Realization and manipulation of compact localized states in a two-dimensional photonic crystal with a Lieb lattice

Compact localized states (CLSs) associated with flat bands (FBs) exhibit significant potential for wave localization and enhanced wave-matter interactions. The Lieb lattice, characterized by its unique bipartite and chiral symmetries, features a dispersionless FB cutting through the Dirac points, distinguishing it from other lattices and providing substantial flexibility for controlling CLS configurations. Herein, we investigate theoretically the generation and manipulation of CLSs in a two-dimensional dielectric photonic crystal (PC) with a Lieb lattice. Particularly, to address the inevitable non-nearest-neighboring interactions of the lattice sites, we propose an optimized strategy by embedding perfect electric conductors between dielectric sites, enabling the first observation of an ideal FB in Lieb PCs; this closely matches the tight-binding model that considers only the nearest-neighbor coupling. Furthermore, by leveraging the robust CLS in Lieb PCs, we demonstrate the on-demand design of diverse localized mode patterns through CLS engineering and showcase their selective optical excitation. These advancements offer promising applications in on-chip optical routing and switching, as well as in the design of high-performance cavity-based photonic devices.