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arXiv:1905.02347 · Journal of the Optical Society of America B

Four-wave mixing-based orbital angular momentum translation

Nawaz Sarif Mallick, Tarak Nath Dey

Published May 4, 2020• 24 citations
arXivHTMLPDF

Abstract

We theoretically study the generation of orbital angular momentum (OAM) based on the four-wave mixing process in a diamond-type homogeneously broadened 85 R b atomic system. We use density matrix formalism at a weak field limit to explain the origin of vortex translation between different optical fields and a generated signal. We show how the singularities, which are omnipresent in the phases of the input optical vortex beams, can be profoundly mapped to atomic coherence in the transverse plane, which holds the origin of OAM translation. This translation process works well even for a moderately intense probe and control field, which enhances medium nonlinearity. The generation and manipulation of OAM of the light beam in a nonlinear medium may have important applications in optical tweezers and quantum information processing systems.

DOI
10.1364/josab.390280

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We theoretically study the generation of orbital angular momentum (OAM) based on the four-wave mixing process in a diamond-type homogeneously broadened 85 R b atomic system. We use density matrix formalism at a weak field limit to explain the origin of vortex translation between different optical fields and a generated signal. We show how the singularities, which are omnipresent in the phases of the input optical vortex beams, can be profoundly mapped to atomic coherence in the transverse plane, which holds the origin of OAM translation. This translation process works well even for a moderately intense probe and control field, which enhances medium nonlinearity. The generation and manipulation of OAM of the light beam in a nonlinear medium may have important applications in optical tweezers and quantum information processing systems.
Abstract This study presents a theoretical exploration of generating 420 nm Bessel-Gaussian beam with orbital angular momentum (OAM) via nonlinear processes in a four-level 85 Rb atomic system. A non-degenerate four-wave mixing (FWM) configuration, driven by two strong control fields at wavelengths 780 nm and 776 nm along with a weak field, enables the generation of the desired blue Bessel-Gaussian beam. Our analysis examines how the Bessel-Gaussian properties of the initial beams including intensity, phase profiles, and topological charges are transferred into the generated 420 nm beam at specific transverse positions. Using Maxwell’s wave equations, we explicitly explore how these spatial profiles evolve with varying topological charges over different propagation distances, providing deeper insights into Bessel-Gaussian information transfer mechanisms. The generation and characterization of 420 nm structured beam highlight promising applications, particularly in the precise manipulation of microparticles, due to their enhanced resolution and superior trapping abilities. This comprehensive theoretical framework establishes a foundation for future experimental and applied research in optical manipulation and high-resolution imaging.
Vortex light, a unique optical field that carries orbital angular momentum (OAM), has attracted considerable attention in recent years. In this paper, we present a detailed theoretical analysis of OAM transfer from the input field to the generated signal field in a four-level double-Lambda system via the four-wave mixing (FWM) process, showing that their OAMs follow a specific algebraic relationship. We identify the optimal conditions for efficient vortex light transmission, analyze the influence of detuning on transmission efficiency and phase distortion, and specifically examine the scenario where the control field carries OAM the latter being essential for a complete characterization of OAM conservation in the FWM process, while all three aspects have been largely overlooked in the existing literature. Furthermore, we investigated the tunability of the group velocity between the probe and signal fields by modulating the Rabi frequencies of the two control fields and the relative phase between the probe and signal fields during the FWM process. We demonstrate that the conversion between matched vortex slow and fast light can be realized an effect that has not been widely explored in dual-Lambda-type systems. These results may hold promise for applications in quantum information storage and processing, quantum computing, and ultrasensitive detection.
We explore the generation of orbital angular momentum (OAM) carrying mid-infrared Bessel-Gaussian beams through nonlinear interactions within a non-uniformly broadened 85 Rb atomic ensemble. Utilizing an efficient four-wave mixing (FWM) scheme driven by two strong control fields and a weak probe field, we achieve coherent emission at a wavelength of 5.23 µm. By employing the density matrix approach, we obtain an analytical expression for the nonlinear atomic coherence involved in the four-wave mixing process, elucidating how the Bessel-Gaussian profile of the probe field is transferred into the mid-infrared signal. Numerical simulations of Maxwell’s wave equation ensure the generation of phase-matched, non-diffracting Bessel-Gaussian beams, which can be precisely controlled by manipulating the spatial susceptibility of the atomic medium. Furthermore, this study demonstrates the potential of higher-order Bessel-Gaussian beams with OAM to significantly advance applications in high-speed communication, biomedical imaging, and optical manipulation, owing to their robust beam integrity and enhanced data transmission capabilities in the mid-infrared spectrum.
We investigate the generation of mid-infrared (mid-IR) vortex beams carrying orbital angular momentum (OAM) through nonlinear processes in an inhomogeneously broadened 85 Rb atomic ensemble. By employing a four-level atomic system featuring two strong control fields and a weak probe field, we generate a non-degenerate four-wave mixing signal at a wavelength of 5.23 µm. Applying the density-matrix formalism, we derive an analytical expression for the nonlinear atomic coherence which facilitates the transfer of vortex characteristics such as topological charge and intensity and phase profiles from the probe field to the mid-IR signal. Numerical solutions of Maxwell’s wave equation confirm the generation of mid-IR vortex beams with adjustable topological charges and beam widths at different spatial positions. This technique offers significant potential for applications in mid-IR communication, providing additional bandwidth and improved data transmission rates, as well as in fields such as microfluidics, biophysics, and nanotechnology, where OAM-carrying beams can manipulate microparticles with precision.
Abstract In this paper, we suggest a theoretical model for the exchange of the orbital angular momentum (OAM) state of laser fields in a real cold atomic system for realization in an experimental setup. By using four-wave mixing (FWM) processes, we study the spatial dependence of the new weak generated signal light under electromagnetically induced transparency conditions when one of the laser lights becomes an optical vortex. We discuss the spatial dependence of FWM processes via experimental parameters for different conditions of the OAM of vortex light. We have found that the intensity and phase distributions of the new generated light depends strongly on the OAM number of the optical vortex light. Moreover, we investigate the absorption spectrum of the new generated signal light for different OAM of the optical vortex light. Our obtained results may have potential applications in quantum information science.
We investigate the spatial and quantum intensity correlations between the probe and Stokes optical fields produced via four-wave mixing in a double-Λ configuration, when both incoming probe and control fields carry non-zero optical orbital angular momentum (OAM). We observed that the topological charge of the generated Stokes field obeyed the OAM conservation law. However, the maximum values and optimal conditions for the intensity squeezing between the probe and Stokes fields were largely independent of the angular momenta of the beams, even when these two fields had significantly different OAM charges. We also investigated the case of a composite-vortex pump field, containing two closely positioned optical vortices, and showed that the generated Stokes field carried the OAM corresponding to the total topological charge of the pump field, further expanding the range of possible OAM manipulation techniques.