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Analytical hybrid-mode dispersion relations of a lossy coaxial waveguide were rigorously analyzed using a mode-matching technique. In order to model a practical coaxial line with inevitable losses, we adopted an all-dielectric coaxial waveguide surrounded by the perfect electric conductor (PEC) boundary. The rigorous dispersion characteristics of the TM 01 , TE 01 , and EH 11  modes were investigated for lossy coaxial waveguides filled with different electrical conductivities. Based on the exact solutions, approximate but accurate dispersion equations were proposed for the TM 0 p  , TE 0 p   , EH  mp  , and HE  mp   modes in order to estimate and compare the behaviors of complex propagation constants in the microwave and visible spectra.

Analytical Dispersion Equations of a Lossy Coaxial Waveguide in the Microwave and Visible Spectra