arXiv subjects

Dumitru Mihalache

Publications and source records attributed to Dumitru Mihalache.

64 records · Page 4Linked to original sources

arXiv2010

Vortices and ring dark solitons in nonlinear amplifying waveguides

We consider the generation and propagation of (2+1)-dimensional beams in a nonlinear waveguide with the linear gain. Simple self-similar evolution of the beams is achieved at the asymptotic stage, if the input beams represent the fundamental mode. On the contrary, if they carry vorticity or amplitude nodes (or phase slips), vortex tori and ring dark solitons (RDSs) are generated, featuring another type of the self-similar evolution, with an exponentially shrinking vortex core or notch of the RDS. Numerical and analytical considerations reveal that these self-similar structures are robust entities in amplifying waveguides, being \emph{stable} against azimuthal perturbations.

physics.optics↗

arXiv2009

Elliptic Vortices in Composite Mathieu Lattices

We address the elliptically shaped vortex solitons in defocusing nonlinear media imprinted with a composite Mathieu lattice. Elliptic vortices feature anisotropic patterns both in intensity and phase, and can only exist when their energy flow exceed some certain threshold. Single-charged elliptic vortices are found to arise via bifurcation from dipole modes, which, to the best of our knowledge is the first example in the context of optics studies of symmetry breaking bifurcations for the phase dislocations of different dimensionalities. Higher-order elliptic vortices with topological charge could exhibit spatially separated single-charged phase singularities, leading to their stabilization. The salient features of reported elliptic vortices qualitatively hold for other elliptic shaped confining potentials.

nlin.PS↗

arXiv2006

Generation of surface soliton arrays

We discover that at the edge of optical lattice imprinted in saturable nonlinear media one-dimensional surface solitons exist only within a band of light intensities, and that they cease to exist when the lattice depth exceeds an upper threshold. We also reveal the generation of arrays of two-dimensional surface solitons mediated by transverse modulational instability of one-dimensional solitons, a process that is found to exhibit specific features associated to properties of the optical lattice.

physics.optics↗

arXiv2006

Vortex stability in nearly two-dimensional Bose-Einstein condensates with attraction

We perform accurate investigation of stability of localized vortices in an effectively two-dimensional ("pancake-shaped") trapped BEC with negative scattering length. The analysis combines computation of the stability eigenvalues and direct simulations. The states with vorticity S=1 are stable in a third of their existence region, $0 $ $\allowbreak 0.43N_{\max}^{(S=1)}$, the fragments do not recombine, as each one collapses by itself. The results are compared with those in the full 3D Gross-Pitaevskii equation. In a moderately anisotropic 3D configuration, with the aspect ratio $\sqrt{10}$, the stability interval of the S=1 vortices occupies $\approx 40%$ of their existence region, hence the 2D limit provides for a reasonable approximation in this case. For the isotropic 3D configuration, the stability interval expands to 65% of the existence domain. Overall, the vorticity heightens the actual collapse threshold by a factor of up to 2. All vortices with $S\geq 2$ are unstable.

cond-mat.other↗

arXiv2006

Surface waves at the interface between left-handed and birefringent materials

We theoretically investigate the existence and properties of hybrid surface waves forming at interfaces between left-handed materials and dielectric birefringent media. The existence conditions of such waves are found to be highly relaxed in comparison to the original hybrid surface waves, discovered by Dyakonov, in configurations involving birefringent materials and right-handed media. Hybrid surface waves in left-handed materials feature remarkable properties: (i) a high degree of localization and (ii) coexistence of several guided solutions. The existence of several hybrid surface waves for the same parameter set is linked to the birefringent nature of the medium whereas the strong localization is related to the presence of the left-handed material. The hybrid surface modes appear for large areas in the parameter space.

physics.optics↗

arXiv2006

Exact soliton solutions and nonlinear modulation instability in spinor Bose-Einstein condensates

We find one-, two-, and three-component solitons of the polar and ferromagnetic (FM) types in the general (non-integrable) model of a spinor (three-component) model of the Bose-Einstein condensate (BEC), based on a system of three nonlinearly coupled Gross-Pitaevskii equations. The stability of the solitons is studied by means of direct simulations, and, in a part, analytically, using linearized equations for small perturbations. Global stability of the solitons is considered by means of the energy comparison. As a result, ground-state and metastable soliton states of the FM and polar types are identified. For the special integrable version of the model, we develop the Darboux transformation (DT). As an application of the DT, analytical solutions are obtained that display full nonlinear evolution of the modulational instability (MI) of a continuous-wave (CW) state seeded by a small spatially periodic perturbation. Additionally, by dint of direct simulations, we demonstrate that solitons of both the polar and FM types, found in the integrable system, are structurally stable, i.e., they are robust under random changes of the relevant nonlinear coefficient in time.

nlin.PS↗

arXiv2004

Multicolor vortex solitons in two-dimensional photonic lattices

We report on the existence and stability of multicolor lattice vortex solitons constituted by coupled fundamental frequency and second-harmonic waves in optical lattices in quadratic nonlinear media. It is shown that the solitons are stable almost in the entire domain of their existence, and that the instability domain decreases with the increase of the lattice depth. We also show the generation of the solitons, and the feasibility of the concept of lattice soliton algebra.

nlin.PS↗

arXiv2004

Spatiotemporal discrete multicolor solitons

We have found various families of two-dimensional spatiotemporal solitons in quadratically nonlinear waveguide arrays. The families of unstaggered odd, even and twisted stationary solutions are thoroughly characterized and their stability against perturbations is investigated. We show that the twisted and even solutions display instability, while most of the odd solitons show remarkable stability upon evolution.

nlin.PS↗

arXiv2003

Soliton "molecules": robust clusters of light bullets

We show how to generate robust self-sustained clusters of soliton bullets-spatiotemporal (optical or matter-wave) solitons. The clusters carry an orbital angular momentum being supported by competing nonlinearities. The "atoms" forming the "molecule" are fully three-dimensional solitons linked via a staircase-like macroscopic phase. Recent progress in generating atomic-molecular coherent mixing in Bose-Einstein condensates might open potential scenarios for the experimental generation of these soliton molecules with matter-waves.

nlin.PS↗

arXiv2002

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 Bose-Einstein condensates. Clusters with multipolar global wave fronts are non-stationary or at best flipping.

physics.optics↗