Determination of dielectric permittivity at microwaves using the eigenvalue problem

A simple method for solving the inverse medium problem to determine the complex dielectric permittivity of a dielectric material at microwave frequencies is presented. The arbitrarily shaped dielectric sample is considered to be placed in a rectangular waveguide. The finite-difference technique and harmonic functions are applied to get a system of linear equations with measured reflection and/or transition coefficients added and solved through the eigenvalue problem. An algorithm to distinguish proper results from the system eigenvalues is defined by considering numerical solution properties. The system is tested using another method