We introduce an advanced methodology for determining the topological charge of a vortex Bessel beam via light-atom interactions in a closed-loop three-level atomic system. This technique exploits the interplay between an optical Bessel beam with topological charge \(\ell _p\) and a microwave Bessel beam with topological charge \(\ell _{\mu }\) , which collectively induce a spatially varying, phase-sensitive atomic susceptibility. This interaction manifests in a distinct pattern of alternating absorption and transparency regions in the transverse plane, governed by the medium’s resultant topological charge, \(\ell = \ell _{\mu } - \ell _{p}\) . The transparency windows selectively allow specific beam portions to propagate, while absorption windows block others, transforming the beam’s concentric rings into structured patterns of alternating bright and dark strips. The number of these strips directly correlates with the Bessel beam’s topological charge. Analytical expressions for atomic susceptibility elucidate the mechanism underlying this transformation, enabling simultaneous and precise measurement of the topological charges of both beams. The superior sensitivity of this approach opens up transformative possibilities for applications in communications, microscopy, and optical metrology. Furthermore, varying the relative phase between the optical and microwave beams induces a controlled angular rotation of the structured beam, offering enhanced maneuverability over beam orientation. This robust approach not only facilitates precise characterization of structured light but also supports advanced applications in optical computing, information processing, and sensing technologies.
