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We have proposed a novel approximate analytical expression for saturation intensity for tapered traveling-wave semiconductor laser amplifier structures. The application of this analytical expression of saturation intensity has been demonstrated by considering the effect of gain saturation on polarization sensitivity of two tapered amplifier structures, linear and exponential tapered amplifier structures. It is found that polarization sensitivity of the tapered amplifier structure is several decibels higher than that of passive tapered waveguides in unsaturated condition. Polarization sensitivity of the two tapered amplifier structures has also been investigated in a highly saturated condition. The combined effects of mode conversion and gain saturation on fundamental TE gain have also been investigated using the proposed analytical expression for saturation intensity.