  Generation of ultrarelativistic polarized leptons during interaction of an
ultrarelativistic electron beam with a counterpropagating ultraintense laser
pulse is investigated in the quantum radiation-dominated domain. While the
symmetry of the laser field tends to average the radiative polarization of
leptons to zero, we demonstrate the feasibility of sizable radiative
polarization through breaking the symmetry of the process in the reflection
regime. After the reflection, the off-axis particles escape the tightly focused
beam with polarization correlated to the emission angle, while the particles at
the beam center are more likely to be captured in the laser field with
unmatched polarization and kinetic motion. Meanwhile, polarization along the
electric field emerges due to the spin rotation in the transverse plane via
precession. In this way, the combined effects of radiative polarization, spin
precession and the laser field focusing are shaping the angle-dependent
polarization for outgoing leptons. Our spin-resolved Monte Carlo simulations
demonstrate an angle-dependent polarization degree up to $\sim20\%$ for both
electrons and positrons, with a yield of one pair per seed electron. It
provides a new approach for producing polarized high density electron and
positron jets at ultraintense laser facilities.
