Determining distribution of complex dielectric permittivity over cylindrical body of intricate cross section from electromagnetic field measurement

A long cylinder of any given intricate cross section, with a dielectric permittivity and an electrical conductivity independent of the axial coordinate, is placed in the electromagnetic field of a monochromatic wave with the generatrix parallel to the electric field vector. The distribution of dielectric permittivity over cross sections of this cylinder is calculated from readings of the field components at points within a cross section. The first step of the algorithm is calculating the axial component of current density as the sum of density of the conduction current and the axial component of the polarization vector, the latter multiplied by the frequency. The second step of the algorithm is calculating the resultant internal electric field as the sum of the primary electric field and the electric field induced by the cylinder current of already known density. The third and last step of the algorithm is calculating the dielectric permittivity at any given point from the already known current density and the primary electric field.