An approach to permittivity determination at microwave frequencies throughthe eigenvalue problem

A simple method of solving the inverse medium problem in order to determine the complex dielectric constant of a lossy dielectric material at microwav e frequencies is presented. The arbitrarily shaped dielectric sample placed in a rectangular waveguide is considered. Electromagnetic fields in the wa veguide are expanded in series of harmonic functions. A set of linear equat ions is obtained using the finite-difference technique. An additional empir ical condition, which is related to the measured reflection and/or transmis sion coefficients and results in an overdetermined system, is added and the n the system is defined by the addition of a trivial extra parameter. The s ample's dielectric properties are obtained by solving the resulting eigenva lue problem. An algorithm to extract proper results from the set of eigenva lues is defined by considering the properties of numerical solution. The sy stem is tested by using an alternative method.