1：Experimental Design and Method Selection:

The methodology involves deriving the wave equation from Maxwell's Equations for bi-anisotropic waveguides, applying the weighted residuals method (Galerkin method) to obtain integral equations, and using a Finite Element Method (FEM) with mixed interpolating functions (edge elements for transverse components and Lagrange elements for axial components) to discretize the equations into a quadratic eigensystem, which is then transformed into a generalised sparse eigensystem for solution.

2：Sample Selection and Data Sources:

The analysis is applied to various waveguide geometries, including circular, rectangular, and trapezoidal cross-sections, filled with different bi-anisotropic materials (e.g., chiral, gyrotropic chirowaveguides), with parameters specified based on previous studies or defined for reference.

3：List of Experimental Equipment and Materials:

No specific experimental equipment or materials are mentioned; the work is computational, focusing on numerical analysis using FEM.

4：Experimental Procedures and Operational Workflow:

The procedure includes defining the waveguide geometry and material properties, meshing the cross-section with a 3-simplex mesh, interpolating fields using Whitney forms, discretizing the integral equations, solving the resulting eigensystem using software (SLEPc), and applying boundary conditions for perfect electric or magnetic conductors.

5：Data Analysis Methods:

The eigensystem is solved to find propagation constants (phase and attenuation constants) for waveguide modes, with results compared to previously published data or presented as new references.