In this paper, we numerically analyze nonlinear asymmetric switching using a semiconductor optical amplifier (SOA) phase-shifter-based Mach–Zehnder interferometer (MZI), for the first time, to the best of our knowledge. The self-phase modulation (SPM) effect and nonlinear phase shift in each MZI arm are investigated for different input pulse intensities and linear gains in both picosecond and femtosecond regimes. The input light signal is split unequally over the two arms, where SOAs are placed and act as nonlinear phase shifters in each arm. The finite difference beam propagation method is used to solve the modified nonlinear Schrodinger equation to analyze the wave propagation. In this work, the main nonlinear effects in SOA, such as group velocity dispersion, Kerr effect, two-photon absorption, carrier heating, and spectral hole burning, are considered. Furthermore, the effect of SPM on distortion of the pulse shape and its spectrum, which can be used for pulse shaping in a picosecond-switching scheme, is studied. We depicted red and blue shifts that each pulse experiences in the process of switching in picosecond and femtosecond regimes, respectively. Based on the results for sub-picosecond input pulses, by controlling the bias current level in the MZI arms, the pulse distortion due to nonlinear effects of SOAs can be decreased at the switch output port, and symmetric pulse can be obtained. Switching with higher speed is possible in bulk SOAs in the femtosecond regime using asymmetric MZI-switching structure.