Terahertz antennas have garnered significant attention, particularly in the fields of photonics and wireless communication. Graphene, renowned for its exceptional strength and thinness, exhibits remarkable properties when employed as an antenna element for radiation. Its conductivity varies with thickness and can be controlled through biasing voltage. To mitigate surface wave effects, photonic band gap crystals serve as suitable substrates. This study proposes an antenna structure comprising a miniaturized patch fabricated from graphene material on a photonic band gap (PBG) substrate of Arlon, operating in the terahertz frequency range. A comparative analysis of the antenna structure with and without PBG is conducted, and the obtained results are discussed. The proposed antenna demonstrates optimal performance in terms of return loss, gain, and voltage standing wave ratio (VSWR) across multiple frequency bands within the terahertz spectrum. At 1 THz and 1.18 THz, it achieves an effective gain of 4.53 dB and a return loss of 22 dB. Additionally, various electrical properties, such as surface current, current density, and VSWR, are analysed. The simulations are conducted using the High-Frequency Structure Simulator (HFSS). With a compact volume of 500 µm x 500 µm x 200 µm, the proposed antenna structure is suitable for various optical applications, including nano-sensor networks and imaging. Encouraging results are demonstrated at higher optical ranges within the terahertz band.