准相位匹配光子晶体中稳固光学涡旋液滴的方形整形
Square-shaping of sturdy optical vortex droplets in quasi-phase-matched photonic crystals
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中文总结 AI 辅助
本文提出在准相位匹配光子晶体中，利用竞争非线性和方形几何约束，实现方形涡旋液滴的稳定形成，揭示涡旋稳健性不依赖圆对称的普适性。
中文摘要 AI 辅助
我们阐述了一种在准相位匹配三维光子晶体中，结合自聚焦二次非线性和自散焦三次材料非线性，对自俘获涡旋态进行可控整形的方案。该设置产生了稳固的液滴状涡旋模式，能够适应外部施加的强几何约束。在横向$(x,y)$平面施加方形调制，并沿传播方向$z$对二次非线性系数$d_z$进行周期性准相位匹配，导致了具有四重旋转对称性($C_4$)的方形涡旋液滴(VDs)的形成。这些态保持了涡旋相位循环，并在广泛的参数区域内表现出稳健的传播。在由三次自散焦主导的过饱和区域中，方形涡旋液滴遵循反Vakhitov--Kolokolov稳定性判据。结果主要针对拓扑荷$S=1$的涡旋液滴产生，也部分针对$S=2$和$4$产生，揭示了意想不到的普适性：涡旋的稳健性不依赖于圆对称性。因此，竞争非线性与几何约束的结合不仅为自俘获涡旋态的形成提供了有效方法，也为非线性光学场中拓扑保护的普适性提供了新见解。
英文摘要
We elaborate a scheme for controllable shaping of self-trapped vortex states in a quasi-phase-matched three-dimensional photonic crystal with the combination of self-focusing quadratic and defocusing cubic material nonlinearities. The setting gives rise to sturdy droplet-like vortex modes, capable to adapt to externally imposed strong geometric constraints. The application of a square-shaped modulation in the transverse $\left(x,y\right) $ plane and periodic quasi-phase-matching to the quadratic nonlinear coefficient $d_{z}$ along the propagation direction $z$ leads to the formation of square vortex droplets (VDs) with fourfold rotational symmetry ($C_{4}$). These states preserve the vortical phase circulation and exhibit robust propagation in a broad parameter region. In the oversaturated regime dominated by the cubic self-defocusing, the square-shaped VDs obey the anti-Vakhitov--Kolokolov stability criterion. The results, which are produced, chiefly, for the VDs with topological charge $S=1$, and also, in a partial form, for $S=2$ and $4$, reveal an unexpected universality: the vortex robustness is not contingent upon the circular symmetry. Thus, the combination of the competing nonlinearities and geometric confinement provides not only an effective method for the formation of self-trapped vortex states, but also new insight into generality of the topological protection in nonlinear optical fields.
发表机构
- Foshan University（佛山大学）
- Guangdong-Hong Kong-Macao Joint Laboratory for Intelligent Micro-Nano Optoelectronic Technology, Foshan University（佛山大学广东港澳智能微纳光电技术联合实验室）
- Tel Aviv University（特拉维夫大学）
- Instituto de Alta Investigación, Universidad de Tarapacá（塔拉帕卡大学高等研究所）
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