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Physical Review A

Nonperturbative vector solitary waves in four-level coherent media

Adrian Alexandrescu, José R. Salgueiro, Víctor M. Pérez‐García, Humberto Michinel

Published Jun 30, 2009• 6 citations
Publisher

Abstract

The propagation of probe and coupling optical beams through a four-level coherent media is modeled by two coupled nonlinear Schr\"odinger equations. The nonlinear susceptibilities exhibited by the four-level media are calculated in the nonperturbative regime, i.e., considering the probe and coupling fields as having comparable amplitudes. We address the existence and stability of vector solitons build by the probe and coupling beams in the coupled nonlinear Schr\"odinger equations.

DOI
10.1103/physreva.79.063843

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The propagation of probe and coupling optical beams through a four-level coherent media is modeled by two coupled nonlinear Schr"odinger equations. The nonlinear susceptibilities exhibited by the four-level media are calculated in the nonperturbative regime, i.e., considering the probe and coupling fields as having comparable amplitudes. We address the existence and stability of vector solitons build by the probe and coupling beams in the coupled nonlinear Schr"odinger equations.
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.
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.
We study the interaction of the medium composed of three-level atoms in A configuration interacting with two laser fields: weak probe field and strong control field. The probe field enters the medium under a certain angle, and it is initially in the form of the spatial soliton, while the control field is periodically modulated. The system of optical Bloch equations is analytically solved in the stationary regime by the perturbation method in order to obtain linear and third-order nonlinear susceptibility of the medium with respect to the probe field. After a straightforward algebraic procedure, using the approximation of the slow-varying field envelope, the nonlinear Schrödinger equation for the probe field is obtained. It is numerically solved by applying the spectral Fourier split-step method. It is found that, for properly chosen values of the probe and control field detunings and control Rabi frequency, the probe field behaves as a solitary wave whose direction does not depend on the incident angle. Moreover, the regime consisting of Bloch-like oscillations can be identified. The simulation is performed by choosing the corresponding levels of Mg atoms.
Multicomponent nonlinear Schrödinger equations constitute fundamental models for coherent matter waves in multicomponent Bose--Einstein condensates, spinor quantum fluids, and vector nonlinear optical systems. We develop a vector formulation of the Hirota bilinear formalism for the completely integrable Manakov system that treats the coupled nonlinear Schrödinger equations directly at the vector level rather than through the conventional component-wise decomposition. This framework naturally retains the intrinsic multicomponent representation of the model while providing compact analytical expressions for exact vector soliton solutions. Within this approach, we systematically construct bright, dark, and mixed one-, two-, and three-soliton solutions and show how the underlying vector structure provides a unified description of their nonlinear interactions. In particular, the proposed formalism makes the coupling between the different components explicit while preserving the geometric organization of the vector system throughout the bilinearization procedure. Beyond its analytical simplicity, the framework offers a natural perspective for the study of coherent multicomponent nonlinear excitations and provides a foundation for extending vector Hirota methods to other classes of exact solutions, including rogue waves, periodic waves, and rational solutions.