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 Wannier solitons. These solitons showcase novel possibilities for light localization and transmission within nonlinear flat-band systems.

中文翻译：

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超蜂窝晶格中的二维平带孤子


平带周期性材料的特征是线性光谱包含至少一个带，其中传播常数几乎保持恒定，而与布里渊区的布洛赫动量无关。这些材料为研究与光定位相关的现象提供了独特的平台。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被探索，特别是在带平坦度稍微偏离零的连续系统中，与具有完全平坦带的简化离散系统相比。在这里，我们使用光谱中具有平带的连续超蜂窝晶格，从理论上和数值上引入了一系列稳定的平带孤子。这些解决方案包括基波孤子、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幂范围内都是稳定的。它们不会从平带中分叉，并且可以使用 Wannier 函数展开进行分析，从而将它们指定为万尼尔孤子。这些孤子展示了非线性平带系统中光定位和传输的新可能性。