Directional coupling to a $\lambda/5000$ nano-waveguide

Silicon-based micro-devices are considered promising candidates for consolidating several terahertz technologies into a common and practical platform. The practicality stems from the relatively low loss, device compactness, ease of fabrication, and wide range of available passive and active functionalities. Nevertheless, typical device footprints are limited by diffraction to several hundreds of micrometers, which hinders emerging nanoscale applications of terahertz frequencies. While metallic gap modes provide nanoscale terahertz confinement, efficiently coupling to them is difficult. Here we present and experimentally demonstrate a strategy for efficiently interfacing sub-terahertz radiation ({\lambda}=1 mm) to a waveguide formed by a nanogap, etched in a gold film, that is 200 nm ({\lambda}/5000) wide and up to 4.5 mm long. The design principle relies on phase matching dielectric and nanogap waveguide modes, resulting in efficient directional coupling between them when placed side-by-side. Broadband far field terahertz transmission experiments through the dielectric waveguide reveal a transmission dip near the designed wavelength due to resonant coupling. Near field measurements on the surface of the gold layer confirm that such a dip is accompanied by a transfer of power to the nanogap, with an estimated coupling efficiency of ~10%. Our approach provides a pathway for efficiently interfacing millimeter-wave and near-infrared photonic circuits, providing controlled and tailored nanoscale terahertz confinement, with important implications for on-chip nanospectroscopy, telecommunications, and quantum technologies.