Spatial Solitons Research Articles

Observation of a different type of splitting solitons induced by interaction of second order spatial solitons

In this work the behavior of the split solitons derived from the interaction between two (1 + 1)- Dimensional second-order bright spatial solitons, is numerically investigated. Each individual interaction occurs when the two second-order solitons are initially propagating in the parallel way, while the variety of relative phases and the different initial transversal separation are adjusted. When the initial separation distance is on the appropriate distance where they feel the presence of other soliton, both second-order solitons breakup into a couple of first order (fundamental) low- and high-amplitude solitons, and consequently their initial parallel path suffers a lot. Although the propagation path of high- amplitude solitons receive low effects due to interaction and consequently almost follow their initial propagation path, the propagation path of the low-amplitude solitons suffers based on their initial relative phase. The derived low-amplitude fundamental solitons interact with each other and their propagation path also, as usual of their basic interaction properties, while the high-amplitude fundamental solitons, do not show the interaction, and almost continue their own parallel paths. As the initial separation distance decreases, and almost the initial overlap occurs, the propagation paths suffer for both (high and low amplitude) fundamental solitons. Behavior of the broken solitons induced by the interaction between the second order spatial solitons are investigated by solving the Nonlinear Schrodinger equation (NLSE), and it is simulated numerically by MATLAB program by using the well-known Split-Step Fourier Transform method.

Self-organized structures of two-component laser fields and their active control in a cold Rydberg atomic gas

We investigate the formation and control of stationary optical patterns in a cold Rydberg atomic gas via double electromagnetically induced transparency. We show that, through the modulational instability of plane-wave state of a laser field with two polarization components, the system undergoes a spontaneous symmetry breaking and hence the emergence of plentiful self-organized spatial optical structures, which can be manipulated by the ratio between the cross- and self-Kerr nonlinearities, the nonlocality degree of the Kerr nonlinearities, and the populations initially prepared in the two atomic ground states. Interestingly, a crossover from mixture to separation in space (optical phase separation) of the two polarization components occurs when the ratio between the cross- and self-Kerr nonlinearities exceeds a critical value. We also show that the system supports nonlocal two-component spatial optical solitons and vortices when the parameters of the system are selected suitably. The rich diversity and active controllability of the self-organized optical structures reported here provide a way for realizing novel optical patterns and solitons and their structural phase transitions based on Rydberg atomic gases.

Solution of coupled nonlinear Schrödinger equations in focusing-defocusing medium by modified perturbation theory

The interaction of bright solitons of different orders and two different wavelengths propagating in the medium focusing for one wavelength and defocusing for the other is considered. The system of nonlinear Schrödinger equations is solved by means of perturbation theory. Application of an additional postulate to adjust both widths of the solitons and to modify the amplitude by a factor determined by the overlap integral greatly improves the accuracy of the description. The good accuracy of description is confirmed by numerical calculations. Full Text: PDF ReferencesY. Kivshar, G. P. Agrawal, Optical Solitons. From Fibers to Photonic Crystals, (Amsterdam, Academic Press 2003). CrossRef F. Abdullaev, S. Darmanyan, P. Khabibullaev, Optical Solitons, (Springer-Verlag, Berlin, 1993) CrossRef G.I.A Stegema, D.N. Christodoulides, M. Segev, IEEE J. Selected Topics Quantum Electron. 6, (2000), 1419 CrossRef J. Yang, "Nonlinear Waves in Integrable and Nonintegrable Systems", (SIAM, Philadelphia 2010). CrossRef Y. Kivshar, B. Malomed, "Dynamics of solitons in nearly integrable systems", Rev. Mod. Phys. 61, 763 (1989). CrossRef P.G. Kevrekidis, D.J. Frantzeskakis, "Solitons in coupled nonlinear Schrödinger models: A survey of recent developments", Reviews in Physics 1 (2016), 140 CrossRef R. de la Fuente, A. Barthelemy, "Spatial soliton-induced guiding by cross-phase modulation", IEEE J. Quantum Electron. 28, 547 (1992). CrossRef H. T. Tran, R. A. Sammut, "Families of multiwavelength spatial solitons in nonlinear Kerr media", Phys. Rev. A 52, 3170 (1995). CrossRef S. Leble, B. Reichel, "Coupled nonlinear Schrödinger equations in optic fibers theory", Eur. Phys. J. Special Topics 173, 5 (2009). CrossRef M. Vijayajayanthi, T.Kanna, M. Lakshmanan, "Multisoliton solutions and energy sharing collisions in coupled nonlinear Schrödinger equations with focusing, defocusing and mixed type nonlinearities", Eur. Phys. J. Special Topics 173, 57 (2009). CrossRef S. V. Manakov, "On the theory of two-dimensional stationary self-focusing of electromagnetic waves ", Sov. Phys. JETP 38 (1973), 248 DirectLink J. Yang, Phys. Rev. E 65, 036606 (2002). CrossRef T.Kanna, M. Lakshmanan, "Exact Soliton Solutions, Shape Changing Collisions, and Partially Coherent Solitons in Coupled Nonlinear Schrödinger Equations", Phys. Rev. Lett. 86, 5043 (2001). CrossRef M. Jakubowski, K. Steiglitz, R. Squier, "State transformations of colliding optical solitons and possible application to computation in bulk media", Phys. Rev. E 58, 6752 (1998). 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 (2017). CrossRef P. S. Jung, M. A. Karpierz, M. Trippenbach, D. N. Christodoulides, and W. Krolikowski, "Supermode spatial solitons via competing nonlocal nonlinearities", Photonics Lett. Pol. 10 (2018). CrossRef A. Ramaniuk, M. Trippenbach, P.S. Jung, D.N. Christodoulides, W.Krolikowski, G. Assanto, "Scalar and vector supermode solitons owing to competing nonlocal nonlinearities", Opt. Express 29, 8015 (2021) CrossRef

The combined spatial soliton and breather solutions in the (2+1)- dimensional NLS equation of PT symmetric media

Using a bilinear transformation and the variable separation approach, The abundant localized structures for the (2+1)-dimensional NLS equation of PT-symmetric media are explored. And Some special soliton solutions such as periodic soliton solution, dromion solutions, ring, peak, breathers and instantons type of solitons are presented by selecting the different functions appropriately. and then, the combined spatial soliton and breather solutions of the (2+1)-dimensional coupled inhomogeneous PT- symmetric nonlinear media with variable coefficients are also obtained, The propagation dynamics of combined solitons are investigated analytically and numerically, and the simulation results show they are applicable for certain potential applications in nonlinear optics and plasma physics.

Multiple Self-Organized Phases and Spatial Solitons in Cold Atoms Mediated by Optical Feedback.

We study the transverse self-structuring of cold atomic clouds with effective atomic interactions mediated by a coherent driving beam retroreflected by means of a single mirror. The resulting self-structuring due to optomechanical forces is much richer than that of an effective-Kerr medium, displaying hexagonal, stripe and honeycomb phases depending on the interaction strength parametrized by the linear susceptibility. Phase domains are described by Ginzburg-Landau amplitude equations with real coefficients. In the stripe phase the system recovers inversion symmetry. Moreover, the subcritical character of the honeycomb phase allows for light-density feedback solitons functioning as self-sustained dark atomic traps with motion controlled by phase gradients in the driving beam.

Topological solitons in arrays of modelocked lasers.

We report spatiotemporal topological solitons in an array of modelocked lasers. In its conservative limit, our model reduces to the famous Su-Schrieffer-Heeger system possessing topological states inside the gap of its linear spectrum. We report one-dimensional spatial and two-dimensional spatiotemporal topological solitons, i.e., bullets, with the operational frequencies locked to the values inside the topological gap.

Scalar and vector supermode solitons owing to competing nonlocal nonlinearities.

We investigate scalar and vector multi-hump spatial solitons resulting from competing Kerr-like nonlinear responses excited in a nonlocal medium by either one or two (mutually incoherent) light beams. Two-color vector supermode solitons are more amenable to control but exhibit an intriguing form of spontaneous symmetry breaking in propagation.

Linear stability analysis and spatial solitons in the one-dimensional and the two-dimensional generalized nonlinear Schrödinger equation with third-order dispersion and $$\mathcal {PT}$$-symmetric potentials

Linear stability analysis and spatial solitons in the one-dimensional and the two-dimensional generalized nonlinear Schrödinger equation with third-order dispersion and $$\mathcal {PT}$$-symmetric potentials

Analysis of light coupling in AlxGa1-xAs waveguide arrays.

Light propagation in arrays of AlxGa1-xAs waveguides is studied. The power coupling constant between two adjacent waveguides is precisely measured as waveguide material and structure is varied. Aluminum concentration contrast between waveguide core/cladding layers and waveguide width/height produce an asymmetric effective refractive index between linearly polarized modes, which in turn causes a polarization dependence of the coupling constants. Experimental measurement results agree well with an analytical model. The sensitivity of coupling constant to the waveguide parameters is analyzed. Through a careful geometric design, comparable coupling constants can be achieved in three waveguide arrays with different structure. Similar formation processes of discrete spatial optical solitons are observed respectively, confirming that the parameterization in the discrete nonlinear Schrödinger equation characterizes waveguide arrays.

Tunable evolutions of bright beams in a separate spatial soliton pair due to the crystal temperature

We numerically investigate the temperature characteristics of the bright soliton and a Gaussian beam in a photorefractive crystal circuit, in which two photorefractive crystals are connected with an external voltage source. The results indicate that the dynamical evolution of the bright soliton and the Gaussian beam formed in one crystal depend strongly on the temperature of the other crystal, in which the dark soliton is formed. For the bright soliton, the full width at half maximum (FWHM) of the soliton increases and the center deflection decreases with the increase of the dark soliton crystal temperature. The Gaussian beam shows the similar evolution behaviors and experiences periodic compression and expansion during propagation. The deviation between the bright soliton and the Gaussian beam, however, becomes obvious as the increase of the temperature of the dark soliton crystal. A Gaussian beam that is mismatched with the bright soliton supported by the crystal could evolve into a bright solitary wave by tuning the temperature of the dark soliton crystal properly.

Quantum field fluctuations in the vicinity of a classical laser soliton

An analysis of weak quantum fluctuations of a spatial soliton in a laser with fast saturable absorption in the possible presence of weak holding radiation is carried out. In the c-number representation with adiabatic elimination of atomic variables, the master Heisenberg–Langevin equation is linearized in the vicinity of a stable classical (in the absence of fluctuations) laser soliton. The linearized equation’s solution is constructed on the basis of the spectral expansion in eigenfunctions of the evolution operator unperturbed by fluctuations. The discrete spectrum of this operator is found and used to determine the mean values of the squared fluctuations of the coordinates of the soliton center and its momentum. A comparison is made with similar fluctuations in driven interferometers with Kerr non-linearity of the medium.

Investigation of the interaction of a pair of bright optical spatial pyroelectric solitons during their in-phase propagation in an undoped lithium niobate crystal at a wavelength of 532 nm

The formation of two-dimensional bright spatial solitons by in-phase laser beams with a wavelength of 532 nm propagating in the bulk of photorefractive lithium niobate crystal under the reversal of the sign of the nonlinear optical response of the material with the contribution of the pyroelectric effect has been experimentally demonstrated. It is shown that varying the distance between the beams at the input face of the crystal leads to the interaction of pyroelectric solitons, which allows the formation of non-rectilinear propagation paths of light beams.

All-optical computing circuits half-subtractor and comparator based on soliton interactions

The speed limitations of electronic processors have created a demand for a high bandwidth and ultra-fast computing circuits. By replacing the electric logic gates with photonic ones, a high bandwidth and fast photonic microprocessor will be achieved which will overcome the speed limitations of electronic circuits. Digital photonic logic circuits are key elements in the next generation optical computers. In this paper, all-optical logical half-subtractor and digital comparator are designed based on spatial optical solitons. These computational gates are designed simply with repulsive and attractive interactions of three inphase and out of phase spatial optical solitons in a bulky nonlinear Kerr medium. With tuning the phase input solitons and exploiting inphase and out of phase soliton interactions a high functional circuit with broad operational bandwidth, high switching speed and high contrast ratio between ON/OFF states is achieved by a simple structure.

Interaction of a Spatial Soliton on an Interface between Two Nonlinear Media

Spatial solitons are the solutions of nonlinear partial differential equations describing the propagation of optical beams in Kerr type nonlinear medium. This paper studies the scattering of a spatial solitons of the Cubic-Quintic Nonlinear Schrodinger Equation (C-Q NLSE) on an interface between two nonlinear media. The scattering process will be investigated by variational approximation method and by direct numerical solution of C-Q NLSE. This variational approximation method has been used to analyse the dynamic of the width and center of mass position of a soliton during the scattering process. Meanwhile, a direct numerical simulation of C-Q NLSE is run to check the accuracy of the approximation by using the same range of parameters and initial condition. The results for direct numerical simulation of CQNLSE for soliton parameters are quite similar with the variational equation. The studies showed that soliton can be reflected by or transmitted through the interface, also the nonlinear surface wave can be formed depending on the parameters of interface and initial soliton.

Optical solitons in a saturable nonlinear medium in the presence of an asymmetric complex potential

We report on the existence of families of stable spatial solitons in a saturable nonlinear medium characterized by a refractive index with asymmetric distribution of gain and loss. The properties of the nonlinear modes bifurcating from the eigenvalue of the underlying linear problem are thoroughly investigated. The eigenvalue ranges in the power-eigenvalue diagrams for different gain/loss profiles are inspected. We find that the saturable nonlinearity severely restricts these ranges, as the eigenvalues tend to move quite fast to an asymptotic profile, as power increases. Numerical simulations of the wave equations are carried out and examples of the dynamics of the asymmetric solitons obtained exhibit a remarkable agreement with the analytic stability results.

Coupled spatial periodic waves and solitons in the photovoltaic photorefractive crystals

The evolution of spatial solitons in the photovoltaic photorefractive crystal can be governed by the specific coupled nonlinear Schrodinger equations. Under the photovoltaic field with the external bias field, the coupled cn–sn-type periodic wave solution and the corresponding photorefractive bright–dark soliton pair were constructed to describe the evolution of beam. The influence of the external bias field on solitonic dynamics is analyzed. In the photovoltaic crystal, coupled sn–cn-type, sn–dn-type periodic wave solutions, solution constructed by products of elliptic functions and the corresponding dark–bright soliton pair and coupled double-peaked soliton solutions are found to describe the evolution of a spatial-phase-modulated photovoltaic soliton and a non-phase-modulated beam.

Fractional quantum couplers

Fractional quantum coupler, a new type of quantum couplers that is composed of arrays of two coupled waveguides or a dual-core waveguide with intermodal coupling, within which the light waves diffraction is of the fractional-order differentiation, is put forward in the territory of fractional quantum mechanics. The modelling equations of such fractional couplers are derived in the framework of coupled nonlinear fractional Schrödinger equations with the space derivative of fractional order denoted by Lévy index α, and localized wave solutions as spatial optical solitons of these equations are constructed and their nonlinear propagation properties are discussed. Linear perturbation method based on linear stability analysis, and direct simulations are conducted to identify the stability and instability regions of the predicted solitons.

Численное моделирование когерентных и турбулентных структур излучения методом нелинейных интегральных отображений

The propagation of stable coherent entities of an electromagnetic field in nonlinear media with parameters varying in space can be described in the framework of iterations of nonlinear integral transformations. It is shown that for a set of geometries relevant to typical problems of nonlinear optics, numerical modeling by reducing to dynamical systems with discrete time and continuous spatial variables to iterates of local nonlinear Feigenbaum and Ikeda mappings and nonlocal diffusion-dispersion linear integral transforms is equivalent to partial differential equations of the Ginzburg-Landau type in a fairly wide range of parameters. Such nonlocal mappings , which are the products of matrix operators in the numerical implementation, turn out to be stable numerical-difference schemes, provide fast convergence and an adequate approximation of solutions. The realism of this approach allows one to take into account the effect of noise on nonlinear dynamics by superimposing a spatial noise specified in the form of a multimode random process at each iteration and selecting the stable wave configurations. The nonlinear wave formations described by this method include optical phase singularities, spatial solitons, and turbulent states with fast decay of correlations. The particular interest is in the periodic configurations of the electromagnetic field obtained by this numerical method that arise as a result of phase synchronization, such as optical lattices and self-organized vortex clusters.

Observation and analysis of creation, decay, and regeneration of annular soliton clusters in a lossy cubic-quintic optical medium

We observe and analyze formation, decay, and subsequent regeneration of ring-shaped clusters of (2+1)-dimensional spatial solitons (filaments) in a medium with the cubic-quintic (focusing-defocusing) self-interaction and strong dissipative nonlinearity. The cluster of filaments, that remains stable over ~17.5 Rayleigh lengths, is produced by the azimuthal modulational instability from a parent ring-shaped beam with embedded vorticity l = 1. In the course of still longer propagation, the stability of the soliton cluster is lost under the action of nonlinear losses. The annular cluster is then spontaneously regenerated due to power transfer from the reservoir provided by the unsplit part of the parent vortex ring. A (secondary) interval of the robust propagation of the regenerated cluster is identified. The experiments use a laser beam (at wavelength 800 nm), built of pulses with temporal duration 150 fs, at the repetition rate of 1 kHz, propagating in a cell filled by liquid carbon disulfide. Numerical calculations, based on a modified nonlinear Schr\"odinger equation which includes the cubic-quintic refractive terms and nonlinear losses, provide results in close agreement with the experimental findings.

Solitons supported by parity-time-symmetric optical lattices with saturable nonlinearity in fractional Schrödinger equation

We report on the existence and the stability of spatial solitons supported by one-dimensional (1D) parity-time (PT)-symmetric optical lattices with self-focusing saturable nonlinearity in the fractional Schrödinger equation. These spatial optical solitons are found to exist in the semi-infinite gap and are stable in several continuous regions. In addition, the effects of the Lévy index and the saturation parameter on soliton stability are also studied. Our results demonstrate that the system described here can produce unique properties for soliton stability and propagation. We also perform a stability analysis for these solitons and the analysis results are confirmed by the soliton propagations.