We report on the formation of plasmonic bandgaps in two-dimensional periodic arrangements of gold patches. Orthogonal arrays of subwavelength slits with different periodicities have been studied by means of a three-dimensional finite-difference time-domain (FDTD) code, changing incident polarization and geometrical parameters. Spectral response of gold patches having different a form factor and surrounded by different media have been also investigated and compared in order to give a full description of bandgap shifts paving the way for the design of polarization-sensitive devices.