Detuning Tunable OAM Generation via Double-$Λ$ Four-Wave Mixing in Hot Rubidium Vapor

We demonstrate detuning-tunable generation of orbital-angular-momentum (OAM) light using a double Lambda four-wave-mixing (FWM) process in Doppler broadened rubidium vapor. Two near-resonant pumps on the D1 line drive non degenerate FWM that produces bright probe conjugate beams whose transverse modes evolve with pump detuning. A paraxial density-matrix model coupled to split-step propagation predicts detuning-dependent spatial gain shaping that sets the OAM content; experiments with a mode cleaned pump laser and a 12-mm AR-coated vapor cell validate these predictions. We quantify mode formation by imaging, spectroscopy, and power measurements, and verify OAM conservation between the generated beams. The results establish resonant atomic vapor as a compact, tunable platform for structured-light generation with applications to high-dimensional quantum communications and imaging.