Optical vortex transfer and dispersion-controlled light propagation in an Er³⁺: YAG three-level quantum system

We investigate coherent orbital-angular-momentum (OAM) transfer and dispersion-controlled light propagation in a ladder-type Er³⁺: YAG three-level system. Using the density-matrix formalism and coupled Maxwell-Bloch equations, we derive analytical expressions for the probe and generated beams that explicitly incorporate Er³⁺-ion concentration. We show that an incident vortex-carrying probe beam transfers its OAM to a generated signal beam through a concentration-dependent sum-frequency nonlinear process, with complete phase and topological-charge preservation. By analyzing conversion efficiency, spatial phase, and intensity distributions, we identify an optimal Er³⁺ concentration (3%) that maximizes vortex-transfer efficiency. Furthermore, the absorption and dispersion spectra of the probe and generated beams reveal the mechanism underpinning the vortex transfer and indicate the potential for concentration-selectable transitions between fast and slow propagation regimes. These results establish Er³⁺: YAG as a viable solid-state platform for coherent manipulation of structured light, enabling efficient vortex-beam frequency conversion and dispersion engineering, with potential relevance to classical and quantum OAM-based communication protocols, wavelength-compatible OAM interfaces, and slow-light photonic signal processing.