We present the strict design parameters of the experiment for the 780 nm tunable continuous-wave second harmonic (SH) generation by the nonlinear resonator containing a MgO doped periodically poled LiNbO3 (MgO:PPLN) crystal. Optimization of such critical parameters, including focusing and impedance matching, more than 84% SH conversion efficiency and 3.1 W available output power at 780 nm were obtained from the fundamental wave at 1560 nm with two different input couplers. The thermal saturated behavior of the SH output power has been observed in the experiment. The beam quality factor M2 of the generated SH wave is 1.04 (1.03), and the RMS power stability is 1.29% in 3 h. The SH wave was further used to detect the D 2 transitions of Rb atom, exhibiting a fine tunable characteristic. Such laser source can be a suitable candidate in the atomic physics and quantum optics.