  Increasing demand for practical applications is forcing deeper research into
optical vortices (OVs): from the generation and measurement to shaping and
multiple singularities manipulation of OVs. Herein, we propose a new type of
phase structure called the high-order cross phase (HOCP) can be employed to
modulate OVs to implement both polygonal shaping and singularities
manipulation. Theoretically, we investigate the propagation characteristics of
OVs with the HOCP. In experiments, we achieve the shaping and singularities
manipulation of OVs by utilizing the HOCP. On this basis, we discuss the
interference patterns of superposed OVs after the modulation. This work
provides an alternative method to achieve both polygonal shaping and multiple
singularities manipulation, which will facilitate applications in optical
micro-manipulation, optical communication, and high-dimensional quantum
entanglement.
