On Hybrid Approach in Microwave Scattering Theory for Wire-filled Composites

Abstract

A hybrid approach to the scattering theory in composite materials with conductive wire inclusions has been discussed that allows considering their material properties such as conductivity and magnetic domain structure. The wire geometry of the inclusions makes it possible to determine a unique parameter – the surface impedance, which can be accurately measured over a wide frequency range, from kilohertz to tens of gigahertz. The surface impedance includes both conductive and magnetic properties of wires that determine their microwave scattering properties. The scattered EM field from a single wire can then be rigorously calculated by solving the integro-differential antenna equation for the linear current density with the impedance boundary condition. The field within the skin-layer in conductive ferromagnetic wires is strongly affected by external stimuli, such as DC magnetic field, tensile stress, and temperature, which open up additional channels to tune the scattered microwave radiation. Within the framework of the proposed hybrid approach, combining metrological measurements of individual properties of wires and accurate solution of an external electrodynamic problem, there is no need to consider the most complex internal problem. The developed approach has been used to calculate the dipole moment induced by an external wave in a short ferromagnetic wire. The surface impedance of the wire in the presence of a longitudinal DC magnetic field and tensile stress was measured in a specially designed PCB cell. The numerical algorithm for solving the antenna equation with the impedance boundary condition was implemented in PyCharm IDE. The single-particle scattering problem is the key stage to constructing a general theory that considers the collective response of many particles, as well as their EM coupling.