Dumitru Mihalache

Spatiotemporal optical solitons

In the course of the past several years, a new level of understanding has been achieved about conditions for the existence, stability, and generation of spatiotemporal optical solitons, which are nondiffracting and nondispersing wavepackets propagating in nonlinear optical media. Experimentally, effectively two-dimensional (2D) spatiotemporal solitons that overcome diffraction in one transverse spatial dimension have been created in quadratic nonlinear media. With regard to the theory, fundamentally new features of light pulses that self-trap in one or two transverse spatial dimensions and do not spread out in time, when propagating in various optical media, were thoroughly investigated in models with various nonlinearities. Stable vorticity-carrying spatiotemporal solitons have been predicted too, in media with competing nonlinearities (quadratic–cubic or cubic–quintic). This article offers an up-to-date survey of experimental and theoretical results in this field. Both achievements and outstanding difficulties are reviewed, and open problems are highlighted. Also briefly described are recent predictions for stable 2D and 3D solitons in Bose–Einstein condensates supported by full or low-dimensional optical lattices.

Subwavelength plasmonic lattice solitons in arrays of metallic nanowires.

We predict theoretically that stable subwavelength plasmonic lattice solitons (PLSs) are formed in arrays of metallic nanowires embedded in a nonlinear medium. The tight confinement of the guiding modes of the metallic nanowires, combined with the strong nonlinearity induced by the enhanced field at the metal surface, provide the main physical mechanisms for balancing the wave diffraction and the formation of PLSs. As the conditions required for the formation of PLSs are satisfied in a variety of plasmonic systems, we expect these nonlinear modes to have important applications to subwavelength nanophotonics. In particular, we show that the subwavelength PLSs can be used to optically manipulate with nanometer accuracy the power flow in ultracompact photonic systems.

Multipole vector solitons in nonlocal nonlinear media.

We show that multipole solitons can be made stable via vectorial coupling in bulk nonlocal nonlinear media. Such vector solitons are composed of mutually incoherent nodeless and multipole components jointly inducing a nonlinear refractive index profile. We found that stabilization of the otherwise highly unstable multipoles occurs below certain maximum energy flow. Such a threshold is determined by the nonlocality degree.

Varieties of Stable Vortical Solitons in Ginzburg-Landau Media with Radially Inhomogeneous Losses

Using a combination of the variation approximation and direct simulations, we consider the model of the light transmission in nonlinearly amplified bulk media, taking into account the localization of the gain, i.e., the linear loss shaped as a parabolic function of the transverse radius, with a minimum at the center. The balance of the transverse diffraction, self-focusing, gain, and the inhomogeneous loss provides for the hitherto elusive stabilization of vortex solitons, in a large zone of the parameter space. Adjacent to it, stability domains are found for several novel kinds of localized vortices, including spinning elliptically shaped ones, eccentric elliptic vortices which feature double rotation, spinning crescents, and breathing vortices.

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.

On multidimensional solitons and their legacy in contemporary Atomic, Molecular and Optical physics

This viewpoint relates to an article by B A Malomed, D Mihalache, F Wise, and L Torner (2005 J. Opt. B: Quantum Semiclass. Opt. 7 R53–R72) and was published as part of a series of viewpoints celebrating 50 of the most influential papers published in the Journal of Physics series, which is celebrating its 50th anniversary.

Stationary trapping of light beams in bulk second-order nonlinear media

The mutual trapping of fundamental and second harmonic, continuous-wave light beams propagating in bulk second-order nonlinear media is studied. We find numerically families of stationary, radially symmetric solitary waves. The transverse profiles of the trapped beams, their scaling properties, and their stability under propagation are investigated as a function of the total power and the linear wavevector-mismatch between the waves. We show that at phase-matching mutually trapped solitary waves exist for any total wave power, whereas they exist only above a threshold power for both positive and negative phase-mismatches.

Generation of surface soliton arrays

We discover that, at the edge of an optical lattice imprinted in a saturable nonlinear medium, 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 the transverse modulational instability of one-dimensional solitons, a process that is found to exhibit specific features associated to properties of the optical lattice.

Stability of spatial solitary waves in quadratic media.

We investigate the stability of bright solitary waves formed by the mutual trapping of the fundamental and second-harmonic waves propagating in a nonlinear quadratic medium. First, we find that most of the solitary waves are stable under propagation. Second, we study the evolution of the solitary waves in the presence of small linear absorption. At phase matching the adiabatic evolution of the solitary waves obeys an amplitude × width-squared rule.

Vector rogue waves in the Manakov system: diversity and compossibility

We employ a nonrecursive Darboux transformation formalism for obtaining a hierarchy of rogue wave solutions to the focusing vector nonlinear Schrodinger equations (Manakov system). The exact explicit rogue wave solutions up to the second order are presented. Typical rogue wave patterns such as Peregrine-type, triple, quadruple, and sextuple vector rogue waves, either bright–dark or bright–bright in their respective components, are put forward. Despite the diversity, there exists a universal compossibility that different rogue wave states could coexist for the same background parameters. It is also shown that the higher-order rogue wave hierarchy can indeed be thought of as a nonlinear superposition of a fixed well prescribed number of fundamental rogue waves. These results may help understand the protean rogue wave manifestations in areas ranging from hydrodynamics to nonlinear optics.