Corner states of light in photonic waveguides

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Abstract

The recently established paradigm of higher-order topological states of matter has shown that not only edge and surface states1,2 but also states localized to corners, can have robust and exotic properties3,4,5,6,7,8,9. Here we report on the experimental realization of novel corner states made out of visible light in three-dimensional photonic structures inscribed in glass samples using femtosecond laser technology10,11. By creating and analysing waveguide arrays, which form two-dimensional breathing kagome lattices in various sample geometries, we establish this as a platform for corner states exhibiting a remarkable degree of flexibility and control. In each sample geometry we measure eigenmodes that are localized at the corners in a finite frequency range, in complete analogy with a theoretical model of the breathing kagome7,8,9,12,13,14. Here, measurements reveal that light can be ‘fractionalized,’ corresponding to simultaneous localization to each corner of a triangular sample, even in the presence of defects.

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Fig. 1: Experimental set-up and breathing kagome lattice.
Fig. 2: Observation of light output from the output facet of rhombic and triangular lattices of waveguide arrays.
Fig. 3: Observation of corner states in the rhombic lattice of a waveguide array (d1 = 12 μm and d2 = 7 μm) with edges consisting of 11 waveguides.
Fig. 4: Observation of the ‘fractionalized’ corner states in a triangular lattice of a waveguide array with d1 = 11 μm and d2 = 6 μm with edges consisting of six waveguides.
Fig. 5: Observation of the ‘fractionalized’ corner states in a triangular lattice with a defect in a waveguide array with d1 = 11 μm and d2 = 6 μm with edges consisting of six waveguides.

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

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Acknowledgements

This work is supported by the Swedish Research Council (VR) and the Knut and Alice Wallenberg Foundation. E.J.B. is a Wallenberg Academy Fellow.

Author information

E.J.B. initiated the research. F.K.K. and E.J.B. derived the theoretical results. A.E.H., A.M., G.A. and M.B. designed and carried out the experiment and performed the data analysis. M.B. supervised the experimental part. E.J.B. and F.K.K. wrote the main text. M.B. and A.E.H. wrote the experimental part. All authors discussed the results and contributed to the final version of the manuscript.

Correspondence to Emil J. Bergholtz.

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Supplementary Information

Supplementary discussion and derivations, Figs. 1–11 and refs. 1–8.

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