Integer and fractional electromagnetically induced Talbot effects in a ladder-type coherent atomic system

Geometric pattern evolution of photonic graphene in coherent atomic medium

The photonic graphene in atoms not only has the typical photonic band structures but also exhibits controllable optical properties that are difficult to achieve in the natural graphene. Here, the evolution process of discrete diffraction patterns of a photonic graphene, which is constructed through a three-beam interference, is demonstrated experimentally in a 5S_1/2 - 5P_3/2 - 5D_5/2 ⁸⁵Rb atomic vapor. The input probe beam experiences a periodic refractive index modulation when traveling through the atomic vapor, and the evolution of output patterns with honeycomb, hybrid-hexagonal, and hexagonal geometric profiles is obtained by controlling the experimental parameters of two-photon detuning and the power of the coupling field. Moreover, the Talbot images of such three kinds of periodic structure patterns at different propagating planes are observed experimentally. This work provides an ideal platform to investigate manipulation the propagation of light in artificial photonic lattices with tunable periodically varying refractive index.

Talbot effect of an electromagnetically induced square photonic lattice assisted by a spatial light modulator

We demonstrate the Talbot effect of an electromagnetically induced square photonic lattice formed under the electromagnetically induced transparency (EIT) condition both experimentally and theoretically in a three-level ⁸⁵Rb atomic configuration. The two-dimensional lattice patterns result from the diffraction of a Gaussian probe field traveling through the vapor cell, in which the refractive index is modulated by a coupling field with a two-dimensional periodic intensity distribution generated by a spatial light modulator. The experimental observations are consistent with the theoretical predictions. This investigation not only provides a new avenue for producing desired electromagnetically induced photonic lattices beyond the commonly adopted multi-beam interfering method but also broadens studies of electromagnetically induced Talbot effect to two-dimensional space.

Optics metrology and at-wavelength wavefront characterization by a microfocus X-ray grating interferometer

A microfocus X-ray grating interferometer (MFXGI) is proposed to measure the profile of the X-ray wavefront and slope error of X-ray optical elements. This device consists of a phase grating G₁ to modulate the incoming wavefront and an absorption grating G₂ as a transmission mask for the position-sensitive detector. The wavefront distortions caused by the deformable mirror were analyzed under operating conditions for in situ investigation of X-ray optical elements. The MFXGI can obtain direct and reflected beams in one recorded image at the same time through a microfocus X-ray source. The direct beam can be used to calculate the parameter errors and spherical shape for error compensation and retrieve the aspherical shape of the height profile. This instrument is expected to be a valuable tool for further technical progress in X-ray adaptive optics and X-ray mirror manufacturing and mounting.

Tunneling-induced Talbot effect

We investigate the reforming of a plane wave into a periodic waveform in its propagation through a structural asymmetry four-level quantum dot molecule (QDM) system that is induced by an inter-dot tunneling process and present the resulting tunneling-induced Talbot effect. The tunneling process between two neighborhood dots is provided with the aid of a gate voltage. Using a periodic coupling field the response of the medium to the propagating plane probe beam becomes periodic. The needed periodic coupling field is generated with the interference of two coherent plane waves having a small angle and propagating almost parallel to the probe beam direction. In the presence of the tunneling effect of an electron between two adjacent QDs, for the probe beam propagating through the QDM system, the medium becomes transparent where the coupling fields interfere constructively. As a result, the spatial periodicity of the coupling field modulates the passing plane probe beam. We determine the minimum length of the QDM system to generate a periodic intensity profile with a visibility value equal to 1 for the probe field at the exit plane of the medium. It is also shown that by increasing the propagation length of the probe beam through the QDM medium, the profile of the maximum intensity areas becomes sharper. This feature is quantified by considering a sharpness factor for the intensity profile of the probe beam at the transverse plane. Finally, we investigate free space propagation of the induced periodic field and present the Talbot images of the tunneling-induced periodic patterns at different propagation distances for different values of the QDM medium lengths. The presented dynamically designing method of the periodic coherent intensity patterns might find applications in science and technology. For instance, in optical lithography, the need to use micro/nanofabricated physical transmission diffraction gratings, in which preparation of them is expensive and time-consuming, can be eliminated.

Measurement of the Kerr nonlinear refractive index of the Rb vapor based on an optical frequency comb using the z-scan method

We report the measurement of the Kerr nonlinear refractive index of the rubidium vapor via the high sensitivity z-scan method by using an optical frequency comb. The novel self-focusing and self-defocusing effects of the vapor are presented with red and blue detunings of the laser frequency. The optical nonlinear characteristics of the rubidium vapor are clearly interpreted under different experimental parameters. Furthermore, the Kerr nonlinear refractive index n₂ is obtained from the measured dispersion curve, and it basically occurs on the order of 10^-6 cm²/W. The evolutions of the Kerr nonlinear coefficient n₂ with the laser power and frequency detuning, respectively, are studied. To the best of our knowledge, the use of pulsed lasers to measure the Kerr nonlinear refractive index n₂ of atomic vapor has not been reported yet. The direct measurement of the Kerr nonlinear coefficient will greatly help us understand and optimize nonlinear optical processes and find its more potential applications in quantum optics.

Observation of an Electromagnetically Induced Grating in Cold 85Rb Atoms

Electromagnetically induced grating (EIG) is extensively investigated as an artificial periodic structure in recent years owed to its simple reconfiguration and flexible adjustability. We report the experimental observation of EIG in cold rubidium atoms. The coupling and probe lasers are corresponding to the 5S1/2−5P1/2 and 5S1/2−5P3/2 transitions of a V-type electromagnetically induced transparency (EIT) configuration, respectively. A clear spatial intensity distribution of the probe laser with distinguished third-order diffraction pattern is recorded to character the EIG. The influence of the pertinent experimental parameters, such as coupling laser intensity and two-photon detuning on the diffraction pattern is investigated in detail. This is the first observation in visual form of the EIG in cold rubidium atoms. These results may potentially provide a nondestructive method to image cold atoms and pave the way for investigating non-Hermitian physics and the control of light dynamics.

Optically tunable grating in a V+Ξ configuration involving a Rydberg state

A novel tunable all-optical grating is realized experimentally in a V+Ξ configuration coherent rubidium thermal vapor. This new energy level structure employs a Rydberg level as the uppermost level and contains two typical electromagnetically induced transparency energy level configurations with the same probe field. Compared with the traditional V-type three-level grating, a significant improvement of the diffraction efficiency of this novel grating was observed. Its improvement was then also demonstrated experimentally by the transition spectrum and theoretically by a comprehensive simulation. The diffraction efficiency gain introduced by the control laser field was tuned with several experimental parameters, such as the atomic density and the control field intensity. And the maximum enhancement rate of first-order diffraction efficiency is proved to be as high as 30%. Such a novel all-optical tunable grating promises to be the new driving force in the advancement of all-optical communications and information technology.

Observation of diffraction pattern in two-dimensional optically induced atomic lattice

The diffraction pattern of a two-dimensional optically induced atomic lattice is reported experimentally in a three-level atomic system. Such a two-dimensional optical lattice is established by two orthogonal standing-wave fields induced by the interference of two pairs of coupling laser beams. When the probe beam is launched into it, a spatially modulated discrete diffraction pattern can be obtained at the output plane of the vapor cell under the electromagnetically induced transparency condition. We investigate the diffraction pattern under different experimental parameters and find that it can be effectively controlled by tuning the coupling laser power and two-photon detuning. Our work may potentially pave the way for studying the control of light and other intriguing physical phenomena based on such a periodically modulated atomic lattice.