Abstract
We propose a theoretical scheme for creating a two-dimensional Electromagnetically Induced Grating in a three-level Lambda -type atomic system interacting with a weak probe field and two simultaneous position-dependent coupling fields—a two dimensional standing wave and an optical vortex beam. Upon derivation of the Maxwell wave equation, describing the dynamic response of the probe light in the atomic medium, we perform numerical calculations of the amplitude, phase modulations and Fraunhofer diffraction pattern of the probe field under different system parameters. We show that due to the azimuthal modulation of the Laguerre–Gaussian field, a two-dimensional asymmetric grating is observed, giving an increase of the zeroth and high orders of diffraction, thus transferring the probe energy to the high orders of direction. The asymmetry is especially seen in the case of combining a resonant probe with an off-resonant standing wave coupling and optical vortex fields. Unlike in previously reported asymmetric diffraction gratings for PT symmetric structures, the parity time symmetric structure is not necessary for the asymmetric diffraction grating presented here. The asymmetry is due to the constructive and destructive interference between the amplitude and phase modulations of the grating system, resulting in complete blocking of the diffracted photons at negative or positive angles, due to the coupling of the vortex beam. A detailed analysis of the probe field energy transfer to different orders of diffraction in the case of off-resonant standing wave coupling field proves the possibility of direct control over the performance of the grating.
Highlights
We propose a theoretical scheme for creating a two-dimensional Electromagnetically Induced Grating in a three-level -type atomic system interacting with a weak probe field and two simultaneous position-dependent coupling fields—a two dimensional standing wave and an optical vortex beam
In the present work we study the effects of the simultaneous interaction of atomic three-level Electromagnetically Induced Grating (EIG) scheme with a standing wave coupling field and a laser beam carrying Orbital Angular Momentum (OAM)
In this work we have studied analytically and numerically the effects of the simultaneous coupling of an atomic three-level -type scheme by a standing wave field along the x, y-direction and a laser beam carrying OAM in a EIG configuration
Summary
We consider a three-level atomic system arranged in a − configuration of atomic levels involving two ground states |1 and |3 , and an excited state |2 , as shown in Fig. 1 A weak probe field in the form of a travelling wave induces the atomic transition |1 → |2 , while the transition |2 → |3 is driven simultaneously by a coupling field in the form of a standing wave (SW) along x, y- direction and a vortex Laguerre–Gaussian (LG) field. (9) and (10) and the diffraction pattern of the probe light can be controlled by changing the OAM number of the vortex light, leading to the possibility for adjusting the EIG pattern on demand It is worth noting, that the simultaneous coupling by the s and LG fields is exactly the one giving the opportunity for such a control. If the levels |2 and |3 were interacting with the standing field only, while another atomic transition was coupled by the vortex field, the parameters | c|2 and | LG|2 would appear in the equations separately and the results would be independent of the azimuthal angle of the vortex field. Θx and θy stand for the diffraction angles with respect to the z direction, Rx = x/ , Ry = y/ , and M(N) is the number of spatial periods of the grating irradiated by the probe beam. Eqs. (11)–(14) represent the typical grating equations found in most EIG-related works, we include them here for the sake of the completeness
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