We introduce a semiconductor optical amplifier (SOA) chip with high gain (>40 dB) and high saturation power (>21 dBm) with moderate drive current (1.3A). A design model for optimizing the new dual-section SOA concept is presented. The model predictions are in very good agreement with the measurement results on fabricated chips. Using the gain and saturation output power product as the figure of merit, it shows the best-reported trade-off result so far. However, due to the slight degradation of the noise figure that ensued, an advanced design is introduced, enabling the optimization of the noise figure in addition to the gain and saturation output power.