Fano Resonances in Flat Band Networks

TL;DR

This paper explores Fano resonances in flat band networks, highlighting how defects and nonlinearities influence wave propagation, localization, and resonance phenomena in engineered lattice systems.

Contribution

It provides a comprehensive analysis of Fano resonances in flat band lattices, including effects of defects, disorder, and nonlinearities on wave dynamics and localization.

Findings

Defects couple flat band modes to dispersive states, creating Fano resonances.

Disorder induces a dense set of Fano defects, affecting localization.

Nonlinearities can preserve flat band modes and tune Fano resonances.

Abstract

Linear wave equations on Hamiltonian lattices with translational invariance are characterized by an eigenvalue band structure in reciprocal space. Flat band lattices have at least one of the bands completely dispersionless. Such bands are coined flat bands. Flat bands occur in fine-tuned networks, and can be protected by (e.g. chiral) symmetries. Recently a number of such systems were realized in structured optical systems, exciton-polariton condensates, and ultracold atomic gases. Flat band networks support compact localized modes. Local defects couple these compact modes to dispersive states and generate Fano resonances in the wave propagation. Disorder (i.e. a finite density of defects) leads to a dense set of Fano defects, and to novel scaling laws in the localization length of disordered dispersive states. Nonlinearities can preserve the compactness of flat band modes, along with renormalizing (tuning) their frequencies. These strictly compact nonlinear excitations induce tunable Fano resonances in the wave propagation of a nonlinear flat band lattice.