Necklace Solitons Research Articles

Accessible solitons in three-dimensional parabolic cylindrical coordinates

A class of self-similar beams, named three-dimensional (3D) spatiotemporal parabolic accessible solitons, are introduced in the 3D highly nonlocal nonlinear media. We obtain exact solutions of the 3D spatiotemporal linear Schrödinger equation in parabolic cylindrical coordinates by using the method of separation of variables. The 3D localized structures are constructed with the help of the confluent hypergeometric Tricomi functions and the Hermite polynomials. Based on such an exact solution, we graphically display three different types of 3D beams: the Gaussian solitons, the ring necklace solitons, and the parabolic solitons, by choosing different mode parameters. We also perform direct numerical simulation to discuss the stability of local solutions. The procedure we follow provides a new method for the manipulation of spatiotemporal solitons.

Accessible solitons of fractional dimension

We demonstrate that accessible solitons described by an extended Schrödinger equation with the Laplacian of fractional dimension can exist in strongly nonlocal nonlinear media. The soliton solutions of the model are constructed by two special functions, the associated Legendre polynomials and the Laguerre polynomials in the fraction-dimensional space. Our results show that these fractional accessible solitons form a soliton family which includes crescent solitons, and asymmetric single-layer and multi-layer necklace solitons.

Light bullets in three-dimensional complex Ginzburg-Landau equation with modulated Kummer-Gauss photonic lattice

We investigate the existence of spatiotemporal necklace vortex solitons or light bullets in the complex Ginzburg-Landau equation with the modulated Kummer-Gauss (KG) external lattice potential and the spiraling phase of vorticities , and 2. We find localized vortex necklaces in a three-dimensional nonlinear medium, trapped by the KG external potential with different orders of vorticity. Stable and quasi-stable solitons form from input pulses with embedded vorticity. The stability is established by calculating growth rates of the perturbed eigenmodes. We establish that spatiotemporal necklace solitons may coexist in a large domain of the parameter space.

Necklace solitons in Bessel photonic lattice: Stability and internal oscillation

Stability, internal modes and internal oscillation of 12-pearled necklace solitons in photorefractive crystal with imprinted Bessel photonic lattices are investigated. It is shown that the imaginary parts of internal modes are negligible comparing with real parts. The stable solitons perform long-distance and quasi-periodic oscillation of intensity and shape under the perturbation of internal modes.

Internal oscillation of necklace solitons in Bessel photonic lattice imprinted in defocusing and focusing materials

Internal modes and internal oscillation of necklace solitons in Bessel photonic lattices imprinted in self-defocusing and self-focusing materials are investigated. Under the same parameters, necklace solitons in self-focusing material possess larger power than that of self-defocusing material, and the stability of solitons in defocusing material is better than in focusing material. It is shown that the internal modes have both real and imaginary parts in such cases, differing from the one-dimensional case. While white noise gives rise to jitter of the intensity of stable necklace solitons, the stable solitons perform long-distance and quasi-periodic oscillation of intensity and shape under the perturbation of internal modes, and the solitons in self-defocusing material experience larger oscillation amplitude than that in self-focusing material.

Internal modes of necklace solitons in the Bessel photonic lattice

Internal modes and internal oscillation of ten-pearled necklace solitons in Bessel photonic lattices with defocusing Kerr nonlinearity are investigated after the derivation of solutions of such solitons and the analysis of their stability. It is shown that the internal modes have both real and imaginary parts in such cases, which is different from the one-dimensional case. While white noise gives rise to the jitter of the intensity of stable necklace solitons, the stable solitons perform long-distance and quasi-periodic oscillation of intensity and shape under the perturbation of internal modes.

Accessible solitary wave families of the generalized nonlocal nonlinear Schrödinger equation

Two-dimensional accessible solitary wave families of the generalized nonlocal nonlinear Schrodinger equation are obtained by utilizing superpositions of various single accessible solitary solutions. Specific values of soliton parameters are selected as initial conditions and the superposition of known single solitary solutions in the highly nonlocal regime are launched into the nonlocal nonlinear medium with a Gaussian response function, to obtain novel numerical solitary solutions of improved stability. Our results reveal that in nonlocal media with the Gaussian response the higher-order spatial accessible solitary families can exist in various forms, such as asymmetric necklace, asymmetric fractional, and symmetric multipolar necklace solitons.

Internal oscillation of vector solitons and necklace solitons

Internal modes and internal oscillation of vector solitons associated with photoisomerization and necklace solitons in Bessel lattices are researched. While white noise gives rise to the unsmoothness of the vector solitons, the perturbation of internal modes results in the long-distance quasi-periodic oscillation of soliton shape. Internal modes of two-dimensional necklace solitons in Bessel lattices have both real and imaginary parts, which is different with the internal modes of one-dimensional solitons which have only real part.

Stabilization of multibeam necklace solitons in circular arrays with spatially modulated nonlinearity

We address necklace solitons supported by circular waveguide arrays with out-of-phase modulation of nonlinearity and linear refractive index. Such two-dimensional necklace solitons appear as rings of multiple out-of-phase bright spots. We show that necklace solitons are stable if their peak intensity is low or moderate and that the domain of stability shrinks with increasing nonlinearity modulation depth. However, we find that the stability domains expand with increasing number of necklace spots.

Three-dimensional optical vortex and necklace solitons in highly nonlocal nonlinear media

We demonstrate the existence of localized optical vortex and necklace solitons in three-dimensional (3D) highly nonlocal nonlinear media, both analytically and numerically. The 3D solitons are constructed with the help of Kummer's functions in spherical coordinates and their unique properties are discussed. The procedure we follow offers ways for generation, control, and manipulation of spatial solitons.

Two-dimensional Whittaker solitons in nonlocal nonlinear media

Two-dimensional Whittaker solitons (WSs) are introduced and investigated numerically in nonlocal nonlinear media. Different classes of stable and unstable higher-order spatial optical solitons are discovered among the solutions of the generalized nonlocal nonlinear Schr\odinger equation, in analogy with the linear Whittaker eigenmodes of the quantum harmonic oscillator. Specific values of the modulation depth parameter for different values of the topological charge are discussed. Our results reveal that in media with a Gaussian response function higher-order spatial WSs can exist in various families, such as two-dimensional Gaussian solitons, vortex-ring solitons, half-moon solitons, and symmetric and asymmetric single-layer and multilayer necklace solitons. The stability of WSs is addressed numerically. We establish that two-dimensional Gaussian solitons and vortex-ring solitons are stable, while other families of spatial WSs are unstable, although their stability can be improved by moving into the strongly nonlocal regime.

Two-Dimensional Laguerre–Gaussian Asymmetric Soliton Family in Strongly Nonlocal Media

We demonstrate the existence of a broad class of higher-order Laguerre–Gaussian asymmetric spatial optical solitons in strongly nonlocal nonlinear media. Furthermore, we discuss specific values (q = 0) of the modulation depth parameter for different rational values of the topological charge in detail. Our results show that higher-order asymmetry spatial soliton family can exist in various forms, such as two-dimensional defect half-solitons, asymmetric single-layer and multi-layer necklace solitons.

Necklace solitons and ring solitons in Bessel optical lattices

We put forward the existence of localized necklace solitons and ring solitons in a defocusing cubic nonlinear medium with an imprinted Bessel optical lattice. Novel families of necklace solitons are found and their unique properties, including multistable states are revealed. We show that both necklace solitons and ring solitons could reside on any ring of the Bessel lattices. They are dynamically stable provided that the lattice is modulated deep enough. The uncovered phenomena may open a new way for soliton control and manipulation.

Necklacelike Solitons in Optically Induced Photonic Lattices

We report the first observation of stationary necklacelike solitons. Such necklace structures were realized when a high-order vortex beam was launched appropriately into a two-dimensional optically induced photonic lattice. Our theoretical results obtained with continuous and discrete models show that the necklace solitons resulting from a charge-4 vortex have a pi phase difference between adjacent "pearls" and are formed in an octagon shape. Their stability region is identified.