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This paper presents a novel numerical scheme for the extraction of dielectric material parameters using the transmission line method. This method is performed by formulating the discretized Maxwell equations as an eigenpermittivity, permeability or an eigenconductivity problem of the considered sample within an arbitrary and generally inhomogeneous filled waveguide cross section. This allows the direct calculation of the desired material parameter by performing only one full wave simulation. Hence, it is very useful if simplified analytical approaches do not provide the aimed accuracy or even fail completely. This procedure will be demonstrated by applying a modified 2D Finite Differences Frequency Domain scheme to the complex permittivity simulation of arbitrary shaped and placed samples within a waveguide cross section.