Rational number vortex beam multiplier and divider based on an Archimedean spiral mapping

Orbital angular momentum (OAM), as an extra dimension of light, holds substantial potential in both classical and quantum optical communication systems. In such systems, the ability to arbitrarily convert the OAM of light is of great importance. In this work, we demonstrate an arbitrary rational number of multiplication and division of the OAM of light based on an Archimedean spiral mapping. Both the simulation and experimental results have demonstrated the effectiveness of this scheme. This work provides a practical method to manipulate the OAM mode space of light that is directly applicable to high-dimensional optical communication systems.