Coexistence of Multiple Flat Bands in Non-Hermitian Parity-Time Symmetric Lattices

Controlling the localization of light has been studied through many approaches, including flat bands in Hermitian and non-Hermitian systems. It has been formerly investigated that in non-Hermitian systems, an entirely flat band can emerge at the exceptional point of a Parity-Time (PT) symmetric lattice. Although these flat bands were known to be bound states in continuum (BIC), we demonstrate that by engineering the lattice couplings, this would not necessarily hold true. We observe a flat band which is a bound state emerging at a critical point before reaching the exceptional point, and the curvature of the dispersive band changes before and beyond this critical point. Also, by implementing similar derivations into an array of waveguides composed of tetramers, we discover the coexistence of two flat bands, one of which is always a BIC.