  Structured optical fields embedded with polarization singularities (PSs) have
attracted extensive attention due to their capability to retain topological
invariance during propagation. Many advances in PSs research have been made
over the past 20 years in the areas of mathematical description, generation and
detection technologies, propagation dynamics, and applications. However, one of
the most crucial and difficult tasks continues to be manipulating PSs with
multiple degrees of freedom, especially in three-dimensional (3D) tailored
optical fields. We propose and demonstrate the longitudinal PS lines obtained
by superimposing Bessel-like modes with orthogonal polarization states on
composite vector optical fields (VOFs). The embedded PSs in the fields can be
manipulated to propagate robustly along arbitrary trajectories, or to
annihilate, revive, and transform each other at on-demand positions in 3D
space, allowing complex PSs topological morphology and intensity pattern to be
flexibly customized. Our findings could spur further research into singular
optics and help with applications such as micromanipulation, microstructure
fabrication, and optical encryption.
