The development of bias-free terahertz (THz) photoconductive antenna (PCA) emitters is crucial for various telecommunication and biomedical uses. However, these emitters face a primary challenge in their limited terahertz emission power, resulting in lower efficiency compared to biased THz PCAs. This paper introduces a novel design for an antenna-coupled unbiased continuous-wave (CW) THz photomixer emitter array that operates in the optical near-field range without any voltage bias. This unbiased design incorporates a plasmonic nano-resonator to enhance the conversion efficiency of input optical power into photo-generated carriers that contribute to THz photocurrent. The nano-resonator consists of plasmonic nano-electrodes and a distributed Bragg reflector structure strategically positioned above and below the photoconductive material in the active region of the emitter. In the optimally designed PCA, the first plasmonic mode in the nano-gap cavity between nano-electrodes efficiently channels maximal optical power into the photoconductive material. A well-designed DBR beneath this material reflects the optical beam into the GaAs layer, ensuring maximum absorption near the nano-electrodes, where the high built-in electric field accelerates the photocarriers to generate a THz photocurrent. The simulation results for this plasmonic nano-resonator-based emitter predicts a peak THz power of 838 µW with a remarkable conversion efficiency of 2% at a 0.5-THz frequency, setting a new benchmark that surpasses previous bias-free emitters in terms of THz power output and conversion efficiency. The enhanced capabilities of the proposed photomixer show great promise for various biomedical applications, including bioimaging, with the potential to improve patient safety by eliminating risky external biasing circuits.