Modulation of spatial Raman gain induced by Laguerre-Gaussian vortex beams

Electromagnetically induced transparency (EIT) provides an effective platform for coherent control of optical responses in atomic media. Here, we investigate a microwave-assisted closed-loop three-level system driven by a Laguerre-Gaussian (LG) control beam and a Gaussian probe field. Unlike previous work such as O. N. Verma and N. Kant, All-optical generation of structured light beams via microwave-field-controlled electromagnetically induced transparency, Phys. Rev. A, 2024, 110(1), 013701, which focused on overall optical gain in open-loop configurations, our study examines how structured light modulates the spatial distribution of Raman gain. Using a density-matrix approach, we numerically obtain two-dimensional maps and cross-sectional profiles of Raman gain. The results show that three parameters-the orbital angular momentum (OAM) of the LG beam, the single-photon detuning, and the relative phase of the control fields-collectively determine the spatial morphology of the gain. OAM controls the transition between single-lobe and multi-lobe structures, modulates the gain magnitude and spatial complexity, and the relative phase induces rotational or mirror-symmetric transformations. This work provides the first systematic analysis of spatial Raman-gain modulation in a closed-loop three-level system, demonstrating the strong capability of structured light to tailor nonlinear gain processes. The findings extend the theoretical framework beyond PRA 2024 and offer insights for spatially selective amplification and structured-light-based photonic device design.