Optical solitons: Perspectives and applications

This article serves as an introduction to the focus issue on optical solitons. After a short review of the history of solitons and the field of integrable systems, a brief overview of the development of nonlinear optics and optical solitons is provided. Next, the various contributions to this focus issue are presented, and a few separate remarks are devoted to optical communications, where solitons promise to play a decisive role in the next generation of commercial systems. (c) 2000 American Institute of Physics.     

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.     

On conservative and dissipative solitons in media with a periodic spatial modulation

A comparative theoretical analysis of properties of conservative and dissipative optical solitons in media with a periodic spatial modulation of optical characteristics is performed. It is shown that, in the case of modulation in the longitudinal (with respect to the axis of predominant propagation) direction, the mechanism of decay of conservative solitons because of the delocalization of their Fourier harmonics takes place, whereas, for dissipative solitons, this mechanism is absent. In the case of modulation in the transverse direction, the presence of discrete dissipative solitons in a set of optical fibers with nonlinear (saturable) amplification and absorption is shown, which, to a considerable extent, are similar to conservative discrete solitons.     

Generation of high order multi-bound solitons and propagation in optical fibers

We demonstrate experimental generation of multi-bound solitons of up to sextuple in an active FM mode-locked fiber ring laser operating under power saturation in the locking state. The ring laser consists of two booster optical amplifiers operating in saturation regime, an electro-optic phase modulator driven by a sinusoidal electrical wave and a length of dispersive fiber. The periodic phase modulation generates phase chirp of the generated lightwaves in the ring laser. The chirped phase state plays an important role in the phase matching condition for mode-locking as well as the stabilization and the determination of the bound states of multi-solitons. The formation of such high order multi-bound solitons is explained based on the chirping of the phase and the behavior of the optical pulse sequence in the near field region of the dispersive fiber. The propagation of these multi-bound solitons through single mode optical fibers is observed. Experimental and simulation results of bound solitons have been shown to follow similar trends.The propagation of these multi-bound solitons through single mode optical fibers is described. Their mutual interaction through such quadratic phase media shows the influence of the quadratic phase property on the differential phase of individual solitons of the bound group. Simulated results confirm the evolution of the bound solitons over dispersive single mode optical fibers.     

光晶格势阱中二元凝聚体的矢量孤子的振荡和分裂

考虑外部囚禁势阱为光晶格势阱,研究了二元玻色-爱因斯坦凝聚体中亮-亮孤子的动力学行为.结果表明,亮-亮孤子的运动方向和振荡行为可以分别通过调节光晶格势阱的晶格常数和势阱深度来控制.进一步地,亮-亮孤子还可以被局域在光晶格势阱中,并且随着势阱深度的增加,局域孤子会产生分裂行为.     

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.     

Solitons and intrinsic localized modes in a one-dimensional antiferromagnetic chain

By use of the Hartree approximation and the method of multiple scales, we investigate quantum solitons and intrinsic localized modes in a one-dimensional antiferromagnetic chain. It is shown that there exist solitons of two different quantum frequency bands: i.e., magnetic optical solitons and acoustic solitons. At the boundary of the Brillouin zone, these solitons become quantum intrinsic localized modes: their quantum eigenfrequencies are below the bottom of the harmonic optical frequency band and above the top of the harmonic acoustic frequency band.     

Dynamic and static position control of optical feedback solitons

We report on the experimental implementation of an external control for optical feedback solitons using incoherent spatial intensity distributions in a liquid crystal light valve (LCLV) optical single feedback system. The external control provides excellent experimental possibilities for static and dynamic control of the lateral positions of the optical feedback solitons which will be demonstrated. Particularly, the influence of different gradients onto the drift motion of spatial solitons is experimentally investigated in detail. In agreement with theoretical predictions, the drift velocity of the soliton increases according to the steepness of the gradient. Additionally, a completely incoherent addressing scheme including creation and erasure of feedback solitons is demonstrated for the LCLV setup.     

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.     

Gradient induced motion control of drifting solitary structures in a nonlinear optical single feedback experiment

We realize an absolute position control of drifting dissipative optical solitons by injecting an incoherent amplitude parameter gradient onto the nonlinear optical system. This allows for two-dimensional, arbitrary control patterns. The control of the soliton drift velocity is studied applying a periodic, hexagonally shaped modulation. The guiding of dissipative solitons by one- and two-dimensional parameter modulations is demonstrated. Furthermore, one-dimensional, line-shaped parameter modulations are designed to act as barriers for dissipative solitons, allowing implementations of position selectors for solitons. The interaction of dissipative optical solitons with barriers is studied for different barrier parameters.     

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.     

向列相液晶中强非局域空间光孤子的实验观察

通过实验对向列相液晶中的非局域空间光孤子的传输进行了研究。理论上基于非线性的液晶孤子传输方程,采用高斯形式的试探解,得到了孤子传输的解析解,以及对液晶中的非局域孤子和Snyder等提出的强非局域孤子模型的结果进行了比较。实验上,观察了空间光孤子在向列相液晶中的传输,找到了不同束宽下空间光孤子的临界功率。比如束宽为2μm时临界功率为2.0mW。观察了向列相液晶中空间光孤子的弛豫过程,并注意到液晶分子的响应时间长达几秒钟,液晶中的孤子形成速度较慢。     

空间调制作用下Bessel型光晶格中物质波孤立子的稳定性

利用变分法和数值计算方法研究了空间调制作用下Bessel型光晶格中玻色-爱因斯坦凝聚体系中孤立子的稳定性, 给出了存在随空间非周期变化的线性Bessel型光晶格和非线性光晶格(原子之间非线性相互作用的空间调制)时, 各种参数组合下涡旋和非涡旋孤立子的稳定性条件. 首先, 利用圆对称的高斯型试探波函数得出描述体系稳定性参数满足的Euler-Lagrange方程和变分法分析体系稳定性所需要的有效作用势能的表达式. 然后, 根据有效作用势能是否具有局域最小值判断体系是否具有稳定状态, 得出体系具有稳定状态时参数所满足的条件. 最后, 利用有限差分法求解Gross-Pitaevskii方程验证变分法结果的正确性, 所得结果和变分法结果一致. 关键词： Bessel型光晶格 非线性光晶格 孤立子 稳定性     

Spatial solitons in Kerr and Kerr-like media

This is a review paper of basic knowledge and recent advances in the area of spatial solitons in Kerr and Kerr-like media. We consider spatial bright and dark solitons, solitons in waveguide geometries, optical bullets, vortex solitons and, briefly, dissipative cases. In our treatment, we use a Hamiltonian approach when considering stability issues.     

Polarization vortex spatial optical solitons in Bessel optical lattices

We investigate the formation of polarization vortex spatial optical solitons in optical lattice induced by a non-diffracting Bessel beam. The properties of these solitons in zeroth-order and first-order Bessel lattices with focusing and defocusing Kerr nonlinearity are discussed. It is found that these solitons have some analogies with phase vortex solitons carrying single positive or negative topological charge in these lattices. Besides, these polarization vortex solitons have complicated dynamical characteristic and can be stabilized in some parameter region.     

强非局域介质中基于古依相位的旋转涡旋光孤子

利用强非局域非线性介质中傍轴光束传输的修正Snyder-Mitchell模型讨论了两束共线(即光束中心和传输方向都相同)拉盖尔-高斯型光孤子(CLGS)构成的涡旋光孤子传输过程。在一定条件下,涡旋光束在传输过程中,光束截面光斑发生旋转现象,但光束的束宽保持不变,称之为旋转涡旋光孤子。涡旋光孤子旋转的现象可以通过叠加光场中的古依相位来解释。结果展现了几个旋转涡旋光孤子在传输过程中的旋转现象和强非局域介质中多环形旋转涡旋光孤子的传输。     

Parametric solitons

We develop a general framework for understanding the characteristics of multi-frequency (multi-colour) parametric solitons. We identify two special classes of such solitons: cascaded parametric solitons, where the optical energy is shared between several harmonically-related frequency bands; and isolated-bandwidth solitons, where all of the optical energy is localized within a single frequency band. As an example, we consider the case of a five-colour isolated-bandwidth parametric soliton in a Kerr medium.     

Laguerre and Hermite soliton clusters in nonlocal nonlinear media

We introduce novel classes of higher-order spatial optical solitons in analogy with Laguerre-Gaussian and Hermite-Gaussian linear eigenmodes. We reveal that stable higher-order optical solitons can exist in nonlocal nonlinear media in the various forms of soliton necklaces and soliton matrices. Modulational instability can lead to nontrivial transformations between energetically close solitons with different symmetries through the intermediate states resembling generalized Hermite-Laguerre-Gaussian modes.     

Stabilization of optical solitons in chirped PT-symmetric lattices

We investigate the stability properties of optical solitons in a chirped PT-symmetric lattice whose frequency changes in the transverse direction. Linear-stability analysis together with the direct propagation simulations demonstrates that the chirped lattice can improve the stability of optical solitons dramatically. The instability of fundamental solitons can be completely suppressed if the chirp rate exceeds a critical value. A broad stability area of dipole solitons appears if the lattice is appropriately chirped. Thus, we propose an effective way to suppress the instability of solitons in PT-symmetric potentials.