Pure TE and TM modes in the metallic waveguide filled homogeneously with fully anisotropic and lossless medium

This letter gives a sufficient condition for the existence of the pure transverse electric (TE) and transverse magnetic (TM) modes in the metallic waveguide filled with a homogeneous, fully anisotropic and lossless medium. The condition is a relation between the permittivity and permeability tensors of the fully anisotropic medium. The theory given in the letter is an extension of the classic electromagnetic waveguide theory. Furthermore, a mixed spectral element method is applied to simulate this type of anisotropic waveguide problem. At last, a numerical experiment shows that the sufficient condition supported in the letter does confirm the existence of the pure TE and TM modes in the anisotropic waveguide.