Vector statistics of multiply scattered waves in random systems

Statistical distribution functions are derived for the polarization of optical waves transmitted through a random medium. Excellent agreement is obtained with experiment. Our most significant result is the distribution function for the ellipticity {ε}, the ratio between the major and minor axes of the elliptically polarized scattered light. This has a maximum at {ε}=0 and vanishes for {ε}=1, indicating that linear polarization is the most probable state and that circular polarization has vanishing probability. The averaged ellipticity is found to be 〈{ε}〉=1-ln2=0.307.