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     

Stochastic perturbation of non-Kerr law optical solitons

The dynamics of optical solitons with non-Kerr law non-linearities, in presence of stochastic perturbation terms, is studied in this paper. The Langevin equations are derived and it is proved that the solitons travel through a fiber with a fixed mean velocity. The non-linearities that are considered here are the power law, parabolic law and the dual-power law types.     

Evolution of optical solitons in nonlinear dispersive lossy fibres

A variational technique has been applied to the evolution of optical solitons in a nonlinear dispersive lossy fibre. An analytical model has been developed to describe the interaction of two co-propagating orthogonally polarized optical pulses in a lossy fibre, governed by a pair of coupled nonlinear Schroedinger equations, and the threshold amplitude at which the solitons form a bound state has been obtained.     

Nonlinear compression of optical solitons

In this paper, we consider nonlinear Schrödinger (NLS) equations, both in the anomalous and normal dispersive regimes, which govern the propagation of a single field in a fiber medium with phase modulation and fibre gain (or loss). The integrability conditions are arrived from linear eigen value problem. The variable transformations which connect the integrable form of modified NLS equations are presented. We succeed in Hirota bilinearzing the equations and on solving, exact bright and dark soliton solutions are obtained. From the results, we show that the soliton is alive, i.e. pulse area can be conserved by the inclusion of gain (or loss) and phase modulation effects.     

(1+2)维各向同性介质中的旋转椭圆空间光孤子

从(1+2)维非局域非线性薛定谔方程出发, 通过坐标变换得到了旋转坐标系下的非局域非线性薛定谔方程. 假设响应函数为高斯型, 用虚时间法数值求解了旋转坐标系下的非局域非线性薛定谔方程的静态孤子解, 迭代出了不同非局域程度条件下的静态椭圆孤子数值解. 最后采用分步傅里叶算法, 以迭代的孤子解作为初始输入波形, 模拟了在不同的非局域程度条件下, (1+2)维椭圆空间光孤子的旋转传输特性. 强非局域时, 椭圆光孤子的长轴方向和短轴方向波形都是高斯型, 其他的非局域程度下, 不是高斯型. 由此表明：(1+2)维椭圆光孤子对非局域程度依赖性很强. 旋转角速度和功率均与非局域程度以及孤子的椭圆度有关.     

Defect solitons supported by the interface between simple lattices and superlattices

We study surface defect solitons (SDSs) at an interface between superlattices and simple lattices with focusing saturable nonlinearity. The properties of the SDSs formed in such kinds of mixed structures are obviously different from those in single superlattices or single ordinary lattices. Research results show that surface solitons with a zero defect or a positive defect are stable in the semi-infinite gap and cannot exist in the first gap. For the case of a negative defect, the stable region of surface solitons will be narrower in the semi-infinite gap with the increase of the defect depth. Surface gap solitons (SGSs) can stably exist in the first gap for a deeper negative defect depth.     

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.     

Collision of optical solitons with Kerr law nonlinearity

The intra-channel collision of optical solitons, with Kerr law nonlinearity, is studied by the aid of quasi-particle theory. The perturbation terms considered in this paper are all of Hamiltonian type. It is shown that the soliton–soliton interaction can be suppressed in the presence of these perturbations, namely, the self-steepening, the third-order dispersion, the fourth-order dispersion and the frequency separation between the soliton carrier and the gain-center frequency. The prediction of quasi-particle theory are fully confirmed by direct numerical simulations.     

Dark solitons in optical fiber with inhomogeneous effects

We study the nonlinear wave propagation in an inhomogeneous optical fiber core in the normal dispersive regime. In order to include the inhomogeneous physical effects, the nonlinear Schrödinger equation (NLSE), which governs the solitary pulse propagation in optical fiber, is modified by adding terms for phase modulation and power gain or loss. The modified NLSEs are bilinearized and exact dark soliton solutions are obtained. The results are discussed.     

Spinning solitons in cubic-quintic nonlinear media

We review recent theoretical results concerning the existence, stability and unique features of families of bright vortex solitons (doughnuts, or ‘spinning’ solitons) in both conservative and dissipative cubic-quintic nonlinear media.     

Femtosecond second-order solitons in optical fiber transmission

A propagation of the femtosecond second-order solitons in an optical fiber is studied. We show that a generalized nonlinear Schrödinger equation well describes the propagation of the second-order soliton even containing only a few optical cycles. The propagations of a 50 fs and a 10 fs second-order soliton in an optical fiber are numerically simulated. It is found that, for the case of 10 fs second-order soliton, the soliton decay is dominated by the third-order dispersion, in contrast to the case of 50 fs second-order solitons, where the soliton decay is dominated by the delayed Raman response. It is also found that the exact delayed Raman response form must be used for the propagation of the 50 fs or less than 50 fs second-order soliton.     

Optical solitons and optical rogons of generalized resonant dispersive nonlinear Schrödinger's equation with power law nonlinearity

This paper obtains solitons and singular periodic solutions to the generalized resonant dispersive nonlinear Schrödinger’ equation with power law nonlinearity. There are several integration tools that are adopted to extract these solutions. They are simplest equation method, functional variable method, sine–cosine function method, tanh function method and the G′/G-expansion method. These integration techniques reveal bright and singular solitons as well as the corresponding singular periodic solutions to the nonlinear evolution equation. These solitons solutions are important in the nonlinear fiber optics community as well as in the study of rogue waves.     

Dipole solitons in an optical lattice with longitudinal modulation

In this paper, we numerically demonstrate the (1+1)-dimensional dipole solitons can exist in a new Kerr-type optical lattice with longitudinal modulation that fades away and boosts up alternately. The solitons whose two dipoles simultaneously located at one lattice site and at two adjacent lattice sites are investigated, respectively. The results show that, in the two cases, the dipole solitons can be stably trapped in this kind of lattice by properly adjusting lattice parameters and soliton parameters when the repulsive force of dipoles balances the centripetal force resulting from the lattice potential effect on dipole solitons. In addition, the trapping of dipole solitons with an incident angle or the initial center position is discussed.     

A new conserved quantity for non-Kerr law optical solitons

This paper talks about a new conservation law in non-Kerr law media. This new integral of motion is used to provide an equation for the phase of the soliton. This law is also used to obtain the adiabatic variation of the soliton phase due to perturbation terms in a non-Kerr law media that includes the power law, parabolic law and the dual-power law.     

e指数型横场效应对孤子传输的影响

当横场具有e指数型时,精确的孤子将不再存在。本文分析了e指数型横场效应对孤子传输的影响。结果表明e指数型横场效应对孤子传输的影响与损耗对弧子传输的影响是相同的。     

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.     

Amplifying optical signals with discrete solitons in waveguide arrays

We present a design and protocol to achieve an essential feature of an optical transistor, namely the amplification of input signal with the use of discrete solitons in waveguide arrays. We consider the scattering of a discrete soliton by a reflectionless potential in the presence of a control soliton. We show that at the sharp transition region between full reflectance and full transmittance, the intensity of the reflected or transmitted soliton is highly sensitive to the intensity of the control soliton. This suggests a setup of signal amplifier. For realistic purposes, we modulate the parameters of the reflectionless potential well to achieve a performance of amplifier with a controllable amplification. To facilitate the experimental realization, we calculate the amplification factor in terms of the parameters of the potential well and the input power of the control soliton. The suggested signal amplifier device will be an important component in the all-optical data processing.     

A collective variable approach for optical solitons in the cubic-quintic complex Ginzburg-Landau equation with third-order dispersion

Considering the theory of electromagnetic, especially from the Maxwell equations, a basic equation modeling the propagation of ultrashort optical solitons in optical fibers is derived, namely a cubic-quintic complex Ginzburg-Landau equation (CQGLE) with third-order dispersion (TOD). Considering this one-dimensional CQGLE, we derive the equations of motion of pulse parameters called collective variables (CVs), of a pulse propagating in dispersion-managed (DM) fiber optic-links. Equations obtained are investigated numerically in order to view the evolution of pulse parameters along the propagation distance. A fully numerical simulation of the CQGLE finally tests the results of the CV theory. It appears chaotic pulses, attenuate pulses and stable pulses under some parameter values.     

Space solitons in gas mixtures

Evidences that there are incoherent space solitons at discharges in gas mixtures at normal conditions are presented. A new mechanism of optical quadratic nonlinearity responsible for an increase in the refraction index of gas mixture is considered. It is shown that an intense light produced at a discharge in a gas mixture is instable and optical incoherent spatial solitons appear in a form of thin spherical layers where an intense white light circulates in all possible directions and provides concentration of the mixture molecules with maximal refraction index.     

Multi-peak solitons in PT-symmetric Bessel optical lattices with defects

This paper presents a theoretical analysis of the existence and stability of multi-peak solitons in parity–time-symmetric Bessel optical lattices with defects in nonlinear media. The results demonstrate that there always exists a critical propagation constant μ _c for the existence of multi-peak solitons regardless of whether the nonlinearity is self-focusing or self-defocusing. In self-focusing media, multi-peak solitons exist when the propagation constant μ > μ _c . In the self-defocusing case, solitons exist only when μ < μ _c . Only low-power solitons can propagate stably when random noise perturbations are present. Positive defects help stabilize the propagation of multi-peak solitons when the nonlinearity is self-focusing. When the nonlinearity is self-defocusing, however, multi-peak solitons in negative defects have wider stable regions than those in positive defects.