Phase-controlled electromagnetically induced focusing in a closed-loop atomic system

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In atomic systems, the spatially nonuniform distribution of a coupling field leads to the focusing of a probe beam producing a recipe for electromagnetically induced focusing (EIF). A diffraction-like pattern for the output probe beam can arise, and the probe radiation experiences focusing and defocusing across an electromagnetically induced transparency window. This phenomenon has critical implications for experiments on atomic coherence effects. Here, we study the EIF in a four-level closed-loop atomic system and show that full width at half-maximum (FWHM) of focused output probe intensity in the focal plane can be controlled by both intensity profile and relative phase of applied fields. We also demonstrate that the FWHM of the focused output probe intensity in focal length is much smaller than that of the input probe intensity, and in addition, through a special set of parameters, the minimum value of the FWHM can be obtained. Moreover, the FWHM can be made small by increasing Rabi frequency of the Gaussian signal field. Furthermore, the Gaussian probe intensity profile switches to a doughnut-like one just by changing the relative phase of applied fields. Finally, we apply a Laguerre–Gaussian signal field and find that the characteristics of the output probe field depend on the intensity profile of the signal field. Our results can be used to design a lens-like device with a controllable focal length and focusing strength that would pave the way toward all-optical switching devices.