Space-time bullet trains via modulation instability and nonlocal solitons

Design of nematic liquid crystals to control microscale dynamics

The dynamics of small particles, both living such as swimming bacteria and inanimate, such as colloidal spheres, has fascinated scientists for centuries. If one could learn how to control and streamline their chaotic motion, that would open technological opportunities in the transformation of stored or environmental energy into systematic motion, with applications in micro-robotics, transport of matter, guided morphogenesis. This review presents an approach to command microscale dynamics by replacing an isotropic medium with a liquid crystal. Orientational order and associated properties, such as elasticity, surface anchoring, and bulk anisotropy, enable new dynamic effects, ranging from the appearance and propagation of particle-like solitary waves to self-locomotion of an active droplet. By using photoalignment, the liquid crystal can be patterned into predesigned structures. In the presence of the electric field, these patterns enable the transport of solid and fluid particles through nonlinear electrokinetics rooted in anisotropy of conductivity and permittivity. Director patterns command the dynamics of swimming bacteria, guiding their trajectories, polarity of swimming, and distribution in space. This guidance is of a higher level of complexity than a simple following of the director by rod-like microorganisms. Namely, the director gradients mediate hydrodynamic interactions of bacteria to produce an active force and collective polar modes of swimming. The patterned director could also be engraved in a liquid crystal elastomer. When an elastomer coating is activated by heat or light, these patterns produce a deterministic surface topography. The director gradients define an activation force that shapes the elastomer in a manner similar to the active stresses triggering flows in active nematics. The patterned elastomer substrates could be used to define the orientation of cells in living tissues. The liquid-crystal guidance holds a major promise in achieving the goal of commanding microscale active flows.

Temperature control of nematicon trajectories

Using modulation theory, we develop a simple [(2+1)-dimensional] model to describe the synergy between the thermo-optical and reorientational responses of nematic liquid crystals to light beams to describe the routing of spatial optical solitary waves (nematicons) in such a uniaxial environment. Introducing several approximations based on the nonlocal physics of the material, we are able to predict the trajectories of nematicons and their angular steering with temperature, accounting for the energy exchange between the input beam and the medium through one-photon absorption. The theoretical results are then compared to experimental data from previous studies, showing excellent agreement.

Electrically driven three-dimensional solitary waves as director bullets in nematic liquid crystals

Electric field-induced collective reorientation of nematic molecules is of importance for fundamental science and practical applications. This reorientation is either homogeneous over the area of electrodes, as in displays, or periodically modulated, as in electroconvection. The question is whether spatially localized three-dimensional solitary waves of molecular reorientation could be created. Here we demonstrate that the electric field can produce particle-like propagating solitary waves representing self-trapped "bullets" of oscillating molecular director. These director bullets lack fore-aft symmetry and move with very high speed perpendicularly to the electric field and to the initial alignment direction. The bullets are true solitons that preserve spatially confined shapes and survive collisions. The solitons are topologically equivalent to the uniform state and have no static analogs, thus exhibiting a particle-wave duality. Their shape, speed, and interactions depend strongly on the material parameters, which opens the door for a broad range of future studies.

Nonlinear competition in nematicon propagation

We investigate the role of competing nonlinear responses in the formation and propagation of bright spatial solitons. We use nematic liquid crystals (NLCs) exhibiting both thermo-optic and reorientational nonlinearities with continuous-wave beams. In a suitably prepared dye-doped sample and dual beam collinear geometry, thermal heating in the visible affects reorientational self-focusing in the near infrared, altering light propagation and self-trapping.

Self-phase modulation spectral broadening in two-dimensional spatial solitons: toward three-dimensional spatiotemporal pulse-train solitons

We demonstrate self-phase modulation (SPM) spectral broadening in two-dimensional solitons in homogeneous media using two different schemes. In the active mode, a train of pulses are collectively trapped and form a spatial soliton through a photorefractive, slowly responding, and electronically controlled self-focusing nonlinearity, and each pulse experiences spectral broadening by the fast SPM nonlinearity. In the passive mode, the pulse-train beam is guided in a waveguide that is optically induced by a continuous-wave thermal spatial soliton. The soliton formation increased the normalized spectral broadening factor from 0.5% up to 197%. This experiment presents significant progress toward the experimental demonstration of three-dimensional spatiotemporal pulse-train solitons.

Enhancement of third-harmonic generation in nonlocal spatial solitons

We report on the observation of Type I third-harmonic generation induced by a train of femtosecond laser pulses in nematic liquid crystals. We find that as the average power of the train is increased, the frequency conversion process is enhanced as a consequence of the tight confinement of the pulses into a nonlocal spatial soliton.