  We predict the existence of surface waves in layered superconductors in the
THz frequency range, below the Josephson plasma frequency $\omega_J$. This wave
propagates along the vacuum-superconductor interface and dampens in both
transverse directions out of the surface (i.e., towards the superconductor and
towards the vacuum). This is the first prediction of propagating surface waves
in any superconductor. These predicted surface Josephson plasma waves are
important for different phenomena, including the complete suppression of the
specular reflection from a sample (Wood's anomalies) and a huge enhancement of
the wave absorption (which can be used as a THz detector).
