Abstract
We review several two- and three-dimensional metamaterial designs which serve as photonic simulators of topological phenomena in condensed matter physics. Based on a coupled-mode theory we show that lattices of interacting cavities can simulate Haldane lattices which exhibit one-way guided modes and mode coalescence in the absence of external magnetic field. Furthermore, periodic holey metals filled with a magnetoelectric material exhibit a nonreciprocal photonic band structure in the optical regime. Lastly, we show that a three-dimensional lattice of interacting cavities respecting time-reversal symmetry and a certain point-group symmetry can simulate a topological crystalline insulator.
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