Study of Mueller Matrix Containing PDL/G and S-NPR Effect in SOAs

A Mueller matrix containing polarization dependent loss/gain (PDL/G) is derived, and the 16 elements of the matrix are directly represented by the five unknown parameters representing PDL/G, birefringence, and polarization mode coupling. A method is proposed to measure the Mueller matrix using two independent sets of Stokes parameters. The method is applied to a system containing a semiconductor optical amplifier (SOA) with a significant PDG, and its Mueller matrix is measured, which avoids the complex polar decomposition process and improves the measurement accuracy compared with the conventional MMM method. The nonlinearities of the polarization characteristics of the SOA are further investigated by using the quaternion method. The self-induced nonlinear polarization rotation (S-NPR), which is the nonlinear variation of the polarization-dependent phase shift and the PDG with injected optical power, is investigated, and both theory and experiment show that with the increase of the injected optical power, rotation axis of the S-NPR remains unchanged, and only the magnitude of the rotation shows nonlinearity. The influence of the intrinsic parameters of the SOA on the two nonlinearities, phase shift and PDG, is also investigated, and the relationships between phase shift, PDG, and the internal parameters of the SOA (such as small-signal gain, saturation power, LEF, etc.) are obtained.