The hallmark of topological insulators (TIs) is the scatter-free propagation of waves in topologically protected edge channels1. This transport is strictly chiral on the outer edge of the medium and therefore capable of bypassing sharp corners and imperfections, even in the presence of substantial disorder. In photonics, two-dimensional (2D) topological edge states have been demonstrated on several different platforms2,3,4 and are emerging as a promising tool for robust lasers5, quantum devices6,7,8 and other applications. More recently, 3D TIs were demonstrated in microwaves9 and acoustic waves10,11,12,13, where the topological protection in the latter is induced by dislocations. However, at optical frequencies, 3D photonic TIs have so far remained out of experimental reach. Here we demonstrate a photonic TI with protected topological surface states in three dimensions. The topological protection is enabled by a screw dislocation. For this purpose, we use the concept of synthetic dimensions14,15,16,17 in a 2D photonic waveguide array18 by introducing a further modal dimension to transform the system into a 3D topological system. The lattice dislocation endows the system with edge states propagating along 3D trajectories, with topological protection akin to strong photonic TIs19,20. Our work paves the way for utilizing 3D topology in photonic science and technology.
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We would like to thank C. Otto for preparing the high-quality fused silica samples used for the inscription of all photonic structures in this work. The Technion team gratefully acknowledges the support of an Advanced Grant from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 789339) and the support of a research grant from the Air Force Office of Scientific Research (AFOSR) of the USA. The Rostock team gratefully acknowledges the support of the Deutsche Forschungsgemeinschaft (grants SCHE 612/6-1, SZ 276/12-1, BL 574/13-1, SZ 276/15-1, SZ 276/20-1 and SFB 1477 ‘Light-Matter Interactions at Interfaces’, project number 441234705) and the Alfried Krupp von Bohlen und Halbach Foundation.
The authors declare no competing interests.
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Extended data figures and tables
a, The dashed green line is the projection of the trajectory of the two columns of waveguides (blue and red) on the x–y plane. The directions of the helical motion follow the green arrowheads. The two columns are presented here at their closest proximity to one another along the trajectory. The size of each waveguide indicates the different ‘depth’ of refractive index (the largest circle is the deepest waveguide). b, Coupling between adjacent waveguides as a function of their x separation, obtained by different speeds of the laser-writing process, which translates into different refractive index contrast. c, Same as a but at the dislocation, at which the shift creates coupling between localized modes of different 2D layers.
Extended Data Fig. 2 Spectrum of the topological surface states and their typical structure in the presence of intermodal coupling.
a, The amplitude as a function of location and mode in the 3D synthetic space without dislocation for moderate intermodal coupling of 20% of the spatial coupling. b, Same as a but for a lattice with a dislocation. c,d, Floquet spectrum as a function of the state number of a and b, respectively. e–h, Same as a–d but for strong intermodal coupling of 60% of the spatial coupling.
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Lustig, E., Maczewsky, L.J., Beck, J. et al. Photonic topological insulator induced by a dislocation in three dimensions. Nature 609, 931–935 (2022). https://doi.org/10.1038/s41586-022-05129-7
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