Rigorous Retrievals of Complex Permittivity and Permeability by Using Partially Filled Waveguide

Determination of the permittivity and permeability for penetrable materials is very important in many applications. The partially filled waveguide (PFW) method enjoys the feature of reduced fabrication precision requirement for the material under test (MUT). In order to retrieve both permittivity and permeability, rigorous multimodal analysis of PFW is required to derive the formulas for the S-parameters. In the original paper proposing the PFW method, a small-edge-partially-filled waveguide (PFW-s) was analyzed by considering only the longitudinal section magnetic modes, which is obviously wrong. To amend it, the S-parameters of the MUT are rigorously computed in this article by including both longitudinal section electric modes and longitudinal section magnetic modes. The propagation constant of each PFW mode is determined by solving a 1-D finite element eigenvalue problem, avoiding the difficulty of initial guess selection for solving the transcendental dispersive equation with the Newton-Raphson method. By matching the computed S-parameters with the measured ones, nonlinear equations about the unknown permittivity and permeability are established, which are then solved by the Newton-Raphson method. The derived formulations for the PFW-s configuration are then extended straightforwardly to the asymmetric big-edge-partially-filled waveguide (PFW-b) configuration, which enjoys the feature of easy positioning of the material sample compared with the common center-loaded PFW-b configuration. Numerical tests and experiments show that the derived formulas can successfully retrieve simultaneously both permittivity and permeability distributed on the full complex plane.