  We predict a new branch of surface Josephson plasma waves (SJPWs) in layered
superconductors for frequencies higher than the Josephson plasma frequency. In
this frequency range, the permittivity tensor components along and transverse
to the layers have different signs, which is usually associated with negative
refraction. However, for these frequencies, the bulk Josephson plasma waves
cannot be matched with the incident and reflected waves in the vacuum, and,
instead of the negative-refractive properties, abnormal surface modes appear
within the frequency band expected for bulk modes. We also discuss the
excitation of high-frequency SJPWs by means of the attenuated-total-reflection
method.
