Curvilinear motion of laser soliton complexes

Conditions under which the center of inertia of stable complexes of dissipative optical solitons moves curvilinearly have been determined. Such a character of the motion of dissipative structures is caused by asymmetry in the distribution of the intensity and energy fluxes, and it is pronounced for laser solitons with strong interaction. The results of the numerical simulation of these complexes in the model of surface emitting lasers or laser amplifiers with saturated amplification and absorption are presented. Such complexes may be observed in various spatially distributed nonlinear dissipative systems, in particular, in the form of discrete solitons.     

Two-dimensional laser soliton complexes with weak, strong, and mixed coupling

A review is given of features and motion of two-dimensional dissipative solitons in lasers and laser amplifiers with saturable absorption. We present a rich variety of stable complexes with weak, strong, and mixed coupling of individual laser solitons. The type of coupling is determined by the topology of the distribution of energy flows within the complex. We reveal the existence of stable dissipative soliton complexes with curvilinear motion of their centre of mass. This type of motion results from the field distribution asymmetry and is well pronounced for complexes of laser solitons with strong and mixed types of coupling. Similar complexes are expected to exist in different spatially distributed nonlinear dissipative systems, including schemes with discrete dissipative solitons. PACS 42.65.Tg     

Curvilinear motion of multivortex laser-soliton complexes with strong and weak coupling

We reveal the existence of stable dissipative soliton complexes with curvilinear motion of their center of mass. This type of motion results from the field distribution asymmetry and is well pronounced for asymmetric complexes of laser solitons with strong coupling. We present results of numerical simulations of such complexes in a model of wide-aperture lasers or laser amplifiers with saturable gain and absorption. The complex consists of a pair of strongly coupled vortex solitons weakly coupled with a number of other vortex solitons. Similar complexes are expected to exist in different spatially distributed nonlinear dissipative systems, including schemes with discrete dissipative solitons.     

Motion of dissipative soliton complexes in a nonlinear interferometer with driving radiation

A numerical analysis has been made of the motion of spatial dissipative soliton complexes in a wide-aperture interferometer with the Kerr nonlinearity, which is excited by continuous coherent driving radiation. It has been demonstrated that, depending on the symmetry of the radiation intensity distribution, the complex can exhibit four variants of dynamics, including the curvilinear motion of its center. The results obtained have been compared with the case of laser soliton complexes (without coherent driving radiation) and with the predictions made from the phenomenological model of the motion of soliton complexes.     

Clusters of three-dimensional laser solitons and their collisions

A new class of clusters of three-dimensional dissipative inphase-and antiphase-coupled solitons is numerically found in a laser system with a saturable absorber. The orientation of clusters and their motion depend on the symmetry of spatiotemporal characteristic of the system and on the symmetry of arrangement of solitons in the cluster. An example of a nonplanar (spiral-like) trajectory of the center of a seven-soliton cluster possessing no symmetry elements is demonstrated. Collisions of moving soliton clusters, including those accompanied by exchange of solitons between clusters, are studied. Experimentally, three-dimensional dissipative optical solitons can be realized in a laser amplifier with a saturable absorber or in an extended resonator filled with a medium with nonlinear gain and absorption.     

Dissipative solitons of the Bose-Einstein condensate of excitons

A mirrorless scheme for forming dissipative solitons has been proposed. It consists of a thin layer of a nonlinear medium excited by coherent laser radiation. The existence of dark dissipative solitons of the Bose-Einstein condensate of excitons in such a semiconductor film has been numerically demonstrated. The sizes of an excition soliton and required laser-radiation level are two orders of magnitude smaller than the respective quantities for the case of optical dissipative solitons.     

Motion of molecular dissipative solitons in oriented linear <Emphasis Type="Italic">J</Emphasis> aggregates upon oblique incidence of exciting laser radiation

Motion of dissipative solitons in a molecular chain resonantly excited by laser radiation obliquely incident on the chain is computer simulated. The soliton motion with the velocity proportional to the small inclination angle is demonstrated.     

全正色散多波长被动锁模耗散孤子掺镱光纤激光器

报道了一种带有周期性双折射光纤滤波器的全正色散多波长被动锁模耗散孤子掺镱光纤激光器. 通过数值模拟发现加入滤波器后激光器能输出多波长耗散孤子脉冲, 调节滤波器带宽大小可以得到不同波长个数和波长间隔的多波长锁模耗散孤子脉冲. 在激光器产生的四波长和五波长耗散孤子脉冲中观察到了耗散孤子分子, 并且通过调节滤波器参数和饱和功率可以改变多波长脉冲中耗散孤子分子的个数和波长. 这是在被动锁模光纤激光器中首次实现包含有耗散孤子分子的多波长脉冲. 另外还在实验上实现了全正色散双波长被动锁模耗散孤子的产生. 关键词： 全正色散 耗散孤子 多波长脉冲 孤子分子     

Kinetic properties of multiquanta Davydov-like solitons in molecular chains

The Fokker-Planck equation for multivibron solitons interacting with lattice vibrations in a molecular chain has been derived by means of the nonequilibrium statistical operator method. It was shown that a soliton undergoes diffusive motion characterized by two substantially different diffusion coefficients. The first one corresponds to the ordinary (Einsteinian or dissipative) diffusion and characterizes the soliton Brownian motion, while the second one corresponds to the anomalous diffusion connected with frictionless displacement of the soliton center of mass coordinate due to the interaction with phonons. Both processes are the consequence of the Cherenkov-like radiation of phonon quanta arising when soliton velocity approaches the phase speed of sound.     

Motion of dissipative solitons in a laser cavity with a smooth transverse inhomogeneity

The effect of the inhomogeneity gradient in a large-aperture class A laser with a saturable absorber on the transverse motion of dissipative solitons and their clusters in the laser cavity is analytically and numerically studied. A soliton with a nonzero topological charge is found to move rectilinearly in the steady-state regime but in a direction that differs from the direction of the cavity length gradient, which is connected with a nontrivial internal structure of the soliton. The steady-state motion of soliton clusters can be curvilinear, including translational and rotational motions of their center.     

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.     

Three-dimensional dissipative optical solitons

A brief overview of recent theoretical results in the area of three-dimensional dissipative optical solitons is given. A systematic analysis demonstrates the existence and stability of both fundamental (spinless) and spinning three-dimensional dissipative solitons in both normal and anomalous group-velocity regimes. Direct numerical simulations of the evolution of stationary solitons of the three-dimensional cubic-quintic Ginzburg-Landau equation show full agreement with the predictions based on computation of the instability eigenvalues from the linearized equations for small perturbations. It is shown that the diffusivity in the transverse plane is necessary for the stability of vortex solitons against azimuthal perturbations, while fundamental (zero-vorticity) solitons may be stable in the absence of diffusivity. It has also been found that, at values of the nonlinear gain above the upper border of the soliton existence domain, the three-dimensional dissipative solitons either develop intrinsic pulsations or start to expand in the temporal (longitudinal) direction keeping their structure in the transverse spatial plane. Presented at 9-th International Workshop on Nonlinear Optics Applications, NOA 2007, May 17–20, 2007, Świnoujście, Poland     

Collisions between spinning and nonspinning co-axial three-dimensional Ginzburg-Landau solitons

We report results of the first analysis of collisions between stable fundamental (alias spinless) and vortical (spinning) three-dimensional dissipative solitons in a model of a laser cavity. The systematic analysis is carried out for values S=1 and S=2 of the vorticity of the latter soliton. With the increase of the collision momentum, Χ, the same generic scenarios are observed in either case: merger into a single fundamental soliton at both small and relatively large values of Χ, and the formation of two fundamental solitons in an intermediate interval of variation of the collision momentum Χ. At very large values of Χ, the collision seems quasi-elastic, but the vortex soliton eventually splits into two nonspinning fragments.     

Spatiotemporal optical solitons in nonlinear dissipative media: from stationary light bullets to pulsating complexes

Nonlinear dissipative systems display the full (3+1)D spatiotemporal dynamics of stable optical solitons. We review recent results that were obtained within the complex cubic-quintic Ginzburg-Landau equation model. Numerical simulations reveal the existence of stationary bell-shaped (3+1)D solitons for both anomalous and normal chromatic dispersion regimes, as well as the formation of double soliton complexes. We provide additional insight concerning the possible dynamics of these soliton complexes, consider collision cases between two solitons, and discuss the ways nonstationary evolution can lead to optical pattern formation.     

钛宝石飞秒激光器中孤子分子的内部动态探测

孤子是自然界中一种基本的非线性波动传递形式,孤子间的相互作用能够映射出复杂非线性系统的多体动力学过程,具有重要的基础研究价值.被动锁模激光器是研究孤子相互作用的理想平台.光孤子之间的吸引、排斥作用能够形成孤子分子,而时间拉伸色散傅里叶变换(TS-DFT)技术使得实时探测孤子分子动力学成为可能.基于TS-DFT技术,本文实验研究了钛宝石飞秒激光器产生的孤子分子的内部动态,通过改变抽运功率,分别观察到了间隔为180 fs的稳定的孤子分子和间隔为105 fs的具有微弱相位振荡的孤子分子,后者的振动幅度仅为0.05 rad.实验发现受到环境影响,稳定态的孤子分子还能够转变为相位滑动状态.这些间隔为百飞秒量级的光学孤子分子对于研究孤子的近程非线性相互作用具有突出的意义.     

Properties of a vector soliton laser passively mode-locked by a fiber-based semiconductor saturable absorber operating in transmission

We experimentally demonstrate a passively mode-locked fiber laser employing a fiber-based semiconductor saturable absorber (SSA) operating in transmission. Polarization rotation locked vector solitons are observed in the laser. Due to the intrinsic dynamic feature of the laser, period-doubling of these vector solitons has also been observed. Furthermore, extra spectral sidebands are formed on the optical spectrum, caused by the energy exchange between the two orthogonal polarization components of the vector solitons. By careful reduction of the pump power together with fine adjustment to the cavity birefringence, period-one state can further be obtained. Additionally, the phase noise properties of the vector soliton fiber laser have also been characterized experimentally and analytically.     

Effect of polarization on a spin particle trajectory

It is demonstrated that the problem of determining the parameters of trajectories of spin particles and beam of rays in the case of radiation with allowance for polarization is reduced to a variational problem with higher derivatives. It is demonstrated that in the limit of small values of the curvature and torsion, the higher derivatives can be expressed through the parameters of the medium. In this case, the curvature and torsion together with the polarization projection onto the trajectory determine an analog of the 4-potential which in its turn specifies an analog of the electromagnetic field tensor where the projection of polarization onto the trajectory plays the role of charge for a charged particle. It is demonstrated that the Magnus optical effect for dissipative solitons is determined not only by helicity σ, but also by topological index m (by the projection of the orbital soliton momentum onto the soliton trajectory). In an inhomogeneous medium, a relationship between the Magnus optical effect and nonholonomicity of the field of unit vectors tangent to the trajectory is established.     

Diffusion-induced deflection and the effect of two-wave mixing gain on dissipative photovoltaic solitons

In an open-circuit dissipative photovoltaic (PV) crystal, by considering the diffusion effect, the deflection of bright dissipative photovoltaic (DPV) solitons has been investigated by employing numerical technique and perturbational procedure. The relevant results show that the centre of the optical beam moves along a parabolic trajectory, while the central spatial-frequency component shifts linearly with the propagation distance; furthermore, both the spatial deflection and the angular derivation are associated with the photovoltaic field. Such DPV solitons have a fixed deflection degree completely determined by the parameters of the dissipative system. The small bending cannot affect the formation of the DPV soliton via two-wave mixing.     

Soliton Rectangular Pulses and Bound States in a Dissipative System Modeled by the Variable-Coefficients Complex Cubic-Quintic Ginzburg-Landau Equation

The complex cubic-quintic Ginzburg-Landau equation(CQGLE) is a universal model for describing a dissipative system,especially fiber laser.The analytic one-soliton solution of the variable-coefficients CQGLE is calculated by a modified Hirota method.Then,phenomena of soliton pulses splitting and stable bound states of two solitons are investigated.Moreover,rectangular dissipative soliton pulses of the variable-coefficients CQGLE are realized and controlled effectively in the theoretical research for the first time,which breaks through energy limitation of soliton pulses and is expected to provide theoretical basis for preparation of high-energy soliton pulses in fiber lasers.     

基于非线性放大环镜和Lyot滤波器的多波长与耗散孤子锁模态开关型掺铥光纤激光器

报道了一种基于非线性放大环镜和Lyot滤波器技术的态开关型掺铥光纤激光器.通过仔细调节偏振控制器和泵浦功率,掺铥光纤激光器可以分别在多波长态和耗散孤子锁模态运行,并且两种态之间可以相互切换.对于多波长态,在光谱半功率值范围内能生成8个稳定的波长;对于耗散孤子锁模态,在1996 nm的中心波长处产生脉冲能量高达41.49 nJ,脉冲持续时间为2.4 ns,光谱带宽为29 nm的耗散孤子.不同运行态间的切换归因于偏振控制器导致的非线性放大环镜的功能的改变.