Investigation of the effects of lateral displacement and radial index on orbital angular momentum transfer

Vortex beams have attracted considerable interest due to their compatibility with orbital angular momentum (OAM) modes. Based on an OAM mode decomposition approach, this study systematically investigates the mode composition of Laguerre-Gaussian (LG) and perfect Laguerre-Gaussian (PLG) beams with lateral displacement. It is demonstrated that a laterally displaced beam relative to the detection axis can be described as a linear superposition of multiple coaxial beams. The lateral displacement broadens the topological charge (TC) spectrum. Notably, by modulating the radial index of the beam, directed TC transfer in the spectrum can be achieved. This behavior is confirmed in both single-mode and dual-mode LG beams. Furthermore, in specific superposed beam structures, the adjacent modes in the TC spectrum exhibit a constant spacing of 2, revealing a unique mode distribution feature. For comparison purposes, PLG beams exhibit significantly higher sensitivity to lateral displacement, with their TC spectrum broadening more prominently and showing less controllable transfer behavior despite the advantage of constant transverse size. This work provides a novel strategy to address beam misalignment issues in optical detection and communication, holding significant potential for advanced practical applications of OAM-based technologies.