Novel phenomena in flatband photonic structures: from localized states to real-space topology

Abstract

In recent years, flatband systems have aroused considerable interest in different branches of physics, from condensed-matter physics to engineered flatband structures such as in ultracold atoms, various metamaterials, electronic materials, and photonic waveguide arrays. Flatband localization, as an important phenomenon in solid state physics, is of broad interest in the exploration of many fundamental physics of many-body systems. We briefly review the recent experimental advances in light localization in engineered flatband lattices, with the emphasis on the optical induction technique of various photonic lattices and unconventional flatband states. The photonic lattices, established by various optical induction techniques, include quasi-one-dimensional diamond lattices and two-dimensional super-honeycomb, Lieb and Kagome lattices. Nontrivial flatband line states, independent of linear superpositions of conventional compact localized states, are demonstrated in photonic Lieb and super-honeycomb lattices, and they can be considered as an indirect illustration of the non-contractible loop states. Furthermore, we discuss alternative approaches to directly observing the non-contractible loop states in photonic Kagome lattices. These robust loop states are direct manifestation of real-space topology in such flatband systems. In this paper we do not intend to comprehensively account the vast flatband literature, but we briefly review the relevant work on photonic lattices mainly from our group. We hope that the mentioned concepts and techniques can be further explored and developed for subsequent applications in other structured photonic media such as photonic crystals, metamaterials, and other synthetic nanophotonic materials.