Change of photon polarization in magnetic field

The process of photon propagation in external strong magnetic field has been studied. Resonance conditions in approximation of strong magnetic field and weakly excited electron (positron) states have been found. The process probability as a function of polarization parameters has been obtained. In resonance the polarization of the final photon practically does not depend on the polarization of initial photon. Final photon has linear polarization in the plane of wave vector and magnetic field.