On the existence conditions for a fast surface wave

Conditions are obtained for the existence of a fast-moving surface electromagnetic wave (with a speed close to the speed of light in the vacuum) on a flat interface between the vacuum and an isotropic dissipative medium with a permittivity $\varepsilon = \varepsilon' + \mathrm i\varepsilon''$. The interfaces considered include vacuum–seawater, vacuum–metal, vacuum–plasma, and vacuum–dielectric. Conditions for the existence of negligibly damped surface waves are considered for extremely high (vacuum–seawater, vacuum–metal) and very low (vacuum–plasma, vacuum–dielectric) $\varepsilon''$ values. It is shown that at least in these two limit cases, the phase wave velocity $V_{\mathrm p}$ and the group wave velocity $V_{\mathrm g}$ pass synchronously through the speed of light $c$ in the vacuum, which can be considered the reason why surface waves exist at the interface between vacuum and a collisionless plasma (with $\varepsilon' <-1$ and $V_{\mathrm {p,g}} < c$) and do not exist at the interface between the vacuum and a weakly absorbing dielectric (with $\varepsilon' >1$ and $V_{\mathrm {p, g}} >c$). In the first limit case, it is shown that both the phase and group velocities pass $c$ at $\varepsilon' =-3/4$, implying that a surface wave exists at the vacuum–metal interface (with $\varepsilon <-3/4$), but that a surface wave (Zenneck's wave) cannot exist at the vacuum–seawater interface (with $\varepsilon' > -3/4$).