Coupling or Transition between the Zenneck, Sommerfeld, Goubau, and K-Waves

The K-wave is a naturai wave associated with a bare wire with finite conductivity or dielectric coated conducting wire above a ground and can be a quasi-TEM, hybrid (EH-type) or TM wave, depending on the frequency and medium parameters of the ground (conducting, semiconducting, or dielectric). Mutual relations between the Zenneck, Sommerfeld, Goubau, and K-waves are investigated on the basis of their propagation characteristics in frequency. The Z-wave couples to neither the S-nor G-wave, since the former is a fast wave, while the latter, S or G, is a slow wave. However, the Z-wave couples weakly to the K-wave for a bare conducting wire at a certain frequency where attenuation characteristics both waves cross each other and where the phase velocity of the K-wave tends to a fast wave from a slow wave at lower frequencies, approaching but never reaching the phase velocity of the faster Z-wave. For a dielectric coated conducting wire, however, there is no coupling between the Z- and K-waves unless its dielectric layer is extremely thin. The K-wave can be both a slow and a fast wave for a bare conducting wire; a fast wave in the so-called 'transition region’ and a slow wave in the rest range of frequencies, and transfers smoothly to a ΤΈΜ-type of the Carson-Pollaczek wave with decreasing frequency and to the S- or G-wave in a TM-type of surface wave with increasing frequency. All the above statements are confirmed theoretically, providing some numerical examples and experimental evidence.