This work, presents a design of a nano-antenna based plasmonic materials at the frequency range from 192THz to 195THz for modern applications, including THz communication systems. The proposed antenna is constructed from the 3rd iteration of the Hilbert curve patch fed with a modified coplanar 50Ω port. The back layer of the antenna was covered with a partial ground plane defective with a metamaterial-based electromagnetic band gap (EBG) layer. The antenna shows high directivity up to 68dBi at 193.4THz with an excellent matching over the entire frequency band of interest. The proposed antenna is considered of gold conductive layer mounted on a silicon dioxide (SiO2) layer. The proposed EBG was designed as the second order of the Minkowski fractal geometry. The obtained results in terms of S11 were below -10dB for the frequency band of 3THz. These results were validated using numerical techniques based on CST MWS by invoking the time domain (TD) and frequency domain (FD) solvers. The results achieved from the considered techniques agreed very well with each other.