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

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.

References in corpus (11)

• Topological Photonics
• Nearly-flat bands with nontrivial topology
• Observation of a localized flat-band state in a photonic Lieb lattice
• Observation of bound states in Lieb photonic lattices
• Localization and delocalization of light in photonic moire lattices
• Topological Photonic Quasicrystals: Fractal Topological Spectrum and Protected Transport
• Flat Bands Under Correlated Perturbations
• Photonic Floquet topological insulators in a fractal lattice
• Geometric characterization of anomalous Landau levels of isolated flat bands
• General construction of flat bands with and without band crossings based on wave function singularity
• Isolated flat bands in an interlocking-circles lattice

Cited by in corpus (15)

• Observation of nonlinear fractal higher-order topological insulator
• Topological edge and corner states in Bi fractals on InSb
• Localized states emerging from singular and nonsingular flat bands in a frustrated fractal-like photonic lattice
• Localized dynamics arising from multiple flat bands in a decorated photonic Lieb lattice
• Designer quantum states on a fractal substrate: compact localization, flat bands and the edge modes
• Multiple flat bands and localized states in photonic super-Kagome lattices
• Non-singular and singular flat bands in tunable acoustic metamaterials
• Robust incoherent perfect absorption
• Engineering flux-controlled flat bands and topological states in a Stagome lattice
• Mode conversion and resonant absorption in inhomogeneous materials with flat bands
• The Fractal-Lattice Hubbard Model
• Aharonov-Bohm caging of an electron in a quantum fractal
• A fractal geometry immersed in a hierarchical magnetic flux distribution
• Proximity-induced flat bands and topological properties in a decorated diamond chain
• Fractal Polariton Topological Insulator