Geometric Engineering of Flat Bands in a Single-layer Photonic Graphene

TL;DR

This paper presents a simple, versatile method to engineer radiative flat bands in single-layer honeycomb photonic crystals using density wave-like geometric perturbations, enabling topological phase control and flat band applications.

Contribution

The authors introduce a novel, fabrication-friendly approach to create and manipulate flat bands and topological phases in photonic crystals through periodic lattice perturbations.

Findings

Successfully coupled flat band states into the radiative continuum.

Achieved linear Dirac-like dispersion and flat dispersion in orthogonal directions.

Demonstrated topological phase switching and interface states with flat band characteristics.

Abstract

Photonic flat bands offer significant potential for strong light-matter interactions, nonlinear optics, and sensing thanks to their localization of light and high density of states. However, realizing these flat bands typically requires intricate fabrication, perfect alignment and/or specialized geometries, and a general design strategy is missing. In this work, we demonstrate a simple yet versatile strategy to engineer radiative flat bands above the light line, using only a single-layer honeycomb photonic crystal slab. By applying a density wave like geometric perturbation-a spatially periodic displacement of the lattice air holes-we couple intrinsic flat band states from below the light cone into the radiative continuum. This structural modulation creates a highly anisotropic band structure that exhibits linear, Dirac-like dispersion in one direction and nearly flat dispersion in the orthogonal direction, forming an extended van Hove singularity at band extrema. Furthermore, by tuning the Fourier components of the modulation, we can manipulate the Dirac mass term to realize band inversion and switch between two topologically distinct phases. As an application, we demonstrate a Jackiw-Rebbi interface state positioned at the junction of two domains with opposite Dirac mass, that also shows flat band dispersion along the interface. This density-wave perturbation approach provides a conceptually clear and fabrication friendly platform for programming complex photonic band dispersions, opening new avenues for both topological photonics and practical flat-band optoelectronic devices.