Photonic Floquet topological insulators

Topological insulators are a new phase of matter(1), with the striking property that conduction of electrons occurs only on their surfaces(1-3). In two dimensions, electrons on the surface of a topological insulator are not scattered despite defects and disorder, providing robustness akin to that of superconductors. Topological insulators are predicted to have wide-ranging applications in fault-tolerant quantum computing and spintronics. Substantial effort has been directed towards realizing topological insulators for electromagnetic waves(4-13). One-dimensional systems with topological edge states have been demonstrated, but these states are zero-dimensional and therefore exhibit no transport properties(11,12,14). Topological protection of microwaves has been observed using a mechanism similar to the quantum Hall effect(15), by placing a gyromagnetic photonic crystal in an external magnetic field(5). But because magnetic effects are very weak at optical frequencies, realizing photonic topological insulators with scatter-free edge states requires a fundamentally different mechanism-one that is free of magnetic fields. A number of proposals for photonic topological transport have been put forward recently(6-10). One suggested temporal modulation of a photonic crystal, thus breaking time-reversal symmetry and inducing one-way edge states(10). This is in the spirit of the proposed Floquet topological insulators(16-19), in which temporal variations in solid-state systems induce topological edge states. Here we propose and experimentally demonstrate a photonic topological insulator free of external fields and with scatter-free edge transport-a photonic lattice exhibiting topologically protected transport of visible light on the lattice edges. Our system is composed of an array of evanescently coupled helical waveguides(20) arranged in a graphene-like honeycomblattice(21-26). Paraxial diffraction of light is described by a Schrodinger equation where the propagation coordinate (z) acts as 'time'(27). Thus the helicity of the waveguides breaks z-reversal symmetry as proposed for Floquet topological insulators. This structure results in one-way edge states that are topologically protected from scattering.