This paper introduces a silicon-micromachined lens antenna, fabricated for operation in the 500-750 GHz range, featuring an optimized Graded Index Fresnel Zone Planner Lens (FZPL) design. The antenna efficiently radiates a circularly polarized wavefront without the need for additional phase compensation components. Through fabrication, the antenna achieves a high gain of 36 dBi and maintains a -15 dB return loss across the entire waveguide band. Significantly, this all-dielectric lens antenna exhibits minimal loss, ensuring elevated efficiency in Terahertz (THz) communication applications. With its low profile and compact design, this antenna emerges as a promising solution for upcoming wideband THz communication applications. This work not only emphasizes the innovative design but also underscores the practical realization of high-performance antennas with a compact footprint, leveraging silicon micromachining in the THz frequency bands.