Meng et al. previously investigated the transmission characteristics of wave modes in a rectangular waveguide filled with a lossless anisotropic metamaterial. They derived and analyzed wave equations and dispersion relations for \(\hbox {TE}_{z}\) and \(\hbox {TM}_{z}\) (i.e., TE and TM waves related to the z-axis) modes under general conditions and then focused on a specific case where the permittivity and permeability tensors were isotropic in the transverse plane (i.e., when \(\varepsilon _{x}=\varepsilon _{y}=\varepsilon _{t}\) and \(\mu _{x}=\mu _{y}=\mu _{t}\) ). In this comment, we highlight a critical issue: under general anisotropic conditions, a rectangular waveguide cannot support independent \(\hbox {TE}_{z}\) and \(\hbox {TM}_{z}\) modes. Instead, hybrid wave propagation is expected. As a result, the dispersion relations presented for the general case in the original study are incorrect. This comment provides a detailed analysis to clarify the conditions under which these modes can propagate accurately in rectangular waveguides filled with anisotropic metamaterials.
