Vacuum electronic devices utilizing free-electron-based mechanisms are a crucial class of terahertz radiation sources that operate by modulating electron beams. In this study, we introduce what we believe is a novel approach to enhance the second harmonic of electron beams and substantially increase the output power at higher frequencies. Our method employs a planar grating for fundamental modulation and a transmission grating operating in the backward region to augment the harmonic coupling. The outcome is a high power output of the second harmonic signal. Contrasting with traditional linear electron beam harmonic devices, the proposed structure can achieve an output power increase of an order of magnitude. We have investigated this configuration computationally within the G-band. Our findings indicate that an electron beam density of 50 A/cm2 at 31.5 kV can produce a 0.202 THz center frequency signal with an output power of 4.59 W. As the electron beam voltage is adjusted from 23 kV to 38.5 kV, the output signal frequency shifts from 0.195 THz to 0.205 THz, generating several watts of power output. The starting oscillation current density at the center frequency point is 28 A/cm2, which is significantly lower in the G-band compared to conventional electron devices. This reduced current density has substantial implications for the advancement of terahertz vacuum devices.