发表机构
Institute of Spectroscopy, Russian Academy of Sciences（俄罗斯科学院光谱学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究二维星形网络中的涡旋孤子，发现其拓扑荷受离散旋转对称性限制，且稳定性与拓扑荷及对称性密切相关，不同于常规环状阵列。
AI 中文摘要
我研究了二维星形网络中的涡旋孤子，该网络由若干一维线波导阵列（或射线）紧密靠近而成。每个阵列中的第一个波导属于特定半径的环，其模场与该环上其他射线波导的模场重叠，同时也与该线阵列中波导的模场重叠。这形成了一个具有离散旋转对称性的系统，由于中心环上（线阵列在此相互靠近）波导之间的局部耦合，该系统能够支持各种局域线性涡旋态。随着中心环半径的变化，局域涡旋态从沿结构射线扩展的态连续谱中涌现。我展示了当结构中的射线数量增加，从而其离散旋转对称性增加时，不同拓扑荷逐渐增大的涡旋模式如何出现。每个这样的线性局域模式在非线性光学介质中产生一族无阈值的涡旋孤子，其拓扑荷受系统离散旋转对称性的限制。星形网络中的涡旋孤子随着功率增加表现出定性不同的行为，这取决于产生孤子族的线性涡旋的传播常数是位于扩展态带之上还是之下。涡旋孤子的稳定性性质非平凡地依赖于其拓扑荷和系统的离散旋转对称性，显示出与通常的环状波导阵列非常不同的图景。
英文摘要
I consider vortex solitons in two-dimensional star networks created by several one-dimensional line waveguide arrays (or rays) brought in close proximity. First waveguide in each array belongs to the ring of certain radius and its modal field overlaps with modal fields of waveguides from other rays laying on this ring, as well as with modal fields of waveguides in this line array. This creates a system with discrete rotational symmetry that is capable of supporting various localized linear vortex states due to local coupling between waveguides on the central ring, where line arrays approach each other. Localized vortex states emerge from the continuum of the states extended along the rays of the structure upon variation of the radius of the central ring. I show how different vortex modes with progressively increasing topological charges emerge when the number of rays in structure and, therefore, its discrete rotational symmetry increases. Each such linear localized mode gives rise to a family of thresholdless vortex solitons in nonlinear optical medium, whose topological charges are limited by the discrete rotational symmetry of the system. Vortex solitons in star networks exhibit qualitatively different behavior with increasing power depending on whether the propagation constant of linear vortex that gives rise to a family of solitons is located above or below the band of extended states. Stability properties of vortex solitons nontrivially depend on their topological charge and discrete rotational symmetry of the system, showing very different picture from usual ring-like waveguide arrays.
Comments7 pages, 4 figures
Journal refChaos, Solitons and Fractals 212, 119010 (2026)
DOI：10.1016/j.chaos.2026.119010
