Shen Shuang, Zhang Yiqi, Kartashov Yaroslav V, Li Yongdong, Konotop Vladimir V
Key Laboratory for Physical Electronics and Devices, Ministry of Education, School of Electronic Science and Engineering, Xi'an Jiaotong University, Xi'an 710049, China.
Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow, 108840, Russia.
Nanophotonics. 2024 Aug 7;13(21):4047-4056. doi: 10.1515/nanoph-2024-0299. eCollection 2024 Sep.
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 flat-band 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 . These solitons showcase novel possibilities for light localization and transmission within nonlinear flat-band systems.
平带周期材料的特征在于其线性光谱包含至少一个能带，在该能带中，无论布里渊区内的布洛赫动量如何，传播常数几乎保持不变。这些材料为研究与光局域化相关的现象提供了一个独特的平台。与此同时，连续系统中平带物理与非线性之间的相互作用在很大程度上仍未得到探索，特别是在能带平坦度略微偏离零的连续系统中，这与具有精确平带的简化离散系统形成对比。在这里，我们使用一种在其光谱中具有平带的连续超蜂窝晶格，从理论和数值上引入了一系列稳定的平带孤子。这些解包括基态孤子、偶极孤子、多峰孤子甚至涡旋孤子。数值分析表明，这些孤子在很宽的功率范围内都是稳定的。它们不会从平带中分岔出来，并且可以使用万尼尔函数展开进行分析，从而将它们命名为 。这些孤子展示了非线性平带系统中光局域化和传输的新可能性。
