Lluís Torner Sabata

Nonlocal surface dipoles and vortices

We predict the existence and address the stability of two-dimensional surface solitons featuring topologically complex shapes, including dipoles, vortices, and bound states of vortex solitons, at the interface of nonlocal thermal media. Unlike their counterparts in bulk media, surface dipoles are found to be stable in the entire existence domain. Surface vortices are found to exhibit strongly asymmetric intensity and phase distributions, and are shown to be stable, too. Bound states of surface vortex solitons belong to a class of surface solitons having no counterparts in bulk media. Such states are found to be stable provided that their energy flow does not exceed an upper threshold. Our findings constitute an example of topologically complex solitons located at nonlocal two-dimensional interfaces.

Enhaced soliton interactions by inhomogeneous nonlinearity and nonlocality (artno 33812)

We address the interactions between optical solitons in the system with longitudinally varying nonlocality degree and nonlinearity strength. We consider a physical model describing light propagation in nematic liquid crystals featuring a strongly nonlocal nonlinear response. We reveal that the variation of the nonlocality and nonlinearity along the propagation direction can substantially enhance or weaken the interaction between out-of-phase solitons. This phenomenon manifests itself as a slowdown or acceleration of the soliton collision dynamics in one-dimensional geometries or of the soliton spiraling rate in bulk media. Therefore, one finds that by engineering the nonlocality and nonlinearity variation rate one can control the output soliton location.

Diffraction control in P T -symmetric photonic lattices: from beam rectification to dynamic localization

We address the propagation of light beams in longitudinally modulated PT-symmetric lattices, built as arrays of couplers with periodically varying separation between their channels, and show a number of possibilities for efficient diffraction control available in such nonconservative structures. The dynamics of light in such lattices crucially depends on the ratio of the switching length for the straight segments of each coupler and the longitudinal lattice period. Depending on the longitudinal period, one can achieve either beam rectification when the input light propagates at a fixed angle across the structure without diffractive broadening or dynamic localization when the initial intensity distribution is periodically restored after each longitudinal period. Importantly, the transition between these two different propagation regimes can be achieved by tuning only gain and losses acting in the system, provided that the PT symmetry remains unbroken. The impact of Kerr nonlinearity is also discussed.

Stable vortex-soliton tori with multiple nested phase singularities in dissipative media

We show the existence of stable two- and three-dimensional vortex solitons carrying multiple, spatially separated, single-charge topological dislocations nested in a common vortex-ring core. Such nonlinear states are supported by elliptical gain landscapes in focusing nonlinear media with two-photon absorption. The separation between the phase dislocations is dictated mostly by the geometry of the gain landscape, and it only slightly changes upon variation of the gain or absorption strength.

Diagrammatic analysis of nonlinear planar waveguides

We show that universal V–b diagrams provide a powerful tool for analyzing the properties of nonlinear TE-polarized waves guided by optical planar structures. Here we focus on a waveguide consisting of an optically linear film bounded by a saturable nonlinear substrate and cladding. Relevant information on existence conditions and stability of the different allowed nonlinear guided waves is summarized in a few diagrams, and waveguiding properties can be immediately read off them. Critical, power-independent values of the various waveguide parameters for the different kinds of wave that exist have been identified, and we give the condition in parameter space that ensures stable propagation in a symmetric structure.

Diffraction management of focused light beams in optical lattices with a quadratic frequency modulation

We reveal that the effective diffraction experienced by light beams launched along the central guiding channel of optical lattice with a quadratic frequency modulation can be tuned in strength and sign. Complete suppression of the linear diffraction in the broad band of spatial frequencies is shown to be possible, thus profoundly affecting properties of nonlinear self-sustained beams as well. In particular, we report on the properties of a new class of stable solitons supported by such lattices in defocusing media.

Rotating vortex clusters in media with inhomogeneous defocusing nonlinearity

We show that media with inhomogeneous defocusing cubic nonlinearity growing toward the periphery can support a variety of stable vortex clusters nested in a common localized envelope. Nonrotating symmetric clusters are built from an even number of vortices with opposite topological charges, located at equal distances from the origin. Rotation makes the clusters strongly asymmetric, as the centrifugal force shifts some vortices to the periphery, while others approach the origin, depending on the topological charge. We obtain such asymmetric clusters as stationary states in the rotating coordinate frame, identify their existence domains, and show that the rotation may stabilize some of them.

Dynamic localization in optical and Zeeman lattices in the presence of spin-orbit coupling

The dynamic localization of a two-level atom in a periodic potential under the action of spin-orbit coupling and a weak harmonically varying linear force is studied. We consider optical and Zeeman potentials that are either in phase or out of phase in two spinor components, respectively. The expectation value for the position of the atom after one oscillation period of the linear force is recovered in authentic resonances or in pseudoresonances. The frequencies of the linear force corresponding to authentic resonances are determined by the band structure of the periodic potential and are affected by the spin-orbit coupling. The width or dispersion of the wave packet in authentic resonances is usually minimal. The frequencies corresponding to pseudoresonances do not depend on the type of potential and on the strength of the spin-orbit coupling, while the evolution of excitations at the corresponding frequencies is usually accompanied by significant dispersion. Pseudoresonances are determined by the initial phase of the linear force and by the quasimomentum of the wave packet. Due to the spinor nature of the system, the motion of the atom is accompanied by periodic, but not harmonic, spin oscillations. Under the action of spin-orbit coupling the oscillations of the wave packet can be nearly completely suppressed in optical lattices. Dynamic localization in Zeeman lattices is characterized by doubling of the resonant oscillation periods due to band crossing at the boundary of the Brillouin zone. We also show that higher harmonics in the Fourier expansion of the energy band lead to effective dispersion, which can be strong enough to prevent dynamic localization of the Bloch wave packet.

Topological light bullets supported by spatiotemporal gain

We reveal that the competition between diffraction, cubic nonlinearity, two-photon absorption, and gain localized in both space and time results in arrest of collapse, suppression of azimuthal modula-tion instabilities for spatiotemporal wavepackets, and formation of stable three-dimensional light bul-lets. We show that Gaussian spatiotemporal gain landscapes support bright, fundamental light bullets, while gain landscapes featuring a ring-like spatial and a Gaussian temporal shapes may support stable vortex bullets carrying topological phase dislocations.

Ultranarrow optical beams in quadratically nonlinear media

The vector Maxwell equations for the first-and second-harmonic planar beams are solved with allowance made for the nonlinear diffraction that weakens quadratic nonlinearity. The structure of the transverse and longitudinal components of the electromagnetic field of a parametric soliton is calculated for different values of the wave vector and phase mismatch. Exact analytic expressions are obtained for the self-similar profiles of extremally narrow solitons, and it is shown that the width has a fundamental limit of the order of a wavelength in a linear medium.