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This letter gives a condition for the existence of the pure TE and TM modesin the metallic waveguide filled with a homogeneous, fully anisotropic andlossless medium. The condition is a relation between the permittivity andpermeability tensors of the fully anisotropic medium. The theory given in theletter is the extension of the classic electromagnetic waveguide theory. Atlast, we employ the commercial software COMSOL Multiphysics to simulate themetallic waveguide problem filled with a homogeneous, fully anisotropic andlossless medium. Numerical experiment shows that the condition supported in theletter does confirm the existence of the pure TE and TM modes in theanisotropic waveguide.

TE and TM Modes in Metallic Waveguide Filled With a Lossless and Fully Anisotropic Medium