Patterned electrode steering of nematicons

Using He-Ne laser, semiconductor laser，and Ar+ laser as the light sources, we observed the self-focusing phenomena of light wave at low power and the forming of spatial solitons in nematic liquid crystal. The spatial solitons with a length over five millimeters and multiple-mode spatial optical solitons were viewed. Furthermore, the forming conditions and characteristics of these solitons were also discussed.

We investigate interactions between spatial nonlocal bright solitons in nematic liquid crystals using an analytical ("effective particle") approach as well as direct numerical simulations. The model predicts attraction of out-of-phase solitons and the existence of their stable bound state. This nontrivial property is solely due to the nonlocal nature of the nonlinear response of the liquid crystals. We further predict and verify numerically the critical outwards angle and degree of nonlocality which determine the transition between attraction and repulsion of out-of-phase solitons.

A great deal of interest over the years has been directed to the optical space solitons for the possibility of realizing 3D waveguides with very low propagation losses. A great limitation in their use for writing complex circuits is represented by the impossibility of making curved structures. In the past, solitons in nematic liquid crystals, called nematicons, were reflected on electrical interfaces, and more recently photorefractive spatial solitons have been, as well. In the present work, we investigate refraction and total reflection of spatial solitons with saturable electro-optic nonlinearity, such as the photorefractive ones, on an electric wall acting as a reflector. Using a custom FDTD code, the propagation of a self-confined beam was analyzed as a function of the applied electric bias. The electrical reflector was simulated by applying different biases in two adjacent volumes. We observed both smaller and larger angles of refraction, up to the critical π/2-refraction condition, and then the total reflection. The radii of curvature of the associated guides can be varied from centimeters down to hundreds of microns. The straight guides showed losses as low as 0.07 dB/cm as previously observed, while the losses associated with single curves were estimated to be as low as 0.2 dB.

The present research explores nematicons in liquid crystals (LCs) with quadruple power law nonlinearity utilizing the modified extended Fan sub-equation technique as an analytical tool to investigate the optical spatial soliton solutions. For the inaugural time, a novel version of nonlinearity is investigated in relation to LCs. There are distinct applications for the several wave solutions that have been created in optical handling data. The aforementioned modified extended Fan subequation approach offers novel, comprehensive solutions that are relatively easy to deploy in comparison to earlier, regular methodologies. This approach translates a coupled non-linear partial differential equation into a coupled ordinary differential equation through implementing a traveling wave conversion. This approach indicates that a large variety of traveling and solitary solutions that rely upon five parameters can be incorporated by the nematicons in LCs. In addition, the investigation yields solutions of the single and mixed non-degenerate Jacobi elliptic function form. Novel solutions, such as the periodic pattern, kink and anti-kink patterns, N-pattern, W-pattern, anti-Z-pattern, M-pattern, V-pattern, complexion pattern and anti-bell pattern, or dark soliton solutions of nematic LCs, have been constructed by means of modified extended Fan subequation technique through granting suitable values for the parameters. The computer software Mathematica 14 is used to illustrate several modulus, real and imaginary solutions visually in the form of contour, 2D, and 3D visualizations that help understand the concrete importance of the nematicons in LCs. This research additionally offers a physical comprehension of the obtained solutions and applications of model. The imposed approach is ultimately thought to be more potent and effective than alternative approaches, and the solutions found in this work could be beneficial in our understanding of soliton structures in LCs.

We discuss and report refraction and total internal reflection of optical spatial solitons in nematic liquid crystals at the interface between two differently-biased regions, with angular steering as large as –18 and +22 degrees, respectively.

We study a 2D system that couples a Schrödinger evolution equation to a nonlinear elliptic equation and models the propagation of a laser beam in a nematic liquid crystal. The nonlinear elliptic equation describes the response of the director angle to the laser beam electric field. We obtain results on well-posedness and solitary wave solutions of this system, generalizing results for a well-studied simpler system with a linear elliptic equation for the director field. The analysis of the nonlinear elliptic problem shows the existence of an isolated global branch of solutions with director angles that remain bounded for arbitrary electric field. The results on the director equation are also used to show local and global existence, as well as decay for initial conditions with sufficiently small L2−norm. For sufficiently large L2−norm we show the existence of energy minimizing optical solitons with radial, positive and monotone profiles.

We study experimentally the interaction of spatial optical solitons with curved dielectric surfaces in unbiased nematic liquid crystals. We demonstrate that this interaction depends on the curvature of the surface and the walk-off, and it can be employed for efficient routing and control of the soliton trajectories. We also observe a large-angle total internal reflection of the soliton beam from an interface between liquid crystal and air.

Disclinations are among the most common topological defects in nematic liquid crystals. Their controlled generation is essential for both fundamental studies of defect physics and the development of functional soft-matter systems. However, achieving such control remains challenging. Here, we use laser thermal tweezers in a nematic liquid crystal cell with a free surface to generate a hybrid planar soliton, a structure topologically equivalent to a disclination, as both belong to the same homotopy group, π 1 ( R P 2 ). This soliton acts as a template for guiding the formation of disclinations with prescribed geometries and positions. To the best of our knowledge, this represents the first practical implementation of soliton–disclination conversion for direct and predictable defect control. These results elucidate the topological connection between planar solitons and disclinations and provide a foundation for precise topological patterning in liquid crystal systems.

In this work, a study is carried out to analyze nematicons in liquid crystals in the presence of Kerr and parabolic law nonlinearity. Exp(− $$\phi ({\xi })$$ )-Expansion method is incorporated in this regard. Solutions obtained include hyperbolic, periodic and rational solutions along with their combo type solutions in both cases of nonlinearity and their existence is guaranteed by the constraints retrieved during the process.

Among photofunctional materials that can be employed to control the propagation of light by modifying their properties, soft dielectrics such as nematic liquid crystals (NLCs) stand out for their large all-optical response. Through reorientation, the molecular distribution of NLCs can be modified by the electric field of light, permitting functional operations and supporting self-localized light beams or spatial optical solitons. To date, the generation and routing of such solitons have been limited by the boundary conditions employed to tailor the properties of NLCs in planar cells or capillaries. Here we report on spatial solitons in bulk NLCs with no lateral anchoring, where the application of an external magnetic field effectively controls the direction of propagation and the angular steering of the self-trapped wavepackets. Our results entail a completely new approach to the routing of self-localized beams and light-induced waveguides in three dimensions, without the usual limitations imposed by transverse boundary conditions.

Photo-alignment is a versatile tool to pattern the alignment at the confining substrates in a liquid crystal (LC) cell. Arbitrary alignment patterns can be created by using projection with a spatial light modulator (SLM) for the illumination. We demonstrate that a careful design of the alignment patterns allows the stabilization of topological solitons in nematic liquid crystal (NLC) cells, without the need for chirality or strong confinement. The created LC configurations are stabilized by the anchoring conditions imposed at the substrates. The photo-aligned background at both substrates is uniformly planar aligned, and ring-shaped regions with a 180° azimuthal rotation are patterned with an opposite sense of rotation at the top and bottom substrate. A disclination-free structure containing a closed ring of vertically oriented directors is formed when the patterned rings at the top and bottom substrate overlap. Thanks to the topological stability, a vertical director orientation in the bulk is observed even when the centra of both patterned rings are shifted over relatively large distances. The combination of numerical simulations with experimental measurements allows identification of the 3D director configuration in the bulk. A finite element (FE) Q-tensor simulation model is applied to find the equilibrium director configuration and optical simulations are used to confirm the correspondence with experimental microscopy measurements. The created LC configurations offer opportunities in the field of optical devices, light guiding and switching, particle trapping and studies of topological LC structures.

In a numerical study we investigate the influence of noise on the shape-invariant solitons in nematic liquid crystals. We use the modified Petviashvili’s method for finding eigenvalues and eigenfunctions of the evolution partial differential equations, to determine the shape-invariant solitons in a realistic scalar three-dimensional model that includes the highly nonlocal nature of uniaxial nematic liquid crystals. We check the stability of such solutions by propagating them for long distances, without or within the presence of white noise. Without noise, we find them stable. In the presence of noise (added to the medium), we find them breathing, which renders shape-invariant solitons difficult to observe. After prolonged propagation, the noise leads to the dissipation of solitons.KeywordsNematic Liquid CrystalOptical FieldLiquid Crystal CellSpatial SolitonMolecular ReorientationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Existence and stability of vector vortex solitons in nematic liquid crystals

We report on the first experimental observation of stable vortex solitons in nematic liquid crystals with nonlocal nonlinear reorientational response. We show how these nonlinear vortex beams can be formed and confined in extraordinary optical waves by employing the cell with no lateral boundary conditions and the application of an external magnetic field that effectively controls the molecular direction and propagation of the self-trapped beams. We also find that these vortex solitons can be generated in certain ranges of the input beam power.

Exact self-bending soliton solutions for the equation of a beam in a photorefractive medium with diffusion and drift components of the nonlinear response are obtained and their stability is analysed. It is shown that the interaction of solitons in a medium with nonlocal nonlinearity is accompanied by energy exchange, which causes, as a rule, the annihilation of one of the solitons.