Topological photonics

821 Frequency, wavevector, polarization and phase are degrees of freedom that are often used to describe a photonic system. Over the past few years, topology — a property of a photonic material that characterizes the quantized global behaviour of the wavefunctions on its entire dispersion band — has emerged as another indispensable degree of freedom, thus opening a path towards the discovery of fundamentally new states of light and possible revolutionary applications. Potential practical applications of topological photonics include photonic circuitry that is less dependent on isolators and slow light that is insensitive to disorder. Topological ideas in photonics branch from exciting developments in solid-state materials, along with the discovery of new phases of matter called topological insulators1,2. Topological insulators, being insulating in the bulk, conduct electricity on their surface without dissipation or back-scattering, even in the presence of large impurities. The first example of this was the integer quantum Hall effect, discovered in 1980. In quantum Hall states, two-dimensional (2D) electrons in a uniform magnetic field form quantized cyclotron orbits of discrete energies called Landau levels. When the electron energy sits within the energy gap between the Landau levels, the measured edge conductance remains constant within an accuracy of around one part in a billion, regardless of sample size, composition and purity. In 1988, Haldane proposed a theoretical model for achieving the same phenomenon in a periodic system without Landau levels3 — the quantum anomalous Hall effect. In 2005, Haldane and Raghu transferred the key feature of this electronic model to the realm of photonics4,5. They theoretically proposed the photonic analogue of the quantum (anomalous) Hall effect in photonic crystals6 (the periodic variation of optical materials that affects photons in the same manner as solids modulate electrons). Three years later, this idea was confirmed by Wang et al., who provided realistic material designs7 and experimental observations8. These studies spurred numerous subsequent theoretical9–13 and experimental investigations14–16. In ordinary waveguides, back-reflection is a major source of unwanted feedback and loss that hinders large-scale optical integration. The works cited above demonstrate that unidirectional edge waveguides transmit electromagnetic waves without back-reflection even in the presence of arbitrarily large disorder. This is an ideal transport property that is unprecedented in photonics. Topological photonics promises to offer unique, robust designs and new device functionalities for photonic systems by providing immunity to performance degradation induced by fabrication imperfections or environmental changes. Topological photonics