We demonstrate experimentally that the interactions between a pair of nonlocal spatial optical solitons in a nematic liquid crystal (NLC) can be controlled by the degree of nonlocality. For a given beam width, the degree of nonlocality can be modulated by varying the pretilt angle of NLC molecules via the change of the bias. When the pretilt angle is smaller than pi/4, the nonlocality is strong enough to guarantee the independence of the interactions on the phase difference of the solitons. As the pretilt angle increases, the degree of nonlocality decreases. When the degree is below its critical value, the two solitons behavior in the way like their local counterpart: the two in-phase solitons attract and the two out-of-phase solitons repulse.
We develop a general theory of spatial solitons in a liquid crystalline medium exhibiting a nonlinearity with an arbitrary degree of effective nonlocality. The model accounts the observability of "accessible solitons" and establishes an important link with parametric solitons.
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 birefringence-induced astigmatism can eventually destabilize these vortex solitons. However, for low and moderate birefringence, vortex solitons can propagate stably over experimentally relevant distances.
We question physical existence of shape invariant solitons in three dimensional nematic liquid crystals. Using modified Petviashvili's method for finding eigenvalues and eigenfunctions, we determine shape invariant solitons in a realistic physical model that includes the highly nonlocal nature of the liquid crystal system. We check the stability of such solutions by propagating them for long distances. We establish that any noise added to the medium or to the fundamental solitons induces them to breathe, rendering them practically unobservable.
We investigate one-dimensional Helmholtz solitons with nonlocal nonlinearity. We show an exact analytical solution to the nonlocal nonlinear nonparaxial propagation equation in the cases of high and weak nonlocality. We also numerically find that the degree of nonlocality can affect the width of nonlocal Helmholtz soliton beams, but have no effect on their stability. Contrarily, nonparaxiality can affect their stability, but have no effect on their width.
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…
We address the impact of asymmetric nonlocal diffusion nonlinearity on the properties of gap solitons supported by photorefractive crystal with an imprinted optical lattice. We reveal how the asymmetric nonlocal response alters the domains of existence and the stability of solitons originating from different gaps. We find that in such media gap solitons cease to exist above a threshold of the nonlocality degree. We discuss how the interplay between nonlocality and lattice strength modifies the gap soliton mobility.
A model for a non-Kerr cylindrical nematic fiber is presented. We use the multiple scales method to show the possibility of constructing different kinds of wavepackets of transverse magnetic (TM) modes propagating through the fiber. This procedure allows us to generate different hierarchies of nonlinear partial differential equations (PDEs) which describe the propagation of optical pulses along the fiber. We go beyond the usual weakly nonlinear limit of a Kerr medium and derive an extended Nonlinear Schrodinger equation (eNLS) with a third order derivative nonlinearity, governing the dynamics …
We analyze the existence and stability of two-component vector solitons in nematic liquid crystals for which one of the components carries angular momentum and describes a vortex beam. We demonstrate that the nonlocal, nonlinear response can dramatically enhance the field coupling leading to the stabilization of the vortex beam when the amplitude of the second beam exceeds some threshold value. We develop a variational approach to describe this effect analytically.
In uniaxial soft matter with a reorientational nonlinearity, such as nematic liquid crystals, a light beam in the extraordinary polarization walks off its wavevector due to birefringence, while it undergoes self-focusing via an increase in refractive index and eventually forms a spatial soliton. Hereby the trajectory evolution of solitons in nematic liquid crystals- nematicons- in the presence of a linearly varying transverse orientation of the optic axis is analysed. In this study we use and compare two approaches: i) a slowly varying (adiabatic) approximation based on momentum conservation o…
The conditions under which stable evolution of two nonlinear interacting waves are derived within the context of nematic crystals. Two cases are considered: plane waves and solitons. In the first case, the modulation instability analysis reveals that while the nonlocal term suppresses the growth rates, substantially, the coupled system exhibits significantly higher growth rates than its scalar counterpart. In the soliton case, the necessary conditions are derived that lead the solitons to exhibit stable, undistorted evolution, suppressing any breathing behavior and radiation, leading to solito…
It is studied the bright spatial solitons in nonlocal defocusing Kerr media with parity-time (PT) symmetric potentials. We find that these solitons can exist and be stable over a different range of potential parameters. The influence of the degree of nonlocality on the solitons and the transverse energy flow within the stable solitons are also examined.
We report a theoretical and experimental work on the nematicon in the planar cell containing the nematic liquid crystal with negative dielectric anisotropy, aligned homeotropically in the presence of an externally applied voltage. The formation of the soliton is resulted from the balance between the linear difrraction and the nonlocal nonlinearity due to molecular reorientation.
We study effects of nonlocality of the cubic self-focusing nonlinearity on the stability and symmetry-breaking bifurcation (SBB) of solitons in the model of a planar dual-core optical waveg- uide with nonlocal (thermal) nonlinearity. In comparison with the well-known coupled systems with the local nonlinearity, the present setting is affected by the competition of different spatial scales, viz., the coupling length and correlation radius of the nonlocality, $\sqrt{d}$. By means of numer- ical methods and variational approximation (VA, which is relevant for small d), we find that, with the incr…
The large phase shift of strongly nonlocal spatial optical soliton(SNSOS) in the (1+1)-dimensional [(1+1)D] lead glass is investigated using the perturbation method. The fundamental soliton solution of the nonlocal nonlinear Schodinger equation(NNLSE) under the second approximation in strongly nonlocal case is obtained. It is found that the phase shift rate along the propagation direction of such soliton is proportional to the degree of nonlocality, which indicates that one can realize Pi-phase-shift within one Rayleigh distance in (1+1)D lead glass. A full comprehension of the nonlocality-enh…
We consider the impact of anisotropic nonlocality on the arrest of the collapse and stabilization of dipole-mode (DM) solitons in two-dimensional (2D) models of optical media with the diffusive nonlinearity. The nonlocal nonlinearity is made anisotropic through elliptic diffusivity. The medium becomes semi-local in the limit case of 1D diffusivity. Families of fundamental and DM solitons are found by means of the variational approximation (VA) and in a numerical form. We demonstrate that the collapse of 2D beams is arrested even in the semi-local system. The anisotropic nonlocality readily sta…
We study the transverse instability and dynamics of bright soliton stripes in two-dimensional nonlocal nonlinear media. Using a multiscale perturbation method, we derive analytically the first-order correction to the soliton shape, which features an exponential growth in time -- a signature of the transverse instability. The soliton's characteristic timescale associated with its exponential growth,is found to depend on the square root of the nonlocality parameter. This, in turn, highlights the nonlocality-induced suppression of the transverse instability. Our analytical predictions are corrobo…
A novel phenomenon is discovered that the short-range interaction between strongly nonlocal spatial solitons depends sinusoidally on their phase difference. The two neighbouring solitons at close proximate can be inter-trapped via the strong nonlocality, and propagate together as a whole. The trajectory of the propagation is a straight line with its slope controlled by the phase difference. The experimental results carried out in nematic liquid crystals agree quantitatively with the prediction. Our study suggests that the phenomenon to steer optical beams by controlling the phase difference co…
The existence and stability of defect solitons supported by parity-time (PT) symmetric superlattices with nonlocal nonlinearity are investigated. In the semi-infinite gap, in-phase solitons are found to exist stably for positive or zero defects, but can not exist in the presence of negative defects with strong nonlocality. In the first gap, out-of-phase solitons are stable for positive or zero defects, whereas in-phase solitons are stable for negative defects. The dependence of soliton stabilities on modulation depth of the PT potentials is studied. It is interesting that solitons can exist st…
We study numerically formation of spatial optical solitons in nematic liquid crystals with competing nonlocal nonlinearities. We demonstrate that at the sufficiently high input power the interplay between focusing and thermally induced defocusing may lead to the formation of two-peak fundamental spatial solitons. These solitons have constant spatial phase and hence represent supermodes of the self-induced extended waveguide structure. We show that these two-peak solitons are stable in propagation and exhibit adiabatic transition to a single peak state under weak absorption.
Thanks to their unique properties, nematic liquid crystals feature a variety of mechanisms for light-matter interactions. For continuous-wave optical excitations, the two dominant contributions stem from reorientational and thermal nonlinearities. We thoroughly analyze the competing roles of these two nonlinear responses with reference to self-focusing/defocusing and, eventually, the formation of nonlinear diffraction-free wavepackets, the so-called spatial optical solitons. To this extent we refer to dye-doped nematic liquid crystals in planar cells and continuous-wave beams at two distinct w…
We study gray solitons in nonlocal nonlinear media and show that they are stable and can form bound states. We reveal that gray soliton velocity depends on the nonlocality degree, and that it can be drastically reduced in highly nonlocal media. This is in contrast to the case of local media, where the maximal velocity is dictated solely by the asymptotic soliton amplitude.
We investigate the impact of nonlocality, owing to diffusive behavior, on transverse instabilities of a dark stripe propagating in a defocusing cubic medium. The nonlocal response turns out to have a strongly stabilizing effect both in the case of a single soliton input and in the regime where dispersive shock waves develop "multisoliton regime". Such conclusions are supported by the linear stability analysis and numerical simulation of the propagation.
We report on the observation and quantitative assessment of self-trapped pulsating beams in a highly non-local nonlinear regime. The experiments were conducted in nematic liquid crystals and allow a meaningful comparison with the prediction of a scalar theory in the perturbative limit, while addressing the need for beyond-paraxial analytical treatments.
Production of stable multidimensional solitary waves is a grand challenge in modern science. Steering their propagation is an even harder problem. In this work we demonstrate three-dimensional solitary waves in a nematic, trajectories of which can be steered by the electric field in a plane perpendicular to the field. The steering does not modify the properties of the ground state that remains uniform. These localized waves, called director bullets, are topologically unprotected multidimensional solitons of (3+2)D type that show fore-aft and right-left asymmetry with respect to the background …
The reorientational nonlinearity of nematic liquid crystals enables a self-localized spatial soliton and its waveguide to be deflected or destroyed by a control beam propagating across the cell. We demonstrate a simple all-optical readdressing scheme by exploiting the lens-like perturbation induced by an external beam on both a nematicon and a co-polarized guided signal of different wavelength. Angular steering as large as 2.2 degrees was obtained for control powers as low as 32mW in the near infrared.
Intense light propagating in a nonlinear medium can generate an ensemble of interacting filaments of light, or spatial solitons. Using nematic liquid crystals, we demonstrate that they undergo a collective behavior typical of complex systems, including the formation of clusters and sound-like vibrations, as well as the reduction of the configurational entropy, controlled by the degree of nonlocality of the medium.
With reference to spatially non-local nematic liquid crystals, we develop a theory of optical spatial solitons and modulational instability in anisotropic media with arbitrarily large birefringence. Asymmetric spatial profiles and multivalued features are predicted for self-localized light versus walk-off angle. The results hold valid for generic self-focusing birefringent media and apply to large angle steering of individual and multiple self-trapped optical beams.
We model discrete spatial solitons in a periodic nonlinear medium encompassing any degree of transverse non locality. Making a convenient reference to a widely used material -nematic liquid crystals-, we derive a new form of the discrete nonlinear Schrodinger equation and find a novel family of discrete solitons. Such self-localized solutions in optical lattices can exist with an arbitrary degree of imprinted chirp and a have breathing character. We verify numerically that both local and non local discrete light propagation and solitons can be observed in liquid crystalline arrays.
We investigate theoretically and experimentally the optical beam propagation in the nematic liquid crystal with negative dielectric anisotropy, which is aligned homeotropically in a $80μm$-thickness planar cell in the presence of an externally voltage. It is predicted that the nonlocal nonlinearity of liquid crystal undergo an oscillatory response function with a negative nonlinear refractive index coefficient. We found that the oscillatory nonlocal nonlinearity can support stable bright solitons, which are observed in experiment. We also found that abnormal modulation instability occurs with …
We consider the interplay between nonlocal nonlinearity and randomness for two different nonlinear Schrödinger models. We show that stability of bright solitons in presence of random perturbations increases dramatically with the nonlocality-induced finite correlation length of the noise in the transverse plane, by means of both numerical simulations and analytical estimates. In fact, solitons are practically insensitive to noise when the correlation length of the noise becomes comparable to the extent of the wave packet. We characterize soliton stability using two different criteria based on t…
The control of light by light is one of the main aims in modern photonics. In this context, a fundamental cornerstone is the realization of light-written waveguides in real time, resulting in all-optical reconfigurability of communication networks. Light-written waveguides are often associated with spatial solitons, that is, non-diffracting waves due to a nonlinear self-focusing effect in the harmonic regime. From an applicative point of view, it is important to establish the temporal dynamics for the formation of such light-written guides. Here we investigate theoretically the temporal dynami…
We demonstrate the existence of two species of stable bright solitons, fundamental and dipole ones, in one-dimensional self-defocusing nonlocal media, with the local value of nonlinearity coefficient having one or several minima and growing at any rate faster than |x| at large values of coordinate x. The model can be derived for a slab optical waveguide with thermal nonlinearity. The most essential difference from the local counterpart of this system is the competition between two different spatial scales, the one determining the modulation pattern of the nonlinearity coefficient, and the corr…
Spontaneous symmetry breaking and formation of self-organized structures in nonlinear systems are intriguing and important phenomena in nature. Advancing such research to new nonlinear optical regimes is of much interest for both fundamental physics and practical applications. Here we propose a scheme to realize optical pattern formation in a cold Rydberg atomic gas via electromagnetically induced transparency. We show that, by coupling two Rydberg states with a microwave field (microwave dressing), the nonlocal Kerr nonlinearity of the Rydberg gas can be enhanced significantly and may be tune…
