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General time-domain traveling wave rate equations are employed for the simulation of the intra-cavity second harmonic generation (IC-SHG) of semiconductor lasers by a periodically poled nonlinear crystal waveguide. A 1060 nm high power, single-mode, ridge waveguide semiconductor laser is used in the simulation. The SHG crystal is a MgO-doped periodically poled lithium niobate with a single-mode ridge waveguide. Comparisons are made between the computed and experimental results of single-pass SHG for the purposes of model validation. The design of an IC-SHG green laser is further compared to the single-pass SHG laser in terms of the SHG output power, conversion efficiency, temperature tolerance, and high speed modulation capability. It is theoretically found that by using the IC-SHG configuration, SHG power and efficiency can be improved with a relatively short nonlinear crystal. [ABSTRACT FROM AUTHOR]