A metallic slot waveguide, with a dielectric strip embedded within, is investigated for the purpose of enhancing
the optics-to-THz conversion efficiency using the difference-frequency generation (DFG) process. To describe
the frequency conversion process in such lossy waveguides, a fully-vectorial coupled-mode theory is developed.
Using the coupled-mode theory, we outline the basic theoretical requirements for efficient frequency conversion,
which include the needs to achieve large coupling coefficients, phase matching, and low propagation loss for both
the optical and THz waves. Following these requirements, a metallic waveguide is designed by considering the
trade-off between modal confinement and propagation loss. Our numerical calculation shows that the conversion
efficiency in these waveguide structures can be more than one order of magnitude larger than what has been
achieved using dielectric waveguides. Based on the distinct impact of the slot width on the optical and THz
modal dispersion, we propose a two-step method to realize the phase matching for general pump wavelengths.