Narrow Results

We investigate 2-dimensional spatial optical solitons in media exhibiting a large nonlocal response coupled with a self-focusing nonlinearity. To this extent, with reference to a specific system in undoped nematic liquid crystals, we develop a general theory of spatial solitons in media with an arbitrary degree of nonlocality and carry out experimental observations to validate the model. The remarkable agreement between predictions and data yields evidence of narrow-waist solitons, revealing an important connection between nonparaxiality and nonlocality and emphasizing the role of nonlocality.

We start by reviewing the basic physical properties of cavity solitons, embedding this phenomenon in the general framework of optical instabilities and optical pattern formation. Next, we focus on the case of semiconductor microcavities and consider a first principle model. Its homogeneous stationary solutions and their stability are evaluated analytically. With the help of numerical simulations, we discuss two case studies, one in the passive and one in the active configuration.

Experiments are reviewed on quadratic solution generation, and soliton interactions between each other and with a nonlinear interface in non-critical birefringence phase-matched KNbO₃ and periodically poled KTP. Spatially symmetric and asymmetric patterns of multiple soliton-like beam generation were observed and interpreted when only a high intensity fundamental beam is used as the input. The nonlinear reflection of quadratic solitons from a nonlinear interface characterized by a half wavelength shift in the poling structure was obtained. Finally the interactions between pairs of solitons were measured in KNbO₃, including the creation of new solitons in non-coplanar geometries.

Optical propagation in nematic liquid crystals is characterized by a large and highly-nonlocal Kerr-like nonlinearity. We investigate the fundamental role played by spatial nonlocality in nonlinear optical propagation, and develop a model able to predict the main features of spatial solitons and modulational instability in nematic liquid crystals. The model unifies solitons in physical systems exhibiting different degrees of nonlocality, disclosing a connection between nonlocal solitons and parametric solitons in quadratic media. Finally, soliton breathing as well as other characteristics of nonlocal propagation are experimentally demonstrated in a specifically-engineered liquid crystal cell.

Extraordinary-wave nematicons can be launched and steered in angle by acting on the applied voltage. In specifically designed glass cells for planarly aligned nematic liquid crystals, their direction of propagation can be externally-controlled over angles as large as seven degrees.

We present a comprehensive review on the routing of self-confined light-beams in liquid crystals, i.e., generation, propagation and angular steering of self-induced waveguides or spatial solitons in a nonlinear non local dielectric with a large electro-optic response. We describe all-optical routing through soliton-soliton or soliton-beam interactions, as well as voltage-controlled steering in an anisotropic geometry via birefringence or refraction/reflection at a graded interface.

The study of optical solitons and light filaments steering in liquid crystal requires the utilization of particular cells designed for top view investigation and realized with an input interface which enables the control of the molecular director configuration, preventing light scattering. Actually, the director orientation imposed by this additional interface is estimated only by experimental observations. We report a simple model describing the distribution of the director orientation inside a liquid crystal sample under the anchoring action of multiple interfaces. The model is based on the elastic continuum theory, and strong anchoring is taken into account for boundary conditions. Results are in good agreement with experimental observations.

We study light localization in nonlinear non-local nematic liquid crystals capable of optical gain. We address the role of optical amplification on nonlinear beam propagation, considering various forms of gain and configurations.

We review the mathematical modelling of propagation and specific interactions of solitary beams in nematic liquid crystals — so-called nematicons. The theory is first developed for the evolution of a single nematicon; then it is extended to the interaction of two nematicons of different wavelengths, employing linear momentum conservation equations to predict that two colour nematicons can form a vector bound state. Considering optical vortices, we show that the nonlocal response of liquid crystals stabilises a single vortex, unstable in local media. Moreover, the interaction with a nematicon in another colour can stabilise a vortex for nonlocalities far below those at which an isolated vortex remains unstable. When multiple nematicons of the same wavelength interact, the radiation they shed can join them together, still resulting in a vortex. Finally, we discuss the escape of a nematicon from a nonlinear waveguide, using simple modulation theory based on momentum conservation to model the effect and get excellent agreement with the experimental results.

A nonlinear Helmholtz equation is proposed for modelling scalar optical beams in uniform planar waveguides whose refractive index exhibits a purely-focusing dual power-law dependence on the electric field amplitude. Two families of exact analytical solitons, describing forward- and backward-propagating beams, are derived. These solutions are physically and mathematically distinct from those recently discovered for related nonlinearities. The geometry of the new solitons is examined, conservation laws are reported, and classic paraxial predictions are recovered in a simultaneous multiple limit. Conventional semi-analytical techniques assist in studying the stability of these nonparaxial solitons, whose propagation properties are investigated through extensive simulations.

We report on power-dependent self-transverse acceleration of optical spatial solitons in two settings: pure nematic liquid crystals, where the self-steering is a consequence of all-optical reorientation through nonlinear changes in birefringent walk-off, and dye-doped nematic liquid crystals, where the guest-host interaction amplifies reorientation and enhances the transverse force acting on the soliton, thus changing its trajectory.

We investigate spatial XPM-paired solitons in nonlinear metamaterials (MMs) based on the (1 + 1)-dimensional coupled nonlinear Schrodinger equation (NLSE) describing the co-propagation of two optical beams of different frequencies in the MM with a Kerr-type nonlinear polarization. Three types of XPM-paired solitons including bright-bright, bright-dark and dark-dark solitons for different combination of the signs of refractive index experienced by the two beams, respectively, are obtained by using a generalized hyperbolic function method, which makes the temporal XPM-paired solitons in optical fibers find their spatial counterparts in MMs. Numerical simulations are performed to confirm the theoretical predictions and further identify the propagation properties of the spatial XPM-paired solitons in MMs described by Drude model.

In this work, we study nematicons propagation at the disclination lines in a wedge-shaped planarly oriented sample. Using optimal beam parameters for light self-trapping and varying the input beam position and direction of the wave vector k with respect to the z-axis, we gain insight in the nematicons propagation in the highly disturbed area around two different types of disclination lines in chiral nematic.

We consider the nonlinear propagation of an optical beam in a two-dimensional waveguide matrix, which is described by the discrete nonlinear Schrödinger equation with a self-focusing nonlinearity. Our study focuses on the stability domain of the discrete vortex solitons with its topological invariant S equal to 1. Such domain is identified with the propagation constant k and the coupling constant C. Our simulations show that there is a critical value C_cr for any fixed value of k. At C ≤ C_cr, the stable domain is continuous. However, at C > C_cr, the stable domain becomes discontinuous and fuzzy. The distribution of the continuous stable regions is identified and plotted. Moreover, we give the relation of the total power P to C and k, which enable us to figure out the continuous stability area through the (P, C) plane.

A highly nonlocal optical response in space has been shown to heal several shortcomings of beam self-action in nonlinear optics. At the same time, nonlocality is often connected to limits and constraints in both temporal and spatial domains. We provide a brief and rather subjective review of what we consider the main benefits and some drawbacks of a highly nonlocal response in light localization through nonlinear optics, with several examples related to reorientational soft matter, specifically nematic liquid crystals.

We report on the formation and stability of induced surface solitons in parity–time (${𝒫}{𝒯}$) symmetric periodic systems with spatially modulated nonlinearity. We discover that the spatially modulation of the nonlinearity can affect the existence and stability of surface solitons. These surface solitons can be formed in the semi-infinite and first bandgap. Stability analysis shows that odd surface solitons belonging to semi-infinite bandgap are linearly stably in low power domain, and the stable domain becomes narrow with increasing the strength of spatially modulated nonlinearity, both even surface solitons in semi-infinite bandgap and surface solitons in first bandgap are unstable in their existence domain.

We present, to the best of our knowledge, the first exact dark spatial solitons of a nonlinear Helmholtz equation with a self-defocusing saturable refractive-index model. These solutions capture oblique (arbitrary-angle) propagation in both the forward and backward directions, and they can also exhibit a bistability characteristic. A detailed derivation is presented, obtained by combining coordinate transformations and direct-integration methods, and the corresponding solutions of paraxial theory are recovered asymptotically as a subset. Simulations examine the robustness of the new Helmholtz solitons, with stationary states emerging from a range of perturbed input beams.