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This work presents a computational study of a hybrid plasmonic–photonic Panda-ring antenna embedded with a gold grating for dual-mode optical and terahertz (THz) transmission. The proposed structure integrates whispering gallery modes (WGMs) supported by a multi-ring resonator with surface plasmon polariton (SPP) excitation at a metal–dielectric interface, enabling strong near-field confinement and efficient far-field radiation. A systematic structural evolution—from a linear silicon waveguide to single-ring, add-drop, and Panda-ring configurations—is investigated to clarify the role of resonant coupling and power routing. Full-wave simulations using Optiwave FDTD and CST Microwave Studio are employed to analyze electric-field distributions, spectral power intensity, and radiation characteristics. The results demonstrate that the embedded gold grating facilitates effective SPP–WGM hybridization, allowing confined photonic energy to be converted into directional radiation with a peak gain exceeding 5 dBi near 1.52–1.55 µm. The proposed antenna exhibits stable dual-mode operation, making it a promising candidate for Li-Fi transmitters, THz wireless links, and integrated photonic–plasmonic communication systems.