  The recently established paradigm of higher-order topological states of
matter has shown that not only, as previously thought, edge and surface states
but also states localised to corners can have robust and exotic properties.
Here we report on the experimental realisation of novel corner states made out
of classical light in three-dimensional photonic structures inscribed in glass
samples using femtosecond (fs) laser technology. By creating and analysing
waveguide arrays forming 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 localised at the corners in a finite frequency
range in complete analogy with a theoretical model of the breathing kagome.
Here, the measurements reveal that light can be "fractionalised", corresponding
to simultaneous localisation to each corner of a triangular sample, even in the
presence of defects. The fabrication method applied in this work exposes the
advantage of using fs-laser writing for producing compact three-dimensional
devices thus paving the way for technological applications by simulating novel
higher-order states of matter.
