The majority of sources of coherent optical radiation rely on laser oscillators driven by population inversion. Despite their technological importance in communications, medicine, industry, and other fields, it remains a challenge to access the spectral range of 0.1-10 THz (the terahertz gap), a frequency band for applications ranging from spectroscopy to security and high-speed wireless communications. Here, we propose a way to produce coherent radiation spanning the THz gap by efficient second-harmonic generation (SHG) in low-loss dielectric structures, starting from technologically mature electronic oscillators (EOs) in the ~100 GHz range. To achieve this goal, we introduce hybrid THz-band dielectric cavity designs that combine (1) extreme field concentration in high-quality-factor resonators with (2) nonlinear materials enhanced by phonon resonances. We theoretically predict conversion efficiencies of >$10^3$ %/W and the potential to bridge the THz gap with 1 W of input power. This approach enables efficient, cascaded parametric frequency converters, representing a new generation of light sources extensible into the mid-IR spectrum and beyond.
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