Liangwei Dong

Stabilization of multipole-mode solitons in mixed linear-nonlinear lattices with a 𝒫𝒯 symmetry

We report the evolution of higher-order nonlinear states in a focusing cubic medium, where both the linear refractive index and the nonlinearity are spatially modulated by a complex optical lattice exhibiting a parity-time (PT) symmetry. We reveal that introduction of out-of-phase nonlinearity modulation makes possible the stabilization of higher-order solitons with number of poles up to 7, which are highly unstable in linear PT lattices. Under appropriate conditions, multipole-mode solitons with out-of-phase components in the neighboring lattice sites are completely stable provided that their power or propagation constant exceeds a critical value. Thus, our findings suggest an effective way for the realization of stable multipole-mode solitons in periodic potentials with gain-loss components.

Multipeaked gap solitons in PT-symmetric optical lattices

We report the existence and stability properties of multipeaked solitons in a defocusing Kerr medium with an imprinted complex optical lattice featuring a parity-time (PT) symmetry. Various families of soliton solutions with a different number of peaks are found in the first finite gap of the lattice. Linear stability analysis corroborated by direct propagation simulations reveals that multipeaked gap solitons can propagate stably in a wide range, provided that their propagation constant exceeds a critical value. Our findings demonstrate, for the first time, the existence of stable multipeaked gap solitons in a PT-symmetric lattice.

Multi-stable solitons in 𝒫𝒯-symmetric optical lattices

We address the existence and stability properties of optical solitons in a competing cubic-quintic medium with an imprinted complex lattice featuring a parity-time (𝒫𝒯) symmetry. Various families of solitons with even and odd geometrical symmetries are found in both the semi-infinite and the first finite gaps. Linear stability analysis corroborated by direct propagation simulations reveals that solitons with different symmetries and different number of humps can propagate stably at the same propagation constants, i.e., multi-stable solitons can exist in this scheme. Interestingly enough, in sharp contrast to the stability of solitons in a conventional (real) lattice, both even and odd solitons with the same propagation constant belonging to different branches can be stable in the first gap of 𝒫𝒯 lattice, which indicates that the imaginary part of lattice plays an important role for the stabilization of solitons.

Surface solitons in nonlinear lattices

We investigate the existence of spatial optical solitons supported by an interface between two nonlinear lattices with different saturation parameters. Dipole, quadrupole, and vortex solitons are found in the nonlinear surface lattices. The slight different saturation degree between two sides of the interface leads to a remarkable asymmetry of solitons with higher power. We reveal that multipole and vortex solitons are stable when their power exceeds a threshold value, and stable localized surface nonlinear modes with very high peaks are possible.

Gap solitons in the nonlinear fractional Schrödinger equation with an optical lattice

We predict the existence of gap solitons in the nonlinear fractional Schrödinger equation (NLFSE) with an imprinted optically harmonic lattice. Symmetric/antisymmetric nonlinear localized modes bifurcate from the lower/upper edge of the first/second band in defocusing/focusing Kerr media. A unique feature we revealed is that, in focusing Kerr media, stable solitons appear in the finite bandgaps with the decrease of the Lévy index, which is in sharp contrast to the standard NLSE with a focusing nonlinearity. Nonlinear bound states composed by in-phase and out-of-phase soliton units supported by the NLFSE are also uncovered. Our work may pave the way for the study of spatial lattice solitons in fractional dimensions.

Localization of light in a parabolically bending waveguide array in thermal nonlinear media

A parabolically longitudinally bending waveguide array imprinted into thermal nonlinear media is found to support the localized stationary solitons. The localization results from the suppression of a curvature effect by the nonlinearity with an infinite-range nonlocality. The localization criterion is given analytically. Solitons propagate stably along a curved trajectory without bending loss, and their locations are significantly influenced by the waveguide curvature. These solitons represent the first example of stationary localized solitons encountered in curved waveguides.

Stable vortex solitons in a ring-shaped partially-PT-symmetric potential

We address the existence and stability of vortex solitons in a ring-shaped partially-parity-time (pPT) configuration. In sharp contrast to the reported nonlinear modes in PT- or pPT-symmetric systems, stable vortex solitons with different topological charges can be supported by the proposed pPT potential, despite the system always being beyond the symmetry-breaking point. Vortex solitons are characterized by the number of phase singularities which equals the corresponding topological charge. At higher power, unstable higher-charged vortices degenerate into stable vortices with lower charges. Robust nonlinear vortices can be easily excited by an input Gaussian beam. Our results provide, to the best of our knowledge, the first example of stable solitons in a symmetry-breaking system.

Higher-charged vortices in mixed linear-nonlinear circular arrays

We report on the dynamics of vortex solitons in circular waveguide arrays featuring modulation of both the linear and nonlinear refractive indices. Out-of-phase competition between both effects supports multipeaked vortex solitons with higher topological charges. A vortex solution can be found only when its charge is less than half of the number of waveguides. It may expand or shrink radially with the propagation constant, depending on the ratio between the topological charge and the number of waveguides. Surprisingly, vortex solitons with higher charges are more stable than those with lower charges, which is very rare and contrary to the stability of vortices in uniform or lattice-modulated media. Our findings suggest an alternative way for the realization of stable vortex solitons with higher charges.

Elliptic vortices in optical waveguides and self-attractive Bose-Einstein condensates

We investigate vortex solitons in models representing “pancake-shaped” Bose-Einstein condensates (BECs) with attractive interatomic interactions and an anisotropic harmonic trapping potential, or polarization-preserving waveguides, such as a photonic-crystal or radial-bandgap fiber with an elliptically deformed core. Elliptic-vortex states bifurcate from dipole modes. In spite of strongly asymmetric shapes, the elliptic vortices with topological charge 1 are stable in a wide region in their existence domain. The dependence of the stability region on the eccentricity of the elliptic trap is reported. Input circular wave functions with embedded vorticity slowly relax into stationary elliptic vortices, featuring persistent rotation in the course of the evolution. All higher-order vortices are unstable.

Multipeaked fundamental and vortex solitons in azimuthally modulated Bessel lattices

We demonstrate the existence of multipeaked fundamental and vortex solitons in defocusing Kerr media with an imprinted azimuthally modulated Bessel lattice. Multipeaked solitons emanating from the fundamental linear lattice modes are stable in their entire existence domains. The number of soliton peaks is determined by the azimuthal index. Multipeaked vortex solitons with high topological charges in lattices exhibit special amplitude and phase distributions that resemble those of azimuthons. We reveal that the “stability rule” for vortex solitons in defocusing Kerr media is exactly opposite to that in focusing media. Multipeaked vortex solitons we obtained may provide a missing link between the radially symmetric vortices and nonrotating soliton clusters.