Effects of Photon Polarizations in Non-Linear Compton Process

The polarization of recoil photon ( \(\gamma {\kern 1pt} '\) ) in the non-linear Compton process \(e + \vec {L} \to \vec {\gamma }{\kern 1pt} '\,\, + e{\kern 1pt} '\) in the interaction of a relativistic electron with a linearly polarized laser beam ( \(\vec {L}\) ) is analized. Our consideration is done in the line of envisaged LUXE experiment.