Statistics of polarization and Stokes parameters of stochastic waves

The polarization statistics of the superposition of multiple wave populations is discussed. Each wave population was considered to be a coherent mode with fixed polarization angle and axial ratio. In the analysis, two wave vectors having fixed polarization angle but random phase difference were superposed. The integral expressions were developed for the probability distribution functions (PDF) P_S of the Stokes parameters S, using this representation. The results show that the integral for each Stokes PDF P_S contains a square-root singularity in electric field space for two wave populations.