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We present a model for polarization-dependent gain saturation in strained bulk semiconductor optical amplifiers. We assume that the polarized optical field can be decomposed into transverse electric and transverse magnetic components that have indirect interaction with each other via the gain saturation. The gain anisotropy due to tensile strain in the amplifier is accounted for by a population imbalance factor. The model is applied to a nonlinear polarization switch, for which results are obtained, that are in excellent agreement with experimental data. Finally, we describe an all-optical flip-flop memory that is based on two coupled nonlinear polarization switches.