Collision of solitary waves in media with a second-order nonlinearity

Damping of persistent oscillations of quadratic optical solitons

We investigate the dynamics of optical soliton formation in media with quadratic nonlinearity under conditions of long-living oscillations produced by the soliton's internal modes. We compare the predictions of the second-order perturbation approach, combining it with the energy conservation law, with the direct numerical simulations using the transparent boundary conditions. We demonstrate that these two approaches correlate well and describe the nonlinear radiation damping of the internal modes.

Chaotic character of two-soliton collisions in the weakly perturbed nonlinear Schrödinger equation

We analyze the exact two-soliton solution to the unperturbed nonlinear Schrödinger equation and predict that in a weakly perturbed system (i) soliton collisions can be strongly inelastic, (ii) inelastic collisions are of almost nonradiating type, (iii) results of a collision are extremely sensitive to the relative phase of solitons, and (iv) the effect is independent on the particular type of perturbation. In the numerical study we consider two different types of perturbation and confirm the predictions. We also show that this effect is a reason for chaotic soliton scattering. For applications, where the inelasticity of collision, induced by a weak perturbation, is undesirable, we propose a method of compensating it by perturbation of another type.

Short-lived two-soliton bound states in weakly perturbed nonlinear Schrodinger equation

Resonant soliton collisions in the weakly discrete nonlinear Schrodinger equation are studied numerically. The fractal nature of the soliton scattering, described in our previous works, is investigated in detail. We demonstrate that the fractal scattering pattern is related to the existence of the short-lived two-soliton bound states. The bound state can be regarded as a two-soliton quasiparticle of a new type, different from the breather. We establish that the probability P of a bound state with the lifetime L follows the law P approximately L(-3). In the frame of a simple two-particle model, we derive the nonlinear map, which generates the fractal pattern similar to that observed in the numerical study of soliton collisions. (c) 2002 American Institute of Physics.

Complexity and regularity of vector-soliton collisions

In this paper, we extensively investigate the collision of vector solitons in the coupled nonlinear Schrödinger equations. First, we show that for collisions of orthogonally polarized and equal-amplitude vector solitons, when the cross-phase modulational coefficient beta is small, a sequence of reflection windows similar to that in the phi(4) model arises. When beta increases, a fractal structure unlike phi(4)'s gradually emerges. But when beta is greater than one, this fractal structure disappears. Analytically, we explain these collision behaviors by a variational model that qualitatively reproduces the main features of these collisions. This variational model helps to establish that these window sequences and fractal structures are caused entirely or partially by a resonance mechanism between the translational motion and width oscillations of vector solitons. Next, we investigate collision dependence on initial polarizations of vector solitons. We discovered a sequence of reflection windows that is phase induced rather than resonance induced. Analytically, we have derived a simple formula for the locations of these phase-induced windows, and this formula agrees well with the numerical data. Last, we discuss collision dependence on relative amplitudes of initial vector solitons. We show that when vector solitons have different amplitudes, the collision structure simplifies. Feasibility of experimental observation of these results is also discussed at the end of the paper.

Optical Spatial Solitons and Their Interactions: Universality and Diversity

Spatial solitons, beams that do not spread owing to diffraction when they propagate, have been demonstrated to exist by virtue of a variety of nonlinear self-trapping mechanisms. Despite the diversity of these mechanisms, many of the features of soliton interactions and collisions are universal. Spatial solitons exhibit a richness of phenomena not found with temporal solitons in fibers, including effects such as fusion, fission, annihilation, and stable orbiting in three dimensions. Here the current state of knowledge on spatial soliton interactions is reviewed.

Generation of soliton oscillations in nonlinear quadratic materials

We show analytically and numerically that the generation of long-lasting soliton oscillations in resonant chi(2) optical materials possesses a threshold for the amplitude of a fundamental wave. The persistent oscillations of solitary waves reported by Etrich et al. [Phys. Rev. E 54, 4321 (1996)] are found to appear for finite values of the wave amplitude.

Collisions between type II two-dimensional quadratic solitons

We report experimental and numerical results that describe collisions between two-dimensional type II quadratic solitons excited in a KTP crystal by fundamental waves of orthogonal polarization. Our results provide experimental evidence of the possibility of both inelastic collision (when two quadratic solitons merge at input into a single soliton at output) and quasi-elastic collision.

Trapping of slowly moving or stationary two-color gap solitons

We address the important problem of excitation of gap solitons of a parametric nature, which are sustained in periodically corrugated frequency-doubling media near Bragg resonance with both the fundamental frequency and its second harmonic. We demonstrate that a zero-velocity soliton can be trapped in a finite Bragg structure by the quiescence of two counterpropagating moving solitons, which in turn might be formed by injection of appropriate light pulses at a single carrier frequency.

Interactions between one-dimensional quadratic solitons

The interaction between two one-dimensional quadratic solitons has been investigated experimentally in lithium niobate planar waveguides for both parallel- and crossing-launched solitons.

Polarization-multiplexed x((2)) solitary-wave interactions

We investigate interactions between vectorial solitary waves through typeII second-harmonic generation. We demonstrate that one can tune the collision distance of two initially codirectional solitary waves changing their polarization state. Moreover, by adiabatic perturbation analysis, it is possible to predict such a collision distance as a function of solitary-wave separation, in good agreement with numerical simulations.

Multiple soliton bound states and symmetry breaking in quadratic media

We present a study of the dynamics of multiple soliton bound states in diffractive media with second-order nonlinearity. A numerical stability analysis of these bound states reveals that wave propagation in quadratic materials exhibits spatial symmetry-breaking instabilities.

Intensity-controlled interactions between vectorial spatial solitary waves in quadratic nonlinear media

We numerically investigate the interaction of vectorial solitary waves propagating in a bulk crystal with a phase-matchable quadratic nonlinearity. We obtain coalescence, steering, crossing, or repulsion by controlling the launched intensities in two orthogonal polarizations without any coherent seed at the second harmonic.