Tight-binding photonics

Abstract: Photonics, dealing with the generation, manipulation, and detection of photons in various systems, lays the foundation of many advanced technologies. A key task of photonics is to know how photons propagate in complex media such as periodic and aperiodic photonic crystals. The conventional wisdom is to numerically solve the Maxwell equations either by dedicated numerical techniques or brute-force finite-element calculations. Recently, the strict analogy between photonic crystals and theoretical tight-binding models provides an unprecedentedly convenient wayof understanding the spectra and wavefunctions of photonic systems by mapping the complicated differential equationsinto matrixed Hamiltonians that can be easily solved through the band theory and exact diagonalization. in this paper, we present a timely review of tight-binding-like photonics in various platforms, covering fundamental theories, experimental realizations, unique physical efiects, and their potential applications. We also provide a brief outlook on the future trends of this active area. Our review offers an in-depth and comprehensive picture on this rapidly developing field and may shed light on the future design on advanced tight-binding-like photonic devices.