Polarization of high-energy γ-quanta traversing a bunch of polarized laser photons

The elastic light-light scattering below the threshold of the e+e− pair production leads to a variation in polarization of hard γ-quanta traversing (without loss in intensity) a region where the laser light is focused. This effect can be used to control the γ-quantum polarization. Equations are obtained which determine the variation of Stokes parameters of γ-quanta in this case, and their solutions are given. It is pointed out that this effect can be observed in the experiment of the type of E- 144 at SLAC. It should be taken into account and, perhaps, it can be used in experiments at future γγ colliders.