Nonlocal Media Research Articles

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

Nonlocal logarithmic nonlinear optical soliton

The propagation of optical beam in (1 + 2)-dimensional nonlocal logarithmic nonlinear media is studied. The numerical simulation shows that the intensity profiles of solitons undergo a gradual and continuous transition from a Gaussian-shaped function in the general nonlocal media to an approximately hyperbolic secant function in the local case. Due to the nonlocal effect, the stability of solitons increases with the increase of nonlocality degree. Concretely speaking, the quasi-stable solitons can be formed in local and weakly nonlocal (nonlocality degree α < 0.5) logarithmic nonlinear media. In general nonlocal case (0.5 ≤ α≤1), the completely stable solitons can be formed. In special case (α = 1), even the initial power increase largely, the solitons can still exist even the initial power has large change for the saturable nonlinear contract effect. However, when α = 1.1, the solitons cannot be formed at any initial power because nonlinear effect is too small to balance diffraction effect.

Tomographic imaging of non-local media based on space-fractional diffusion models

We investigate a generalized tomographic imaging framework applicable to a class of inhomogeneous media characterized by non-local diffusive energy transport. Under these conditions, the transport mechanism is well described by fractional-order continuum models capable of capturing anomalous diffusion that would otherwise remain undetected when using traditional integer-order models. Although the underlying idea of the proposed framework is applicable to any transport mechanism, the case of fractional heat conduction is presented as a specific example to illustrate the methodology. By using numerical simulations, we show how complex inhomogeneous media involving non-local transport can be successfully imaged if fractional order models are used. In particular, results will show that by properly recognizing and accounting for the fractional character of the host medium not only allows achieving increased resolution but, in case of strong and spatially distributed non-locality, it represents the only viable approach to achieve a successful reconstruction.

Elliptic Optical Soliton in Anisotropic Nonlocal Competing Cubic–Quintic Nonlinear Media

The propagation of elliptic optical beam in (1 + 2)-dimensional nonlocal competing cubic–quintic (CQ) nonlinear media was investigated analytically and numerically. The evolution equations for the parameters of the optical beam and the critical powers of stable propagation in x - and y -directions are obtained. Both the analytical and numerical solutions show that the stable elliptic optical solitons can be formed in nonlocal cubic, quantic, and competing CQ nonlinear media. The stability of soliton depends on the initial power, beamwidth, and characteristic length of the response function. In particular, there are bistable elliptic optical solitons in nonlocal media with self-focusing cubic and self-defocusing quintic nonlinearities when these nonlocal and nonlinear parameters are in the appropriate value domain.

Single evolution equation in a light-matter pairing system

The coupled system including wave mixing and nonlinear dynamics of a nonlocal optical medium is usually studied (1) numerically, with the medium being regarded as a black box, or (2) experimentally, making use of some empirical assumptions. In this paper we deduce for the first time a single evolution equation describing the dynamics of the pairing system as a holistic complex. For a non-degenerate set of parameters, we obtain the nonlinear Schrödinger equation with coefficients being written out explicitly. Analytical solutions of this equation can be experimentally realized in any photorefractive medium, e.g. in photorefractive, liquid or photonic crystals. For instance, a soliton-like solution can be used in dynamical holography for designing an artificial grating with maximal amplification of an image.

Analytic expression and propagation properties of hollow Gaussian beams for the off-waist incident case in strongly nonlocal media

Abstract In this paper, the propagation properties of hollow Gaussian beams (HGBs) are discussed in detail when they are off-waist incident in strongly nonlocal media. A set of mathematic expressions are given to describe the evolutions of the beam intensity, the beam width, and the real beam radius. Numerical simulations are carried out to illustrate these propagation properties depended on the off-waist incidence. It is found that a HGB always periodically transforms its transverse patterns during propagation. Accordingly, the beam width and the real beam radius are also periodic during propagation.

Flexoelectric effect on vibration responses of piezoelectric nanobeams embedded in viscoelastic medium based on nonlocal elasticity theory

In this study, vibration characteristics of a piezoelectric nanobeam embedded in a viscoelastic medium are investigated based on nonlocal Euler–Bernoulli beam theory. In doing this, the governing equations of motion and boundary conditions for vibration analysis are first derived using Hamilton’s principle, where nonlocal effect, piezoelectric effect, flexoelectric effect, and viscoelastic medium are considered simultaneously. Subsequently, the transfer function method is employed to obtain the natural frequencies and corresponding mode shapes in closed form for the embedded piezoelectric nanobeam with arbitrary boundary conditions. The proposed mechanics model is validated by comparing the obtained results with those available in the literature, where good agreement is achieved. The effects of nonlocal parameter, boundary conditions, slenderness ratio, flexoelectric coefficient, and viscoelastic medium on vibration responses are also examined carefully for the embedded nanobeam. The results demonstrate the efficiency and robustness of the developed model for vibration analysis of a complicated multi-physics system comprising piezoelectric nanobeam with flexoelectric effect, viscoelastic medium, and electrical loadings.

Stochastic models associated to a Nonlocal Porous Medium Equation

The nonlocal porous medium equation considered in this paper is a degenerate nonlinear evolution equation involving a space pseudo-differential operator of fractional order. This space-fractional equation admits an explicit, nonnegative, compactly supported weak solution representing a probability density function. In this paper we analyze the link between isotropic transport processes, or random flights, and the nonlocal porous medium equation. In particular, we focus our attention on the interpretation of the weak solution of the nonlinear diffusion equation by means of random flights.

Stable vortex soliton in nonlocal media with orientational nonlinearity.

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.

Chirped Airy beams in strongly nonlocal media with focusing and defocusing nonlinearity

In this paper, we derive an analytical solution of linearly chirped Airy beams (CAB) propagating in strongly nonlocal media with focusing and defocusing nonlinearity. Our analytical results show the periodic evolution pattern of CAB supported by strongly nonlocal focusing nonlinearity is made to be gradually reshaped each other between Airy distribution and conventional standard Gaussian distribution. Meanwhile, we further disclose how initial chirp affects the periodic evolution of optical beam. It is found that we can change ballistic trajectory gradually from conventional parabolic to trigonometric shapes through increasing initial chirp; however the corresponding period is only determined by the degree of nonlocality but independent on the former. Moreover, another interesting property is that initial chirp will lead to a positive or negative transverse displacement of the resulting Gaussian distribution depending on the direction of input beam, but does not affect its shape and longitudinal location. On the other hand, for defocusing nonlinearity, CAB is found to exhibit the conventional nonperiodic self-accelerating behavior, which direction is decided by the initial chirp. Our analytical results agree with the existing results and can be confirmed by numerical prediction.

Exact solitons, periodic peakons and compactons in an optical soliton model

To study the properties of one-dimensional spatial solitons in thermal nonlocal media, we investigate the dynamical behaviour and bifurcation of solutions of the planar systems deduced from the model for one-dimensional beams. By approach of dynamical systems, we obtain the exact forms of parametric representations for solitary wave solution, kink wave solution, periodic wave solution, periodic peakon and compacton solution. Different wave profiles have been recovered by using the associated planar dynamical systems, showing new types of wave solutions which have not been observed in previous studies for the similar models.

Propagation characteristics of modified hollow Gaussian beams in nonlocal media under off-waist incident condition

In this paper, we focus on the evolutions of modified hollow Gaussian beams in highly nonlocal media under the off-waist incident condition. Two alternative analytical expressions describing the beam evolution are deduced, and the analytical expressions of the on-axis intensity, the second-order moment beam width, and the mean radius of curvature of the beam are all given. Numerical simulations are carried out to illustrate the propagation characteristics. The results show that, under the off-waist incident condition, the evolution of the beam width is always periodical whatever the beam power is, even when the beam power is equal to the critical power. The transversal pattern evolution is not symmetric about the middle of the evolution period. These results are much different from those under the on-waist incident condition.

Tailoring optical pulling force on gain coated nanoparticles with nonlocal effective medium theory.

We study the optical scattering force on the coated nanoparticles with gain core and nonlocal plasmonic shell in the long-wavelength limit, and demonstrate negative optical force acting on the nanoparticles near the symmetric and/or antisymmetric surface plasmon resonances. To understand the optical force behavior, we propose nonlocal effective medium theory to derive the equivalent permittivity for the coated nanoparticles with nonlocality. We show that the imaginary part of the equivalent permittivity is negative near the surface resonant wavelength, resulting in the negative optical force. The introduction of nonlocality may shift the resonant wavelength of the optical force, and strengthen the negative optical force. Two examples of Fano-like resonant scattering in such coated nanoparticles are considered, and Fano resonance-induced negative optical force is found too. Our findings could have some potential applications in plasmonics, nano-optical manipulation, and optical selection.

Perfectly matched layers for nonlocal media with hydrodynamic-Drude description: a transformation optics approach.

We develop a transformation optics theory for the nonlocal media in the hydrodynamic Drude model by generalizing the free-electron current density equation to a transformation invariant form. Applying the transformation optics theory, perfectly matched layers (PMLs) for the nonlocal media are theoretically formulated and implemented in frequency domain with finite element method. The nonlocal PMLs are shown to absorb outgoing surface and volume plasmons without inducing unphysical reflections. The effectiveness of the nonlocal PMLs is quantitatively demonstrated by the behaviors that the numerical errors continuously approach zero with increasing linear mesh density.

Analytical theory of two-dimensional ring dark soliton in nonlocal nonlinear media

Completely stable two-dimensional ring dark soliton in nonlocal media with an arbitrary degree of nonlocality are investigated. The exact solution of the ring dark solitons is obtained with the variational method and a cylindrical nonlocal response function. The analytical results are confirmed by directly numerical simulations. We also analytically and numerically study the expansion dynamics of the gray ring dark solitons in detail.

Effect of uncertainty in material properties on wave propagation characteristics of nanorod embedded in elastic medium

The effect of uncertainty in material properties on wave propagation characteristics of nanorod embedded in an elastic medium is investigated by developing a nonlocal nanorod model with uncertainties. Considering limited experimental data, uncertain-but-bounded variables are employed to quantify the uncertain material properties in this paper. According to the nonlocal elasticity theory, the governing equations are derived by applying the Hamilton’s principle. An iterative algorithm based interval analysis method is presented to evaluate the lower and upper bounds of the wave dispersion curves. Simultaneously, the presented method is verified by comparing with Monte-Carlo simulation. Furthermore, combined effects of material uncertainties and various parameters such as nonlocal scale, elastic medium and lateral inertia on wave dispersion characteristics of nanorod are studied in detail. Numerical results not only make further understanding of wave propagation characteristics of nanostructures with uncertain material properties, but also provide significant guidance for the reliability and robust design of the next generation of nanodevices.

Suppression of collapse for two-dimensional Airy beam in nonlocal nonlinear media

Dynamics and collapse of two-dimensional Airy beams are investigated numerically in nonlocal nonlinear media with split step Fourier transform method. In particular, the stability and self-healing properties of the Airy beams depend crucially on the location and topological charge of the vortex when the beams carry angular momentum. The propagation of abruptly autofocusing Airy beams is also demonstrated in local and nonlocal media. In strongly self-focusing regime, with the help of nonlocality, stationary propagation of two-dimensional Airy beams can be obtained, which always collapse in local nonlinear media.

Light Meets Water in Nonlocal Media: Surface Tension Analogue in Optics.

Shallow water wave phenomena find their analogue in optics through a nonlocal nonlinear Schrödinger (NLS) model in 2+1 dimensions. We identify an analogue of surface tension in optics, namely, a single parameter depending on the degree of nonlocality, which changes the sign of dispersion, much like surface tension does in the shallow water wave problem. Using multiscale expansions, we reduce the NLS model to a Kadomtsev-Petviashvili (KP) equation, which is of the KPII (KPI) type, for strong (weak) nonlocality. We demonstrate the emergence of robust optical antidark solitons forming Y-, X-, and H-shaped wave patterns, which are approximated by colliding KPII line solitons, similar to those observed in shallow waters.

Stabilization of two-dimensional dark and anti-dark solitons in a nonlocal media

The existence and elastic collision of ring dark and anti-dark solitons in a nonlocal media with an exponential nonlocal response function was first investigated by Horikis and Frantzeskakis (2016 Opt. Lett. 41 583), who found that the initial rings expand outward, keeping their shape during evolution for relatively short propagation distances. In this paper, we study the stability of two-dimensional dark and anti-dark soliton in a nonlocal media by direct numerical simulations. We found that the shapes of the nonlocal response function have a great effect on the propagation of these solitons. In particular, the ring dark solitons can be completely stabilized in a nonlinear media with a cylindrical nonlocal response function due to the boundary force. We also investigate the dynamics of gray ring dark solitons and elliptic dark solitons in detail.

Scalar and vector Hermite–Gaussian soliton in strong nonlocal media with exponential-decay response

This paper investigates the propagation of scalar and vector Hermite–Gaussian (HG) solitons in strong nonlocal media with exponential-decay response. The evolution equations for the parameters of the single HG beam are obtained by variational approach and the analytical results are confirmed by numerical simulation in section 2. Both the analytical and numerical solutions show that the critical power is increase with the increase of the order. Section 3 numerically studied the vector HG soliton and found that, the total critical power and the initial powers of the components should satisfy a complex relation. Because of the mutual attraction between the components, the stability of the quasi high-order vector HG soliton is better than the corresponding single HG beam during propagation.