Numerical analysis of the stability of optical bullets (2 + 1) in a planar waveguide with cubic–quintic nonlinearity

In this paper, we have presented a numerical analysis of the stability of optical bullets (2 + 1), or spatiotemporal solitons (2 + 1), in a planar waveguide with cubic–quintic nonlinearity. The optical spatiotemporal solitons are the result of the balance between the nonlinear parameters, of dispersion (dispersion length, L _D) and diffraction (diffraction length, L _d) with temporal and spatial auto-focusing behavior, respectively. With the objective of ensure the stability and preventing the collapse or the spreading of pulses, in this study we explore the cubic–quintic nonlinearity with the optical fields coupled by cross-phase modulation and considering several values for the non linear parameter α We have shown the existence of stable light bullets in planar waveguide with cubic–quintic nonlinearity through the study of spatiotemporal collisions of the light bullets.     

Bilinear Forms and Dark-Dark Solitons for the Coupled Cubic-Quintic Nonlinear SchrÕdinger Equations with Variable Coefficients in a Twin-Core Optical Fiber or Non-Kerr Medium*

Twin-core optical fibers are applied in such fields as the optical sensing and optical communication,and propagation of the pulses,Gauss beams and laser beams in the non-Kerr media is reported.Studied in this paper are the coupled cubic-quintic nonlinear Schrodinger equations with variable coefficients,which describe the effects of quintic nonlinearity for the ultrashort optical pulse propagation in a twin-core optical fiber or non-Kerr medium.Based on the integrable conditions,bilinear forms are derived,and dark-dark soliton solutions can be constructed in terms of the Gramian via the Kadomtsev-Petviashvili hierarchy reduction.Propagation and interaction of the dark-dark solitons are presented and discussed through the graphic analysis.With different values of the delayed nonlinear response effect b(z),where z represents direction of the propagation,the linear-and parabolic-shaped one dark-dark soltions can be derived.Interactions between the parabolic-and periodic-shaped two dark-dark solitons are presented with b(z) as the linear and periodic functions,respectively.Directions of velocities of the two dark-dark solitons vary with z and the amplitudes of the solitons remain unchanged can be observed.Interactions between the two dark-dark solitons of different types are displayed,and we observe that the velocity of one soliton is zero and direction of the velocity of the other soliton vary with z.We find that those interactions are elastic.     

Step-like structure and assisted tunneling in two coupled modulated waveguides

The propagation of an initially-localized optical beam along two coupled modulated waveguides is investigated. A universal step-like structure emerges in the propagation process once |d|\delta v/v₀|v_0| ~ 1 and T = 2 π/m v₀m v_0, both for the linear and nonlinear optical waveguides. The reason is that the coupling between the two waveguides can be completely suppressed at z = m T or (2 m+1)T/2. When the nonlinearity is strong, assisted tunneling can be found for the initially-localized optical beam by slightly increasing the strength of the modulation.     

Stabilization of two-dimensional solitons and vortices against supercritical collapse by lattice potentials

It is known that optical-lattice (OL) potentials can stabilize solitons and solitary vortices against the critical collapse, generated by cubic attractive nonlinearity in the 2D geometry. We demonstrate that OLs can also stabilize various species of fundamental and vortical solitons against the supercritical collapse, driven by the double-attractive cubic-quintic nonlinearity (however, solitons remain unstable in the case of the pure quintic nonlinearity). Two types of OLs are considered, producing similar results: the 2D Kronig-Penney “checkerboard”, and the sinusoidal potential. Soliton families are obtained by means of a variational approximation, and as numerical solutions. The stability of all families, which include fundamental and multi-humped solitons, vortices of oblique and straight types, vortices built of quadrupoles, and supervortices, strictly obeys the Vakhitov-Kolokolov criterion. The model applies to optical media and BEC in “pancake” traps.     

Stability of Bragg grating solitons in a cubic-quintic nonlinear medium with dispersive reflectivity

We investigate the existence and stability of Bragg grating solitons in a cubic-quintic medium with dispersive reflectivity. It is found that the model supports two disjoint families of solitons. One family can be viewed as the generalization of the Bragg grating solitons in Kerr nonlinearity with dispersive reflectivity. On the other hand, the quintic nonlinearity is dominant in the other family. Stability regions are identified by means of systematic numerical stability analysis. In the case of the first family, the size of the stability region increases up to moderate values of dispersive reflectivity. However for the second family (i.e. region where quintic nonlinearity dominates), the size of the stability region increases even for strong dispersive reflectivity. For all values of m, there exists a subset of the unstable solitons belonging to the first family for which the instability development leads to deformation and subsequent splitting of the soliton into two moving solitons with different amplitudes and velocities.     

亚强非局域空间光孤子的相互作用

研究了亚强非局域空间光孤子的相互作用规律,从光线方程出发得到了孤子光束中心的演化性质以及相互作用周期的解析解.发现亚强非局域条件下孤子的初始间距和非局域特征长度的关系对孤子的相互作用周期有很大的影响,在斜入射时存在一个最大入射角, 小于这个角度孤子才会吸引.数值模拟验证了理论解析的结果. 关键词： 亚强非局域 相互作用 空间光孤子 全光开关     

The evolution of two-frequency solitons in an optical fiber with a longitudinally nonuniform nonlinearity

The evolution of two-frequency solitons in an optical fiber, as well as the practically important special case of absence of the second-harmonic wave, in the presence of a longitudinal nonuniformity of the coefficients characterizing the propagation nonlinearity are considered. The solitons found for media with constant values of the nonlinearity coefficients are used as initial distributions for media with a periodic dependence of the nonlinearity coefficients on the longitudinal coordinate. Modulation of the coefficient of cubic or quadratic nonlinearity is shown to result in oscillations of the peak intensity of the solitons (in both their components if two-color solitons are considered). In the case of a weak modulation of the nonlinearity coefficients, oscillations of the peak intensity occur at the frequency coinciding with the frequency of modulation of the nonlinearity coefficients. Under the weak influence of a periodically modulated cubic nonlinearity, parameters of quadratic solitons also oscillate upon the propagation. Regions of stability of solitons in the space of the modulation parameters are established.     

Nonlinear focusing of picosecond baseband pulses in paraelectric crystals

The nonlinear baseband electromagnetic pulses of a wide spectrum that lies in terahertz (THz) range are investigated theoretically in the paraelectric crystals like SrTiO₃ at the temperatures ~ 77 K. The frequency dispersion is important in THz range there. The dominating nonlinearity of the crystal is cubic. The frequency dispersion and nonlinearity correspond to existence of envelope solitons and the modulation instability of long input envelope pulses, whereas in the transverse direction the modulation instability is absent. When the nonlinear wave is uniform in the transverse direction, the existence of soliton-like baseband pulses without a carrier frequency has been demonstrated. There exists a possibility to generate the regular sequences of short baseband pulses due to the nonlinearity in the paraelectric crystals. The nonlinear focusing of input long baseband pulses by the exciting antenna results in the formation of extremely short baseband pulses localized both in the longitudinal and transverse directions.     

Dispersion-Managed Optical Solitons with Higher-Order Nonlinearity

In this paper we have investigated the propagation characteristics of optical solitons in dispersion managed optical communication systems taking into account of the effect of quintic nonlinearity. Using variational formalism, several ordinary differential equations have been established for pulse parameters. These equations have been solved numerically to investigate the propagation characteristics. It has been noticed that stable periodic pulse propagation is possible over long distance. Numerical simulation has been undertaken to show that parabolic nonlinearity reduces collision distance between neighbouring pulses of the same channel.     

Solitons generated by self-organization in bismuth germanium oxide single crystals during the interaction with laser beam

We present here the experimental, theoretical, and numerical investigations of Kerr solitons generated by self-organization in black and yellow high quality bismuth germanium oxide (Bi₁₂GeO₂₀) single crystals. A picosecond laser beam of increasing power induces competing cubic and quintic nonlinearities. The numerical evolution of two-dimensional complex cubic-quintic nonlinear Schrödinger equation with measured values of nonlinearities shows the compensation of diffraction by competing cubic and quintic nonlinearities of opposite sign, i.e., the self-generation and stable propagation of solitons. Experiments as well as numerical simulations show higher nonlinearity in the black Bi₁₂GeO₂₀ than in the more transparent yellow one.     

A collective variable approach for optical solitons in the cubic-quintic complex Ginzburg-Landau equation with third-order dispersion

Considering the theory of electromagnetic, especially from the Maxwell equations, a basic equation modeling the propagation of ultrashort optical solitons in optical fibers is derived, namely a cubic-quintic complex Ginzburg-Landau equation (CQGLE) with third-order dispersion (TOD). Considering this one-dimensional CQGLE, we derive the equations of motion of pulse parameters called collective variables (CVs), of a pulse propagating in dispersion-managed (DM) fiber optic-links. Equations obtained are investigated numerically in order to view the evolution of pulse parameters along the propagation distance. A fully numerical simulation of the CQGLE finally tests the results of the CV theory. It appears chaotic pulses, attenuate pulses and stable pulses under some parameter values.     

Matter-wave propagation in optical lattices

Coherent propagation of atomic-matter waves in a one-dimensional optical lattice is studied. Wave packets of cold two-level atoms propagate simultaneously in two optical potentials in a dressed-state basis. Three regimes of the wave-packet propagation are specified by the quantity Δ² /ω _D , where Δ and ω _D are the dimensionless atom–laser detuning and the Doppler shift, respectively. At Δ² /ω _D ≫ 1, the propagation is essentially adiabatic, at Δ² /ω _D ≪ 1, it is (almost) resonant, and at Δ² ≃ ω _D , the wave packets propagate nonadiabatically, splitting at each node of the standing wave. The latter means that the atom makes a transition from one potential to the other one when crossing each node, and the probability of that transition is given by a Landau–Zener-like formula. All the regimes of propagation are studied with δ-like and Gaussian wave packets in the momentum and position spaces. Varying the control parameters, we can create wave packets trapped in a well of optical potentials and moving ballistically in a given direction in close analogy with point-like atoms. Within some range of the parameters, we force the atom to move in a pure quamtum-mechanical manner in such a way that a part of the packet is trapped in a well, and the other part propagates ballistically. The propagation modes are found to be characterized by different types of time evolution of the uncertainty product and the Wigner function.     

Spatiotemporal chaos control in two-wave driven systems

Spatiotemporal chaos control is considered by taking a one-dimensional driven/damped nonlinear drift-wave equation as a model. We apply an additional sinusoidal wave to suppress spatiotemporal chaos, and the system becomes a two-sinusoidal-wave driven system (the original driving wave with frequency ω and an additional controlling wave with frequency Ω). Numerical simulations show that when the frequency of the controlling wave is in the proper range, spatiotemporal chaos can be modified into a regular state where the amplitudes of all modes vary periodically with frequency Ω-ω while the phases of all modes evolve quasi-periodically with a running frequency Ω overlapped by a small modulation of frequency Ω-ω. The physical reason for this peculiar phenomenon is attributed to a frequency entrainment in the competition of the two external waves.     

Dispersion and nonlinear management for femtosecond optical solitons

We consider the concept of femtosecond propagation for optical solitons in a dispersion management fiber and study the optimal amplification of optical solitons through dispersion wells and barriers and also for the dispersion tailored profile case. For the former, we observed periodic soliton trapping for the in-phase injection case when their respective velocities were equal and opposite with their amplitudes being unequal and no soliton trapping for the off-phase injection case when the two pulses are having a phase difference of π. For the latter, we observed an enormous amplification of the soliton pulses which is one of our main results in this Letter.     

Generation of stable multi-vortex clusters in a dissipative medium with anti-cubic nonlinearity

We demonstrate the generation of vortex solitons in a model of dissipative optical media with the singular anti-cubic (AC) nonlinearity, by launching a vorticity-carrying Gaussian input into the medium modeled by the cubic-quintic complex Ginzburg-Landau equation. The effect of the AC term on the beam propagation is investigated in detail. An analytical result is produced for the asymptotic form of fundamental and vortical solitons at the point of $r\to 0$, which is imposed by the AC term. Numerical simulations identify parameter domains that maintain stable dissipative solitons in the form of vortex clusters. The number of vortices in the clusters is equal to the vorticity embedded in the Gaussian input.     

Thirring combo-solitons with cubic nonlinearity and spatio-temporal dispersion

Abstract

The vector-coupled nonlinear Schrödinger equation, which can be applied to describe the propagation of Thirring optical solitons in birefringent ?bers with Kerr law nonlinearity, detuning, intermodal dispersion and spatiotemporal dispersion, has been studied analytically. By means of the complex envelope function ansatz, exact Thirring bright-dark combosolitons are reported, and the properties of these solitons are discussed.     

Multi-peak solitons in PT-symmetric Bessel optical lattices with defects

This paper presents a theoretical analysis of the existence and stability of multi-peak solitons in parity–time-symmetric Bessel optical lattices with defects in nonlinear media. The results demonstrate that there always exists a critical propagation constant μ _c for the existence of multi-peak solitons regardless of whether the nonlinearity is self-focusing or self-defocusing. In self-focusing media, multi-peak solitons exist when the propagation constant μ > μ _c . In the self-defocusing case, solitons exist only when μ < μ _c . Only low-power solitons can propagate stably when random noise perturbations are present. Positive defects help stabilize the propagation of multi-peak solitons when the nonlinearity is self-focusing. When the nonlinearity is self-defocusing, however, multi-peak solitons in negative defects have wider stable regions than those in positive defects.     

Time-resolved two-color interferometric photoemission of image-potential states on Cu(100)

We describe an interferometric time-resolved photoemission technique that makes it possible to simultaneously observe the decay of optical induced polarizations and populations at surfaces in a two-color excitation scheme. In this scheme initially unoccupied electronic surface states are coherently excited by the interaction of laser pulses with frequency ω_a and the two-photon polarization which is induced by laser pulses with frequency ω_a/2. Interference is observed by changing the delay between both laser pulses using an actively stabilized two-color Mach–Zehnder interferometer. We demonstrate this technique for excitation of the n=1 image-potential state on a Cu(100) surface. PACS 78.47.+p; 79.60.Bm; 73.20.-r; 82.53.Kp; 42.50.Md     

Coupled nonlinear Schrödinger equations with cubic-quintic nonlinearity: Integrability and soliton interaction in non-Kerr media

We propose an integrable system of coupled nonlinear Schr?dinger equations with cubic-quintic terms describing the effects of quintic nonlinearity on the ultrashort optical soliton pulse propagation in non-Kerr media. Lax pairs, conserved quantities and exact soliton solutions for the proposed integrable model are given. The explicit form of two solitons are used to study soliton interaction showing many intriguing features including inelastic (shape changing or intensity redistribution) scattering. Another system of coupled equations with fifth-degree nonlinearity is derived, which represents vector generalization of the known chiral-soliton bearing system.     

Stable high-dimensional solitons in nonlocal competing cubic-quintic nonlinear media

We find and stabilize high-dimensional dipole and quadrupole solitons in nonlocal competing cubic-quintic nonlinear media. By adjusting the propagation constant, cubic, and quintic nonlinear coefficients, the stable intervals for dipole and quadrupole solitons that are parallel to the x-axis and those after rotating 45° counterclockwise around the origin of coordinate are found. For the dipole solitons and those after rotation, their stability is controlled by the propagation constant, the coefficients of cubic and quintic nonlinearity. The stability of quadrupole solitons is controlled by the propagation constant and the coefficient of cubic nonlinearity, rather than the coefficient of quintic nonlinearity, though there is a small effect of the quintic nonlinear coefficient on the stability. Our proposal may provide a way to generate and stabilize some novel high-dimensional nonlinear modes in a nonlocal system.