Picosecond gain and refractive index nonlinearities in semiconductor optical amplifiers (SOAs) are simulated for repeated pulse injection case in which the repeatition period is shorter than SOA carrier lifetime. The simulation is implemented by using a multi-section model and starting from the rate equation. The aberration of the temporal profile of the output pulse, gain and phase change induced by pulse injection, and frequency chirp on the output pulse are given for each injected pulse. Gain and phase change induced by return-to-zero (RZ) optical signal stream is also given.