Solitons in nonintegrable systems

We introduce the concept of this special focus issue on solitons in nonintegrable systems. A brief overview of some recent developments is provided, and the various contributions are described. The topics covered in this focus issue are the modulation of solitons, bores, and shocks, the dynamical evolution of solitary waves, and existence and stability of solitary waves and embedded solitons.     

Wavelet based spectral analysis of optical solitons

The propagation of solitons or a pulse or a signal through optical fibers has been a major area of research given its potential applicability in all optical communication systems. In a modern optical communication system, the transmission link is composed of optical fibers and amplifiers. This manifests in noise, clutters and distortion when the signal propagates through optical fibers, consequently affecting the capacity and performance of the optical system. The dynamics of solitons has therefore become an active field of research in nonlinear optics for couple of decades. The nonlinear Schrodinger's equation (NLSE) with log law nonlinearity governs the propagation of optical solitons through optical fibers and its dynamics. Most of the studies reveal that the optical solitons have Gaussian wave profile called Gaussons. This entails the use of wavelet techniques for the processing of optical solitons.     

Spatial solitons in an optical lattice with varying diffraction and spatially inhomogeneous nonlinearity

In this paper, we present the (1+1)-dimensional inhomogeneous nonlinear Schrödinger (NLS) equation that describes the propagation of optical waves in nonlinear optical systems exhibiting optical lattice, inhomogeneous nonlinearity and varying diffraction at the same time. A series of interesting properties of spatial solitons are found from the numerical calculations, such as the stable propagation in the a nonperiodic optical lattice induced by periodic diffraction variations and periodic nonlinearity variations. Finally, the interaction of neighboring spatial solitons in a nonperiodic optical lattice is discussed, and the results reveal that two spatial solitons can propagate periodically and separately in the optical lattice without interaction.     

Conservative and dissipative fiber Bragg solitons (a review)

We present a comparative review of two classes of optical solitons—conservative and dissipative solitons—propagating in single-mode optical fibers in which refractive-index gratings are induced such that their period is comparable with the radiation wavelength. Fibers that have the Kerr nonlinearity and negligibly small losses and that do not gain radiation (conservative system) are described by traditional equations of the approximation of slowly varying amplitudes, and effects caused by the nonlinearity of the medium, such as nonlinear switching, optical bistability, and formation of conservative Bragg solitons are considered. It is shown that the passage beyond the scope of the approximation of slowly varying amplitudes makes it possible to describe new important effects, including localization of soliton centers near maxima of the refractive-index grating. Bright and dark conservative solitons are demonstrated, which are formed when the Kerr nonlinearity is replaced by the nonlinearity of two-level atomic systems. The properties of conservative solitons in resonance semiconductor Bragg structures with quantum wells are considered. Results of experimental studies of nonlinear effects in fibers with Bragg gratings are presented. For an active single-mode fiber with a Bragg refractive-index grating and nonlinear gain and absorption, dissipative solitons are described using the approximation of slowly varying amplitudes and inertialess nonlinearity. It is shown that the dissipative factors qualitatively change the properties of solitons compared to the conservative case. Using the Maxwell-Bloch equations, it is demonstrated that the ratio between the gain and absorption relaxation times significantly affects the stability of localized structures. The interaction of dissipative optical Bragg solitons is described. It is shown that, beyond the scope of the approximation of slowly varying amplitudes, the average velocity of propagating dissipative Bragg solitons acquires only discrete values, and formation of pairs of solitons with two values of the phase difference becomes possible. For a birefringent fiber, dissipative vector optical Bragg solitons are demonstrated.     

Regular and stochastic motion of dissipative optical solitons

Investigations of the motion of dissipative optical solitons and their complexes in wide-aperture nonlinearly optical (with coherent pump radiation) and laser (with incoherent pump radiation) systems have been reviewed. An important characteristic of dissipative solitons is the topology of the energy fluxes, which determines the internal structure of individual solitons and makes it possible to certainly separate the cases of the weak and strong interactions between the solitons. It has been shown that the character of the regular motion of dissipative soliton structures in a homogeneous system is determined by the symmetry of the transverse distributions of the intensity and energy flux; the motion of asymmetric structures is curvilinear. This is also valid for complexes of three-dimensional dissipative optical solitons, “laser bullets.” The extreme possibilities of localization of solitons are determined by quantum noises. The corresponding Brownian motion of the center of the dissipative optical soliton is characterized by a much lower level of the statistic dispersion of the coordinates of its center and velocity than that in the case of conservative solitons.     

Spatial resonator solitons

Spatial solitons can exist in various kinds of nonlinear optical resonators with and without amplification. In the past years different types of these localized structures such as vortices, bright, dark solitons, and phase solitons have been experimentally shown to exist. Many links appear to exist to fields different from optics, such as fluids, phase transitions, or particle physics. These spatial resonator solitons are bistable and due to their mobility suggest schemes of information processing not possible with the fixed bistable elements forming the basic ingredient of traditional electronic processing. The recent demonstration of existence and manipulation of spatial solitons in semiconductor microresonators represents a step in the direction of such optical parallel processing applications. We review some proof of principle soliton experiments on slow systems, and describe in more detail the experiments on semiconductor resonator solitons which are aimed at applications.     

Quantum many-body simulations using Gaussian phase-space representations

Phase-space representations are of increasing importance as a viable and successful means to study exponentially complex quantum many-body systems from first principles. This paper traces the background of these methods, starting from the early work of Wigner, Glauber and Sudarshan. We focus on modern phase-space approaches using non-classical phase-space representations. These lead to the Gaussian representation, which unifies bosonic and fermionic phase-space. Examples treated include quantum solitons in optical fibers, colliding Bose-Einstein condensates, and strongly correlated fermions on lattices. The text was submitted by the authors in English.     

Spatial optical (2+1)‐dimensional scalar‐ and vector‐solitons in saturable nonlinear media

(2+1)‐dimensional optical spatial solitons have become a major field of research in nonlinear physics throughout the last decade due to their potential in adaptive optical communication technologies. With the help of photorefractive crystals that supply the required type of nonlinearity for soliton generation, we are able to demonstrate experimentally the formation, the dynamic properties, and especially the interaction of solitary waves, which were so far only known from general soliton theory. Among the complex interaction scenarios of scalar solitons, we reveal a distinct behavior denoted as anomalous interaction, which is unique in soliton‐supporting systems. Further on, we realize highly parallel, light‐induced waveguide configurations based on photorefractive screening solitons that give rise to technical applications towards waveguide couplers and dividers as well as all‐optical information processing devices where light is controlled by light itself. Finally, we demonstrate the generation, stability and propagation dynamics of multi‐component or vector solitons, multipole transverse optical structures bearing a complex geometry. In analogy to the particle‐light dualism of scalar solitons, various types of vector solitons can ‐ in a broader sense ‐ be interpreted as molecules of light.     

基于运动光栅光折变双光束耦合的刚性全息明孤子的动态演化

研究基于运动光栅双光束耦合的耗散光折变系统中的空间光孤子的动态演化问题.数值计算 表明，系统参数同这种孤子的稳定性密切相关.在某组系统参数下，孤子可以在晶体内稳定 传播足够远的距离.双光束耦合的相位与强度耦合系数之比越大，孤子的稳定性越好.讨论了 将这种系统应用于光学开关、中继及分路器件的可能性. 关键词： 空间光孤子 光折变非线性光学 耗散系统 全息光栅     

Convection-induced stabilization of optical dissipative solitons

In spatially extended convective systems, the reflection symmetry breaking induced by drift effects leads to a striking nonlinear effect that drastically affects the formation and stability of dissipative solitons in optical parametric oscillators. The phenomenon of nonlinear-induced convection dynamics is revealed using a model of the complex quintic Ginzburg-Landau equation with nonlinear gradient terms in it. Mechanisms leading to stabilization of dissipative solitons by convection are singled out. The predictions are in very good agreement with numerical solutions found from the governing equations of the optical parametric oscillators.     

Resonant and nonresonant optical solitons: Similarities and differences

An analysis of the similarities and differences between resonant and nonresonant optical solitons is conducted. The study focuses on physical aspects of the problem, including self-focusing and self-defocusing. Attention is given to possible applications of both types of solitons in optical information transmission and processing systems.     

DNA adsorption on graphene

We study analytically the properties of the optical absorption and the spatial weak-light solitons in a quantum dot molecule system with the interdot tunneling coupling (ITC). It is shown that, for the linear case, there exists tunneling induced transparency (TIT) in the context of a weak ITC, while the TIT can be replaced by Autler-Townes splitting in the presence of a strong ITC. For the nonlinear case, it is probable to realize the spatial optical solitons even under weak light intensity. Interestingly, we find that there appears transformation behavior between the bright and dark solitons by properly turning both the ITC strength and the detuning of the probe field. Meanwhile, the transformation condition of the bright and dark solitons is obtained. Additionally it is also found that the amplitude of the solitons first descends and then rises with the increasing of ITC strength. Our results may have potential applications for nonlinear optical experiments and optical telecommunication engineering in solid systems.     

Midband dissipative spatial solitons

We show dissipative spatial solitons in nonlinear optical microresonators in which the refractive index is laterally modulated. In addition to "normal" and "staggered" dissipative solitons, similar to those in spatially modulated conservative systems, a narrow "midband" soliton is shown, having no counterparts in conservative systems.     

Optical soliton in a one-dimensional array of a metal nanoparticle-microcavity complex

Quantum coherence can be enhanced by placing metal nanoparticles (MNPs) in optical microcavities. Combining localized-surface plasmon resonances (LSPRs), nonlinear interaction between the LSPR and microcavity arrays of a MNP-microcavity complex offer a unique playground to observe novel optical phenomena and develop novel concepts for quantum manipulation. Here we theoretically demonstrate that optical solitons are achievable with a one-dimensional array which consists of a chain of periodically spaced identical MNP-microcavity complex systems. These differ from the solitons which stem from the MNPs with nonlinear Kerr-like response; the optical soliton here originates from LSPR-microcavity interaction. Using experimentally achievable parameters, we identify the conditions under which the nonlinearity induced by LSPR-microcavity interaction allows us to compensate for the dispersion caused by photon hopping of adjacent microcavities. More interestingly, the dynamics of solitons can be modulated by varying the radius of the MNP. The presented results illustrate the potential to utilize the MNP-microcavity complex for light manipulation, as well as to guide the design of photon switch and on-chip photon architecture.     

Oscillating solitons in nonlinear optics

Oscillating solitons are obtained in nonlinear optics. Analytical study of the variable-coefficient nonlinear Schrödinger equation, which is used to describe the soliton propagation in those systems, is carried out using the Hirota’s bilinear method. The bilinear forms and analytic soliton solutions are derived, and the relevant properties and features of oscillating solitons are illustrated. Oscillating solitons are controlled by the reciprocal of the group velocity and Kerr nonlinearity. Results of this paper will be valuable to the study of dispersion-managed optical communication system and mode-locked fibre lasers.     

Multiband vector lattice solitons

We predict multiband vector solitons in nonlinear periodic systems, using photonic lattices as a prime example. The solitons consist of two optical fields arising from different bands of the transmission spectrum, which involve both bound state and radiation mode components.     

Higher-order solitons in amplitude-disordered waveguide arrays

We investigate the existence and stability of different families of spatial solitons in optical waveguide arrays whose amplitudes obey a disordered distribution. The competition between focusing nonlinearity and linearly disordered refractive index modulation results in the formation of spatial localized nonlinear states. Solitons originating from Anderson modes with few nodes are robust during propagation. While multi-peaked solitons with in-phase neighboring components are completely unstable, multipole-mode solitons whose neighboring components are out-of-phase can propagate stably in wide parameter regions provided that their power exceeds a critical value. Our findings, thus, provide the first example of stable higher-order nonlinear states in disordered systems.     

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.