Spatial Optical Solitons Research Articles

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.

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.

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.

Stabilization of one-dimensional Townes solitons by spin-orbit coupling in a dual-core system

It was recently demonstrated that 2D Townes solitons (TSs) in two-component systems with cubic self-focusing, which are normally made unstable by the critical collapse, can be stabilized by linear spin-orbit coupling (SOC), in Bose-Einstein condensates and optics alike. We demonstrate that 1D TSs, realized as optical spatial solitons in a planar dual-core waveguide with dominant quintic self-focusing, may be stabilized by SOC-like terms emulated by obliquity of the coupling between cores of the waveguide. Thus, SOC offers a universal mechanism for the stabilization of (quasi-) TSs. A combination of systematic numerical considerations and analytical approximations identifies a vast stability area for skew-symmetric solitons in the system’s main (semi-infinite) and annex (finite) bandgaps. Tilted (”moving”) solitons are unstable, spontaneously evolving into robust breathers. For broad solitons, diffraction, represented by second derivatives in the system, may be neglected, leading to a simplified model with a finite bandgap. It is populated by skew-antisymmetric gap solitons, which are nearly stable close to the gap’s bottom.

Phase sensitive, all-optical and self-integrated multi-logic AND, OR, XOR, and NOT gates

The design and simulation of all-optical and self-integrated primary logical AND, OR, XOR and NOT gates based on phase sensitivity of spatial optical solitons have been reported. By tuning the phase of incident solitons into a bulky nonlinear Kerr medium and interaction between the phase tuned solitons, the self-integrated logical gates are achieved simultaneously in a 50 μm long distance by one setup. These are the advantages in the application and design of integrated circuits. In addition, the proposed logical gates can be cascaded and the logical AND and XOR gates can simultaneously have two outputs. The simplicity of constructing, simultaneous functions with one setup, the possibility of integrating, high sensitivity and fabrication ease are the advantages of the proposed logical gates and may be a good candidate for the future of integrated photonic computational circuits.

All-optical Half-Adder circuit with using spatial Optical solitons

All-optical Half-Adder circuit with using spatial Optical solitons

Soliton Maxwell demons and long-tailed statistics in fluctuating optical fields.

We demonstrate experimentally in biased photorefractive crystals that collisions between random-amplitude optical spatial solitons produce long-tailed statistics from input Gaussian fluctuations. The effect is mediated by Raman nonlocal corrections to Kerr self-focusing that turn soliton-soliton interaction into a Maxwell demon for the output wave amplitude.

Coupling of separate solitons in a series circuit of two photon photorefractive crystals exhibiting simultaneous quadratic and linear nonlinearities

Separately coupled optical spatial solitons are shown to exist in a biased series two-photon photorefractive(TPPR) crystal circuit consisting of two TPPR crystals which have the quadratic and linear electro-optic(EO) effect present simultaneously. The space charge field in each photorefractive(PR) crystal in the circuit has been derived. We find that the space charge field in each crystal is coupled with the space charge field in the other crystal. We consider the cases of separately coupled bright, dark and grey solitons and obtain the numerical solutions for the spatial solitons’ profile. The coupling effect due to the soliton peak intensity in each crystal and the gating beam intensity is studied in detail. The light induced current causes a change in the spatial profile of the dark or grey soliton in one of the crystal which results in a change in the spatial profile and propagation of the soliton in the other crystal. We also find that the bright soliton intensity in one crystal does not affect the soliton in the other crystal. A change in the gating beam intensity in one crystal influences the soliton in the other crystal and this is true for all the three cases of dark, grey and bright separate soliton pairs.

Manipulating rogue waves, breathers and solitons in several non-integrable nonlinear Schrödinger equations

We study a non-integrable system in a resonant four-level media at room temperature. Under appropriate parameter conditions, the system can be reduced to the saturated nonlinear Schrodinger equation (SNLSE) and cubic-quintic nonlinear Schrodinger equation (CQNLSE). And we find a scheme to produce (1 + 1)-dimensional [(1 + 1) − D] spatial optical rogue waves, breathers, and solitons in these equations. The generation and disappearance of different nonlinear modes can be manipulated just by adjusting the amplitude and width of the initial Gaussian pulse. We also prove this scheme adapts to not only the integrable model, but also the non-integrable model. In addition, we also find the relation among these different nonlinear modes.

Chaotic self-trapped optical beams produced by interaction of solitons in strongly nonlocal nonlinear medial

We demonstrate the long distance behavior of interactions of spatial optical solitons in the strongly nonlocal nonlinear media that permits several forms of stable solitons. Results show that the short-range interactions of two solitons will evolve into chaotic self-trapped optical beams, which keep the beam width nearly invariant and possess the chaotic properties denoted by the positive Lyapunov exponents and spatial decoherence. However, the dynamics of the long-range interactions of solitons are fundamentally different, which will turn to be unbounded states of the self-induced waveguide for the emission of radiation waves.

Spatial solitons in KTaxNb1-xO3 waveguides produced by swift carbon ion irradiation and femtosecond laser ablation

We report on the fabrication of planar waveguide and ridge waveguides in a KTN crystal by using swift heavy C5+ ions irradiation and femtosecond laser ablation. The reconstructed refractive index profile of the irradiated KTN waveguide illustrates an optical well and barrier distribution. The confocal Raman spectra suggest that the enhanced tetragonality and the lattice damage occurs in the waveguide region and the optical barrier area, respectively. The optical spatial solitons at 632.8 nm are observed from the planar waveguide and the ridge waveguides with a width of 60 μm and 20 μm, respectively, at room temperature.

Temporal behaviour of bright solitons in photorefractive crystals having both the linear and quadratic electro-optic effect

Abstract We investigate the characteristics of formation or time evolution of optical spatial solitons in novel photorefractive media having both the linear and quadratic electro-optic effect. We have derived a one dimensional time dependant wave propagation equation in biased photorefractive media having both the linear and quadratic electro-optic effect. The variation of soliton width with time is investigated for different values of peak intensity ratio and it is shown that these bright solitons can exist both in the quasi steady state and steady state regimes for high saturation values. Two distinct regimes of intensity ratio are identified where the soliton formation characteristics are different. Only steady state solitons are formed if the intensity ratio is small. Soliton characteristics like the initial soliton width, steady state soliton width, and quasi steady state soliton width are investigated for both regimes and found to depend on as varying functions of the intensity ratio. We also find that the individual magnitudes of the linear and quadratic electro-optic coefficients affect the temporal characteristics of formation of the solitons. Appropriate example has been taken for an illustration of our results.

Coupling of optical spatial solitons in photorefractive multiple quantum well planar waveguide

A comprehensive theory predicting the existence of both incoherently coupled and coherently coupled grey and dark optical spatial solitons in multiple quantum well planar (MQW) waveguides is presented. In addition, we also show the existence of dark Manakov soliton pair and the bright-dark Manakov soliton pair in such Multiple Quantum well waveguides for the first time. In the case of a coherently coupled soliton pair, the mutual phase difference, the overlap of the optical mode on the waveguide, the external bias field and beam intensity ratio have a profound effect on the FWHM of the soliton pairs. As a general case, a theory for the interesting and hitherto uninvestigated case of coherently coupled multicomponent solitons has been presented and analyzed for the first time. The effect of the mutual phase difference, the overlap of the optical mode on the waveguide(overlap parameter), the external bias field and beam intensity ratio on the FWHM is studied for these coherently coupled multicomponent solitons also. The Manakov soliton solutions are found analytically and they exist in the limit of low total intensity of the beams. We find that the dark-dark and bright-dark Manakov soliton pairs exist in such MQW waveguides whereas bright-bright Manakov soliton pair does not exist. The Manakov solitons’ spatial profile depends upon the overlap parameter, the intensity of the components, and the external electric field.

微扰法求解铅玻璃中的涡旋空间光孤子

微扰法求解铅玻璃中的涡旋空间光孤子

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

Electro-optic steering of random laser emission in liquid crystals

Electro-optic steering of random laser emission in liquid crystals

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.

Interplay of Thermo-Optic and Reorientational Responses in Nematicon Generation.

Employing several nematic liquid crystal mixtures, we investigate how the thermo-optic response of nonlinear birefringent soft-matter affects the propagation of light beams and the features of self-induced waveguides. We address the formation of optical spatial solitons and the control of their trajectories versus temperature, comparing the measurements with the expectations based on a simplified model, showing an excellent agreement. Moreover, in a guest–host mixture with an absorbing dye dopant, we study the competition between reorientational and thermal nonlinearities, demonstrating that the two processes can be adjusted independently in order to tune the soliton properties, i.e., trajectory and confinement strength. Our results are an important contribution to better comprehend the role played by material properties on linear and nonlinear beam propagation, as well as their exploitation for signal processing and addressing.

Beaming random lasers with soliton control

Random lasers are resonator-less light sources where feedback stems from recurrent scattering at the expense of spatial profile and directionality. Suitably-doped nematic liquid crystals can random lase when optically pumped near resonance(s); moreover, through molecular reorientation within the transparency region, they support self-guided optical spatial solitons, i.e., light-induced waveguides. Here, we synergistically combine solitons and collinear pumping in weakly scattering dye-doped nematic liquid crystals, whereby random lasing and self-confinement concur to beaming the emission, with several improved features: all-optical switching driven by a low-power input, laser directionality and smooth output profile with high-conversion efficiency, externally controlled angular steering. Such effects make soliton-assisted random lasers an outstanding route towards application-oriented random lasers.