Spatial modulation of refractive index in a dense atomic ensemble using Laguerre–Gaussian beams

Abstract

We propose a scheme to investigate the spatial modulation of the refractive index in a dense atomic ensemble under the action of the Laguerre–Gaussian (LG) beams. Theoretical derivations based on a density-matrix approach associated with numerical simulations are utilized to study the behaviors of the index of refraction, showing that the azimuthal and radial mode indices (i.e., l 2 and p 2) of the LG beams significantly affect the real and imaginary parts of the refractive index. To be specific, the number of the dispersive peaks is determined by ( p 2 + 1 ) | l 2 |, and there are 2 | l 2 | lossless petals in conjunction with p 2 concentric absorption rings centered on the vortex center. Furthermore, by tuning the phase values of the electric and magnetic components of the electromagnetic field, the index of refraction can be drastically tuned from negative to zero to positive and accompanied by periodic absorption and amplification. This investigation provides a powerful tool for manipulating the index of refraction through a nonlinear interaction between atoms and the vortex beams and suggests potential applications in optical switching, logic gates, and optical storage with spatially varying refractive indices.