Propagation of partially polarized Gaussian Schell-model beams through aligned and misaligned optical systems

By use of a tensor method, the transform formulae for the beam coherence-polarization matrix of the partially polarized Gaussian Schell-model (GSM) beams through aligned and misaligned optical systems are derived. As an example, the propagation properties of the partially polarized GSM beam passing through a misaligned thin lens are illustrated numerically and discussed in detail. The derived formulae provide a convenient way to study the propagation properties of the partially polarized GSM beams through aligned and misaligned optical systems.