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The gain saturation factor describes the proportionality between the real and imaginary parts of the optical susceptibility associated with the circulating optical field in the laser cavity. This factor depends on where the laser operates relative to the gain peak. The effects of the gain saturation factor on the characteristics of the nonlinear phenomena induced by optical injection are studied to find the optimal operating conditions for various application requirements. Such requirements include high microwave frequency, low phase noise, broadband frequency tunability, high modulation bandwidth, optical single-sideband modulation, and stability. Optically injected semiconductor lasers of positive, negative, and zero gain saturation factors are compared through mappings of their nonlinear dynamical characteristics as functions of the detuning frequency and the injection strength. It is found that the instability of an optically injected laser is enhanced by a smaller or more negative gain saturation factor. In both stable locking and periodic oscillations, a laser of a positive gain saturation factor that is smaller than the linewdith enhancement factor is most suitable for optical transmission requirements.