Optical Vortex Transfer and Dispersion-Controlled Light Propagation in an Er YAG Three-Level Quantum System

We theoretically investigate coherent orbital-angular-momentum (OAM) transfer and dispersion-controlled light propagation in a ladder-type Er 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 Er 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 Er concentration (3 percent) 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 demonstrate tunable transitions between fast and slow regimes. These results establish Er YAG as a viable solid-state platform for the coherent manipulation of structured light, enabling efficient vortex-beam frequency conversion and dispersion engineering for applications in high-dimensional quantum communication, wavelength-compatible OAM interfaces, and slow-light photonic signal processing.