Bending the rules | Nature Photonics

The abstract mathematics of topology is generating excitement in photonics. A new way of thinking about photonics driven by topology — the 'rubber sheet' mathematics that describes

the equivalence and conservation laws of spaces as they are stretched, squashed and deformed — is rewriting the rules of photonic circuit design. It's also generating great excitement

in the process. Research is being inspired by the discovery of topological insulators — materials that are electrically insulating in their interior but conductive at the surface. These

curious materials were first discovered in the 1980s, in the form of the quantum Hall effect, but their topological origins have only been generalized to investigate new topological

materials in the past few years. Indeed, so profound are the effects that many tipped the discovery of such topological phenomena as a probable candidate for this year's Nobel Prize in

Physics (see Editorial below). Since their discovery, researchers have realized that analogous 'edge states' for transporting light can also be formed in carefully designed

periodic media like photonic crystals, metamaterials and coupled resonators. The behaviour of such states is dictated by the rules of topology and concepts of topological invariance and

topological phase transitions. When applied to the frequency bands of periodic optical structures, these rules can yield a host of enticing and unique properties that are 'topologically

protected'. For instance, such edge states are predicted to be intrinsically unidirectional and immune to backscatter. They also naturally circumnavigate and flow around imperfections

that lie in their path. Ultimately this may lead to more robust photonic waveguides that are lower-loss, more tolerant of fabrication defects, self-routing and free from troublesome

reflections. It would also lead to a new way of realizing optical isolators. Now the challenge is to realize suitable materials that have the correct characteristics for practical operation

at optical wavelengths. According to Ling Lu and Marin Soljačić at the Massachusetts Institute of Technology, in the USA, who have a Review Article on topological photonics on page 821 of

this issue, “the field has exploded in the past two years” and is growing exponentially. “Every month there are new papers in photonics related to topology appearing on arXiv,” remarks Lu.

“We're just at the tip of an iceberg in terms of new physics.” Soljačić also makes the point that as topological effects apply to many types of classical or quantum waves, many of the

concepts are being transferred to surface plasmons, excitons, exciton-polaritons, phonons and magnons, inspiring many opportunities for further research. Exciting times indeed. RIGHTS AND

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Published: 31 October 2014 * Issue Date: November 2014 * DOI: https://doi.org/10.1038/nphoton.2014.276 SHARE THIS ARTICLE Anyone you share the following link with will be able to read this

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