Guided modes and continuous modes in parallel-plate waveguides excited by a line source

We describe a new physical picture inside a parallel-plate waveguide excited by a line current source. Generally, the electromagnetic (EM) fields inside the waveguide are represented in closed forms of Sommerfeld-like integrals. When the waveguide is filled with air or lossless layered media, we show that EM fields are contributed by both continuous spectra and poles, which correspond to 'continuous modes' and guided modes inside the waveguide. Due to the pairing appearance of poles, the guided modes are composed of physical and unphysical components. We have further shown that the continuous modes contain propagating and evanescent waves, where the former eliminates exactly the unphysical guided modes and the later contributes the near-field effect of the source. Hence the existence of continuous modes makes the wave propagation inside the waveguide physical. When the guidance condition is not satisfied, only evanescent waves are included in continuous modes, which represents the storage of energies near the source. Theoretical analysis and numerical results are given to validate our conclusions.