A study of the propagation characteristics of electromagnetic waves in a hyperbolic metamaterial-filled circular coaxialwaveguide, with the inner and outer perfect electric conductor (PEC) surfaces, was reported before by Bhardwaj et al. [J. Lightwave Technol. 37, 3064 (2019)]. They showed that the TE z and TM z (i.e., TE and TM waves related to the z -axis) are the eigen modes of the mentioned system, and concluded that radial hyperbolicity ( εr<0 , εz≃εϕ>0 ) is more advantageous than axial hyperbolicity ( εz<0 , εr≃εϕ>0 ) for near-field coupling effects. However, the study by Bhardwaj et al. has a fundamental error, where for the case ( εr<0 , εz≃εϕ>0 ) the proposed system cannot support the propagation of the TE z and TM z waves, and therefore in this case the results derived by Bhardwaj et al. are incorrect.
