Reconstruction of complex permittivity of a longitudinally inhomogeneous material loaded in a rectangular waveguide

In this study, an integral equation technique is presented in order to reconstruct the complex permittivity variation of a material loaded in a rectangular cross section waveguide. The problem is first reduced to the solution of a two-coupled integral equations in terms of S-parameters of the system, which contains the Green's function of the empty waveguide. The resulting inverse scattering problem for the unknown complex permittivity of the loading is solved by Contrast Source Inversion (CSI) technique. The validity and reliability of the proposed method has been demonstrated with numerical applications.