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Physical Review A

Electromagnetically-induced focusing

Richard R. Moseley, Sara Shepherd, David J. Fulton, Bruce Sinclair, Malcolm H. Dunn

Published Jan 1, 1996• 65 citations
Publisher

Abstract

The theoretical basis for electromagnetically-induced focusing (EIF), which is caused by spatial variations in the coupling laser strength in an electromagnetically-induced transparency (EIT) experiment, is studied in detail. Using a numerical model it is shown that radial changes in both absorption and refractive index are important in predicting the probe beam's propagation conditions. Detailed calculations of the focusing and defocusing during EIF under various conditions are presented and compared with appropriate experiments. Diffractionlike patterns are predicted for, and observed on, a probe beam after propagation through a smaller EIT aperture. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.53.408

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Transmissivity of up to 200% has been observed in an absorption imaging study of electromagnetically induced transparency in cold sodium atoms, when a focused coupling beam is applied near the edge of the atom cloud. The signal behavior strongly depends on the frequency difference between the probe beam and the coupling beam. Such high transmissivity can be attributed to the strong focusing effect of the probe beam, when it propagates in a medium with spatially inhomogeneous refractive index induced by the coupling beam. A detailed numerical analysis based upon the Maxwell propagation equations is presented.

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The theoretical basis for electromagnetically-induced focusing (EIF), which is caused by spatial variations in the coupling laser strength in an electromagnetically-induced transparency (EIT) experiment, is studied in detail. Using a numerical model it is shown that radial changes in both absorption and refractive index are important in predicting the probe beam's propagation conditions. Detailed calculations of the focusing and defocusing during EIF under various conditions are presented and compared with appropriate experiments. Diffractionlike patterns are predicted for, and observed on, a probe beam after propagation through a smaller EIT aperture. \textcopyright{} 1996 The American Physical Society.
Electromagnetically induced transparency (EIT) in an inhomogenously broadened medium consisting of Λ-type three-level atoms has been analyzed. It is shown that the Λ system can induce a transparency of the medium when the probe laser and the coupling laser have the same frequency detunings (including zero). Across the EIT window, the radial variation of the strong coupling laser radiation may lead to electromagnetically induced focusing or defocusing of the weak probe laser at separate probe frequency detuning points.
We study the lensing effect experienced by a weak probe field under conditions of electromagnetically induced transparency (EIT) involving a Rydberg state. A Gaussian coupling beam tightly focused on a laser-cooled atomic cloud produces an inhomogeneity in the coupling Rabi frequency along the transverse direction and makes the EIT area acting like a gradient-index medium. We image the probe beam at the position where it exits the atomic cloud and observe that a red-detuned probe light is strongly focused with a greatly enhanced intensity whereas a blue-detuned one is defocused with a reduced intensity. Our experimental results agree very well with the numerical solutions of Maxwell-Bloch equations.
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.
Electromagnetically induced transparency is a technique for eliminating the effect of a medium on a propagating beam of electromagnetic radiation. EIT may also be used, but under more limited conditions, to eliminate optical self-focusing and defocusing and to improve the transmission of laser beams through inhomogeneous refracting gases and metal vapors, as figure 1 illustrates. The technique may be used to create large populations of coherently driven uniformly phased atoms, thereby making possible new types of optoelectronic devices.
Transmissivity of up to 200% has been observed in an absorption imaging study of electromagnetically induced transparency in cold sodium atoms, when a focused coupling beam is applied near the edge of the atom cloud. The signal behavior strongly depends on the frequency difference between the probe beam and the coupling beam. Such high transmissivity can be attributed to the strong focusing effect of the probe beam, when it propagates in a medium with spatially inhomogeneous refractive index induced by the coupling beam. A detailed numerical analysis based upon the Maxwell propagation equations is presented.