This paper presents a Mueller-matrix approach to simulate the azimuth and ellipticity trajectory of a probe light in a tensile-strained bulk semiconductor optical amplifier (SOA) in a conventional pump-probe scheme. The physical mechanisms for the variations of polarization azimuth and ellipticity angle of the probe originate from the significant nonuniform distributions of carrier density across the active region in the presence of an intense pump light. Due to this carrier-density nonuniformity, the effective refractive indexes experienced by transverse-electric (TE) and transverse-magnetic (TM) modes of the probe are different. This results in a phase shift between TE and TM modes of the probe upon leaving the SOA. Simulations of the carrier distributions along the cavity length at different pump-light levels are demonstrated using multisection rate equations, which take into account the longitudinal nonuniform carrier density. The optical gain is considered via the parabolic band approximation. The influences of the spontaneous recombination and carrier-dependent material loss on the amplifier performance are included. The Mueller-matrix formalism is utilized to predict the variations of azimuth and ellipticity angle, which greatly reduces the complexity of the simulations in comparison with Jones-matrix formalism. The suggested approach is beneficial to experimental investigations due to the fact that during the optical-tuning process, Stokes parameters are virtually measurable on the Poincare sphere, and the Stokes vector of the incoming probe can be adjusted by a polarization controller and monitored by a polarization analyzer. Based on these carrier-induced nonlinearities in SOAs, an optical AND gate with extinction ratio larger than 14 dB and Q-factor larger than 25 is presented at a bit rate of 2.5 Gb/s.