In this paper, electromagnetic emission at the plasma frequency produced by a short laser pulse in a finite-size plasma layer with a longitudinal density modulation is studied using both analytical theory and particle-in-cell simulations. The radiation mechanism suggests that a laser pulse excites a long-lived plasma wake which, in the presence of ion density modulation with the appropriate period, generates a superluminal satellite capable of matching in phase with vacuum electromagnetic waves. It is found that such a mechanism can be used for generating tunable narrow-band (5%) multi-mJ terahertz pulses with high efficiency (>0.3%) due to ability of superluminal plasma oscillations at the cut-off frequency to diffuse through a plasma that is several times wider than the radiation wavelength.