Using a hexagonal array of helical waveguides, physicists have observed robust optical waves that move in one direction, bypassing obstacles and imperfections exactly as predicted by the theory of topological insulators. See Letter p.196
Photonics researchers have long been inspired by a conceptual analogy between electromagnetic waves in patterned media and quantum-mechanical electron waves in solids. In the late 1980s, Yablonovitch1 and John2 conceived of the photonic crystal — a spatially periodic nanostructure — as an analogue of an electronic insulator. In a photonic crystal, the frequencies of propagating light can be restricted to distinct bands, which are separated by gaps of forbidden frequency, akin to the electronic bandgaps in insulators within which no electron states exist. Photonic bandgaps are now a staple of optical nanostructure design, with applications ranging from low-loss optical resonators to slow-light waveguides3. On page 196 of this issue, Rechtsman et al.4 report the design and realization of a photonic device that mimics a state of insulating matter known as a topological insulator, which has properties strikingly distinct from those of conventional insulators. This points the way towards the development of fault-tolerant photonic devices that exploit 'topologically protected' light waves.
Like a conventional insulator, a topological insulator has a bandgap. However, its bands are topologically non-trivial: they cannot be continuously deformed into the bands of a conventional insulator as long as they remain separated by a bandgap, just as a torus cannot be transformed into a sphere without tearing its surface5. Consequently, when a topological insulator is connected to a conventional insulator (or a vacuum), a low-dimensional metal emerges at an edge between the two materials. Unusually, this metal is immune to conversion into an insulator by the presence of impurities or distortions on the edge, because its existence is enforced by topological differences between the materials on each side of the edge. Since the theoretical prediction6 and experimental discovery7 of topological-insulator materials in 2006 and 2007, respectively, condensed-matter physicists have been scrambling to exploit the unique properties of the materials in applications such as spintronics and fault-tolerant quantum computing.
In 2009, researchers realized8 a photonic system with topologically non-trivial bands using a magnetic photonic-crystal slab. (Strictly speaking, this system was analogous not to a topological insulator, but to the closely related 'quantum Hall gas'.) They showed8 that this photonic crystal's edge acted as a one-way waveguide, supporting scatter-free, disorder-immune wave propagation — the photonic analogue of the exotic edge metal. This system seemed to have a potential application as an isolator, a device that permits light to flow in only one direction. But it came with two important technical shortcomings. First, the properties of the magnetic material from which the photonic crystal was made limited the operating frequency of the device to microwave frequencies rather than optical frequencies, which are of much greater technological interest. Second, the system required a strong external magnet to function, restricting its application as a stand-alone device.
Rechtsman et al. demonstrate a topologically non-trivial photonic system that overcomes both limitations: it operates at optical frequencies and does not require an external magnetic field. The authors' system is based on a type of topological insulator known as a Floquet topological insulator, which was proposed9 in 2011 and independently, in a photonic context10, in 2012. The authors of these studies noted that when a system is driven by an oscillating potential (such as an oscillating voltage), its state at each discrete period of the oscillation is equivalent to that of an undriven transformed system, which can be described using a nineteenth-century mathematical result known as Floquet's theorem. Crucially, even if the original system has topologically trivial bands, the transformed system can have topologically non-trivial bands if an appropriate driving potential is chosen.
Rechtsman et al. add another twist to this idea. An array of coupled parallel optical waveguides can act as a quantum-wave simulator: the flow of light down the array is formally equivalent to the evolution in time of a quantum-mechanical matter wave with one fewer spatial dimension than the array, with the distance along the waveguide axis playing the part of the time dimension. Such waveguide arrays have been used in experimental demonstrations of 'quantum-wave' phenomena, such as Anderson localization, in an entirely classical electromagnetic context11. Rechtsman and colleagues go on to show that a helical twist in the waveguides is formally equivalent to an oscillating potential, which, through Floquet's theorem, yields topologically non-trivial bands. Their experiments directly demonstrate the existence of an electromagnetic wave that moves in a single direction around the edge of the waveguide array (Fig. 1), bypassing obstacles and imperfections exactly as predicted by the theory of topological insulators.
It is worth noting that this photonic topological insulator cannot be used as an optical isolator. The waveguide array is a three-dimensional photonic crystal composed of non-magnetic material, and a well-known principle based on the time-reversal symmetry of such systems shows that they cannot act as isolators. Thus, for each edge wave travelling in one direction along the edge of the waveguide array, it is possible to excite another wave that moves backwards along the edge and backwards along the waveguide axis. (For those familiar with models of two-dimensional electronic topological insulators, the direction of propagation along the waveguide axis in this system can be regarded as playing the part of the electron's spin orientation.)
Although several other research groups have proposed different schemes for photonic topological insulators (see ref. 4 for references and ref. 12 for a recent experimental demonstration in an optical-chip platform), Rechtsman and colleagues' method is notable for its simplicity and practicality. The robust properties of the topological edge waves indicate several possible device applications, such as carrying signals robustly through optical fibres. Future variants of this photonic topological insulator could also be used to explore many issues of fundamental scientific interest, including how the edge waves behave under conditions of nonlinearity, amplification and damping, all of which are easily achievable and tunable in photonic media.