Multiplication and division of orbital angular momentum beams by Fermat’s spiral transformation

Optical geometrical transformation is a novel and powerful tool to switch orbital angular momentum (OAM) states in modern optics. We demonstrate a scheme to operate multiplication and division in OAM by Fermat’s spiral transformation. The characteristics of the output beams in the case of integer and fraction OAM operations are presented in detail. Additionally, the power weight of the output OAM modes and the interference patterns of the output beams are reported to confirm the expected ability of OAM mode conversion by Fermat’s spiral transformation. We further investigate the evolution of OAM beams in operations theoretically and experimentally. This work provides a practical way to perform an optical transformation mapping on OAM beams. It can find application in optical communications with larger OAM mode numbers as well as quantum information in high-dimensional systems.