorbed wire having a parabolic section and being of the same nature as the substrate. The amplitude of the scattered wave shows a series of enhancement and lowering as a function of the frequency of the incident wave. The angular distribution of the scattered wave is dependent upon the frequency and the incident angle. We also present the local densities of states in the vicinity of this defect which contain well-defined resonances.

We present a few recent or new theoretical results about surface acoustic localized and resonant modes associated with planar or deterministic rough surfaces. The following composite systems are considered: one or two adlayers deposited on a semi-infinite substrate and wires or grooves integrated near a planar surface. The surface modes can be obtained as well-defined features of the density of states resulting from a calculation of the Green functions in these heterostructures. In this work, the materials are described in the framework of the elasticity theory.

Raman-scattering spectroscopy has been used to study the folded longitudinal-acoustic (FLA) phonons in three- and four-layer superlattices comprised variously of slabs of GaAs, Ga 1-x Al x As, and AlAs. For each superlattice, the observed FLA peak frequencies recorded with different exciting wavelengths agree very well with the calculated dispersion relation based on an elastic-continuum model. However, apart from some qualitative trends in the three-layer superlattices, the relative intensities of the Raman FLA peaks are not well reproduced by the photoelastic theory of a perfect superlattice. Reasons for this discrepancy are discussed. The three-layer superlattices exhibited a high photoluminescence efficiency, comparable to that of strained Ga 1-x In x As/GaAs single quantum wells

By using a simple model, we show that the density of states of a metallic overlayer deposited on a metallic substrate contains resonances (size quantization peaks) that do not broaden as an effect of the overlayer-substrate coupling, but remain well-defined features for different values of the coupling parameter. Instead, these modes become sharper by increasing the thickness of the overlayer. We also investigate the influence of the work function on the localized and resonant states associated with the overlayer. This effect, which, in general, is not considered in tight-binding models, is most significant for the highest localized or resonant mode, which becomes a surface mode of the overlayer.

N-layer superlattices are formed out of a periodic repetition of a unit cell containing N (N > 2) different slabs. Polytype superlattices made from three constituents (InAs — GaSb — AlSb) were proposed recently.1 We review here the studies of phonons in N-layer superlattices.2–9 A recent Raman determination10 of folded acoustic phonons in a four-layer superlattice is then compared with the theoretical results. We discuss also the existence of surface phonons for three-layer superlattices and the possible extensions of these studies to more complex composite materials.

A theoretical investigation has been made of magnetoplasmons in infinite and semi-infinite semiconductor superlattices subjected to an external magnetic field with use of a Green-function response theory. The applied magnetic field B0 is taken to be parallel to the interfaces and perpendicular to the direction of propagation (Voigt geometry). Thicknesses of the constituent layers are assumed to be sufficiently large so as to ignore the "quantum size effects." The layers are characterized by the frequency- and magnetic-field-dependent dielectric tensors. The magnetoplasma modes are defined by the electric fields that are localized at, and decay exponentially away from, the interfaces. The response theory applied to study the magnetoplasmons in these systems provides the corresponding response functions associated with the electromagnetic fields, which can in turn be used to derive almost all physical properties of the system at hand. In spite of the mathematical complexity, we have successfully reproduced the previously reported (analytical) results obtained within a different theoretical framework.