  Relativistic spin-polarized (SP) lepton beams are important for investigating
spin-dependent interaction processes. In particular, spatially structured
spin-polarized (SSP) lepton beams may find new applications in material,
atomic, nuclear, high-energy physics and new physics beyond the Standard Model.
However, realizing ultrafast generation and spin-manipulation of relativistic
SSP lepton beams pose significant challenges. Here, we put forward a novel
method of ultrafast (picosecond-timescale) generation of a relativistic SSP
lepton beam via employing a moderate terahertz (THz) wave in a dielectric-lined
waveguide (DWL). We first find that lepton beams with customizable
spin-polarization structures can be generated by utilizing different
electromagnetic modes, and optimizing the lepton velocity and THz phase
velocity can improve efficiency of spin-manipulation and visibility of the SP
structure. These SSP beams play a profound role in studying magnetic effects in
material physics, chiral-selective chemistry, generation of structured
$\gamma$-rays, etc., and open a new avenue for research on relativistic SP
particles.
