Inhomogeneous Dielectric Media: Wave Propagation and Dielectric Permittivity Reconstruction in the Case of a Rectangular Waveguide

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In this paper we study the theoretical part of a novel non-destructive testing method for the reconstruction of the dielectric profile of an inhomogeneous dielectric material. We consider the inhomogeneity to be described by a polynomial of third order, i.e., εr(z)= ε0 + ε1z2 + ε3z3 and we utilize a system of three rectangular waveguides to solve the direct and the inverse problem. We apply Frobenius method to solve the underlying differential equations. We give special attention to the first cut-off frequency on the main mode TE10 and we propose a good estimation of it by using the mean value of the dielectric profile.