Flat-band localization and self-collimation of light in photonic crystals

We investigate the optical properties of a photonic crystal composed of a quasi-one-dimensional flat-band lattice array through finite-difference time-domain simulations. The photonic bands contain flat bands (FBs) at specific frequencies, which correspond to compact localized states as a consequence of destructive interference. The FBs are shown to be nondispersive along the $\mathrm{\Gamma }\to X$ line, but dispersive along the $\mathrm{\Gamma }\to Y$ line. The FB localization of light in a single direction only results in a self-collimation of light propagation throughout the photonic crystal at the FB frequency.