  Robust higher-order optical vortices are much in demand for applications in
optical manipulation, optical communications, quantum entanglement and quantum
computing. However, in numerous experimental settings, a controlled generation
of optical vortices with arbitrary orbital angular momentum (OAM) remains a
substantial challenge. Here, we present a concept of "optical vortex ladder"
for stepwise generation of optical vortices through Sisyphus pumping of
pseudospin modes in photonic graphene. Instead of conical diffraction and
incomplete pseudospin conversion under traditional Gaussian beam excitations,
the vortices produced in the ladder arise from non-trivial topology and feature
diffraction-free Bessel profiles, thanks to the refined excitation of the ring
spectrum around the Dirac cones. By employing a periodic "kick" to the photonic
graphene, effectively inducing the Sisyphus pumping, the ladder enables tunable
generation of optical vortices of any order even when the initial excitation
does not involve any OAM. The optical vortex ladder stands out as an intriguing
non-Hermitian dynamical system, and, among other possibilities, opens up a
pathway for applications of topological singularities in beam shaping and
wavefront engineering.
