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Mathematical Methods in the Applied Sciences

Manipulation of Pulse and Pulse Intensity of Optical Solitons Via Super‐Gaussian Beam in Atomic Medium

Amir Ali, Shreefa O. Hilali, Abdul Majeed, Zeeshan Ali

Published Nov 26, 2025• 5 citations
Publisher

Abstract

ABSTRACT The manipulation of optical solitons and their pulse intensity in a five‐level M‐type Kerr atomic medium driven by control fields of a super‐Gaussian beam is investigated. Here, we study an important problem for the design of tunable nonlinear optical and quantum communication systems that can control soliton characteristics through spatial beam parameters. The theoretical investigation is based on the density‐matrix formalism combined with the Maxwell–Bloch equations to analyze the propagation dynamics of solitonic pulses under different beam orders, variances, detunings, and Rabi frequencies. It is shown that the soliton profile depends strongly on the deviation and order of the super‐Gaussian beam. The pulse amplitude and localization significantly improve, and the system exhibits transitions from multipeak to bright and dark periodic solitons when the power is adjusted between 1 and 10 and the variances between 0 and 1. The measured soliton intensities from to show controlled behavior throughout spatial and temporal coordinates. The results demonstrate that the dispersion and Kerr nonlinearity balance may be externally adjusted using beam shape, enabling flexible soliton generation and control. This work is novel and extends earlier work that was limited to Gaussian or lower level configurations by introducing a structured‐beam‐driven approach to control optical solitons in M‐type atomic system.

DOI
10.1002/mma.70362

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ABSTRACT The manipulation of optical solitons and their pulse intensity in a five‐level M‐type Kerr atomic medium driven by control fields of a super‐Gaussian beam is investigated. Here, we study an important problem for the design of tunable nonlinear optical and quantum communication systems that can control soliton characteristics through spatial beam parameters. The theoretical investigation is based on the density‐matrix formalism combined with the Maxwell–Bloch equations to analyze the propagation dynamics of solitonic pulses under different beam orders, variances, detunings, and Rabi frequencies. It is shown that the soliton profile depends strongly on the deviation and order of the super‐Gaussian beam. The pulse amplitude and localization significantly improve, and the system exhibits transitions from multipeak to bright and dark periodic solitons when the power is adjusted between 1 and 10 and the variances between 0 and 1. The measured soliton intensities from to show controlled behavior throughout spatial and temporal coordinates. The results demonstrate that the dispersion and Kerr nonlinearity balance may be externally adjusted using beam shape, enabling flexible soliton generation and control. This work is novel and extends earlier work that was limited to Gaussian or lower level configurations by introducing a structured‐beam‐driven approach to control optical solitons in M‐type atomic system.
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.
The area devoted to cross-Kerr nonlinearity and coherent driving fields is increasingly used to control optical solitons in atomic media. Recently, this area has been investigated by using the concepts of fractals theory. Since then, fractals theory has various applications in different disciplines of science and engineering. The said area has the capability to describe the complex geometry of dynamical problems. The propagation of light pulse and their solitonic behavior are investigated in a [Formula: see text] medium of four levels. Significant control over the absorption, dispersion, group refractive index and pulse propagation is reported with variation of coupled driving fields. The sublominal group velocity of [Formula: see text] and superlominal propagation of group velocity of [Formula: see text] is controlled. The bright and dark soliton pulse is modified with variation of driving fields in the superluminal and sublominal regions. Due subluminality of light dark soliton is reported and superluminality bright soliton is noted in the medium. The maximum of [Formula: see text] output pulse intensity is controlled. The intensity of the output pulse is an increasing and decreasing function of coupled driving fields’ Rabi frequencies. The modified solitons in this rubidium atomic medium are comparably more informative and significant to solitonic pulse intensity control in four-level cesium atomic medium under Doppler and inverse Doppler broadening effects. The modified results have useful application and soliton radar and communication technologies.
Abstract This paper describes the dynamics of solitonic pulse propagation in a closed loop quantum system comprised of five atomic energy levels. In this system four higher energy levels with four control laser fields form a closed ring-shape loop which is coherently coupled to a ground level state by a tunable probe laser field. Although the propagation of an intense probe pulse suffers losses and broadening in linear regime, there exist specific conditions where the probe pulse is found to become robust during its propagation. We attribute this regime to the formation of an optical soliton with a slow group velocity because of the balance between the dispersion and Kerr optical nonlinearity. Results obtained are based on the theoretical model using the coupled Maxwell–Bloch equations for the nonlinear propagation.
Abstract A coherent atomic medium is proposed for manipulating the absorption, dispersion, transmission and reflection of an optical soliton via two strong coherent control field’s Rabi oscillations, detunings and incident angles. Significant anomalous dispersion regions and a negative group index are investigated. A group index of n g = −1500 and a negative group velocity of v g = −2.0 × 10 5 ms −1 is calculated. This leads to superluminal propagation ( v g > c ) in the anomalous dispersion region. A significant cancellation of linear and nonlinear effects results a bright optical soliton in the coherent atomic medium. Similarly the shape-preserving phenomenon of the bright optical solitons is investigated by launching the input pulse at different incident angles. As a result, the intensity distribution of the optical solitons has no fluctuation in time t / τ 0 with any values of y / ω 0 and shows a significant bright form of solitary waves. These solitons show remarkable applications in optics, particularly in soliton radar technology for medical purposes, controlling the intensity of bright solitons for the modification of optical information processing, high-speed optical switching and quantum communication.
The generation of spatial bright solitons of reflection and transmission pulses and their intensities are investigated in a sodium atomic medium using Gaussian Milnor polynomial control fields. Significant bright and dark ring-shaped solitons are controlled by balancing nonlinearity and dispersion along two spatial coordinates. The intensity is more localized along one of the spatial coordinates due to larger nonlinearity and spread along other spatial coordinates due to smaller nonlinearity in the reflection pulse. A circular, crater-type bright soliton intensity is also maintained around the origin of the x and y coordinates, exhibiting varying intensity along the circumference. A large, bright intensity peak is observed around the origin, with the intensity minima at the center in reflection. The intensity peaks are enhanced in one of the spatial coordinates and localized in another coordinate in reflection. A large Gaussian-type bright solitonic intensity distribution is investigated at approximately y=0λ throughout the variation along the x-axis in the transmission pulse pattern. The reflection and transmission pulse intensities vary from 0% to 40% , and at least 20% of the intensity of the incident pulse is lost by attenuation. The modified results are useful in optical communications, fiber optics, optical computation, signal processing, radar technology, and artificial neural networks.
Abstract The coherent manipulation and control of bright and dark solitons through sodium atomic medium have been investigated in this manuscript. Dark soliton is reported for reflection and bright soliton is reported for transmission pulses with variation in position and driving field parameters through sodium atomic medium. Further the transmission pulse is periodic dark and bright solitonic behaviors and reflection pulse is periodic bright solitonic behavior with variation in the incident angle and Rabi frequency of the control field. Elliptical dark and bright solitons as well as breather types solitons are also investigated for reflection and transmission pulses. The dark soliton in reflection is due to slow light propagation and bright soliton is obtained due to fast light propagation of transmission through the medium. The modified results of the dark and bright solitons are useful for telecommunication and ultra-fast signal routing system.