Envelope self-similar solutions for the nonautonomous and inhomogeneous nonlinear Schrödinger equation

By means of the similarity transformation connecting with the solvable stationary equation, the self-similar combined Jacobian elliptic function solutions and fractional form solutions of the generalized nonlinear Schrödinger equation (NLSE) are obtained when the dispersion, nonlinearity, and gain or absorption are varied. The propagation dynamics in a periodic distributed amplification system is investigated. Self-similar cnoidal waves and corresponding localized waves including bright and dark similaritons (or solitons) for NLSE and arch and kink similaritons (or solitons) for cubic-quintic NLSE are analyzed. The results show that the intensity and the width of chirped cnoidal waves (or similaritons) change more distinctly than that of chirp-free counterparts (or solitons).     

Spatiotemporal self-similar nonlinear tunneling effects in the (3 + 1)-dimensional inhomogeneous nonlinear medium with the linear and nonlinear gain

With the help of two kinds of similarity transformations connected with the elliptic equation, at first we analytically derive spatiotemporal self-similar solutions of the (3 + 1)-dimensional inhomogeneous nonlinear Schrödinger equation with the linear and nonlinear gain. Then we give out the mutually exclusive parameter domains for bright and dark similaritons. Finally, we discuss nonlinear tunneling effects for spatiotemporal similaritons passing through the nonlinear barrier or well. Results show that bright and dark similaritons in the normal and anomalous dispersion regions have opposite dynamic behaviors.     

Similaritons in nonlinear optical systems

By using the lens-type transformation, we find the self-similar evolution of four kinds of optical similaritons in (1+1)-dimensional nonlinear Schrödinger equations. They are the exact solitonic similaritons, quasi solitonic similaritons, asymptotic compact parabolic similaritons and asymptotic Hermite-Gaussian similaritons. Moreover, the interaction of multiple solitonic similaritons are investigated. Approximate but highly accurate analytical methods are developed to describe their center-of-mass motion.     

Spatial similaritons in the (2+1)-dimensional inhomogeneous cubic-quintic nonlinear Schrödinger equation

Along the idea of the similarity transformation, analytical spatial similaritons to a (2+1)-dimensional inhomogeneous cubic-quintic nonlinear Schrödinger equation with distributed diffraction and gain are derived when some certain compatibility conditions are satisfied. Based on these exact solutions, we investigate dynamic behaviors of self-similar cnoidal waves and chirped similaritons in the hyperbolically and Gaussian decreasing diffraction waveguides.     

Controlled generation and steering of spatial gap solitons

We demonstrate the first fully controlled generation of immobile and slow spatial gap solitons in nonlinear periodic systems with band-gap spectra, and observe the key features of gap solitons that distinguish them from discrete solitons, including a dynamical transformation of gap solitons due to nonlinear interband coupling. We also describe theoretically and confirm experimentally the effect of the anomalous steering of gap solitons in optically induced photonic lattices.     

Two-dimensional spatial solitons in highly nonlocal nonlinear media

We investigate, analytically and numerically, a class of novel higher-order spatial solitons in two transverse-dimensions, in highly nonlocal nonlinear media. The stability of these solutions in propagation is confirmed by direct numerical simulation. Our results demonstrate that the higher-order spatial solitons in highly nonlocal nonlinear media can exist in various forms, such as the fundamental solitons, vortex-ring solitons, multipole solitons, and fractional solitons.     

Self-similar optical beam in nonlinear waveguides

By means of the similarity transformation, we obtain exact bright and dark similariton-pair solutions in nonlinear waveguides for the generalized nonlinear Schr?dinger equation exhibiting spatial inhomogeneity, inhomogeneous nonlinearity and gain or loss at the same time. Then we investigate the interaction behaviors of these solitonic similaritons in a periodic distributed amplification system.     

Spatial optical solitons supported by mutual focusing

We study composite spatial optical solitons supported by two-wave mutual focusing induced by cross-phase modulation in Kerr-like nonlinear media. We find the families of both single- and two-hump solitons and discuss their properties and stability. We also reveal remarkable similarities between recently predicted holographic solitons in photorefractive media and parametric solitons in quadratic nonlinear crystals.     

Soliton Properties of Light Pulses on the Surface of Ionic Crystals Generated by Strong Nonlinear Effects

In this paper, we theoretically discuss the soliton properties of light pulse transportation on the surface of an ionic crystal having strong nonlinear interactions between ions of unit cells. We analyze in detail the dark solitons when the nonlinear coefficient g is positive and negative, respectively. It is found that whether the nonlinear coefficient g is positive or negative, the dark solitons can be formed over the whole dispersion relation area of surface polaritons considering nonlinear effects. Attention should be paid to the fact that around ωTO, the light pulse can form advanced dark solitons, and there is a switching area from advanced dark soliton to retarded dark soliton near ωTO. We also discuss the effects of higher nonlinear dispersion on the solitons.     

高阶效应对自相似抛物线脉冲相互作用的影响

讨论高阶效应对自相似抛物线脉冲传输中相互作用的影响.数值研究结果证明高阶效应使得自相似抛物线脉冲形状畸变非常严重,并加剧脉冲间的相互作用.我们分析了不同的高阶效应对脉冲间相互作用的具体影响.而且我们可通过幅度调制和脉冲压缩技术,获得较高质量的自相似抛物线脉冲串传输.这些结果对进一步研究高质量的自相似抛物线脉冲在高功率超短脉冲光纤放大器、激光器和传输系统中的应用有重要的意义.     

Spatiotemporal solitons in inhomogeneous nonlinear media

We investigate the possibility of forming spatiotemporal solitons (optical bullets) in inhomogeneous, dispersive nonlinear media using a graded-index Kerr medium as an example. We use a variational approach to solve the multidimensional, inhomogeneous, nonlinear Schrödinger equation and show that spatiotemporal solitons can be stabilized under certain conditions. We verify their existence by means of a full numerical analysis and show that such solitons should be observable experimentally.     

Spatial weak-light solitons in an electromagnetically induced nonlinear waveguide

We show that a weak probe light beam can form spatial solitons in an electromagnetically induced transparency (EIT) medium composed of four-level atoms and a coupling light field. We find that the coupling light beam can induce a highly controllable nonlinear waveguide and exert very strong effects on the dynamical behavior of the solitons. Hence, in the EIT medium, it is not only possible to produce spatial solitons at very low light intensities but also simultaneously control these solitons by using the coupling-light-induced nonlinear waveguide.     

Similariton fiber laser with a hollow-core photonic bandgap fiber for dispersion control

We report on an ytterbium-doped similariton fiber ring laser with a hollow-core photonic bandgap fiber for intracavity dispersion control. The oscillator is hybrid mode locked with a saturable Bragg reflector and by nonlinear polarization evolution. This scheme allows for an exact adjustment of the transmission characteristic to avoid the formation of bunched noiselike pulses while the self-starting characteristic is preserved. The oscillator generates highly stretched similaritons at 1025 nm with a pulse energy above 1n J at a repetition rate of 21.9 MHz.     

Spectral incoherent solitons: a localized soliton behavior in the frequency domain

We show both theoretically and experimentally in an optical fiber system that a noninstantaneous nonlinear environment supports the existence of spectral incoherent solitons. Contrary to conventional solitons, spectral incoherent solitons do not exhibit a confinement in the spatiotemporal domain, but exclusively in the frequency domain. The theory reveals that the causality condition inherent to the nonlinear response function is the key property underlying the existence of spectral incoherent solitons. These solitons constitute nonequilibrium stable states of the incoherent field and are shown to be robust with respect to binary collisions.     

Dynamics of solitons of the generalized (3+1)-dimensional nonlinear Schrödinger equation with distributed coefficients

We present three families of soliton solutions to the generalized (3+1)-dimensional nonlinear Schrödinger equation with distributed coefficients. We investigate the dynamics of these solitons in nonlinear optics with some selected parameters. Different shapes of bright solitons, a train of bright solitons and dark solitons are observed. The obtained results may raise the possibilities of relevant experiments and potential applications.     

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.     

Spatial optical solitons in inhomogeneous elliptic core saturating nonlinear fiber

We have investigated the propagation characteristics of spatial optical solitons in saturating nonlinear waveguide employing JWKB and paraxial ray approximation. We have obtained two second-order coupled nonlinear differential equations for transverse soliton widths of solitons. Threshold power for stable propagation of the beam has been calculated from these coupled equations. We have undertaken stability analysis, which predicts robustness of these solitons. Both guiding as well as antiguiding cases have been considered and shown that stable spatial soliton propagation is possible in both cases.     

Multicolor lattice solitons

We report on the existence of multicolor solitons supported by periodic lattices made from quadratic nonlinear media. Such lattice solitons bridge the gap between continuous solitons in uniform media and discrete solitons in strongly localized systems and exhibit a wealth of new features. We discovered that, in contrast to uniform media, multipeaked lattice solitons are stable. Thus they open new opportunities for all-optical switching based on soliton packets.     

Analytical solution for photorefractive screening solitons

We study formation and interaction of one-dimensional screening solitons in a photorefractive medium with sublinear dependence of the photoconductivity on light intensity. We find an exact analytical solution to the corresponding nonlinear Schrodinger equation. We show that these solitons are stable in propagation and their interaction is generic for solitons of saturable nonlinearity. In particular, they may fuse or "give birth" to new solitons upon collision.     

Attraction of nonlocal dark optical solitons

We study the formation and interaction of spatial dark optical solitons in materials with a nonlocal nonlinear response. We show that unlike in local materials, where dark solitons typically repel, the nonlocal nonlinearity leads to a long-range attraction and formation of stable bound states of dark solitons.