This letter introduced the Mueller matrix method (MMM) with polar decomposition to precisely analyze the PR activities of semiconductor optical amplifiers (SOAs), where the SOA is described by a Mueller matrix M which is decomposed to a diattenuator MD, a retarder MR, and a depolarizer MΔ. The polarization rotation (PR) is determined by the retarder matrix MR, and the rotation angle θ can be calculated by θ=arccos[Tr(MR)/2-1]. It employed a computer-controlled measurement system to obtain Mueller matrix M of the SOA. Experimental results showed the amplified spontaneous emission noise in SOAs will decrease the degree of polarization of optical signal. And the PR angle was linear to input optical wavelength, while it was nonlinear to injected current and optical power. Moreover we apply a pump-probe scheme to investigate the photoinduced PR and cross-gain modulation effects in the SOA, and we found both PR angle and output power were nonlinear to the controlling optical power while obtain the orthogonal PR by controlling of a ～3.5 mW laser. Based on above results we realized a high-speed polarization switching with response time less than 300 ps, which is applicable to high-speed data communication at Gb/s.