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.

This paper presents an extension of the formulation of wave propagation in transverse electric (TE) and transverse magnetic (TM) modes in the case of metallic circular waveguides filled with anisotropic metamaterials. The determined higher-order modes have been analyzed and exploited to the design of filters. Among the particularities of anisotropic material, the backward waves can propagate below the cut-off frequency. The numerical results for TE and TM modes have been compared with theoretical predictions. Good agreements were obtained. We analyzed a periodic structure containing waveguides filled with anisotropic metamaterial using the mode-matching technique. By using modal analysis, our approach reduced considerably the computation time compared to HFSS.