arXiv subjects

Shuang Shen

Publications and source records attributed to Shuang Shen.

8 recordsLinked to original sources

arXiv2026

Stable vortex soliton arrays in disclination-fractal systems

Vortex light fields carry orbital angular momentum and have attracted significant attention because of their wide applications in light field manipulations, optical communications, and quantum information processing. In nonlinear media, the balance between diffraction and self-action enables the formation of vortex solitons. However, achieving the stability of vortex solitons remains challenging due to radial and azimuthal modulation instabilities. Here, we report stable vortex solitons and vortex-soliton arrays in disclination-fractal configurations with different rotational symmetries, constructed by applying disclination operations to fractal lattice structures. The stable vortex-soliton arrays---composed of several vortex solitons---can exist along domain walls, resulting from the disclination operation applied to the topologically trivial phase. Their stability is verified through both linear stability analysis and direct simulations of perturbed propagation. For comparison, vortex-soliton arrays in conventional disclination configurations are found to be completely unstable, demonstrating the significance of the fractal configuration in stabilizing these nonlinear states. These findings reveal a new nonlinear excitation mechanism arising from the interplay between fractal geometry and disclination defects, thereby providing theoretical underpinnings for both the improved understanding of multi-field excitation phenomena in complex geometric systems and opening new avenues for the design of photonic devices based on fractal disclination structures.

physics.optics↗

arXiv2024

$π$ mode lasing in the non-Hermitian Floquet topological system

$π$ modes are unique topological edge states appearing in Floquet systems with periodic modulations of the underlying lattice structure in evolution variable, such as dynamically modulated Su-Schrieffer-Heeger (SSH) lattices. These edge states are anomalous states usually appearing between Floquet replicas of the same band, even if standard topological index remains zero for this band. While linear and nonlinear $π$ modes were observed in conservative systems, they have never been studied in nonlinear regime in the non-Hermitian systems with structured gain and losses. Here we show that SSH waveguide array with periodically oscillating waveguide positions in propagation direction and with parity-time symmetric refractive index landscape, can support $π$ modes that are damped or amplified at different ends of the array. By including nonlinearity and nonlinear absorption into our continuous system, we achieve stable lasing in $π$ mode at one end of the array. The representative feature of this system is that lasing in it is thresholdless and it occurs even at low gain-loss amplitudes. The degree of localization of lasing $π$ modes can be flexibly controlled by the amplitude of transverse waveguide oscillations. This work therefore introduces a new type of topological Floquet laser and a route to manipulation of $π$ modes by structured gain and losses.

physics.optics↗

arXiv2024

Two-dimensional flat-band solitons in superhoneycomb lattices

Flat-band periodic materials are characterized by a linear spectrum containing at least one band where the propagation constant remains nearly constant irrespective of the Bloch momentum across the Brillouin zone. These materials provide a unique platform for investigating phenomena related to light localization. Meantime, the interaction between flat-band physics and nonlinearity in continuous systems remains largely unexplored, particularly in continuous systems where the band flatness deviates slightly from zero, in contrast to simplified discrete systems with exactly flat bands. Here, we use a continuous superhoneycomb lattice featuring a flat band in its spectrum to theoretically and numerically introduce a range of stable flatband solitons. These solutions encompass fundamental, dipole, multi-peak, and even vortex solitons. Numerical analysis demonstrates that these solitons are stable in a broad range of powers. They do not bifurcate from the flat band and can be analyzed using Wannier function expansion leading to their designation as Wannier solitons. These solitons showcase novel possibilities for light localization and transmission within nonlinear flat-band systems.

nlin.PS↗

arXiv2024

Chiral bulk solitons in photonic graphene with decorated boundaries

We propose a chiral bulk soliton in a nonlinear photonic lattice with decorated boundaries, presenting a novel approach to manipulate photonic transport without extensive bulk modifications. Unlike traditional methods that rely on topological edge and corner modes, our strategy leverages the robust chiral propagation of bulk modes. By introducing nonlinearity into the system, we find a stable bulk soliton, akin to the topological valley Hall effects. The chiral bulk soliton exhibits remarkable stability; the energy does not decay even after a long-distance propagation; and the corresponding Fourier spectrum confirms the absence of inter-valley scattering indicating a valley-locking property. Our findings not only contribute to the fundamental understanding of nonlinear photonic systems but also hold significant practical implications for the design and optimization of photonic devices.

physics.optics↗

arXiv2023

Floquet edge solitons in modulated trimer waveguide arrays

We show that one-dimensional Floquet trimer arrays with periodically oscillating waveguides support two different and co-existing types of topological Floquet edge states in two different topological gaps in Floquet spectrum. In these systems nontrivial topology is introduced by longitudinal periodic oscillations of the waveguide centers, leading to the formation of Floquet edge states in certain range of oscillation amplitudes despite the fact that the structure spends half of the period in ``instantaneously'' nontopological phase, and only during other half-period it is ``instantaneously'' topological. Two co-existing Floquet edge states are characterized by different phase relations between bright spots in the unit cell -- in one mode these spots are in-phase, while in other mode they are out-of-phase. We show that in focusing nonlinear medium topological Floquet edge solitons, representing exactly periodic nonlinear localized Floquet states, can bifurcate from both these types of linear edge states. Both types of Floquet edge solitons can be stable and can be created dynamically using two-site excitations.

physics.optics↗

arXiv2017

Lyapunov exponents for products of matrices

Let ${\bf M}=(M_1,\ldots, M_k)$ be a tuple of real $d\times d$ matrices. Under certain irreducibility assumptions, we give checkable criteria for deciding whether ${\bf M}$ possesses the following property: there exist two constants $λ\in {\Bbb R}$ and $C>0$ such that for any $n\in {\Bbb N}$ and any $i_1, \ldots, i_n \in \{1,\ldots, k\}$, either $M_{i_1} \cdots M_{i_n}={\bf 0}$ or $C^{-1} e^{λn} \leq \| M_{i_1} \cdots M_{i_n} \| \leq C e^{λn}$, where $\|\cdot\|$ is a matrix norm. The proof is based on symbolic dynamics and the thermodynamic formalism for matrix products. As applications, we are able to check the absolute continuity of a class of overlapping self-similar measures on ${\Bbb R}$, the absolute continuity of certain self-affine measures in ${\Bbb R}^d$ and the dimensional regularity of a class of sofic affine-invariant sets in the plane.

math.DS↗

arXiv2014

Extended multifractal formalism of some non-doubling measures

In a previous work \cite{She} we constructed measures on symbolic spaces which satisfy an extended multifractal formalism (in the sense that Olsen's functions $b$ and $B$ differ and that their Legendre transforms have the expected interpretation in terms of dimensions). These measures are composed with a Gray code and projected onto the unit interval so to get doubling measures. Then we were able to show that the projected measure has the same Olsen's functions as the one it comes from and that it also fulfills the extended multifractal formalism. Here we show that the use of a Gray code is not necessary to get these results, although dealing with non doubling measures.

math.MG↗

arXiv2013

Multifractal analysis of some inhomogeneous multinomial measures with distinct analytic Olsen's $b$ and $B$ functions

Inhomogeneous multinomial measures on the mixed symbolic spaces and the real line are given. By counting the zeros of the corresponding generalized Dirichlet polynomials, one obtains a probability measure whose Olsen's functions $b$ and $B$ are analytic and their graphs differ except at two points where they are tangent. Also, interpretations of the Legendre transform of $b$ and $B$ are given in terms of dimensions.

math.MG↗