Writhing photons and Berry phases in polarized multiple scattering

We study theoretically the polarization state of light in multiple scattering media in the limit of low contrast in the refractive index. Linearly polarized photons are randomly rotated due to the Berry phase associated with the scattering path. For circularly polarized light independent speckle patterns are found for the two helical states. The statistics of the geometric phase is related to the writhe distribution of semiflexible polymers such as DNA.