Microwave solitons in molecular magnets via electromagnetically induced transparency

Using the Schrödinger-Maxwell equations, we investigate the formation of microwave solitons in a crystal of molecular magnets. This system is subjected to one dc magnetic field and two (probe and coupling) ac resonant magnetic fields. The results show that the probe magnetic field can freely propagate in a crystal of molecular magnets due to quantum interference. Furthermore, within certain parameter range, both bright and dark microwave solitons can occur in such a highly resonant medium. We also obtain the analytical expressions for the phase shift and absorption coefficient of the probe magnetic field.     

Observation of self-generation of dark envelope solitons for spin waves in ferromagnetic films

We have performed experiments in which self-generation of dark envelope solitons for spin waves at microwave frequencies were obtained. Stable self-generation of dark solitons was observed in a ring consisting of tangentially magnetized yttrium iron garnet film and a microwave signal amplifier. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 3, 229–233 (10 August 1998)     

Dynamics and formation of vortices collapsed from ring dark solitons in a two-dimensional spin–orbit coupled Bose–Einstein condensate

We consider the dynamics and formation of vortices from ring dark solitons in a two-dimensional Bose–Einstein condensate with the Rashba spin–orbit coupling based on the time-dependent coupled Gross–Pitaevskii equation. Compared with previous results, the system exhibits complex dynamical behaviors in the presence of the spin–orbit coupling. With the modulation of the spin–orbit coupling, not only the lifetime of ring dark solitons is greatly prolonged, but also their attenuation kinetics is significantly affected. For two shallow ring dark solitons with the equal strength of the spin–orbit coupling, the radius of ring dark solitons increases to a maximum value over time and then shrinks into a minimum value. Due to the effect of the snake instability, ring dark solitons split into a series of ring-like clusters of vortex pairs, which perform complex oscillations. This indicates that the system is strongly dependent on the presence of the spin–orbit coupling. Furthermore, the effect of different initial modulation depths on the dynamics of ring dark solitons is investigated.     

Exact solutions for bright and dark solitons in spatially inhomogeneous nonlinearity

We present exact analytical results for bright and dark solitons in a type of one-dimensional spatially inhomogeneous nonlinearity. We show that the competition between a homogeneous self-defocusing (SDF) nonlinearity and a localized self-focusing (SF) nonlinearity supports stable fundamental bright solitons. For a specific choice of the nonlinear parameters, exact analytical solutions for fundamental bright solitons have been obtained. By applying both variational approximation and Vakhitov-Kolokolov stability criterion, it is found that exact fundamental bright solitons are stable. Our analytical results are also confirmed numerically. Additionally, we show that a homogeneous SF nonlinearity modulated by a localized SF nonlinearity allows the existence of exact dark solitons, for certain special cases of nonlinear parameters. By making use of linear stability analysis and direct numerical simulation, it is found that these exact dark solitons are linearly unstable.     

Dynamics of ring dark solitons in Bose-Einstein condensates and nonlinear optics

Quasiparticle approach to dynamics of dark solitons is applied to the case of ring solitons. It is shown that the energy conservation law provides the effective equations of motion of ring dark solitons for general form of the nonlinear term in the generalized nonlinear Schrödinger or Gross-Pitaevskii equation. Analytical theory is illustrated by examples of dynamics of ring solitons in light beams propagating through a photorefractive medium and in non-uniform condensates confined in axially symmetric traps. Analytical results agree very well with the results of our numerical simulations.     

Optical spin generated by a soliton pulse in an add–drop filter for optoelectronic and spintronic use

A new concept of an optical spin generation using bright and dark soliton conversion behaviors within a modified optical add–drop filter known as PANDA ring resonator is proposed. The orthogonal solitons can be formed within the system and detected simultaneously at the output ports. Under the resonant condition, the dark and bright soliton pair corresponding to the left-hand and right-hand rotating solitons (photons) can be generated. When a soliton is absorbed by an object, an angular momentum of either +? or ?? is imparted to the object, in which two possible spin states known as optoelectronic(soliton) spins are exhibited. Furthermore, an array of soliton spins, i.e. particles can be generated and detected by the proposed system, which can be used to form large scale spin generation.     

非局域表面暗孤子及其稳定性分析

非局域体介质中的暗孤子及表面亮孤子由于在光通信领域的潜在应用而受到极大关注,然而到目前为止却没有对非局域表面暗孤子的研究.在线性介质和非局域非线性介质的分界面上,数值模拟得到了1+1维非局域基态和二阶表面暗孤子,研究了它们的波形与传播常数和介质非局域程度的关系,基于它们的稳定性分析进行了理论推导和数值模拟.稳定性分析结果表明:1+1维非局域基态表面暗孤子在其存在区域总是稳定的,而二阶表面暗孤子是区域不稳定的,其不稳定区域的宽度与传播常数以及介质的非局域程度有关系,且受传播常数的影响更大.加噪声的初始输入传输图验证了稳定性分析结果的正确性.     

Modulational instability of dark solitons in three wave resonant interaction

We study the propagation of velocity-locked dark triplet solitons in the three wave resonant interaction model. The modulational instability of the plane wave background where the solitons sit prevents the long range propagation. However even a small second order dispersion proves to greatly reduce, or suppress, the modulational instability gain, allowing for effective stable soliton propagation.     

Gap and dark solitons in discrete photorefractive media with?intensity-resonant nonlinearity

Light propagation in one-dimensional nonlinear waveguide arrays with self-defocusing intensity-resonant nonlinearity is investigated theoretically. We study thoroughly conditions for existence and stability of both gap and discrete dark solitons. According to the linear stability analysis both fundamental types (on-site and intersite) of gap solitons may be stable. Discrete dark solitons are unstable except in the low-power regime and, depending on system parameters, evolve into either gray solitons, breathers, or background radiation. Mobility of these solitons is analyzed by the free energy concept: gap solitons are immobile but dark solitons can be easily set in motion.     

Odd and even two-dimensional dark spatial solitons

The formation of two-Dimensional (2D) odd dark spatial solutions is analyzed numerically at an initial helical dark-beam phase distribution. Experimental results are presented for the first time confirming the existence of two-dimensional optical even dark solitons (ring dark solitons). Several aspects of the evolution of input 1D and 2D odd/even dark beams are compared qualitatively.     

Single and combined optical solitons,and conservation laws in (2+1)-dimensions with Kundu–Mukherjee–Naskar equation

In this work, the celebrated (2+1)-dimensional Kundu–Mukherjee–Naskar equation (KMNE) proposed to govern the soliton dynamics in (2+1)-dimensions along excited resonant wave guides that is doped with Erbium atoms is studied with the aid of ansatz approach and sine-Gordon expansion method (SGEM). The integration algorithms revealed both single and combined optical solitons of the model. These solitons are reported as bright, dark, combined dark-bright and singular solitons. The combined dark-bright and combined singular soliton solutions of the KMNE are to the best of our knowledge reported for the first time in this paper. These solutions supplements the existing ones in the literature. Additionally, we studied the conservation laws (Cls) of the equation by applying the multipliers approach and report the non-trivial fluxes associated with the equation. The physical structure of the obtained solutions are shown by graphic illustration in order to give a better understanding on the dynamics of optical solitons.     

非局域暗孤子及其稳定性分析

由于其在通信领域潜在的应用前景, 非局域空间孤子一直是研究热点. 但空间非局域暗孤子由于其边界的特殊性, 对其特别是稳定性方面研究甚少. 提出了非局域暗孤子稳定性分析理论, 并对热非线性体介质中1+1维基态和二阶暗孤子的稳定性进行了数值分析和研究, 得到了稳定性图. 从稳定性分析图可知: 在热非线性体介质中, 1+1维基态暗孤子在其存在区域总是稳定的, 而1+1维二阶暗孤子是震荡不稳定的, 其不稳定区域的宽度与传播常数以及介质的非局域程度有关. 为了验证非局域暗孤子稳定性分析理论的正确性, 对加噪声初始输入的传输进行数值模拟得到了传输图, 传输图表明稳定性分析理论的正确性. 关键词： 非局域 稳定性 暗孤子     

Dynamics of Bright/Dark Solitons in Bose--Einstein Condensates with Time-Dependent Scattering Length and External Potential

We present an analytical study on the dynamics of bright and dark solitons in Bose-Einstein condensates with time-varying atomic scattering length in a time-varying external parabolic potential. A set of exact soliton solutions of the one-dimensional Gross-Pitaevskii equation are obtained, including fundamental bright solitons, higher-order bright solitons, and dark solitons. The results show that the soliton＇s parameters （amplitude, width, and period） can be changed in a controllable manner by changing the scattering length and external potential. This may be helpful to design experiments.     

Formation of multiple dark photovoltaic spatial solitons

We theoretically study the formation of multiple dark photovoltaic soliton splitting in the quasi-steady-state and steady-state regimes under open-circuit conditions. We find that the initial width of the dark notch at the entrance face of the crystal is a key parameter for generating an even (or odd) number sequence of dark coherent photovoltaic solitons. If the initial width of the dark notch is small, only a fundamental soliton or Y-junction soliton pair is generated. As the initial width of the dark notch is increased, the dark notch tends to split into an odd (or even) number of multiple dark photovoltaic solitons, which realizes a progressive transition from a low-order soliton to a sequence of higher-order solitons. The soliton pairs far away from the centre have bigger width and less visibility. In addition, when the distance from the centre of the dark notch increases, the separations between adjacent dark stripes become slightly smaller.     

Ultra-slow Bright and Dark Optical Solitons in Cold Media

We present a systematic study on the formation of ultra-slow bright and dark optical solitons in highly resonant media. By investigating four life-time broadened atomic systems, i.e., three-state Λ-type and cascade-type schemes, and four-state N-type and cascade-type schemes, we show that the formation of such ultra-slow solitons in cold atomic systems is a fairly universal phenomenon.     

Do solitonlike self-similar waves exist in nonlinear optical media?

We show analytically that bright and dark spatial self-similar waves can propagate in graded-index amplifiers exhibiting self-focusing or self-defocusing Kerr nonlinearities. The intensity profiles of the novel waves are identical with those of fundamental bright or dark spatial solitons supported by homogeneous passive waveguides with the same type of nonlinearity. Thus, we reveal a previously unnoticed connection between spatial solitons and self-similar waves. We also suggest that the discovered self-similar waves can be used in a promising scheme for the amplification and focusing of spatial solitons in future all-optical networks.     

Ultraslow optical solitons in a cold four-state medium

We show the formation of ultraslow optical solitons in a lifetime broadened four-state atomic medium under Raman excitation. With appropriate conditions we demonstrate, both analytically and numerically, that both bright and dark ultraslow optical solitons can occur in such a highly resonant medium with remarkable propagation characteristics. This work may open other research opportunities in condensed matter and may result in a substantial impact on technology.     

Enhanced Kerr Nonlinearities Caused by Cross Talk Between Optical and Microwave Transitions

We investigate the enhanced Kerr nonlinearities in four-level atomic vapors driven by a coupling, probe and microwave fields. Under the optical one-photon and two-photon resonant conditions, the linear and nonlinear responses of the weak probe field can be modified by the cross talk among optical and microwave transitions. The enhanced Kerr nonlinearity can form bright optical solitons of the probe field.     

Head-on collision of ring dark solitons in Bose--Einstein condensates

The ring dark solitons and their head-on collisions in a Bose--Einstein condensates with thin disc-shaped potential are studied. It is shown that the system admits a solution with two concentric ring solitons, one moving inwards and the other moving outwards, which in small-amplitude limit, are described by the two cylindrical KdV equations in the respective reference frames. By using the extended Poincar\'e--Lighthill--Kuo perturbation method, the analytical phase shifts following the head-on collisions between two ring dark solitary waves are derived. It is shown that the phase shifts decrease with the radial coordinate $r$ according to the $r^{-1/3}$ law and depend on the initial soliton amplitude and radius.     

Subwavelength spatial solitons

We analyze the effects of additional terms in the nonlinear Schr?dinger equation for spatial solitons, directly derived from the Maxwell's equations with the Kerr nonlinearity, on the shapes of bright and dark solitons with a fixed polarization. Combining analytical and numerical methods, we find that the additional terms always render the solitons broader. The most essential result is a fundamental limitation on the width of the subwavelength soliton: The ratio of the FWHM of the bright soliton to the wavelength cannot be smaller than 1/2, and the same ratio for the FWHM of the dark soliton cannot be smaller than 1/4.