A Sufficient Condition of Having Independent TE and TM Modes in a   Waveguide Filled with Homogenous Anisotropic Lossless Medium
  Based on the idea of the Abelian group theory in mathematics,this paper finds a sufficient condition of having independent TE and TM modes in a waveguide filled with homogenous anisotropic lossless medium. For independent TE modes, we prove the nonzero cut-off wavenumbers obtained from longitudinal scalar magnetic field stimulation and transverse vector electric field stimulation are same in theory. For independent TM modes, we also prove the nonzero cut-off wavenumbers obtained from longitudinal scalar electric field stimulation and transverse vector magnetic field stimulation are same in theory. Finally we carry out several numerical experiments to verify the correctness of the condition given by us.We hope that this condition is useful for the designs of waveguide with homogenous anisotropic lossless medium in microwave engineering community. 
Wei Jiang, Jie Liu, Qing Huo Liu
math.NA