Complete description of polarization effects in e + e - pair productionby a photon in the field of a strong laser wave

We consider production of a e ⁺ e^- pair by a high-energy photon in the field of a strong laser wave. A 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, 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.