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Journal of the Optical Society of America B

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

Zahra Amini Sabegh, Mohammad Ali Maleki, Mohammad Mahmoudi

Published Nov 2, 2017• 1 citation
Publisher

Abstract

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.

DOI
10.1364/josab.34.002446

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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.
The electromagnetically induced grating is investigated in a four-level double V-type quantum system. It is shown that the electromagnetically induced transparency established by the cross-Kerr nonlinear effect can be canceled by the four-wave mixing in a closed-loop atomic system and that the diffraction of the probe beam depends on the relative phase of the applied fields and can be controlled by this parameter. We find that an additional nonlinear contribution is established in the medium response by applying a microwave field to the system and that the electromagnetically induced absorption grating turns to the electromagnetically induced phase grating. This contribution leads to 100% diffraction efficiency in the first-order direction, so we can say that the proposed grating could be considered as a special candidate for the optical networking and communication.
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.
The optical trap potential is studied in a four-level double-Λ closed-loop atomic system in the multiphoton resonance condition. We apply four femtosecond Gaussian laser beams to generate a closed-loop configuration. It is shown that the induced optical dipole force on the system dramatically depends on the relative phase of applied fields, and it switches from focusing to defocusing in the transverse direction, simply by properly changing the relative phase. Through special switching of the relative phase, the trapping potential splits into two positions, which has novel applications in trapping and manipulating the particles. Moreover, it is further demonstrated that trap depth can be manipulated by the relative phase. Finally, a maximum coherent population transfer is achieved for a special value of the relative phase of applied fields.
Abstract We proposed a theoretical scheme for two-dimensional (2D) electromagnetically induced grating (EIG) in a closed-loop four-level atomic system driven by a weak probe field, a traveling-wave control field, two orthogonal standing-wave fields and a microwave field. Due to low amplitude modulation accompanied with large phase modulation, EIG can be obtained and the probe energy can be diffracted into first-order and even high-order directions with high efficiency. The results show that the diffraction pattern and efficiency of the EIG could be adjusted effectively by the probe field detuning, the coherent field intensity, the interaction length. Meanwhile, the quantum interference between the amplitude modulation and phase modulation can be manipulated by the relative phase, which can be used to regulate the diffraction pattern and efficiency of the 2D EIG. Our scheme of 2D EIG may be useful in beam splitting and all-optical switching.
We investigate theoretically a scheme for all-optical generation of structured light beams with and without a microwave field in an electromagnetically induced transparency (EIT) medium composed of rubidium atoms. In a conventional EIT system, two optical fields (namely, a strong control field and a weak probe field) drive two electric-dipole-allowed transitions of an atom to form a three-level system in a $\mathrm{\ensuremath{\Lambda}}$ configuration. At EIT resonance, we found that a Laguerre-Gaussian (LG) control beam induces a radial modulation of probe's absorption profile in such way that a Gaussian probe beam is reshaped into a hollow-Gaussian beam following the position-selective absorption. The transmitted probe beam has a doughnut-shaped intensity structure similar to that LG beam whereas the phase profile is still a spherical wave. Moreover, the presence of a microwave field between two ground states of three-level system leads to a closed-loop system, and probe response is modified with an additional term proportional to the amplitudes of Rabi frequencies of control and microwave fields, and relative phase of three fields. This term acts as driving field which is responsible for the generation of a vortex probe beam having a helical phase profile. We have further shown that the amplitude and helical phase of generated vortex beam can be manipulated by changing the relative phase of applied fields and temperature of the vapor cell. The present study may provide a useful tool for creation of structured light beams with and without orbital angular momentum.
We present a theoretical study of an optical cavity coupled with single four-level atoms in closed loop formed via applied control lasers. The transmitted probe field from the cavity is analyzed. We show that the electromagnetically induced transparency (EIT) in the cavity and the normal mode splitting will be very different with changing the closed interaction phase and the intensity of the free-space control laser. This coupled cavity–atom system presents a variational double-EIT that comes from modulating the splitting of the dark state, which means that we could realize the gradual transfer between one EIT peak and two EIT peaks by adjusting the applied control lasers, and the normal mode splitting sidebands will shift slightly by changing the free-space control laser. This means that we could control the output cavity probe field more freely and it is easer to realize optical switch controlled by more parameters. We also depict the angular dispersion of the intracavity probe field in different free-space control laser. The large phase shift ( ) of the reflected intracavity probe field will be very useful for optical temporal differentiation and quantum phase gate.