标题： 准相位匹配光子晶体中的三阶谐波生成涡旋孤子 显示英文标题

标题： Vortex solitons in quasi-phase-matched photonic crystals with the third harmonic generation

摘要： 我们报告了在具有由准相位匹配的二次非线性产生的三次谐波（TH）生成的三维光子晶体模型中稳定的复合涡旋孤子。 光子晶体设计为在$\left( x\text{,}% y\right) $平面上的棋盘结构，而二阶非线性极化率$d(z)$沿传播方向作为具有两种不同周期的矩形链进行调制。 这种结构可以通过现有技术制造。 复合涡旋孤子由基频（FF）、二次谐波（SH）和三次谐波（TH）成分构成，表现出对应于拓扑电荷为$s=1$的涡旋、对应于$s=2$的四极子以及对应于$s = -1$的反涡旋结构的空间图案。 孤子轮廓呈现出菱形或方形图案，分别对应于相位匹配条件$\varphi =0$或$\pi $，其中菱形孤子具有更宽的稳定区域。 从实验可行性角度来看，我们表明菱形和方形的复合涡旋孤子可能在光子晶体中传播距离高达$\sim 1$m。具有$s=\mp 1$的孤子的TH分量是由级联非线性相互作用产生的，从具有$s=\pm 1$的FF涡旋分量开始，并通过具有$s=2$的四极子SH分量进行。这些发现为在非线性光学中创建和控制稳定的涡旋孤子提供了一种新方法。 显示英文摘要

摘要： We report stable composite vortex solitons in the model of a three-dimensional photonic crystal with the third-harmonic (TH) generation provided by the quasi-phase-matched quadratic nonlinearity. The photonic crystal is designed with a checkerboard structure in the $\left( x\text{,}% y\right) $ plane, while the second-order nonlinear susceptibility, $d(z)$, is modulated along the propagation direction as a chains of rectangles with two different periods. This structure can be fabricated by means of available technologies. The composite vortex solitons are built of fundamental-frequency (FF), second-harmonic (SH), and TH components, exhibiting spatial patterns which correspond to vortex with topological charges $s=1$, a quadrupole with $s=2$, and an anti-vortex structure with $s = -1$, respectively. The soliton profiles feature rhombic or square patterns, corresponding to phase-matching conditions $\varphi =0$ or $\pi $, respectively, the rhombic solitons possessing a broader stability region. From the perspective of the experimental feasibility, we show that both the rhombic and square-shaped composite vortex solitons may readily propagate in the photonic crystals over distances up to $\sim 1$ m. The TH component of the soliton with $s=\mp 1$ is produced by the cascaded nonlinear interactions, starting from the FF vortex component with $s=\pm 1$ and proceeding through the quadrupole SH one with $s=2$. These findings offer a novel approach for the creation and control of stable vortex solitons in nonlinear optics.