Geometric Engineering of Flat Bands in a Single-Layer Photonic Graphene.

Photonic flat-bands offer significant potential for light-matter interactions and nonlinear optics, thanks to their localization of light and high density of states. However, realizing flat-bands requires intricate fabrication, alignment, and/or specialized geometries. Here, we demonstrate a simple yet versatile strategy to engineer flat-bands above the light line, using only a single-layer honeycomb photonic crystal slab. By applying a density wave-like geometric perturbation, we couple intrinsic flat-band states from below the light cone into the radiative continuum that creates an anisotropic band structure exhibiting Dirac-like and flat dispersions along orthogonal directions. Furthermore, we can manipulate the mass term to realize band inversion and switch between two topologically distinct phases. We demonstrate a Jackiw-Rebbi state at the junction of two phases with opposite Dirac mass, exhibiting flat-band dispersion along the interface. Our approach provides a fabrication friendly platform for programming photonic band dispersions, opening avenues for topological photonics and practical flat-band optoelectronics.