Collision dynamics of three-solitons in an optical communication system with third-order dispersion and nonlinearity

In this communication, three different forms of fractional nonlinear Schrödinger equations have been constructed based on the notion of nonlocal generalized fractional momentum operator, the fractional expansion Riccati method and the notion of Laplacian operator in fractal dimensions. Their physical properties are analyzed and their associated solitonic solutions are obtained and discussed. It was observed that the first two approaches give comparable solutions, whereas the third approach give rise to a nonlinear Schrödinger equation characterized by variable coefficients, and hence, a large family of solitons solutions may be obtained accordingly. PACS numbers: 42.65.Tg, 05.45.Df, 02.30.Tb. 

A family of nonlinear Schrodinger equations and their solitons solutions

Optical soliton solutions to the fractional nonlinear Fokas–Lenells and paraxial Schrödinger equations

In this article, we consider the twin-core couplers with Kudryashov's sextic power law of refractive index and perturbation terms. The extended F-expansion method is implemented to construct cubic–quartic solitons in optical metamaterials and other solutions for the proposed model. Bright soliton solutions, singular soliton solutions, periodic solutions and combo periodic solutions are obtained. Moreover, for the physical illustration, some of the obtained solutions are represented graphically. 

Construction cubic-quartic solitons in optical metamaterials for the perturbed twin-core couplers with Kudryashov's sextic power law using extended F-expansion method

Pure-quartic solitons in presence of weak nonlocality

The structure and stability of multipole and vortex solitons in the nonlocal nonlinear fractional Schrödinger equation with a gradually decreasing Lévy index, α, are numerically studied. It is found that the solitons adiabatically compress with the decrease of Lévy index, and new species of stable ones are produced by means of this technique. It is known that, under the action of the normal diffraction (α = 2), the nonlocal cubic self-trapping can support, at most, quadrupole solitons and vortex ones with winding number m = 2 as stable modes in the one- and two-dimensional space, respectively. In contrast to that, we find that the application of the Lévy index management (the gradual decrease of α) leads to the formation of stable five-poles and sextupoles in one-dimensional, and vortices with m = 3 in two-dimensional. Weak dissipation does not essentially affect the observed results. 

Transformation of multipole and vortex solitons in the nonlocal nonlinear fractional Schrödinger equation by means of Lévy-index management

This paper introduces a series of asymmetric multi-vortex solitons, which made up of Gaussian beam and embedded multi off-axis shift vortex, in nonlocal nonlinear media. The analytical expression of the soliton trajectory is derived, and the other propagation properties, such as the intensity distribution, the rotating period, and the orbital angular momentum (OAM) are all investigated. It is found that the initial displacement of the soliton mass center, which can be controlled by selecting the appropriate shift values of the off-axis vortexes, can determine the trajectory of the optics beam. The OAM also depending on the shift values of the vortexes. Obviously, the controllable propagation of the asymmetric multi-vortex beam has important academic value and application prospect in optical switches, or be used as optical tweezers and wrenches.

Asymmetric multi-vortex solitons in nonlocal nonlinear media

This paper numerically investigates the propagation of Laguerre-Gaussian vortex beams launched in nonlocal nonlinear media, such as lead glass. Our results show that the propagation properties depend on the selection of beam parameters m and p, which represent the azimuthal and radial mode numbers. When p=0, these profiles can be stable solitons for m≤2, or break up and then form a set of single-hump profiles for m≥3, which are unbounded states with scattered remnants of the energy. However, for p≥1, the broken beams can evolve into vortex chaoticons, which exhibit both chaotic and solitonlike properties. The chaotic properties are determined by the positive Lyapunov exponents and spatial decoherence, while the solitonlike properties are demonstrated by the invariance of beam width and the interaction of beams in the form of quasielastic collisions. In addition, the power and orbital angular momentum of unbounded beam states both decay in propagation, while those of the chaoticons maintain their values well.

Vortex chaoticons in thermal nonlocal nonlinear media.

This paper studied the propagations of fractional vortex beams in nonlocal nonlinear media, and found that quasi-stable solitons can form when the nonlocality is strong enough and the initial power is equal to the critical power. The propagation properties, including intensity patterns, phase structures, transverse energy flows, and rotation period, were all investigated. The critical power of solitons with different topological charges is the same, however, the orbital angular momentum (OAM) of that increases with the increase of fractional topological charge. In addition, we revealed that fractional vortex solitons have lateral shifts in the y-direction, and the shift values can be controlled by the fractional topological charge. Obviously, the quasi-stable fractional vortex solitons have important academic value and potential application to optical switches, optical wrenches and optical communications, etc.

Qing Wang

Papers

Transformation of multipole and vortex solitons in the nonlocal nonlinear fractional Schrödinger equation by means of Lévy-index management

Asymmetric multi-vortex solitons in nonlocal nonlinear media

Vortex chaoticons in thermal nonlocal nonlinear media.

Quasi-stable fractional vortex solitons in nonlocal nonlinear media