A scheme for monochromatic terahertz (THz) generation via cascading enhanced Cherenkov-type difference frequency generation (DFG) in a sandwich-like waveguide is proposed. The novel scheme has the potential to overcome the quantum-defect limit and to provide an efficient output coupling. This process is elucidated by developing a coupled-mode theory and taking into account the pump depletion, waveguide mode properties, and THz output coupling. The effect of cascading enhancement is analyzed by comparing with non-cascaded DFG situation. It is predicted that THz power can be boosted by nearly 8-fold with a 400 MW/cm<sup>2</sup> pump in a 40-mm-long Si-LiNbO<sub>3</sub>-Si waveguide.
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