Sakli et al. previously studied the propagation characteristics of wave modes in a metallic circular waveguide filled with anisotropic metamaterial [Int. J. Microw. Wirel. Technol. 9, 805–813 (2017)]. They derived and analyzed the wave equation and dispersion relations for TEz and TMz modes (i.e., TE and TM waves related to the z-axis) within the waveguide. However, they did not verify whether the system actually supports these TEz and TMz waves. This work aims to investigate that issue. Our findings indicate that, in general, a metallic circular waveguide filled with anisotropic metamaterial cannot support the propagation of TEz and TMz waves. Consequently, the results presented by Sakli et al. are incorrect.
