The development of practical terahertz systems requires high-gain, broadband and robust integrated antennas. In recent years, many photonics-inspired all-dielectric components have been demonstrated; however, practical implementation of existing devices usually relies on perforated structures that can be fragile and exhibit cut-offs related to their gratings. In this paper, we present a novel, all-dielectric planar antenna that avoids perforations entirely. The antenna employs a dielectric slab parabolic reflector that collimates incident waves towards radiating rods, producing a fan-shaped beam. A thorough investigation of the optimal guided-wave collimating structure is presented utilizing geometric optics, along with a proof of concept for its use as a beam launcher in integrated terahertz circuits. Thereafter, the device is adapted as an antenna. The novel antenna, 19.83 mm × 20.97 mm in footprint and 200 μm thick, is broadband, low-profile, readily integrable with planar, on-chip components, and exhibits a nearly-flat gain across the 220-330 GHz range, with a maximum value of 21.5 dBi. Input reflection coefficient magnitude is below -20 dB across the entire range, indicating excellent 40% fractional bandwidth, and a sidelobe level reaching as low as -28.4 dB for the E-plane and -39.5 dB for the H-plane.