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

We investigate the optical properties of a photonic crystal (PC) 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 Г → X line, prohibiting optical transmission with incident light in x direction. On the other hand, the photonic band for the FB frequency is found to be dispersive along the Г → Y line, resulting in nonzero optical transmission. Such anisotropic optical response of the PC due to the FB localization of light in a single direction only results in a self-collimation of light propagation throughout the PC at the FB frequency.