In this paper, design and implantations of terahertz rectangular DRA using HFSS simulator have been presented. The aspect ratio has played deterministic role for desired resonant modes excitation at terahertz frequencies. The antenna operates at 10 THz, hence can be used for high speed communications and terahertz sensors. Design is simple due to rectangular geometry, efficient due to use of DR, and unique using silicon as radiator. Mathematical modeling of 10 THz frequency using Terahertz DRA is also presented along with simulations results of S11 below -10dB , Gain of 4.89 dBi with good radiation pattern have been validated. These DRAs falls within visible frequency hence they can be used as artificial retinal photoreceptors. DR material has advantages over metallic antennas as they can operate with stability from microwave to optical regime. These optical antennas can be suitable for wireless transmission of TBPS data rate. Terahertz technology has effectively miniaturized the size of DRA. High speed communication at THz frequency can result into wide bandwidth and shall be able to provide Tbps data rate. Coherent states and control at optical frequencies have been formulated mathematically with unique characteristics at terahertz frequency.