  In this presentation, we analytically derive the dispersion equation for
surface waves traveling along reactive boundaries which are periodically
modulated in time. In addition, we show numerical results for the dispersion
curves and importantly uncover that time-varying boundaries generate band gaps
that can be controlled by engineering the modulation spectrum. Furthermore, we
also point out an interesting effect of field amplification related to the
existence of such band gaps for surface waves. The effect of amplification does
not require the synchronization of signal and pumping waves. This unique
property is very promising to be applied in surface-wave communications from
microwave to optical frequencies.
