We experimentally realize fractal-like photonic lattices by use of the cw-laser-writing technique, thereby observing distinct compact localized states (CLSs) associated with different flatbands in the same lattice setting. Such triangle-shaped lattices, akin to the first generation Sierpinski lattices, possess a band structure where singular non-degenerate and nonsingular degenerate flatbands coexist. By proper phase modulation of an input excitation beam, we demonstrate not only the simplest CLSs but also their superimposition into other complex mode structures. Our experimental and numerical results are corroborated by theoretical analysis. Furthermore, we show by numerical simulation a dynamical oscillation of the flatband states due to beating of the CLSs that have different eigenenergies. These results may provide inspiration for exploring fundamental phenomena arising from the interplay of fractal structure, flatband singularity, and real-space topology.

中文翻译：

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奇异和非奇异平带产生的分形光子晶格和局域态

我们通过使用连续激光写入技术实验性地实现了类分形光子晶格，从而观察到与相同晶格设置中的不同平带相关的不同紧凑局部状态 (CLS)。这种三角形晶格类似于第一代谢尔宾斯基晶格，具有带状结构，其中奇异的非简并和非奇异的简并平带共存。通过对输入激发光束进行适当的相位调制，我们不仅展示了最简单的 CLS，还展示了它们与其他复杂模式结构的叠加。我们的实验和数值结果得到了理论分析的证实。此外，我们通过数值模拟显示了由于具有不同特征能量的 CLS 的跳动而导致的平带状态的动态振荡。