Coherence-controlled azimuthal modulation of atomic ensemble susceptibility, grating, and Fraunhofer diffraction

We demonstrate coherence-controlled azimuthal modulation of electromagnetically induced transparency (EIT) and all-optical switching in a four-level atomic ensemble coupled to a Laguerre-Gaussian beam, a control field, and a microwave field. The spatial EIT patterns exhibit doublet, quartet, and sextuplet structures, evolving into more complex structures with increasing orbital angular momentum (OAM). These structures can be dynamically switched between EIT and absorption patterns, preserving mirror image symmetry (with even OAM) and rotation symmetry (with odd OAM) by adjusting the relative phase of the coupling fields. By creating two-dimensional electromagnetically induced gratings (EIGs), we find that the diffractive patterns are influenced by probe field detuning, OAM, and relative phase. Specifically, the diffraction patterns of a probe field exhibit complex behavior across first to fourth orders, with intensities influenced by topological charge and azimuthal angle. The diffraction patterns are further modulated by the relative phase, with patterns at 0 and <i>π</i> being mirror images of each other, while the pattern at <i>π</i>/2 exhibits distinct behavior. These findings highlight the potential for precise control over structural EIT, all optical switching and diffraction patterns in coherent atomic media.