Flat bands from diffraction in periodic systems

Periodic photonic structures enable precise control over the light-matter interaction through band structure engineering. Certain lattice geometries exhibit dispersionless flat bands, characterized by vanishing group velocity and diverging density of states, which present unique opportunities for applications such as slow light, nonlinear optical processes and controlling photoluminescence. However, thus far, flat bands have not been reported in systems where the lattice sites are radiatively coupled over a long range. Here we show that lattices consisting of superposed equispaced one dimensional chains exhibit flat bands with a purely diffractive origin, with the energies and angles of the flat bands controlled by the geometrical parameters of the lattice and the unit cell. The flat bands extend over all angles, can have linewidths on the order of a few nanometers, and are linearly polarized. We experimentally observe flat bands at predicted energies in lattices of gold nanoparticles at near-infrared frequencies using Fourier spectroscopy. Our results provide a general and efficient design strategy for lattices with flat, polarized dispersions for applications such as flat-band lasing, enhancing light-matter interaction, and controlling the emission or absorption of electromagnetic radiation over a wide spectral range.