Abstract
We consider the 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. The probability of this process for circularly or linearly polarized laser photons and for arbitrary polarization of all other particles is calculated. We obtain the complete set of functions which describe such a probability in a compact invariant form. Besides this, we discuss in some detail the polarization effects in the kinematics relevant to the problem of $e\to \gamma$ conversion at $\gamma \gamma$ and $\gamma e$ colliders.
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