Corner states of light in photonic waveguides

The recently established paradigm of higher-order topological states of matter has shown that not only edge and surface states^1,2 but also states localized to corners, can have robust and exotic properties^3–9. 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 technology^10,11. 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 kagome^{7–9,12–14}. 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.