Nonparaxial spiral transformation enabling the division operation of optical vortex topological charges

Orbital angular momentum (OAM) of light offers a versatile degree of freedom for photonic multiplexing, quantum information processing, and optical manipulation. Nevertheless, flexible scaling of OAM states—particularly beyond the paraxial regime—constitutes an unresolved challenge. Here, we establish a nonparaxial spiral transformation framework enabling rational-order topological charge division by integer factors. This transformation is experimentally realized via cascaded phase plates engineered for nonparaxial wavefront control. Simulations and experiments employing perfect vortex beams validate precise OAM scaling for n = 1/2, 1/3, and 1/4, with dominant power residing in target modes. This approach extends OAM manipulation capabilities beyond paraxial constraints, paving the way for high-dimensional photonic technologies.