  Synthetic dimensions based on particles' internal degrees of freedom, such as
frequency, spatial modes and arrival time, have attracted significant
attention. They offer ideal large-scale lattices to simulate nontrivial
topological phenomena. Exploring more synthetic dimensions is one of the paths
toward higher dimensional physics. In this work, we design and experimentally
control the coupling among synthetic dimensions consisting of the intrinsic
photonic orbital angular momentum and spin angular momentum degrees of freedom
in a degenerate optical resonant cavity, which generates a periodically driven
spin-orbital coupling system. We directly characterize the system's properties,
including the density of states, energy band structures and topological
windings, through the transmission intensity measurements. Our work
demonstrates a novel mechanism for exploring the spatial modes of twisted
photons as the synthetic dimension, which paves the way to design rich
topological physics in a highly compact platform.
