Topological states in amorphous magnetic photonic lattices

Since the discovery of topological phases in optical systems, most of the efforts have been focused on the periodic and quasiperiodic optical structures which have both long-range and short-range orders. In this paper, we construct a kind of two-dimensional aperiodic optical systems, named the amorphous magnetic photonic lattices (AMPLs), which only have short-range orders, and investigate the topological states in these AMPLs. By using the supercell method, we build supercell magnetic photonic crystals as approximate equivalents of the AMPLs. Based on the band structure calculation and full wave simulation, we demonstrate the existence of single-mode and multimode topological edge states in these AMPLs. Through calculating the gapless edge states in reciprocal space, our research gives an intuitive understanding of the topology underlying aperiodic optical systems. Our system provides a platform to explore the relationship between short-range orders and topology and also paves an easy way to fabricate topological optical devices in application.