Pulse narrowing mechanism in semiconductor optical amplifier (SOA) based multi stack structure is studied numerically. For analyzing narrowing characteristics of the structure, an efficient finite-difference beam propagation method is utilized to study single pulse and counter propagation pulses in SOA. SOA all interband non-linear gain effects for picosecond input pulses are considered. The effect of SOA and input pulse parameters on the multi stack operation are identified and analyzed. Simulation results demonstrate that key parameters must be suitably selected so as to ensure the satisfaction of the best pulse narrowing conditions.