Shock-augmented ignition (SAI) is a promising optimized scheme recently developed from the shock ignition concept, which may effectively mitigate the laser-plasma interaction (LPI) instabilities by reducing the laser power intensity of the ignition pulse. In this study, numerical simulations are performed on the SAI scheme driven by a second-harmonic (2ω) laser, and the implosion gain window of the SAI scheme is obtained for different compression pulse durations and power dip durations, where the power dip is introduced at the end of compression pulse prior to the ignition pulse. By incorporating implosion results obtained with third-harmonic (3ω) laser drive, we investigate the correlation between implosion gain and power dip duration. The temporal match between the rebounding shock wave and the ignition shock wave is assessed by analyzing the implosion velocity generated by the compression pulse. Here, the gain as a function of shell implosion velocity is analyzed. Our results also reveal that the optimal implosion velocity for SAI is comparable for both 2ω and 3ω driving lasers with the considered ignition pulse. In addition, the effect of the driving laser wavelength on the ignition time window is discussed. It is found that the dip duration decreases with increasing wavelength, and this dependence is corroborated by additional simulations using fourth-harmonic (4ω) laser light.