Localized light in a fractal-like photonic lattice

Abstract

We demonstrate light localization in a frustrated fractal-like photonic lattice owing multiple flat bands fabricated by femtosecond direct laser writing. We investigate the arising flat bands depending on the singularities of their Bloch wave functions.

Demonstration of Robust Boundary Modes in Photonic Decorated Honeycomb Lattices

“…Such a DHL (also called “star lattice” [ 2,4,5 ] ) is different from previous HCL variations such as the super HCLs [ 37 ] that consist of five lattice sites per unit cell and host only a single flat band, although the term “decorated HCL” was somewhat mix‐used in literature. [ 40,41 ] The DHL considered here is also different from the fractal‐like lattices, [ 32,33 ] which also have six lattice sites per unit cell but only with one singular flatband touching. A light beam propagating in a photonic DHL is described by the Schrödinger‐like paraxial wave equation [ 42,43 ] $$\[i{\partial _z}{\bm{\Psi }}(x,y,z) = \left( { - \frac{1}{{2k}}\nabla _ \bot ^2 - \frac{{k\Delta n(x,y)}}{{{n_0}}}} \right){\bm{\Psi }}(x,y,z) = {H_0}{\bm{\Psi }}(x,y,z)\]$$where Ψ ( x , y , z ) is the envelope of the electric field, k is the wavenumber, Δ n is the induced refractive index change that forms a DHL potential, n 0 is the bulk refractive index, and H 0 is the Hamiltonian operator.…”

“…[ 11 ] Flatband systems have attracted considerable attention over the decades, for instance, in the study of Anderson localization, [ 12,13 ] bosonic condensation [ 14 ] and fractional quantum Hall states, [ 15,16 ] and have been realized in a variety of synthetic platforms recently, [ 11 ] including engineered electronic lattices, [ 17–19 ] optical lattices for cold atoms, [ 20 ] polaritonic lattices [ 21 ] and photonic lattices. [ 22–28 ] In particular, an extensively studied phenomenon using photonic lattices is the formation of compact localized states (CLSs), [ 29,30 ] realized with a variety of flatband lattice geometry such as Lieb, [ 22,23 ] Kagome, [ 25 ] rhombic, [ 31 ] and fractal‐like [ 32–34 ] lattices.…”