  We propose a feasible scenario to directly polarize a relativistic electron
beam and obtain overall polarization in various directions through a filter
mechanism for single-shot collision between an ultrarelativistic unpolarized
electron beam and an ultraintense circularly polarized laser pulse. The
electrons are scattered to a large angular range of several degrees and the
polarization states of the electrons are connected with their spatial position
after the collision. Therefore, we can employ a filter to filter out a part of
the scattered electrons based on their position and obtain high-degree overall
polarization for the filtered beam. Through spin-considered Monte-Carlo
simulations, polarization with a degree up to 62% in arbitrary transverse
directions and longitudinal polarization up to 10% are obtained for the
filtered beams at currently achievable laser intensity. We theoretically
analyze the distribution formation of the scattered electrons and investigate
the influence of different initial parameters through simulations to
demonstrate the robustness of our scheme. This scenario provides a simple and
flexible way to produce relativistic polarized electron beams for various
polarization directions.
