Rigorous Formulation for Retrieving Electromagnetic Parameters of Biaxial Composite Material With Rectangular Waveguide

Fiber-reinforced composites are widely used in the aerospace and automotive industries. Most exhibit biaxial anisotropic properties. Complex anisotropic permittivity and permeability are the most important parameters to investigate. A systematical study of the measurement methods for anisotropic material based on rectangular waveguides is carried out in this article. An efficient forward model for wave propagation in a rectangular waveguide partially filled with anisotropic material is proposed. Mode matching with proper boundary conditions makes this model rigorous and efficient. Three inversion methods based on choosing measurements of S-parameters for two modes, frequencies, or waveguides are developed, based on this forward model, for retrieving the complex permittivity and permeability of biaxial material. Numerical simulations for all methods are carried out for systematically discussing the stability and applicability of all three methods. The reason for the instability of the method based on two frequencies is first revealed in this article via an uncertainty analysis. The inversion methods based on two modes or two waveguides are multivalued problems due to the thickness of the sample. An iterative optimization strategy is first proposed in this work to overcome this problem. The proposed double-waveguide method is both stable and easily applicable in practice. Experimental results are carried out to demonstrate the stability and accuracy of the proposed methods.