Gap solitons

Novel effects for few-cycle pulses propagation in quadratic media with dispersion management are considered. First, the process of extraordinary wave generation in uniaxial crystal is tightly related with the process of ordinary wave profile differentiation. Velocity mismatch limits interaction efficiency and leads to splitting of generated waves into two subpulses. Such effect can be suppressed in the medium with periodic modulation of quadratic nonlinearity or with velocity mismatch sign modulation. Second, highly interesting effects arise with the third-order dispersion. Dispersive spreading can be reduced in layered medium with alternating third-order dispersion coefficients. Quadratic photonic crystals with modulated dispersion coefficients or with managed dispersion are very promising for few-cycle pulse nonlinear optics. One- and two-wave soliton trapping and propagation dynamics are also studied in such crystals. The analytical theory is accompanied with the numerical simulation results.

Magnetostatic surface wave (MSSW) bright solitons in a ferrite-dielectric-metal (FDM) structure have been studied experimentally and numerically in the framework of the nonlinear Schro/spl uml/dinger equation. Attention was focused on the influence of the parametric instability on the soliton formation and propagation. We also discussed the contribution of the nonsolitary (dispersive wave) part of the MSSW pulse on the soliton propagation, to show that their mutual interference leads to the leveling off or to the appearance of some peaks in the MSSW pulse output versus the input amplitude. We have also shown that for MSSW pulses with rectangular shape, the linear pulse compression caused by an induced phase modulation of the input pulse must be taken into account. Experiments were performed on FDM microstrip structures loaded by a 14-/spl mu/m-thick yttrium iron garnet film, separated from the ground metal by an air gap with thickness h/sub 1//spl ap/100 /spl mu/m or h/sub 2//spl ap/200 /spl mu/m. It was found experimentally for MSSW with wavelength /spl lambda//spl ap/h that the modulation instability leads to soliton formation for rectangular input pulses with duration /spl tau/ less than the characteristic transient time t/sup */ needed for the onset of the parametric instability, while pulses with /spl tau//spl ges/t/sup */ are mainly subjected to parametric instability. The measured threshold amplitudes for parametric and modulation instabilities are in agreement with the theoretical predictions. An influence of additional pumping in the form of both continuous-wave and pulsed signals on the soliton formation was studied. It was shown that an additional pumping signal with duration /spl tau//spl ges/t/sup */, and amplitude above the threshold of the parametric instability, suppressed the MSSW soliton. Numerical modeling of the pulsewidth dependence on the microwave power during the propagation in the FDM structure yields results that are in agreement with the experimental observations. Moreover, pulse narrowing due to the induced phase modulation of the input pulse was numerically predicted. All of these effects are in agreement with the experimental findings.

Evolution of spatial solitons in quadratic media with fluctuating nonlinearity

We employ a time-dependent mean-field-hydrodynamic model to study the generation of bright solitons in a degenerate fermion–fermion mixture in a cigar-shaped geometry using variational and numerical methods. Due to a strong Pauli-blocking repulsion among identical spin-polarized fermions at short distances there cannot be bright solitons for repulsive interspecies interactions. Employing a linear stability analysis we demonstrate the formation of stable solitons due to modulational instability of a constant-amplitude solution of the model equations for a sufficiently attractive interspecies interaction. We perform a numerical stability analysis of these solitons and also demonstrate the formation of soliton trains by jumping the effective interspecies interaction from repulsive to attractive. These fermionic solitons can be formed and studied in laboratory with present technology.

We theoretically investigate the simultaneous formation and stable propagation of slow optical soliton pairs in semiconductor quantum dots with a four-level biexciton-exciton cascade configuration. Owing to the destructive interference set up by two continuous wave control fields that couple to a biexciton state, the linear as well as nonlinear dispersion can be dramatically enhanced simultaneously with the absorptions of two weak probe fields being almost suppressed. These results reveal that the detrimental distortions of the two weak-pulsed probe fields due to dispersion effects can be well balanced by the self-phase modulation effect under very low input light intensity, which leads to the slow temporal optical soliton pairs with matched group velocity and amplitude. We also show that the propagation of slow optical solitons can be strongly modified by the biexciton coherence.

Numerical studies of various aspects of two-dimensional Langmuir solitons, are made, viz., (i) instability and collapse of a planar soliton perturbed in the perpendicular direction, (ii) the effect of an approximate Landau damping on the collapse, and (iii) the generation and subsequent collapse of planar solitons by an external pump field. These computations verify the flow of energy from long wavelength pump fields, through soliton formation and collapse, to shorter wavelengths, where the energy is transferred to the electrons.

Novel insights into the propagation of the generalized Boussinesq equation: Dynamics of bidirectional symmetric solitary waves

We present experimental and numerical observations of transverse instability in quadratic media under conditions that emphasize the inherently spatiotemporal and multidimensional nature of the wave propagation. Intensity-dependent beam filamentation is shown to be closely connected to the periodic evolution of quadratic solitons, and implications for the generation of three-dimensional spatiotemporal solitons are discussed.

A harmonic balance technique is used to study the formation and interaction of solitons in discrete, lossless, nonlinear transmission lines as a function of the number of harmonics, number of LC-cells, and pulse height and width at the generator. It is shown that the number of harmonics required to accurately determine the soliton formation and propagation increases as the generator's fundamental frequency is decreased, and that about 500 LC-cells are needed to observe the propagation and interaction of solitons. It is also shown that, for the calculations presented, the transmission line is almost perfectly adapted. A Taylor series expansion was used to determine the continuous analog of the discrete transmission line presented. >

Strain solitons are quasi-dislocations that form in van der Waals materials to relieve the energy associated with lattice or rotational mismatch. Novel electronic properties of strain solitons were predicted and observed. To date, strain solitons have been observed only in exfoliated crystals or mechanically strained crystals. The lack of a scalable approach toward the generation of strain solitons poses a significant challenge in the study of and use of their properties. Here, we report the formation of strain solitons with epitaxial growth of bismuth on InSb(111)B by molecular beam epitaxy. The morphology of the strain solitons for films of varying thickness is characterized with scanning tunneling microscopy, and the local strain state is determined from atomic resolution images. Bending in the solitons is attributed to interactions with the interface, and large angle bending is associated with edge dislocations. Our results enable the scalable generation of strain solitons.

The dynamics of a system with three parametrically coupled waves with delayed feedback is considered. Results of the detailed numerical simulation of the onset of self-modulation, as well as complex dynamic and chaotic regimes, are presented. The relation of self-modulation regimes with the formation and propagation of solitons is investigated. It is discovered that as the pump parameter increases, the synchronization of phases of the interacting waves, which is characteristic of stationary generation and periodic self-modulation regimes, is violated, and the system goes to a chaotic regime via intermittency.

Hamiltonian chaos in two coupled three-wave parametric interactions with quadratic nonlinearity

The generation of Langmuir solitons at the resonance layer in a plasma irradiated by a strong high-frequency pump is investigated. The process is modelled by the nonlinear Schrödinger equation including an external pump, a density gradient and linear damping. The evolution equation is reformulated as an exact variational principle and the one-soliton generation process is studied by substituting various trial solutions. The applicability conditions for the nonlinear Schrödinger equation are re-examined and found to be more restrictive than previously stated.

Our aim in this research work is to formulate the exact traveling and solitary wave solutions of nonlinear diffusion reaction (DR) equation with quadratic and cubic nonlinearities by implementing the new technique which is a modified mathematical method. We have investigated the density independent nonlinear diffusion equation with convective flux term. As a result, we have found a variety of new exact traveling and solitary wave solutions in the form of dark solitons, bright solitons, combined dark-bright solitons, traveling wave, periodic wave solutions and we also represent the physical structure of the obtained solutions by two- and three-dimensional graphics by using the Mathematica software. This work proves the power, reliability and fruitfulness of this new technique.

Space plasmas provide abundant evidence of highly energetic particle population, resulting in a long-tailed non-Maxwellian distribution. Furthermore, the first stages in the evolution of plasmas produced during laser–matter interaction are dominated by nonthermal electrons, as confirmed by experimental observation and computer simulations. This phenomenon is efficiently modelled via a kappa-type distribution. We present an overview, from first principles, of the effect of superthermality on the characteristics of electrostatic plasma waves. We rely on a fluid model for ion-acoustic excitations, employing a kappa distribution function to model excess superthermality of the electron distribution. Focusing on nonlinear excitations (solitons), in the form of solitary waves (pulses), shocks and envelope solitons, and employing standard methodological tools of nonlinear plasmadynamical analysis, we discuss the role of excess superthermality in their propagation dynamics (existence laws, stability profile), geometric characteristics and stability. Numerical simulations are employed to confirm theoretical predictions, namely in terms of the stability of electrostatic pulses, as well as the modulational stability profile of bright- and dark-type envelope solitons.