We investigate the transmission properties of arrays of three-dimensional (3-D) gold patches having one- and two-dimensional (1- and 2-D) periodicities, and describe the interaction of cavity and surface plasmon modes. We vary the main geometrical parameters to assess similarities and emphasize differences between 1-D and 2-D periodic patterns. We analyze the spectral response as a function of incident angle and polarization to corroborate our findings. We will also consider form and air filling factors of the grating to assess our ability to control the transmission spectrum. In particular, we observe strong inhibition of the transmission when the impinging wave-vector parallel to the surface of the metal matches the surface plasmon wave-vector of the unperturbed air-gold interface when added to the grating lattice wave-vector. This phenomenon favors the opening of a plasmonic band gap, featuring the suppression of transmission and simultaneous coupling to back-radiation (reflections) of the unperturbed surface plasmon. High-Q, resonating modes occur at the edges of the forbidden band, boosting the energy transfer across the grating thus providing enhanced transmission and broadside directivity at the exit side of the grating.