  We consider emission of a photon by an electron in the field of a strong
laser wave. Polarization effects in this process are important for a number of
physical problems. We discuss a probability of this process for circularly
polarized laser photons and for arbitrary polarization of all other particles.
We obtain the complete set of functions which describe such a probability in a
compact covariant form. Besides, we discuss an application of the obtained
formulas to the problem of electron -> photon conversion at photon-photon and
photon-electron colliders.
