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.     

Optical soliton perturbation in a non-Kerr law media

This paper studies the optical soliton perturbation by the aid of soliton perturbation theory. The various perturbation terms, that arise in the study of optical solitons, are exhaustively studied in this paper. The adiabatic parameter dynamics of optical solitons are obtained in presence of these perturbation terms. The types of nonlinearities that are considered are Kerr law, power law, parabolic law as well as the dual-power law.     

Stochastic perturbation of Kerr law optical solitons

The soliton perturbation theory is used to study and analyze the stochastic perturbation of optical solitons, due to Kerr law nonlinearity, in addition to deterministic perturbations of optical solitons that is governed by the nonlinear Schrödingers equation. The Langevin equations are derived and analyzed. The deterministic perturbations that are considered here are of both Hamiltonian as well as of non-Hamiltonian type.     

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.     

Stochastic Perturbation of Power Law Optical Solitons

The soliton perturbation theory is used to study and analyze the stochastic perturbation of optical solitons, with power law nonlinearity, in addition to deterministic perturbations, that is governed by the nonlinear Schrödinger’s equation. The Langevin equations are derived and analysed. The deterministic perturbations that are considered here are due to filters and nonlinear damping.     

Stochastic perturbation of dispersion-managed optical solitons

The stochastic perturbation of dispersion-managed optical solitons is studied in this paper, in addition to deterministic preturbation terms, by the aid of soliton perturbation theory. The super-Gaussian pulses are considered and the corresponding Langevin equations are derived and analyzed. It is shown that in presence of the perturbation terms, the soliton propagates down the fiber with a fixed mean energy.OCIS Codes: 060.2310; 060.4510; 060.5530; 190.4370     

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.     

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     

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.     

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.     

Dynamics of bound vector solitons induced by stochastic perturbations: Soliton breakup and soliton switching

We respectively investigate breakup and switching of the Manakov-typed bound vector solitons (BVSs) induced by two types of stochastic perturbations: the homogenous and nonhomogenous. Symmetry-recovering is discovered for the asymmetrical homogenous case, while soliton switching is found to relate with the perturbation amplitude and soliton coherence. Simulations show that soliton switching in the circularly-polarized light system is much weaker than that in the Manakov and linearly-polarized systems. In addition, the homogenous perturbations can enhance the soliton switching in both of the Manakov and non-integrable (linearly- and circularly-polarized) systems. Our results might be helpful in interpreting dynamics of the BVSs with stochastic noises in nonlinear optics or with stochastic quantum fluctuations in Bose–Einstein condensates.     

Femtosecond Pulse Propagation in Optical Fibers Under Higher Order Effects: A Collective Variable Approach

Employing collective variable approach, femtosecond pulse propagation has been investigated in optical fibers using the higher order nonlinear Schrödinger equation. In order to view the pulse dynamics along the propagation distance, variation of different pulse parameters, called collective variables, such as pulse amplitude, width, chirp, pulse center and frequency has been investigated by numerically solving the set of ordinary equations obtained from collective variable approach.     

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.     

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.     

槽中双孤子互作用的微扰求解

孤子运动的Miles方程是一个具特征的非线性Schrdinger型方程.借求孤子解的微扰法,导出所遵循的矩阵方程,和孤子解的修正量δu(x,λ).并据双孤子解,计算了它的周期互作用状态 关键词： Miles方程 微扰双孤子解     

Perturbation of Super-Sech Solitons in Dispersion-Managed Optical Fibers

The dynamics of super-sech solitons in dispersion-managed optical fibers is obtained in this paper. The dynamical system of soliton parameters is obtained for such pulses for dispersion-managed fibers, in presence of various perturbation terms. The perturbation terms studied are Hamiltonian, as well as non-Hamiltonian along with non-local types.     

A Hopf-like equation and perturbation theory for differential delay equations

We extend techniques developed for the study of turbulent fluid flows to the statistical study of the dynamics of differential delay equations. Because the phase spaces of differential delay equations are infinite dimensional, phase-space densities for these systems are functionals. We derive a Hopf-like functional differential equation governing the evolution of these densities. The functional differential equation is reduced to an infinite chain of linear partial differential equations using perturbation theory. A necessary condition for a measure to be invariant under the action of a nonlinear differential delay equation is given. Finally, we show that the evolution equation for the density functional is the Fourier transform of the infinite-dimensional version of the Kramers-Moyal expansion.     

Stochastic equations of the Langevin type under a weakly dependent perturbation

Asymptotic expansions for the probability density of the solution of a stochastic differential equation under a weakly dependent perturbation are proposed. In particular, linear partial differential equations for the first two terms of the correlation time expansion are derived. It is shown that in these expansions the boundary layer part appears and non-Gaussianity of the perturbation is important for the Fokker-Planck approximation correction.     

Coupled matter-wave solitons in optical lattices

We make use of a potential model to study the dynamics of two coupled matter-wave or Bose-Einstein condensate (BEC) solitons loaded in optical lattices. With separate attention to linear and nonlinear lattices we find some remarkable differences for response of the system to effects of these lattices. As opposed to the case of linear optical lattice (LOL), the nonlinear lattice (NOL) can be used to control the mutual interaction between the two solitons. For a given lattice wave number k, the effective potentials in which the two solitons move are such that the well (V_eff(NOL)), resulting from the juxtaposition of soliton interaction and nonlinear lattice potential, is deeper than the corresponding well V_eff(LOL). But these effective potentials have opposite k dependence in the sense that the depth of V_eff(LOL) increases as k increases and that of V_eff(NOL) decreases for higher k values. We verify that the effectiveness of optical lattices to regulate the motion of the coupled solitons depends sensitively on the initial locations of the motionless solitons as well as values of the lattice wave number. For both LOL and NOL the two solitons meet each other due to mutual interaction if their initial locations are taken within the potential wells with the difference that the solitons in the NOL approach each other rather rapidly and take roughly half the time to meet as compared with the time needed for such coalescence in the LOL. In the NOL, the soliton profiles can move freely and respond to the lattice periodicity when the separation between their initial locations are as twice as that needed for a similar free movement in the LOL. We observe that, in both cases, slow tuning of the optical lattices by varying k with respect to a time parameter τ drags the oscillatory solitons apart to take them to different locations. In our potential model the oscillatory solitons appear to propagate undistorted. But a fully numerical calculation indicates that during evolution they exhibit decay and revival.     

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.