Fractal-like photonic lattices and localized states arising from singular and nonsingular flatbands

Abstract

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.