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We designed a single-pass quasi-phase-matched second-harmonic generation (SHG) device with a planar waveguide; the device comprised a Y-cut 5 mol% MgO-doped LiNbO3 (MgO:LiNbO3) crystal core that was 3 mum thick and SiO2 cladding. The waveguide provided a high coupling efficiency of 95% between an incident Gaussian beam and the fundamental guided mode of a fundamental wave; it also provided high electric-field confinement in the case of both the fundamental and SHG waves in the core. Thus, a high overlap between nonlinear polarization and an SHG-guided mode was attained. The bonding of the device with the waveguide side positioned downward to a heat sink provided a large heat radiation area when pumping with a near-collimated Gaussian beam, which reduced the temperature rise and its gradient along the waveguide to minimize the phase mismatch. We demonstrated the green light generation of 1.6 W with 40% conversion efficiency using a 7-mm-long sample and 1.2-W SHG with 60% efficiency using an 18-mm-long sample.