Influence of dispersive waves on vector soliton propagation

In the present study, the nonlinear modulation of transverse waves propagating in a cubically nonlinear dispersive elastic medium is studied using a multi-scale expansion of wave solutions. It is found that the propagation of quasi-monochromatic transverse waves is described by a pair of coupled nonlinear Schrodinger (CNLS) equations. In the process of deriving the amplitude equations, it is observed that for a specific choice of material constants and wavenumber, the coefficient of nonlinear terms becomes zero, and the CNLS equations are no longer valid for describing the behaviour of transverse waves. In order to balance the nonlinear effects with the dispersive effects, by intensifying the nonlinearity, a new perturbation expansion is used near the critical wavenumber. It is found that the long time behaviour of the transverse waves about the critical wavenumber is given by a pair of coupled quintic nonlinear Schrodinger (CQNLS) equations. In the absence of one of the transverse waves, the CQNLS equations reduce to the single quintic nonlinear Schrodinger (QNLS) equation which has already been obtained in the context of water waves. By using a modified form of the so-called tanh method, some travelling wave solutions of the CQNLS equations are presented.

In this paper, the lattice Boltzmann method for convection-diffusion equation with source term is applied directly to solve some important nonlinear complex equations, including nonlinear Schrödinger (NLS) equation, coupled NLS equations, Klein-Gordon equation and coupled Klein-Gordon-Schrödinger equations, by using complex-valued distribution function and relaxation time. Detailed simulations of these equations are carried out. Numerical results agree well with the analytical solutions, which show that the lattice Boltzmann method is an effective numerical solver for complex nonlinear systems.

The concept of non-linear pulse is a symptom of such physical phenomenon inherently non linear, and its history is intimately linked to the development of theories of equations of nonlinear waves. As such, we now know that the non-linear pulses occur naturally in most nonlinear systems. This paper is devoted to modeling the evolution of nonlinear pulse during its propagation in a nonlinear directional coupler (NLDC) in terms of intermodal dispersion (IMD) in order to show the impact of these phenomena on the propagation in the (NLDC). In this case modeling the propagation in a nonlinear medium is governed by a system of coupled nonlinear Schrodinger equations (CNLSE). This is a mathematical model using to describe the (NDLC). The study is focused on the propagation of fundamental solitary pulses. Key words: Nonlinear optic, dispersive medium, nonlinear medium, modeling, temporal widening, optical coupler, nonlinear pulses, nonlinear fiber, coupled nonlinear Schrodinger equation (CNLSE), intermodal dispersion (IMD).

Conditions for stationary pulse propagation in the strong dispersion management regime

We address the formation and propagation of vector solitons in optical lattices in the presence of anisotropy-induced walk-off between ordinary and extraordinary polarized field components. Stable vector solitons trapped by the lattice form above a threshold power, while decreasing the lattice depth below a critical value results in the abrupt release of the caged solitons that then move across the lattice and may get trapped in a desired lattice channel.

Beaches with monazitic sands show high natural radiation, and the knowledge of this radiation is fundamental to simulate the effects of natural terrestrial radiation on biological systems. Monazite-rich sand from a beach in the southeastern Brazil were collected and analyzed by X-ray fluorescence, X-ray diffraction, and magnetic susceptibility. The natural terrestrial radiation of the beach sand showed a positive correlation with the Th and Y elements, which are closely associated with Ce, Nd, Ca, and P, suggesting that this grouping is mainly associated with local natural radiation. Based on the sand characterization, a physical simulator of natural gamma radiation was built with parameters similar to those of the monazite beach sand, considering areas with high natural radiation levels. The simulation revealed that the natural radiation of the monazite sands has a significant effect on reducing the growth of the bacteria strains of E. coli and S. aureus present in the beach sand, with a reduction of 23.8% and 18.4%, respectively.

Recent advance of emerging low-dimensional materials for vector soliton generation in fiber lasers

The impact of the first-order and second-order PMD on the performances of optical switching with NOLM is studied by the split-step Fourier method (SSFM) based on the coupled nonlinear Schrodinger equation (CNLSE), including optical eye graphs, power transmission function of the NRZ code and the Q-factor penalty of different code patterns at different working speeds. The simulation results show that the switching performances are deteriorated badly by PMD, and using the right code pattern can reduce the impact of PMD partially. Furthermore, the compensation method of PMD by the polarization-maintaining fiber (PMF) inside the fiber loop of NOLM is put forward. It influences the original switching performances to the least extent when the PMF is located in the middle of the fiber loop.

A set of two coupled nonlinear Schrodinger equations (CNLS) describes the two mode propagation in an optical fibre. The Painleve singularity structure analysis singles out two integrable parametric choices, including the Manakov model. Using the results of Painleve analysis, we succeed in Hirota bilinearizing the CNLS equations in both the anomalous as well as normal dispersion regions for the integrable cases. Solving the Hirota bilinear equations, bright and dark N-soliton solutions are explicitly obtained.

Performance deterioration induced by cross-phase modulation (XPM) in the basic nonlinear optical loop mirror (NOLM) switch unit in the digital optical communication system and analog microwave photonic communication system is studied by using the split-step Fourier method (SSFM) that can solve the coupled nonlinear Schrodinger equation (CNLSE). The simulation results show that the switching performance of basic NOLM unit is distorted by the XPM induced nonreciprocity when the splitting ratio of NOLM coupler f ≠ 0.5 and the distortion effect would be more serious with the increase of the working speed or the modulation bandwidth. In the digital optical communication system, the power transmission function of NOLM decreases in the range of 0 < f < 0.5 and increases in the range of 0.5 < f < 1. In the analog microwave photonic communication system, XPM induces the distortion of waveforms and the leak of side lobes. And the larger the modulation bandwidth is, the larger the leak of side lobes is.

Amplifier noise induces fluctuations on the soliton's mean frequency and amplitude. These fluctuations disturb the soliton phase difference, which modifies the soliton interaction. Amplifier noise jitter and soliton interaction cannot be studied independently for strongly interacting solitons in high-repetition-rate long-distance transmissions. A first-order analytical modeling for the jitter of two interacting solitons with periodic amplification is presented.

Coupled tapering/uptapering of dark soliton pair in nonlinear media

In this paper, we performed analytical, numerical and experimental studies on the generation of soliton waves in discrete nonlinear transmission lines (NLTL) with varactors, as well as the analysis of the losses impact on the propagation of these waves. Using the reductive perturbation method, we derived a nonlinear Schrödinger (NLS) equation with a loss term and determined an analytical expression that completely describes the bright soliton profile. Our theoretical analysis predicts the carrier wave frequency threshold above which a formation of bright solitons can be observed. We also performed numerical simulations to confirm our analytical results and we analyzed the space–time evolution of the soliton waves. A good agreement between analytical and numerical findings was obtained. An experimental prototype of the lossy NLTL, built at the discrete level, was used to validate our proposed model. The experimental shape of the envelope solitons is well fitted by the theoretical waveforms, which take into account the amplitude damping due to the losses in commercially available varactors and inductors used in a prototype. Experimentally observed changes in soliton amplitude and half–maximum width during the propagation along lossy NLTL are in good accordance with the proposed model defined by NLS equation with loss term.

The nonlinear Schrödinger equation in the finite line

Unitary quantum lattice gas algorithm generated from the Dirac collision operator for 1D soliton–soliton collisions