Vortex solitons in quasi-phase-matched photonic crystals with the third harmonic generation
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| Main Authors: | , , , , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866913921444610048 |
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| author | Wang, Xuening Guo, Yuxin Ning, Qiuyi Liu, Bin He, Hexiang Zhang, Li Malomed, Boris A. Li, Yongyao |
| author_facet | Wang, Xuening Guo, Yuxin Ning, Qiuyi Liu, Bin He, Hexiang Zhang, Li Malomed, Boris A. Li, Yongyao |
| contents | 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 $φ=0$ or $π$, 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_00818 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Vortex solitons in quasi-phase-matched photonic crystals with the third harmonic generation Wang, Xuening Guo, Yuxin Ning, Qiuyi Liu, Bin He, Hexiang Zhang, Li Malomed, Boris A. Li, Yongyao Optics Pattern Formation and Solitons 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 $φ=0$ or $π$, 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. |
| title | Vortex solitons in quasi-phase-matched photonic crystals with the third harmonic generation |
| topic | Optics Pattern Formation and Solitons |
| url | https://arxiv.org/abs/2507.00818 |