  The advent of laser-driven high-intensity $\gamma$-photon beams has opened up
new opportunities for designing advanced photon-photon colliders. Such
colliders have the potential to produce a large yield of linear Breit-Wheeler
(LBW) pairs in a single shot, which offers a unique platform for studying the
polarized LBW process. In our recent work [Phys. Rev. D 105, L071902(2022)], we
investigated the polarization characteristics of LBW pair production in CP
$\gamma$-photon collisions. To fully clarify the polarization effects involving
both CP and LP $\gamma$-photons, here we further investigate the LBW process
using the polarized cross section with explicit azimuthal-angle dependence due
to the base rotation of photon polarization vectors. We accomplished this by
defining a new spin basis for positrons and electrons, which enables us to
decouple the transverse and longitudinal spin components of $e^\pm$. By means
of analytical calculations and Monte Carlo simulations, we find that the linear
polarization of photon can induce the highly angle-dependent pair yield and
polarization distributions. The comprehensive knowledge of the polarized LBW
process will also open up avenues for investigating the higher-order
photon-photon scattering, the laser-driven quantum electrodynamic plasmas and
the high-energy astrophysics.
