Two-dimensional spatial solitons in highly nonlocal nonlinear media

We investigate, analytically and numerically, a class of novel higher-order spatial solitons in two transverse-dimensions, in highly nonlocal nonlinear media. The stability of these solutions in propagation is confirmed by direct numerical simulation. Our results demonstrate that the higher-order spatial solitons in highly nonlocal nonlinear media can exist in various forms, such as the fundamental solitons, vortex-ring solitons, multipole solitons, and fractional solitons.     

Multicolor lattice solitons

We report on the existence of multicolor solitons supported by periodic lattices made from quadratic nonlinear media. Such lattice solitons bridge the gap between continuous solitons in uniform media and discrete solitons in strongly localized systems and exhibit a wealth of new features. We discovered that, in contrast to uniform media, multipeaked lattice solitons are stable. Thus they open new opportunities for all-optical switching based on soliton packets.     

Parametric vector solitons in tetragonal crystals

We introduce novel types of spatial vector soliton that can be generated in anisotropic optical media, such as tetragonal crystals with third-order nonlinear susceptibility. We demonstrate that these vector solitons provide a nontrivial generalization to both conventional vector solitons of birefringent cubic media and parametric solitons supported by third-order cascaded nonlinearities.     

Collisions of Two Spatial Solitons in Inhomogeneous Nonlinear Media

Collisions of spatial solitons occurring in the nonlinear Schröinger equation with harmonic potential are studied, using conservation laws and the split-step Fourier method. We find an analytical solution for the separation distance between the spatial solitons in an inhomogeneous nonlinear medium when the light beam is self-trapped in the transverse dimension. In the self-focusing nonlinear media the spatial solitons can be transmitted stably, and the interaction between spatial solitons is enhanced due to the linear focusing effect (and also diminished for the linear defocusing effect). In the self-defocusing nonlinear media, in the absence of self-trapping or in the presence of linear self-defocusing, no transmission of stable spatial solitons is possible. However, in such media the linear focusing effect can be exactly compensated, and the spatial solitons can propagate through.     

Spatiotemporal solitons in inhomogeneous nonlinear media

We investigate the possibility of forming spatiotemporal solitons (optical bullets) in inhomogeneous, dispersive nonlinear media using a graded-index Kerr medium as an example. We use a variational approach to solve the multidimensional, inhomogeneous, nonlinear Schrödinger equation and show that spatiotemporal solitons can be stabilized under certain conditions. We verify their existence by means of a full numerical analysis and show that such solitons should be observable experimentally.     

Upper threshold for stability of multipole-mode solitons in nonlocal nonlinear media

We address the stability of multipole-mode solitons in nonlocal Kerr-type nonlinear media. Such solitons comprise several out-of-phase peaks packed together by the forces acting between them. We discover that dipole-, triple-, and quadrupole-mode solitons can be made stable, whereas all higher-order soliton bound states are unstable.     

Spatial optical solitons in fifth order and seventh order weakly nonlocal nonlinear media

We analytically study the (1 + 1)-dimensional spatial optical solitons in weakly nonlocal nonlinear media with cubic–quintic nonlinearity (fifth order nonlinear media) and cubic–quintic–septic nonlinearity (seventh order nonlinear media). Explicit solutions are derived, which include optical bright solitons, singular solutions and singular triangular periodic solution.     

Two-color surface lattice solitons

We study the properties of surface solitons generated at the edge of a semi-infinite photonic lattice in nonlinear quadratic media, namely two-color surface lattice solitons. We analyze the impact of phase mismatch on the existence and stability of nonlinear surface modes and find novel classes of two-color twisted surface solitons, which are stable in a large domain of their existence.     

Multipole vector solitons in nonlocal nonlinear media

We show that multipole solitons can be made stable via vectorial coupling in bulk nonlocal nonlinear media. Such vector solitons are composed of mutually incoherent nodeless and multipole components jointly inducing a nonlinear refractive index profile. We found that stabilization of the otherwise highly unstable multipoles occurs below certain maximum energy flow. Such a threshold is determined by the nonlocality degree.     

Gaussian solitons in nonlocal media: variational analysis

Exact solutions of Gaussian solitons in nonlinear media with a Gaussian nonlocal response are obtained. Using the variational approach, we obtain the approximate solutions of such solitons when the degree of the nonlocality is arbitrary. Specifically, we study the conditions for Gaussian solitons that propagate in weakly and highly nonlocal media. We also compare the variational result with the known exact solutions for weakly and highly nonlocal media.     

Subwavelength discrete solitons in nonlinear metamaterials

We present the first study of subwavelength discrete solitons in nonlinear metamaterials: nanoscaled periodic structures consisting of metal and nonlinear dielectric slabs. The solitons supported by such media result from a balance between tunneling of surface plasmon modes and nonlinear self-trapping. The dynamics in such systems, arising from the threefold interplay between periodicity, nonlinearity, and surface plasmon polaritons, is substantially different from that in conventional nonlinear dielectric waveguide arrays. We expect these phenomena to inspire fundamental studies as well as potential applications of nonlinear metamaterials, particularly in subwavelength nonlinear optics.     

Vector soliton fission by reflection at nonlinear interfaces

We address the reflection of vector solitons, comprising several components that exhibit multiple field oscillations, at the interface between two nonlinear media. We reveal that reflection causes fission of the input signal into sets of solitons propagating at different angles. We find that the maximum number of solitons that arises upon fission is given by the number of field oscillations in the highest-order input vector soliton.     

强非局域介质中基于古依相位的旋转涡旋光孤子

利用强非局域非线性介质中傍轴光束传输的修正Snyder-Mitchell模型讨论了两束共线(即光束中心和传输方向都相同)拉盖尔-高斯型光孤子(CLGS)构成的涡旋光孤子传输过程。在一定条件下,涡旋光束在传输过程中,光束截面光斑发生旋转现象,但光束的束宽保持不变,称之为旋转涡旋光孤子。涡旋光孤子旋转的现象可以通过叠加光场中的古依相位来解释。结果展现了几个旋转涡旋光孤子在传输过程中的旋转现象和强非局域介质中多环形旋转涡旋光孤子的传输。     

Interaction of incoherent white-light solitons

We study numerically the formation and interactions of incoherent white-light solitons in a nonlinear media with logarithmic saturable nonlinearity based on the coherent density approach. We find that not only the formation but also the interactions of incoherent white-light solitons are fundamentally a collective effect, where all the frequencies participate in the process, and self-adjust their respective contributions to the formation and interactions. We find that the interactions of incoherent white-light solitons in logarithmic media are always attractive.     

Transport of Nonautonomous Solitons in Two‐Dimensional Disordered Media

Transport of localized nonlinear excitations in disordered media is an interesting and important topic in modern physics. Investigated in this work is transport of two‐dimensional (2D) solitons for a nonlinear Schrödinger equation with inhomogeneous nonlocality and disorder. We use the variational method to show that, the shape (size) of solitons can be manipulated through adjusting the nonlocality, which, in turn, affects the soliton mobility. Direct numerical simulations reveal that the influence of disorder on the soliton transport accords with our analysis by the variational method. Besides, we have demonstrated an anisotropic transport of the 2D nonautonomous solitons as well. Our study is expected to shed light on modulating solitons through material properties for specifying their transport in disordered media.     

Surface solitons at the interface between semi-infinite linear and thermal nonlinear optical media

We investigate numerically surface-wave solitons occurring at the interface between semi-infinite linear and thermal nonlinear optical media, with the refractive index of the linear medium being greater than that of the nonlinear medium (in the absence of light). We find that the threshold energy flows of the existence of the surface solitons depend on the linear refractive index difference of the two media. Their fitting empirical formula has been obtained. Furthermore, we elucidate that the optical beams propagating in thermal nonlinear optical media, either as a single surface soliton or as a dipole surface soliton, can be attracted to the surface, even when launched from far away.     

Packing, unpacking, and steering of multicolor solitons in optical lattices

We discuss potential applications of multicolor solitons supported by periodic lattices imprinted in quadratic nonlinear media. Such lattice solitons can be packed together with appropriate relative phases to form stable soliton trains that can be treated as bit sequences. We describe controllable splitting of the trains into their soliton constituents and the angle- and power-controlled steering and trapping of solitons moving across the lattice into the desired guiding channel.     

Periodic solitons in nonlocal nonlinear media

We identify periodic solitons in nonlocal nonlinear media: multi-hump soliton solutions propagating in a fully periodic fashion. We also demonstrate recurrences and breathers whose evolution is statistically periodic and discuss why some systems support periodic solitons while others do not.     

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.