The phenomenological theories of Maxwell-Garnett and Bruggeman taking into account the effects of nonsphericity, as well as the differential Bruggeman theory of the effective medium in the case of arbitrary dimension are generalized. Within the framework of the generalized Maxwell-Garnett theory, it has been shown how weak nonsphericity affects the effective cubic nonlinear susceptibility of a heterosystem. In addition, some practical applications of phenomenological theories for indirect determination of the effective permittivity and effective polarizability using the results of experimental measurements are considered.
The symmetric Bruggeman equation, generalized by the introduction of shape-distributed conditional scatterers, is analyzed, that forms the basis of a new conceptual approach within the effective medium theory. The effect of the shape distribution function on the effective permittivity is studied.
The relationship between the percolation theory and effective medium theory is considered. This relationship is demonstrated by the examples of semi-continuous metal films deposited on a dielectric substrate and Bruggeman composites, taking into account the effects of shape. It is shown how the distribution of conditional scatterers in shape can affect the percolation threshold in Bruggeman composites. In addition, it is shown how the Casimir force acting between two composite plates behaves in the vicinity of the percolation threshold.
The development of the homogenization theory using the Bergman-Milton analytical representation is demonstrated. In particular, the spectral density function for the Lichtenecker equation and in the form of a beta distribution is considered. The Bergman-Milton representation is generalized to the case of three-phase heterosystems containing "core-shell" inclusions, and specific examples show how this generalization can be applied to the study of biological cells.
The concept of designing metamaterials with an extended bandwidth, within which the desired dielectric or optical properties are achieved (extraordinary low or high permittivity, strongly absorbing metamaterials and bandpass filters) is proposed. For this purpose, one-dimensional, quasi-one-dimensional metamaterials, as well as nanocomposites based on nanospheres, nanospheroids and shelled spheres are considered.
The semianalytic technique of homogenization of periodic heterosystems in terms of the reciprocal space representation of a mesoscopic permittivity tensor is analyzed. The advantages, disadvantages, as well as limits of applicability of the technique are considered.
Taking into account the effects of nonlocality, one-dimensional metamaterials (superlattices) are considered under the condition of dielectric loss compensation, which is achieved due to the presence of gain constituents, such as dyes, semiconductor quantum wells or quantum dots, glass doped with rare earth ions. It is shown how both an extraordinary high and extraordinary low refractive index can be achieved. The behavior of the phase and group velocity of light in heterosystems under study is analyzed. An approximate analytical solution to the dispersion equation for the propagation mode, which is superior to existing solutions, has been derived.
The results of this work can be used to correctly interpret experimental data, to retrieve needed information about heterosystem constituents, as well as to design new materials and structures with on-demand physical properties and corresponding devices
