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Communications in Theoretical Physics

Special Property of Group Velocity for Temporal Dark Soliton*

Yingjie Du, Jin-Ying Yu, Jintao Bai

Published Apr 1, 2017• 1 citation
Publisher

Abstract

Abstract We investigate the speed of temporal dark soliton based on an optical coherent medium. It is demonstrated that the temporal dark soliton is described by a nonlinear Schrodinger equation whose coefficients are decided by the coherent medium. It is found that the speed of temporal dark soliton not only relies on the linear responses including GV parameter, group velocity dispersion parameter as well as the amplitude of dark soliton, but also relies on the nonlinear response like self-phase modulation parameter. Additionally, the dark soliton in anomalous-dispersion regime propagates slower than bright soliton, while in normal-dispersion regime it inversely propagates faster than bright soliton. The complicated property of the speed for dark soliton is quite different from the bright soliton whose speed is commonly only related to the group velocity parameter. We attribute this feature to the modulation instability of the nonlinear system.

DOI
10.1088/0253-6102/67/4/425

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Abstract We investigate the speed of temporal dark soliton based on an optical coherent medium. It is demonstrated that the temporal dark soliton is described by a nonlinear Schrodinger equation whose coefficients are decided by the coherent medium. It is found that the speed of temporal dark soliton not only relies on the linear responses including GV parameter, group velocity dispersion parameter as well as the amplitude of dark soliton, but also relies on the nonlinear response like self-phase modulation parameter. Additionally, the dark soliton in anomalous-dispersion regime propagates slower than bright soliton, while in normal-dispersion regime it inversely propagates faster than bright soliton. The complicated property of the speed for dark soliton is quite different from the bright soliton whose speed is commonly only related to the group velocity parameter. We attribute this feature to the modulation instability of the nonlinear system.
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 formation environment and the evolution of dark soliton with environment parameters are investigated by using the electromagnetically induced transparency effect produced high dispersion and nonlinearity. To improve the stability and operability, a dual-well semiconductor is used. Combining the quantum theory and the classical field theory, we derive the nonlinear Schrodinger equation to describe the formations and evolutions of wave and soliton. It is demonstrated that the dark soliton can form and propagate in the medium when the medium is anomalously dispersive and cross phase modulation is negative simultaneously, and that in the evolution of the soliton, the width, gray scale and phase are related to each other, the smaller the pulse duration, the bigger the gray scale is and the faster the growth is. In addition, the modulation instability of the nonlinear system is analyzed, and the gain spectrum of the nonlinear system is also discussed.
We investigate a light-pulse propagation with negative group velocity in a nonlinear coherent medium. We show that the necessary conditions for nonlinear superluminal effects to be observable are realized in a three-level $\ensuremath{\Lambda}$ system interacting with a linearly polarized laser field in the presence of a static magnetic field. The initially prepared Zeeman coherence cancels the resonant absorption of the medium almost completely, but preserves its dispersion anomalous and very high. In this medium the light pulse propagates superluminally in the sense that the peak of the transmitted pulse exits the medium before the peak of the incident pulse enters. At the same time the pulse group velocity is intensity dependent, which leads to the self-steepening of the pulse trailing edge due to the fact that the more intense parts of the pulse travel slower. This is in contrast with the shock wave generation in a nonlinear medium with normal dispersion. The predicted effect can be easily observed in the well-known schemes employed in the studies of nonlinear magneto-optical rotation. The upper bound of sample length is found from the criterion that the pulse self-steepening and group-advance time are observable without pulse distortion caused by the group-velocity dispersion.
Summary form only given. The propagation of light in a dispersive medium is characterized by the group velocity /spl nu//sub g/=c(n+/spl nu//sup dn//d/spl nu/)/sup .1/ where n is the refractive index and /spl nu/ the optical frequency. Depending on the sign and magnitude of /sup dn//d/spl nu/ in the medium, the group velocity can be positive, infinite or negative. The group velocity corresponds to the speed of the propagation of the maximum of an optical pulse travelling into the medium. This remains true whether the dispersion in the medium is normal (/sup dn//d/spl nu/>0) or anomalous (/sup dn//d/spl nu/<0). It has been demonstrated that coherently prepared atomic systems can exhibit steep dispersion leading to small absolute values of the group velocity (slow light). In recent work, we have demonstrated that narrow resonances arising from the coherent interaction of two optical fields with a closed atomic transition between two degenerate levels may correspond to a steep anomalous dispersion and thus to slow and negative group velocity. We report on the experimental study of the propagation of an amplitude modulated wave in a medium presenting negative group velocity.
We present the results of experimental studies of the propagation of light pulses through a specially prepared atomic medium with steep anomalous dispersion and enhanced Kerr nonlinearity. The observed negative group velocity is consistent with the principle of causality. The long-lived bright Zeeman coherence that is responsible for the steep anomalous dispersion gives rise also to a giant nonlinearity of the atomic susceptibility, which contributes substantially to the pulse propagation process. The enhanced atomic Kerr nonlinearity in the bright coherent state has been estimated.
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.