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Scientific Reports

Optically induced diffraction gratings based on periodic modulation of linear and nonlinear effects for atom-light coupling quantum systems near plasmonic nanostructures

Azar Vafafard, Mostafa Sahrai, Vahid Siahpoush, Hamid Reza Hamedi, Seyyed Hossein Asadpour

Published Oct 7, 2020• 21 citations
Publisher

Abstract

We investigate the quantum linear and nonlinear effects in a novel five-level quantum system placed near a plasmonic nanostructure. Such a quantum scheme contains a double-V-type subsystem interacting with a weak probe field. The double-V-subsystem is then coupled to an excited state by a strong coupling field, which can be a position-dependent standing-wave field. We start by analyzing the first-order linear as well as the third and fifth order nonlinear terms of the probe susceptibility by systematically solving the equations for the matter-fields. When the quantum system is near the plasmonic nanostructure, the coherent control of linear and nonlinear susceptibilities becomes inevitable, leading to vanishing absorption effects and enhancing the nonlinearities. We also show that when the coupling light involves a standing-wave pattern, the periodic modulation of linear and nonlinear spectra results in an efficient scheme for the electromagnetically induced grating (EIG). In particular, the diffraction efficiency is influenced by changing the distance between the quantum system and plasmonic nanostructure. The proposed scheme may find potential applications in future nanoscale photonic devices.

DOI
10.1038/s41598-020-73587-y

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We investigate the quantum linear and nonlinear effects in a novel five-level quantum system placed near a plasmonic nanostructure. Such a quantum scheme contains a double-V-type subsystem interacting with a weak probe field. The double-V-subsystem is then coupled to an excited state by a strong coupling field, which can be a position-dependent standing-wave field. We start by analyzing the first-order linear as well as the third and fifth order nonlinear terms of the probe susceptibility by systematically solving the equations for the matter-fields. When the quantum system is near the plasmonic nanostructure, the coherent control of linear and nonlinear susceptibilities becomes inevitable, leading to vanishing absorption effects and enhancing the nonlinearities. We also show that when the coupling light involves a standing-wave pattern, the periodic modulation of linear and nonlinear spectra results in an efficient scheme for the electromagnetically induced grating (EIG). In particular, the diffraction efficiency is influenced by changing the distance between the quantum system and plasmonic nanostructure. The proposed scheme may find potential applications in future nanoscale photonic devices.
Abstract We theoretically study a two-dimensional electromagnetically induced phase grating in a four-level quantum system located near plasmonic metamaterials consisting of a periodic two-dimensional array of metal-coated dielectric nanospheres. The four-level quantum system interacts with a weak-probe laser field and a strong coherent coupling field with a standing-wave pattern. In the presence of plasmonic metamaterials the quantum system becomes sensitive to the relative phase between applied light. Therefore, the linear absorption and Kerr nonlinearity of the medium become phase dependent. Here, due to the standing-wave pattern of coupling light, an absorptive grating or phase grating can be formed in the quantum system. In our proposed model, we show that the diffraction efficiencies of the grating are related to the relative phase between applied fields, when the quantum system is located at different distances from plasmonic metamaterials.
We investigate the nonlinear optical response of a four-level double-V-type quantum system interacting with a pair of weak probe fields while located near a two-dimensional array of metal-coated dielectric nanospheres. Such a quantum system contains a V-type subsystem interacting with surface plasmons, and another V-type subsystem interacting with the free-space vacuum. A distinctive feature of the proposed setup is its sensitivity to the relative phase of the applied fields when placed near the plasmonic nanostructure. We demonstrate that due to the presence of the plasmonic nanostructure, the third-order (Kerr-type) susceptibility for one of the laser fields can be significantly modified while another probe field is acting. Moreover, the Kerr nonlinearity of the system can be controlled and even enhanced by varying the distance of the quantum system from the plasmonic nanostructure.We also show that the Kerr nonlinearity of such a system can be controlled by adjusting the relative phase of the applied fields. The results obtained may find potential applications in on-chip nanoscale photonic devices. We also study the light-matter interaction in the case where one probe field carries an optical vortex, and another probe field has no vortex. We demonstrate that due to the phase sensitivity of the closed-loop double V-type quantum system, the linear and nonlinear susceptibility of the nonvortex probe beam depends on the azimuthal angle and orbital angular momentum (OAM) of the vortex probe beam. This feature is missing in open four-level double V-type quantum system interacting with free-space vacuum, as no quantum interference occurs in this case. We use the azimuthal dependence of optical susceptibility of the quantum system to determine the regions of spatially-structured transmittance.
We study the nonlinear optical properties in an asymmetric double AlGaAs/GaAs quantum well nanostructure by using an external control field and resonant tunneling effects. It is found that the resonant tunneling can modulate the third-order and fifth-order of susceptibilities via detuning frequency of coupling light. In presence of the resonant tunneling and when the coupling light is in resonance with the corresponding transition, the real parts of third-order and fifth-order susceptibilities are enhanced which are accompanied by nonlinear absorption. However, in off-resonance of coupling light, real parts of third-order and fifth-order susceptibilities enhance while the nonlinear absorption vanishes. We investigate also the two-dimensional electromagnetically induced grating (2D-EIG) of the weak probe light by modulating the third-order and fifth-order susceptibilities. In resonance of coupling light, both amplitude and phase grating are formed in the medium due to enhancement of third-order and fifth-order probe absorption and dispersion. When the coupling light is out of resonance, most of probe energy is transferred from zero-order to higher-order directions due to resonant tunneling effect. The efficiency of phase grating for third-order of susceptibility is higher than phase grating for fifth-order susceptibility. Our proposed model may be useful for optical switching and optical sensors based on semiconductor nanostructures.
A nondiffracting propagation of an optical beam through a four-level double-V-type quantum system near a plasmonic nanostructure is investigated. We study the linear absorption and dispersion properties of the quantum system as it interacts with two laser fields. We discuss the effect of the control beam with a Laguerre-Gaussian (LG) profile on the focusing of the probe beam in the presence of a plasmonic nanostructure. An appropriately selected control beam excites one transition of the atomic system and generates a spatially varying refraction index modulation for a weak probe beam that couples to the other transition. We demonstrate that placing a plasmonic nanostructure at a nanometer distance from the atomic system and using a control field with the spatial structure leads to the diffraction-less propagation of the probe beam through the atomic system. Also, it is shown that the optical properties and probe beam focusing can be controlled by adjusting the distance of the plasmonic nanostructure from the atomic system. The proposed all-optical waveguide with high contrast and transmission can be used to implement applications such as image transfer through the medium and image processing.
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.
By investigating the third-order nonlinearity of a four-level ladder-type atomic system, it is found that, with spontaneously generated coherence (SGC) present, the nonlinear absorption or refraction can be significantly enhanced with vanishing linear absorption. We attribute the enhancement of nonlinearity mainly to quantum interference in the two decay pathways from the two upper closely lying levels. With a standing-wave trigger field, absorption or phase grating, which effectively diffracts a weak probe into high-order direction, can be induced by the SGC-enhanced absorptive or refractive nonlinear modulation. In contrast to the schemes for enhancing nonlinearity, no additional coupling field is required. Moreover, the present gratings result from the nonlinear modulation, which differs from the recent investigations based on linear modulation.