A 3-dB gain and input impedance bandwidth enhancement technique for THz periodically corrugated metallic antennas, also known as Bull's Eye antennas, is presented. A novel design that exploits the depth qualities of the corrugations is introduced, by employing two different depth values for two sets of indented rings. While the gain bandwidth of most single-depth planar corrugated antennas is limited, the 3-dB gain bandwidth of the proposed dual-depth design is expanded along with a high maximum gain. The simulated optimum model of 10 rings at around 300 GHz exhibits a 3-dB gain bandwidth of 8.85% with a maximum gain at broadside of 21.3 dBi. A leaky-wave analysis has been performed via a simple transcendental equation at the level of the gap openings in order to explain the antenna principle of operation. A prototype of the optimum antenna design has been fabricated and measured. The typical subwavelength slot feeding of Bull's eye corrugated antennas is substituted with an easy-to-fabricate open waveguide aperture, yielding a broadband matching performance. Measured results demonstrate a good agreement with simulations and validate the proposed antenna design.