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arXiv:2506.05093 · Physical Review A

Comparative study of focusing with scalar and vector beams in an active Raman gain system

Partha Das, Tarak Nath Dey

Published Aug 28, 2025• 1 citation
arXivHTMLPDF

Abstract

We investigate the focusing characteristics of scalar and vector beams within an atomic medium. An active-Raman-gain configuration is employed to achieve significant Kerr nonlinearity in a four-state atomic system. The probe beams can attain focusing within the medium through careful selection of input beam intensities and the spatial profile of the control field. We analytically derive the linear and third-order nonlinear susceptibilities for both scalar and vector probe beams. Our observations indicate that, in addition to the energy transfer from the control beam to the probe beam, the giant cross-Kerr nonlinearity facilitates the focusing of the scalar probe beam into a significantly smaller spot size. Conversely, the vector probe beams exhibit gain-induced narrowing. Furthermore, we evaluate the state of polarization for the vector beam at the minimum beam waist, observing a polarization rotation and a change in ellipticity during propagation. Through the mechanism of focusing, we achieve a reduced spot size for the probe beam, which may have substantial implications for resolution enhancement in microscopy applications.

DOI
10.1103/8j1w-dvc1

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We investigate the focusing characteristics of scalar and vector beams within an atomic medium. An active-Raman-gain configuration is employed to achieve significant Kerr nonlinearity in a four-state atomic system. The probe beams can attain focusing within the medium through careful selection of input beam intensities and the spatial profile of the control field. We analytically derive the linear and third-order nonlinear susceptibilities for both scalar and vector probe beams. Our observations indicate that, in addition to the energy transfer from the control beam to the probe beam, the giant cross-Kerr nonlinearity facilitates the focusing of the scalar probe beam into a significantly smaller spot size. Conversely, the vector probe beams exhibit gain-induced narrowing. Furthermore, we evaluate the state of polarization for the vector beam at the minimum beam waist, observing a polarization rotation and a change in ellipticity during propagation. Through the mechanism of focusing, we achieve a reduced spot size for the probe beam, which may have substantial implications for resolution enhancement in microscopy applications.
We investigate the phase-induced susceptibilities for both components of the probe vector beam (PVB) within an atomic system. The atoms are prepared in a nondegenerate four-level configuration. The transitions are coupled by a $\ensuremath{\pi}$ polarized control field and two orthogonally polarized components of a PVB. We show that the linear susceptibility of the medium depends on the phase shift between the control field and PVB, characterizing loss or gain in the system. Additionally, the phase shift causes polarization rotation in the vector beams (VBs) as they propagate. We further study the effect of nonlinearity on the VB propagation through the medium for a couple of Rayleigh lengths. The self-focusing and defocusing phenomena are observed for radial, azimuthal, and spiral VBs. The special chain-like self-focusing and defocusing leads to the formation of consecutive smaller spot sizes with moderate gain. Therefore, the mechanism of control of susceptibility and self-focusing may hold promise for applications such as transitioning from an absorber to an amplifier, high-resolution microscopy, and optical trap systems.
We consider an active-Raman-gain scheme for realizing giant Kerr nonlinearity and superluminal optical solitons in a four-state atomic system with a gain doublet. We show that this scheme, which is fundamentally different from those based on electromagnetically induced transparency (EIT), is capable of working at room temperature and eliminating nearly all attenuation and distortion.We demonstrate that, due to the appearance of a gain spectrum hole induced by the quantum interference effect induced by a signal field, a significant enhancement of Kerr nonlinearity of probe field can be realized effectively, which can be more than ten times larger than that arrived by the EIT-based scheme with the same energy-level configuration. Based on these important features, we obtain a giant cross-phase modulation effect and hence a stable long-distance propagation of optical solitons, which have superluminal propagating velocity and very low generating power.
We describe cross focusing in a four-level atomic medium under electromagnetically induced transparency. We show that due to the giant Kerr nonlinearity experienced by the atoms, cross focusing between weak signal and probe fields (both fields with intensities below line saturation level) is possible. By applying different intensity masks to the signal field, different lenses (cylindrical, Fresnel, Gaussian) can be induced in the atomic sample. Focusing of the probe beam is analyzed in terms of the excitation parameters (signal Rabi frequency and detuning, as well as optical depth of the atomic medium).
Abstract This research investigates the intricate interplay between Gaussian beams and atomic media, introducing a novel approach by incorporating a Kerr field and spatially dependent refractive index. The study employs a Gaussian probe field as the primary interaction medium with the atomic ensemble, while simultaneously introducing two control fields. One of these control fields acts as a Kerr field, imparting a unique modulation on the propagation characteristics of the Gaussian beam. The key parameters under scrutiny encompass the probe field detuning (∆P /γ), as well as the Rabi frequencies and detunings of the control fields (Ω1,2/γ, ∆1,2/γ). Further exploration involves transforming one of the control fields into a Gaussian beam, resulting in the creation of a spatially dependent refractive index within the atomic medium. The investigation focuses on the spatial coordinates x/ω0 and y/ω0, where ω0 represents the Gaussian beam waist. This intricate configuration provides a unique platform for studying the manipulation and control of light propagation in atomic media. The research not only sheds light on fundamental interactions in quantum optics but also opens avenues for potential applications in quantum information processing and precision measurement. The outcomes of this study contribute valuable insights into the dynamics of Gaussian beams in complex atomic environments, with potential implications for quantum technology and communication.
We investigate linear and nonlinear Faraday effects in a room-temperature, coherently driven four-level active-Raman-gain (ARG) medium. By using the multiple-scale method, we derive two nonlinear coupled envelope equations governing the dynamics of left- and right-polarized components of a linearly polarized probe field. Under the weak probe field approximation, we demonstrate a factor of four increase of the Faraday rotation angle by the linear and nonlinear response of the ARG scheme without probe field loss. We further compare this ARG system with an MMM-type five-state electromagnetically induced transparency (EIT) scheme and demonstrate the superiority of the ARG scheme over the conventional EIT scheme.
Vector beams (VBs) with potential applications are successfully utilized in many fields as light sources with a spatially-varying polarization profile in recent years. Here, we study the transmission of a VB by manipulating atomic polarization via the optical pumping effect. By using hybridly and radially polarized beams as pump and probe beams in a counter-propagating configuration, we observe a four-petal pattern intensity distribution of probe beam, and the four-petal pattern rotates with the polarization state orientation of the pump beam. The results show a polarization dependent absorption in the atomic media. We experimentally demonstrate the absorption characteristics under different polarization combinations of pump and probe beams. The Jones matrix method is used to explain this phenomenon and the simulations are consistent with the experimental observation. Our results may provide a sound foundation for applications in optical manipulation and quantum information in atomic ensembles.