Reconfiguring the propagation dynamics of Airy beams through quantum coherence

We propose a theoretical approach to investigate the control of an Airy beam propagating through a three- level Lambda-type atomic vapor featuring the electromagnetic induced transparency (EIT) properties, with a Gaussian beam as the control field to create a lens-like medium. By using the ABCD Ray transfer matrix theory and the generalized Huygens-Fresnel integral, we deduce an analytical expression for the propagation of an Airy beam within a three-level atomic medium. Our results indicate that the refractive index of the medium is sensitive to both the detuning of the probe field and the Rabi frequency of the control field. By adjusting those parameters, the structural distribution of the atomic medium can be modified, resulting in the medium with a different transverse refractive index. For instance, when the Rabi frequency of the control field exceeds a certain threshold relative to the detuning, the medium behaves like a convex lens, whereas falling below this threshold results in behavior similar to a concave lens. Interestingly, within a specific parameter range, an unstable jump interval exists, resulting in a transition between two distinct structures in the atomic medium. Through precise parameter tuning, the medium can be selectively converted to different lens-like media, allowing for controlled deflection of the Airy beam in a variety of media. Furthermore, we demonstrate that by carefully adjusting these parameters, it is possible to transform the field distribution of the Airy beam from an oscillatory field distribution to a Gaussian- like field distribution at a selected fixed distance, thereby focusing the beam intensity within a specific area.