Lucian-Cornel Crasovan

Stability of spinning ring solitons of the cubic–quintic nonlinear Schrödinger equation

Abstract We investigate stability of (2+1)-dimensional ring solitons of the nonlinear Schrodinger equation with focusing cubic and defocusing quintic nonlinearities. Computing eigenvalues of the linearised equation, we show that rings with spin (topological charge) s=1 and s=2 are linearly stable, provided that they are very broad. The stability regions occupy, respectively, 9% and 8% of the corresponding existence regions. These results finally resolve a controversial stability issue for this class of models.

Stability of vortex solitons in the cubic-quintic model

Abstract We investigate one-parameter families of two-dimensional bright spinning solitons (ring vortices) in dispersive media combining cubic self-focusing and quintic self-defocusing nonlinearities. In direct simulations, the spinning solitons display a symmetry-breaking azimuthal instability, which leads to breakup of a soliton into a set of fragments, each being a stable nonspinning soliton. The fragments fly out tangentially to the circular crest of the original vortex ring. If the soliton’s energy is large enough, the instability develops so slowly that the spinning solitons may be regarded as virtually stable ones, in accord with earlier published results. Growth rates of perturbation eigenmodes with different azimuthal “quantum numbers” are calculated as a function of the soliton’s propagation constant κ from a numerical solution of the linearized equations. As a result, a narrow (in terms of κ ) stability window is found for extremely broad solitons with values of the “spin” s =1 and 2. However, analytical consideration of a special perturbation mode in the form of a spontaneous shift of the soliton’s central “bubble” (core of the vortex embedded in a broad soliton) demonstrates that even extremely broad solitons are subject to an exponentially weak instability against this mode. In actual simulations, a manifestation of this instability is found in a three-dimensional soliton with s =1. In the case when the two-dimensional spinning solitons are subject to tangible azimuthal instability, the number of the nonspinning fragments into which the soliton splits is usually, but not always, equal to the azimuthal number of the instability eigenmode with the largest growth rate.

Tandem light bullets

We put forward a novel strategy to achieve formation of fully three-dimensional light bullets. The new scheme is based on tandem structures where nonlinearity and group-velocity dispersion required for the self-trapping of light are spatially distributed, opening the door for the possibility that they are not necessarily contributed by the same crystal. We show that multicolor light bullets do exist for a variety of tandems with feasible domain lengths.

Erupting, flat-top, and composite spiral solitons in the two-dimensional Ginzburg–Landau equation

Abstract We present three novel varieties of spiraling and nonspiraling axisymmetric solitons in the complex cubic–quintic Ginzburg–Landau equation. These are irregularly “erupting” pulses and two different types of very broad stationary ones found near a border between ordinary pulses and expanding fronts. The region of existence of each pulse is identified numerically. We test their stability and compare their features with those of their counterparts in the one-dimensional and conservative two-dimensional models.

Stationary walking solitons in bulk quadratic nonlinear media

We study the mutual trapping of fundamental and second-harmonic light beams propagating in bulk quadratic nonlinear media in the presence of Poynting vector beam walk-off. We show numerically the existence of a two-parameter family of (2 + 1)-dimensional stationary, spatial walking solitons. We have found that the solitons exist at various values of material parameters with different wave intensities and soliton velocities. We discuss the differences between (2 + 1) and (1 + 1)-dimensional walking solitons and between walking and non-walking solitons.

Optical Dyakonov surface waves at magnetic interfaces

We address the existence and properties of lossless surface waves that form at interfaces between magnetic and birefringent media. We show that the angular domain of existence of Dyakonov surface waves for magnetic interfaces is significantly larger than that for nonmagnetic ones. Our results have important implications for the experimental generation of surface waves and for their potential applications based on guided-to-leaky transitions.

Globally linked vortex clusters in trapped wave fields.

We put forward the existence of a rich variety of fully stationary vortex structures, termed H clusters, made of an increasing number of vortices nested in paraxial wave fields confined by trapping potentials. However, we show that the constituent vortices are globally linked, rather than products of independent vortices. Also, they always feature a monopolar global wave front and exist in nonlinear systems, such as the Bose-Einstein condensates. Clusters with multipolar global wave fronts are nonstationary or, at best, flipping.

MULTIPLE-HUMPED BRIGHT SOLITARY WAVES IN SECOND-ORDER NONLINEAR MEDIA

The propagation of multiple-humped bright solitary waves in a diffractive medium with second-order nonlinearity is studied. It is shown that the multiple-humped bright solitary waves occur only for negative phase mismatches in a small interval of nonlinear wave numbers shifts and above a certain threshold energy flow. Numerical experiments reveal that the multiple-humped stationary solitary waves are unstable on propagation. The evolution of multiple-humped solitary waves shows that the instability leads to one of the following three scenarios of the solitary wave dynamics: (1) the spreading of the solitary wave, (2) the formation of a single-humped solitary wave from a multiple-humped solitary wave in a fusion-like process, and (3) the decay of the multiple-humped solitary waves into several fragments consisting of single-humped solitary waves.

Soliton Eigenvalue Control in Optical Lattices

We address the dynamics of higher-order solitons in optical lattices, and predict their self-splitting into the set of their single-soliton constituents. The splitting is induced by the potential introduced by the lattice, together with the imprinting of a phase tilt onto the initial multisoliton states. The phenomenon allows the controllable generation of several coherent solitons linked via their Zakharov-Shabat eigenvalues. Application of the scheme to the generation of correlated matter waves in Bose-Einstein condensates is discussed.

Soliton clusters in three-dimensional media with competing cubic and quintic nonlinearities

We introduce a class of robust soliton clusters composed of N fundamental solitons in three-dimensional media combining the self-focusing cubic and self-defocusing quintic nonlinearities. The angular momentum is lent to the initial cluster through staircase or continuous ramp-like phase distribution. Formation of these clusters is predicted analytically, by calculating an effective interaction Hamiltonian Hint. If a minimum of Hint is found, direct three-dimensional simulations demonstrate that, when the initial pattern is close to the predicted equilibrium size, a very robust rotating cluster does indeed exist, featuring persistent oscillations around the equilibrium configuration (clusters composed of N = 4,5, and 6 fundamental solitons are investigated in detail). If a strong random noise is added to the initial configuration, the cluster eventually develops instability, either splitting into several fundamental solitons or fusing into a nearly axisymmetric vortex torus. These outcomes match the stability or instability of the three-dimensional vortex solitons with the same energy and spin; in particular, the number of the fragments in the case of the break-up is different from the number of solitons in the original cluster, being instead determined by the dominant mode of the azimuthal instability of the corresponding vortex soliton. The initial form of the phase distribution is important too: under the action of the noise, the cluster with the built-in staircase-like phase profile features azimuthal instability, while the one with the continuous distribution fuses into a vortex torus.