A.Yu. Vetluzhsky, T.D. Shirapova

Important and urgent problem in the theory of wave propagation in random discrete media is to consider the interference of multiply scattered fields. During her rise to the concept of studying the localization of electromagnetic waves, which reflects the most general properties of disordered systems and is a consequence of how the wave nature of the scattered fields and the random nature of scattering media. Initially, the concept of this effect was proposed by Anderson in the middle of last century with regard to the description of the diffusion of electrons in the crystal lattice in a random potential. Beginning in the 1980s, the concept of "localization" first used to describe the effects accompanying the propagation of electromagnetic waves in random discrete media. There are two levels of localization. This is - weak localization or backscattering enhancement associated with the mutual coherence of waves multiply scattered in the same particles propagating in opposite directions, and the strong localization (hereinafter referred to simply localization), which resulted in complete inhibition occurs in the wave propagation a random environment. To date, there are two main criteria the onset of localization of electromagnetic waves: 1. The coefficient of wave propagation through an absorbing structure becomes not exponentially decreasing character, described by T ≈ exp (-L / lloc), where L - the linear extent of the medium, lloc - localization length, which is a parameter determining the degree of localization of the radiation. 2. Criterion Ioffe - Regel: k - l ≤ 1, where k - wave number, l - mean free path of an electromagnetic wave. Theoretical studies of the localization of waves in various media are carried out either on the basis of rigorous numerical methods or approximate, based on effective medium theory. In the latter case it becomes possible to describe the basic localization parameters of relatively simple analytical expressions. To identify the localization of states in the numerical simulation of the propagation lloc must be less than the linear dimensions of the random structure. Thus for small values is convenient to consider localization effects in strongly scattering media. This is possible when considering the resonant cases, for example, due to Mie resonance for the particles forming a discrete structure. An alternative is the analysis of systems in which the lenses have a much larger refractive index than the surrounding homogeneous medium filling. The purpose of this paper is a comparative analysis of two methods for determining the parameters of the localization of waves propagating in a strongly scattering medium: on the basis of a rigorous numerical method and analytical approach. It is shown that the determination of the localization of the radiation parameters of a discrete random medium consisting of strongly scattering elements, it is advisable to carry out on the basis of rigorous numerical methods for calculating the interaction of electromagnetic waves in such media. Approximate methods based on effective medium theory, in this case can only be used as a very rough indicator of localized wave states. Note also that in this paper we consider the excitation of the elements of microwave radiation. Despite this, results and conclusions can be used in the analysis of processes of interaction of radiation with digital media up to terahertz frequencies.