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

TL;DR

This paper experimentally realizes fractal-like photonic lattices with coexisting flatbands, demonstrating localized states, superimposed mode structures, and dynamical oscillations, revealing new insights into flatband physics and fractal photonic systems.

Contribution

It introduces a method to create fractal-like photonic lattices with coexisting flatbands and demonstrates control over localized states and their dynamics, a novel combination in photonics.

Findings

Observation of distinct compact localized states in fractal-like lattices

Experimental demonstration of superimposed mode structures via phase modulation

Numerical simulation of flatband state oscillations due to eigenenergy differences

Abstract

We realize fractal-like photonic lattices using cw-laser-writing technique, thereby observe 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 experimentally not only the simplest CLSs but also their superimposition into other complex mode structures. 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 fractal structure, flatband singularity, and real-space topology.