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V.V. Maksimenko
Karpov Institute of Physical Chemistry, 10, ul.Vorontsovo Pole, 103064, Moscow K-64, Russia
Fractal clusters and complex fractal surfaces separating phases and components of many physical-chemical and biological systems are the brightest examples of fractals in Nature. In this message, we consider their interaction with an external electromagnetic fields.
A fractal cluster (FC) is defined as an agglomerate consisting of nanometric solid particles holding together by the Van der Waals forces. The main feature of FC defining its physical and chemical properties is so called scale invariance. Any small fragment of FC reproduces the structure of the whole cluster under the scale increasing. The first consequence of this invariance are the long distance correlations in arrangement of particles belonging to FC. Due to these correlations, FC possesses by the unique optical and electrodynamic properties.
We consider some features of light interaction with FC. The cluster consists of nonabsorbing particles. Nevertheless this object capable effectively to catch the external electromagnetic radiation. The mechanism of this catching is connected with the light localization inside the cluster. The phenomenon of classical waves localization inside heterogeneously media is known since 1985 year [1]. Now it is the most quickly developing field of physics [2].
The reason for the localization is a specific peculiarity of photon trajectory inside the fractal system of scatterers. Due to the multiple rescattering, this trajectory acquires the features of Antoine's set having zero topological dimension [3]. Respectively, the photon trajectory acquires a «mechanical rigidity» due to a singularity of energy density on it. The interlaced sections (due to the multiple scattering) of the photon trajectory is the reason for the self detention of photon inside FC. This is the reason for the localization. The interlacing of Antoine's trajectories of localized and incident photons leads to the formation of bound state of this pair. As a result, the catching of incident photon by FC becomes possible. The localization cross section is a critical function of the fractal dimension and possesses by the specific frequency dependence. Among other peculiarities are the induced irradiation of photons localized inside cluster and also a possibility of free photon transmission through the fractal system.
Moreover we have considered the light localization in complex heterogeneous systems, for example, in multicomponent solutions in conditions of gel formation , in liquid media near the crystallization threshold etc. Here the localization occures in folds of fractal surface separating phase or components. This surface can be developed as much as it possible. Moreover it can possesses by a finite volume. Such construction are well-known in topology. The most famous two-dimension examples are Peano's curve and Koch's curves having a finite area [4]. There are also exist even more exotic surfaces separating three and a greater number of phases in each its point (the famous Vada's line separating three different «countries» in each point is belong to two-dimension analogues of these surfaces [3]). The interfaces separating of components of some solutions near the gel formation threshold or polymer solutions near the polymerization threshold are organized similarly. The swelling of system under gel formation is a direct consequence of volume finitness of such «crumpled» surfaces.
The localization of light in such systems is the most interesting. Perhaps nowhere it does displayed so brightly and dynamically as here. Moreover just the localization is the physical reason for formation of so complex surfaces. Due to the high concentration, the electromagnetic field localized in primary folds of the surfaces causes a further corrugation of the surface separating the components. Then, new photons localize in these new folds etc.
A similar «folded» system are widely spreaded in biology. The folds of DNA molecule, the cell boundaries, the smallest network of capillaries are among them. The understanding of biochemical processes in living substance is impossible without accounting of the localization. Moreover, just the localization forming these structures in a considerable degree.
In this communication the basic parameters describing the localization of an electromagnetic field in multicomponent three-dimensional Vada's system are calculated: the effective dielectric permeability, the localization cross-section, the cross-section of elastic scattering etc. Is shown that the long distance correlations in an arrangement of the folds result to independence of many characteristics of the system from its material. For example, the effective dielectric permeability depend only on the fractal dimension of the system.
The unusual properties of the localized electromagnetic radiation in the considered systems (the catching of radiation without its dissipation, the possibility its coherent ejection, the wide frequency range of localized light etc.) spill additional light on the debatable problems of Gurvitch's radiation and the problem concerning the existence of a wave genetic code of a cells and the possibility its reading .
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