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Journal of Physics B Atomic Molecular and Optical Physics

Electromagnetically induced angular Talbot effect

Tianhui Qiu, Guojian Yang

Published Oct 28, 2015• 7 citations
Publisher

Abstract

Abstract The discrete angular spectrum (angular Talbot effect) of a periodic grating illuminated by a suitable spherical wave front has been observed recently (Azaña and Chatellus 2104 Phys. Rev. Lett. 112 213902 ). In this paper we study the possibility of such a phenomenon being realized with a medium that has no macroperiodic structure itself. Tunable electromagnetically induced grating (EIG) could be such a kind of medium. We obtain an EIG based on the periodically modulated strong susceptibility due to the third-order nonlinear effect generated in a double Λ-type four-level atomic system, and show the angular Talbot effect of an amplitude EIG, as well as a hybrid EIG, as the condition of the discrete phase-modulation shift of the illumination light front is satisfied. EIG parameters are tunable and the EIG-based angular Talbot effect may have the same potential applications as its periodic grating counterpart has.

DOI
10.1088/0953-4075/48/24/245502

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Communications in Theoretical Physics•Jun 28, 2023•3 citations
Abstract The discrete angular spectrum (angular Talbot effect) of a periodic grating illuminated by a suitable spherical wave front has been observed recently (Azaña and Chatellus 2104 Phys. Rev. Lett. 112 213902 ). In this paper we study the possibility of such a phenomenon being realized with a medium that has no macroperiodic structure itself. Tunable electromagnetically induced grating (EIG) could be such a kind of medium. We obtain an EIG based on the periodically modulated strong susceptibility due to the third-order nonlinear effect generated in a double Λ-type four-level atomic system, and show the angular Talbot effect of an amplitude EIG, as well as a hybrid EIG, as the condition of the discrete phase-modulation shift of the illumination light front is satisfied. EIG parameters are tunable and the EIG-based angular Talbot effect may have the same potential applications as its periodic grating counterpart has.
A strong coupling standing wave, interacting with three-level \ensuremath{\Lambda}-type (or ladder-type) atoms, can diffract a weak probe field (propagating along a direction normal to the standing wave) into high-order diffractions, a phenomenon which we name electromagnetically induced grating (EIG). We develop in this work a theory for studying EIG in a homogeneously broadened medium consisting of three-level \ensuremath{\Lambda}-type atoms. We show that by taking advantage of the absorption and dispersion properties of electromagnetically induced transparency one can create an atomic grating that can effectively diffract light into the first-order direction.
The nonlinear Talbot effect means formation of self-imaging of the periodic structure by utilizing the harmonic wave instead of the fundamental one. Electromagnetically induced optical lattices established in atomic ensembles by optical induction technique have received great attention in recent years. Here, we experimentally demonstrate the nonlinear four wave mixing (FWM) Talbot effect in the Rubidium medium, where the third-order susceptibility χ(3) has periodic distribution due to the modulation from the incident pump light. Two kinds of periodic structure, the square lattice and hexagonal lattice, are employed to investigate the nonlinear FWM Talbot effect. The integer and fractional Talbot images produced by the FWM field are all obtained. The experimental results are qualitatively consistent with theoretical simulations. Different from the self-imaging of the refractive index in the linear optics, the FWM Talbot effect is the self-imaging of the periodic χ(3). The results may offer a high-resolution lensless way for imaging various optical periodic structures.
Understanding and manipulating the non-Hermitian optical property based on coherent atomic gases is of great importance and has attracted much theoretical and experimental attentions. Advancing this study to the nonlinear optics regime is highly desirable due to its importance in fundamental physics and potential applications. In this work, we propose to realize a tunable electromagnetically induced grating (EIG) with parity-time (PT\mathcal{PT}PT) symmetry in a cold gas of Rydberg atoms, where interatomic interactions between Rydberg states are mapped to strong and long-range optical interactions, and investigate nonlinear light diffractions in this system. We show that for far-field diffraction, laser beams incident upon the PT\mathcal{PT}PT-symmetric EIG display distinctive asymmetric diffraction fringes, which can be actively manipulated through tuning the gain-absorption coefficient of the EIG, the incident intensity of the laser beam, and the nonlocality provided by Rydberg atoms. For near-field diffraction, the nonlinear Talbot diffraction carpets emerge and can be modulated by PT\mathcal{PT}PT symmetry in the presence of strong nonlocal interactions, allowing the realization of controllable optical self-imaging. The results are not only imperative for the study of non-Hermitian nonlinear optics but also useful for characterizing the interatomic interaction in Rydberg gases and for designing new optical devices useful in optical information processing and transmission.
In addition to the suppressed absorption in the atomic resonance region, an electromagnetically induced transparency (EIT) medium also possess giant nonlinear dispersion which significantly affects the optical properties of the medium. In this work, we study the influence of third-order nonlinear susceptibility on electromagnetically induced grating (EIG) in a three-level V-type atomic medium. By applying stationary perturbation theory to the density matrix equations describing the time evolution of the quantum states of the system, we have found density matrix solutions to the third-order perturbation corresponding to the third-order susceptibility, and found the transmission function for the probe light. Using the Fourier transform of the transmission function, we can obtain the intensity distribution function of the EIG diffraction spectrum as a function of laser parameters and the atomic medium. To see the influence of third-order susceptibility on EIG diffraction spectrum, we have simulated EIG spectra in two cases with and without third-order susceptibility. We found that the first-order diffraction efficiency was significantly enhanced when third-order susceptibility was introduced.
The electromagnetically induced Talbot effect (EITE) resulting from the repeated self-reconstruction of a spatially intensity-modulated probe field is experimentally demonstrated in a three-level atomic configuration. The probe beam is launched into an optically induced lattice (established by the interference of two coupling fields) inside a rubidium vapor cell and is diffracted by the electromagnetically induced grating that was formed. The diffraction pattern repeats itself at the planes of integer multiple Talbot lengths. In addition, a fractional EITE is also investigated. The experimental observations agree well with the theoretical predictions. This investigation may potentially pave the way for studying the nonlinear and quantum dynamical features that have been predicted for established periodic optical systems.
Abstract We propose a method to implement electromagnetically induced grating in a phaseonium medium that has been coherently generated via atomic mechanisms. Phaseonium atoms have a Λ-type structure and three distinct energy levels; such atoms are originally generated in a coherent superposition of two lower levels. The phaseonium system is comprised of three-level atoms with a Λ-type configuration, which are initially prepared in a coherent superposition of two lower levels. To accomplish this spatial modulation based on the susceptibility of phaseonium medium, a standing-wave field is used. By looking at how an optical field diffracts at different relative phases, we find that the zeroth and first order diffraction intensities increase as the relative phase changes. We also investigate the impact of the Rabi frequency of the field on diffraction intensity and notice that an increasing strength of the Rabi frequency leads to amplification in the intensity of both central zeroth order and first-order diffraction. Furthermore, it has been observed that a significant rise in diffraction intensity occurs at longer interaction lengths between external fields and the atomic medium.