Mathematical model of electromagnetic wave propagation in nanocomposites based on magnetic nanowires

Background. Magnetic nanocomposites possess a big variety of physical properties and considerably differ from properties of a massive material. Physical properties of nanocomposites depend on many factors: chemical composition, methods of synthesis, the size and form of magnetic inclusions, interactions of particles with adjacent particles and a matrix surrounding them. Of considerable interest are magnetic nanowires, received on the basis of the matrix of mesoporous oxide of aluminum. The mesoporous oxide of aluminum, received by anode oxidation of aluminum, is unique by the fact that in the course of its receiving it is possible to supervise the key nanostructural parameters: diameters of cylindrical pores and distance between the centers of adjacent pores. One of methods of receiving magnetic nanocomposites in a matrix of aluminum oxide is electrochemical deposition into the pores of magnetic metals which allows supervising the amount of the deposited metal, varying the length of the received nanowires and their orientation in relation to a substrate. The purpose of the work is to develop a mathematical model of distribution of electromagnetic waves in the nanostructured materials on the basis of magnetic nanowires. Materials and methods. The author developed a decomposition mathematical model of electromagnetic wave propagation in nanostructured composites based on magnetic nanowires and formulated an equation of electrodynamics for the magnetic particles taking into account the field of exchange interaction. The researcher also obtained the linear conductance matrix for the autonomous unit in the form of a rectangular parallelepiped with inclusion of a magnetic nanowire and gave recommendations for the use of the autonomous unit to solve the applied problems of electrodynamics and ultrahigh frequency technology (UHF). Results. The autonomous unit in the form of a rectangular parallelepiped with inclusion of a magnetic nanowire is a universal basic element for the solution of applied problems of electrodynamics and ultrahigh frequency technology. The autonomous unit can be used for definition of constants of distribution of waves in three-dimensional periodic structures from magnetic nanowires. The cell of the periodic structure is modelled by the autonomous unit. By imposing boundary conditions following from the Floquet theorem on the edges of a parallelepiped, the researcher received the characteristic equation concerning constants of distribution of waves. From the solution of the characteristic equation the author defined the main types of waves which can be used for determination of effective values of magnetic and dielectric conductivity of a magnetic nanocomposite. Continuous distributions of waves of the left and right polarization, ordinary and unusual waves in the infinite continuous gyromagnetic environment have to coincide with similar values of constants of distribution of waves in three-dimensional periodic structures of a magnetic nanocomposite. It leads to the system of equations from which it is possible to define the components of an effective tensor of magnetic permeability and a scalar of dielectric permeability. Conclusions. The autonomous unit can be directly used as a basic element in creation of mathematical models of microwave devices with magnetic nanocomposites (circulators, reconstructed filters, etc.). The areas of inserts, substrates of microwave devices from magnetic nanocomposites in addition are to be divided into autonomous units. The mathematical model in this case is a model of high level and allows considering the influence of the field of exchange interaction on the limit characteristics of microwave devices.