Solitons In Nematic Liquid Crystals Research Articles

Interaction of solitons in nonlocal media under competing nonlinearities with gradual nonlocality

We have numerically studied the interaction of in-phase and out-of-phase bright solitons in nematic liquid crystals with competing nonlinearities. In particular, we propose the nonlocality management technique to steer the beam interaction in nematic liquid crystals with competing nonlinearities. By controlling the degree of nonlocality of the material, three methods of regulating the degree of nonlocality were proposed to control soliton interactions. It was found that out-of-phase soliton pairs exhibit approximately adiabatic propagation under cosine function type regression control. To our knowledge, this is the first observation of adiabatic propagation of out-of-phase soliton pairs in nonlocal media with competing nonlinearities. Controlling soliton interactions by regulating the degree of nonlocality may provide theoretical guidance for the experimental realization of all-optical interconnections and all-optical devices.

Generation and Propagation of Flexoelectricity-Induced Solitons in Nematic Liquid Crystals.

Solitons in nematic liquid crystals facilitate the rapid transport and sensing in microfluidic systems. Little is known about the elementary conditions needed to create solitons in nematic materials. In this study, we apply a combination of theory, computational simulations, and experiments to examine the formation and propagation of solitary waves, or "solitons", in nematic liquid crystals under the influence of an alternating current (AC) electric field. We find that these solitary waves exhibit "butterfly"-like or "bullet"-like structures that travel in the direction perpendicular to the applied electric field. Such structures propagate over long distances without losing their initial shape. The theoretical framework adopted here helps identify several key factors leading to the formation of solitons in the absence of electrostatic interactions. These factors include surface irregularities, flexoelectric polarization, unequal elastic constants, and negative anisotropic dielectric permittivity. The results of simulations are shown to be in good agreement with our own experimental observations, serving to establish the validity of the theoretical concepts and ideas advanced in this work.

Dual Role of Beam Polarization and Power in Nematic Liquid Crystals: A Comprehensive Study of TE- and TM-Beam Interactions.

Optical spatial solitons are self-guided wave packets that maintain their transverse profile due to the self-focusing effect of light. In nematic liquid crystals (NLC), such light beams, called nematicons, can be induced by two principal mechanisms: light-induced reorientation of the elongated molecules and thermal changes in the refractive index caused by partial light absorption. This paper presents a detailed investigation of the propagation dynamics of light beams in nematic liquid crystals (NLCs) doped with Sudan Blue dye. Building on the foundational understanding of reorientational and thermal solitons in NLCs and the effective breaking of the action-reaction principle in spatial solitons, this study examines the interaction of infrared (IR) and visible beams in a [-4-(trans-4'-exylcyclohexyl)isothiocyanatobenzene] (6CHBT) NLC. Our experimental results highlight the intricate interplay of beam polarizations, power levels, and the nonlinear properties of NLCs, offering new insights into photonics and nonlinear optics in liquid crystals.

Interplay of reorientational and thermal solitons: unveiling the dynamic coexistence and enhanced nonlinear response in nematic liquid crystals

Spatial solitons in nematic liquid crystals (NLC) are optical beams that maintain their transverse profile due to the self-focusing effect of light. The mechanism leading to the formation of solitons can be either light-induced reorientation of the elongated molecules or thermal changes in the refractive index induced by a light beam. The specific optical properties of nematic liquid crystals cause the reorientational and thermal solitons to coexist in NLC, and their mutual competition can lead to a reduction or enhancement of the overall nonlinear response of the NLC. The study of the interplay between reorientational and thermal solitons allows a better understanding of the conditions under which the solitons can coexist, compete, or enhance each other. Here, we show that the simultaneous existence of both soliton types can lead to a more robust and versatile nonlinear response and can be used in competitive and synergistic configurations by carefully controlling the temperature, intensity, and polarization of the propagating light. As a result of our experimental findings, it may be possible to shape the nature of the interplay between reorientational and thermal solitons and better understand the behavior of reorientational solitons under varying thermal conditions. Furthermore, understanding this mutual interplay may provide insights into the potential of advanced NLC-based photonic devices that exploit the joint effect of reorientational and thermal nonlinearities.

Saturable nonlinearity and bistable solitons in nematic liquid crystals

The saturated nonlocal nonlinearity of positive nematic liquid crystals (NLCs) is discussed in this paper. Based on the nonlinear coupling model satisfied by the beam propagation in a positive NLC, the saturable characteristics of the nonlinear refractive index (NRI) in the cases of <inline-formula><tex-math id="M3">\begin{document}$1+1$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20222088_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20222088_M3.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M4">\begin{document}$1+2$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20222088_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20222088_M4.png"/></alternatives></inline-formula> dimensions are discussed separately, and the numerical solutions of saturated bistable solitons for different pre-declination angles are obtained. The saturated NRI is smaller for larger pre-deflection angles, and the center of the saturated NRI is almost flat for different pre-deflection angles in <inline-formula><tex-math id="M5">\begin{document}$1+2$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20222088_M5.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20222088_M5.png"/></alternatives></inline-formula> dimension. Solitons in the saturated case are no longer standard circular, whose waveforms in the <i>x</i> and <i>y</i> directions are slightly different. We also find that saturated bistable solitons can exist in NLCs for both <inline-formula><tex-math id="M6">\begin{document}$1+1$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20222088_M6.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20222088_M6.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M7">\begin{document}$1+2$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20222088_M7.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20222088_M7.png"/></alternatives></inline-formula> dimensions. With the increase of pre-deflection angle, the existing regions of bistable solitons decrease, while their minimum beamwidth increases. Although the beamwidths of bistable solitons are the same, they have different powers and propagation constants, and their normalized soliton waveforms differ in the <inline-formula><tex-math id="M8">\begin{document}$1+2$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20222088_M8.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20222088_M8.png"/></alternatives></inline-formula> dimensional case.

Investigation of new solitons in nematic liquid crystals with Kerr and non-Kerr law nonlinearities

Nematicons became a key topic of interest in liquid crystal technology in recent years. This paper contributes in understanding the fantastic features of nematicons in optics and further disciplines. This piece of research investigates nematicons for obtaining various exact solutions for Kerr and non-Kerr law nonlinearities with the help of the Kudryashov’s approach and the tanh–coth technique. The acquired outcomes involve rational, periodic and hyperbolic solutions as well as their combo-type solutions for all the four cases of nonlinearity. A comparative study is conducted to show the novelty of present results with results already existing in the literature. The constraint conditions obtained ensured that the existence of these solutions is extraordinarily favorable to further investigate the dynamics of nematicons for various kinds of nonlinearity. The dynamics of the few of the obtained solutions are also discussed by 3D plots.

Formation and stability of vortex solitons in nematic liquid crystals

We study the propagation dynamics of bright optical vortex solitons in nematic liquid crystals with a nonlocal reorientational nonlinear response. We investigate the role of optical birefringence on the stability of these solitons. In agreement with recent experimental observations, we show that the birefringence-induced astigmatism can eventually destabilize these vortex solitons. However, for low and moderate birefringence, vortex solitons can propagate stably over experimentally relevant distances.

Surface Stabilized Topological Solitons in Nematic Liquid Crystals

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.

Spin-optical solitons in liquid crystals

A theoretical and numerical investigation shows the formation of spin-orbit optical solitons in nematic liquid crystals as a consequence of a nonlinear modulation of the optic axis and the resulting geometric phase in the birefringent medium. The unusual self-trapping mechanism may allow for new all-optical waveguiding and switching schemes.

Kinetics of motile solitons in nematic liquid crystals

The generation of spatially localized, soliton-like hydrodynamic disturbances in microscale fluidic systems is an intriguing challenge. Herein, we introduce nonequilibrium solitons in nematic liquid crystals stimulated by an electric field. These dynamic solitons are robust as long as the electric field is maintained. Interestingly, their kinetic behaviours depend on the field condition—Tuning of the amplitude and frequency of the applied electric field alters the solitons to self-assemble into lattice ordering like physical particles or to command them to various dynamic states. Our key property to the realisation is the electrohydrodynamic instability due to the coupling between the fluid elasticity and the background convection. This paper describes a new mechanism for realising dynamic solitons in fluid systems on the basis of the electrohydrodynamic phenomena.

Optical solitons in nematic liquid crystals: Arbitrary deviation angle model

We study a coupled Schrödinger-elliptic evolution system that describes the propagation of a laser beam in nematic liquid crystals. The elliptic equation describes the effects of the beam electric field on the local orientation (director field) of the nematic liquid crystal and has an important regularizing effect, seen experimentally and understood theoretically in related models. In the present work we propose a new nonlinear elliptic equation for the director field that makes no assumption on the size of the director field angle. The analysis of this elliptic equation leads to an upper bound for the size of the director angle that we believe is optimal and physically relevant, and that implies that the elastic response of the medium prevents a complete alignment between the electric field and the orientation of the liquid crystal. The results on the elliptic problem are combined with arguments from dispersive wave theory to show the local and global well-posedness of the evolution problem and the decay of small initial conditions. We also show the existence of constrained minimizers of the Hamiltonian, assuming sufficiently large optical power (L2−norm of the laser field). These minimizers are solitons with radial, monotonically decreasing profiles.

Spatiospectral features of a soliton-assisted random laser in liquid crystals.

We report on novel features of random lasers assisted by near-infrared spatial solitons in nematic liquid crystals. Specifically, we study the role of light-induced reorientational waveguides (nematicons) on the spatial and spectral distributions of the laser modes. We show that the spatially spiky character of the laser emission propagating backwards with respect to the pump tends to disappear in the forward direction, due to the soliton confinement of the generated light. Moreover, the spectral features associated with various random laser resonances appear to merge upon guided-wave propagation along the nematicon, making the nematicon-aided random laser a bidirectional device with distinct emission properties at the two opposite outputs.

Optical solitons in nematic liquid crystals with Kerr and parabolic law nonlinearities

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.

Addressable Refraction and Curved Soliton Waveguides Using Electric Interfaces

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.

Beam splitting in chiral nematic liquid crystals

By lunching the beam into the chiral nematic liquid crystals it is possible to achieve a non-diffractive beam similar to a soliton. This effect is caused by the molecular reorientation i.e. nonlinear response of the material forming the areas of higher refractive index. Diffraction is suppressed by the focusing effect. For appropriate launching conditions it is also possible to achieve a beam which splits into two or more separate beams. Such phenomenon is discussed in this article and analyzed theoretical. To model this effect Fully Vectorial Beam Propagation Method coupled with the Frank-Oseen elastic theory is used. Simulations are performed for various input beam powers, widths, polarization angles and launching positions. Full Text: PDF ReferencesG. Assanto and M. A. Karpierz, "Nematicons: self-localised beams in nematic liquid crystals", Liq. Cryst. 36, 1161–1172 (2009) CrossRef G. Assanto, Nematicons: Spatial Optical Solitons in Nematic Liquid Crystals, John Wiley & Sons Inc. Hoboken, New Jersey (2013) DirectLink A. Piccardi, A. Alberucci, U. Bortolozzo, S. Residori, and G. Assanto, "Soliton gating and switching in liquid crystal light valve", Appl. Phys. Lett. 96, 071104 (2010). CrossRef D. Melo, I. Fernandes, F. Moraes, S. Fumeron, and E. Pereira, "Thermal diode made by nematic liquid crystal", Phys. Lett. A 380, 3121 – 3127 (2016). CrossRef U. Laudyn, M. Kwaśny, F. A. Sala, M. A. Karpierz, N. F. Smyth, G. Assanto, "Curved optical solitons subject to transverse acceleration in reorientational soft matter", Sci. Rep. 7, 12385 (2017) CrossRef M. Kwaśny, U. A. Laudyn, F. A. Sala, A. Alberucci, M. A. Karpierz, G. Assanto, "Self-guided beams in low-birefringence nematic liquid crystals", Phys. Rev. A 86, 013824 (2012) CrossRef F. A. Sala, M. M. Sala-Tefelska, "Optical steering of mutual capacitance in a nematic liquid crystal cell", J. Opt. Soc. Am. B. 35, 133-139 (2018) CrossRef U. A. Laudyn, A. Piccardi, M. Kwasny, M. A. Karpierz, G. Assanto, "Thermo-optic soliton routing in nematic liquid crystals", Opt. Lett. 43, 2296-2299 (2018) CrossRef F. A. Sala, M. M. Sala-Tefelska, M. J. Bujok, J. "Influence of temperature diffusion on molecular reorientation in nematic liquid crystals", Nonlinear Opt. Phys. Mater. 27, 1850011 (2018) CrossRef I-C Khoo Liquid crystals John Wiley & Sons, Inc (2007) DirectLink P. G. de Gennes, J. Prost, The Physics of Liquid Crystals, Clarendon Press (1995) DirectLink U. A. Laudyn, P. S. Jung, M. A. Karpierz, G. Assanto, "Quasi two-dimensional astigmatic solitons in soft chiral metastructures", Sci. Rep. 6, 22923 (2016) CrossRef J. Beeckman, A. Madani, P. J. M. Vanbrabant, P. Henneaux, S-P. Gorza, M. Haelterman, "Switching and intrinsic position bistability of soliton beams in chiral nematic liquid crystals", Phys. Rev. A 83, 033832 (2011) CrossRef A. Madani, J. Beeckman, K. Neyts, "An experimental observation of a spatial optical soliton beam and self splitting of beam into two soliton beams in chiral nematic liquid crystal", Opt. Commun. 298–299, 222-226, (2013) CrossRef G. D. Ziogos, E. E. Kriezis, "Modeling light propagation in liquid crystal devices with a 3-D full-vector finite-element beam propagation method", Opt. Quant. Electron 40, 10 (2008) CrossRef F. A. Sala, M. A. Karpierz, "Chiral and nonchiral nematic liquid-crystal reorientation induced by inhomogeneous electric fields", J. Opt. Soc. Am. B 29, 1465-1472 (2012) CrossRef F. A. Sala, M. A. Karpierz, "Modeling of molecular reorientation and beam propagation in chiral and non-chiral nematic liquid crystals", Opt. Express 20, 13923-13938 (2012) CrossRef F. A. Sala, "Design of false color palettes for grayscale reproduction", Displays, 46, 9-15 (2017) CrossRef

Spatial solitons to mold random lasers in nematic liquid crystals [Invited

Dye-doped nematic liquid crystals support random lasing under optical pumping, as well as reorientational optical spatial solitons acting as all-optical waveguides. By synergistically combining these two responses in a collinear pump-soliton geometry, the resulting soliton-enhanced random laser exhibits higher conversion efficiency and better directional properties. After a short account on random lasers and solitons in nematic liquid crystals–nematicons–we describe our experimental results on nematicon-molded random lasers.

Supermode spatial solitons via competing nonlocal nonlinearities

We study spatial soliton formation in a system with competing nonlinearities. In doing so, we consider a specific nonlinear response that involves both focusing and defocusing nonlocal contributions. We demonstrate that at a sufficiently high input power level, the interplay between these nonlocal nonlinearities may lead to the formation of in-phase, two-hump, fundamental spatial solitons. The conditions required for the existence of these two-peak spatial solitons are also presented. Full Text: PDF ReferencesG. Stegeman and M. Segev, "Optical Spatial Solitons and Their Interactions: Universality and Diversity", Science 286, 1518 (1999). CrossRef Y. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, San Diego, 2003).P. Varatharajah et al., "Stationary nonlinear surface waves and their stability in diffusive Kerr media", Opt. Lett. 13, 690 (1988). CrossRef G. Assanto and M. Peccianti, "Spatial solitons in nematic liquid crystals," IEEE J. Quantum Electron. 39, 13 (2003). CrossRef G. Assanto, ed. Nematicons: Spatial Optical Solitons in Nematic Liquid Crystals (Wiley, 2012). CrossRef O. Bang, W. Krolikowski, J. Wyller, J.J. Rasmussen, "Collapse arrest and soliton stabilization in nonlocal nonlinear media", Phys. Rev. E 66, 046619 (2002). CrossRef X. Hutsebaut, C. Cambournac, M. Haelterman, A. Adamski, K. Neyts, "Single-component higher-order mode solitons in liquid crystals," Opt. Commun. 333, 211 (2004). CrossRef C. Conti, M. Peccianti, and G. Assanto, "Route to nonlocality and observation of accessible solitons," Phys. Rev. Lett. 91, 073901 (2003). CrossRef U. A. Laudyn, P. S. Jung, M.A. Karpierz, and G. Assanto, "Quasi two-dimensional astigmatic solitons in soft chiral metastructures," Sci. Rep. 6, 22923 (2016). CrossRef U. A. Laudyn, P. S. Jung, M. A. Karpierz, G. Assanto, "Power-induced evolution and increased dimensionality of nonlinear modes in reorientational soft matter," Opt. Lett. 39(22), 6399–6402 (2014). CrossRef Y. V. Izdebskaya, V. G. Shvedov, P. S. Jung, and W. Krolikowski, "Stable vortex soliton in nonlocal media with orientational nonlinearity," Opt. Lett. 43, 66-69 (2018) CrossRef P.S. Jung, W. Krolikowski, U.A. Laudyn, M. Trippenbach and M.A. Karpierz, "Supermode spatial optical solitons in liquid crystals with competing nonlinearities", Phys. Rev. A 95, 023820 (2017) CrossRef P.S. Jung, W. Krolikowski, U.A. Laudyn, M.A. Karpierz and M. Trippenbach, "Semi-analytical approach to supermode spatial solitons formation in nematic liquid crystals", Opt. Express 25, 23893 (2017) CrossRef S. Jungling and J. C. Chen, "A study and optimization of eigenmode calculations using the imaginary-distance beam-propagation method", IEEE J. Quantum Electron. 30, 2098 (1994). CrossRef P.S. Jung, K. Rutkowska and M.A. Karpierz, "Evanescent field boundary conditions for modelling of light propagation", Journal of Computational Science 25, 115 (2018) CrossRef A.A. Hardy, W. Streifer, "Coupled mode theory of parallel waveguides," IEEE J. Lightwave Techn. LT-3, 1135 (1985) CrossRef M. Matuszewski, B.A. Malomed, and M. Trippenbach, "Spontaneous symmetry breaking of solitons trapped in a double channel potential," Phys. Rev. A 75, 063621 (2007) CrossRef

Double sine-Gordon solitons in nematic liquid crystals under applied electric and magnetic fields

ABSTRACTIn this paper, we derive the dynamic equation of molecular motion for a twisted nematic liquid crystal (NLC) under applied electric and magnetic fields, and show that it takes the form of a double sine-Gordon (DSG) equation. Two kink and anti-kink solitary solutions of the liquid crystal molecules are obtained by using the F-expansion method to solve the DSG equation. Finally, we confirm that the twist of the NLC molecules can propagate in the form of solitary waves. The propagation velocity and amplitude of the kink and anti-kink solitons induced by the electric and magnetic fields are discussed.

The Sine-Gordon solitons in nematic liquid crystals under the external electric field

Abstract In this paper, we study the dynamic equation of molecular motion in nematic liquid crystals when there exists the twisting disturbance of the molecular arrangement under the external electric field. After a series of derivation, we find that the evolution equation satisfies the form of Sine-Gordon equation which indicates that the molecular twisting deformation may propagate in the form of solitary waves under external electric field, and the kink and anti-kink Sine-Gordon solitary solutions are given then. The existence of a couple of kink and anti-kink Sine-Gordon solitons in nematic liquid crystals is proved. And we also discuss the influence of the velocity of the traveling wave on the solitary propagation.

Thermo-optic soliton routing in nematic liquid crystals

We demonstrate thermo-optic control on the propagation of optical spatial solitons in nematic liquid crystals. By varying the sample temperature, both linear and nonlinear optical properties of the reorientational material are modulated by acting on the refractive indices, the birefringence, and the elastic response. As a result, both the trajectory and transverse confinement of spatial solitons can be adjusted, demonstrating an effective means to tune and readdress self-induced optical waveguides.