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The ongoing rapid progress in the synthesis of a variety of different kinds of nanostructures with fascinating physical properties irreducible to properties of bulk media symbolizes a fundamental breakthrough in the physics and chemistry of condensed matter, significantly extending our knowledge of the nature of solids and our capabilities to control their properties. Solid state nanostructures are constitutive and geometric nanononhomogeneities in semiconductor and dielectric mediums. Fullerenes and nanotubes, semiconductor structures with reduced dimensionality—quantum wells, wires and dots, and sculptured thin films can be mentioned as examples. Despite their different physical natures, these objects share the common property of having extremely small dimensions in one or more directions. These dimensions are about one or two orders of magnitude bigger than the characteristic interatomic distance, so that (1) spatial confinement of charge carriers is fully developed, thereby providing a discrete spectrum of energy states in one or several directions. Apart from that, the intrinsic spatial nonhomogeneity of nanostructures dictates (2) nanoscale nonhomogeneity of electromagnetic fields in them. Whereas the first factor lies in the focus of current research activity in nanosciences, the role of the second factor is often underestimated. This chapter stresses complementary characters of these two key factors whose interplay drastically modifies the electronic and optical properties of nanostructures as compared to bulk media. Conventionally, condensed-matter physics is completely associated with homogeneous media, which are characterized by corresponding dispersion equations for coupled states of the electromagnetic field and material particles. The solutions of a dispersion equation describe the eigenwaves of the media—the so-called quasi-particles - €”which differ from usual (free) particles by the complex behavior of their dispersion characteristics (energy versus quasi-momentum). The embedding of nanoscale nonhomogeneities in a homogeneous media creates conditions for diffraction and scattering of quasi-particles and for their mutual transformation, in the same way as in irregular waveguides. An important role is played by the resonant interactions between different modes and the corresponding matching conditions. The first step in the incorporation of resonant interactions of quasi-particles was made in the theory of quantum semiconductor superlattices. Their high-frequency and optical properties turned out to be very unusual: negative differential conductivity, propagation of longitudinal (plasma) waves, and so on. The interaction of different modes in nanostructures appears to be even more complex due to the greater variety in interacting modes and the complex 3D geometry of the nonhomogeneities. It is no wonder that the electronic and electromagnetic properties of nanomaterials appear to be richer and more diverse.
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