  Photonic crystals have been demonstrated as a versatile platform for the
study of topological phenomena. The recent discovery of higher order
topological insulators introduces new aspects of topological photonic crystals
which are yet to be explored. Here, we propose a dielectric photonic crystal
with unconventional higher order band topology. Besides the conventional
spectral features of gapped edge states and in gap corner states, topological
band theory predicts that the corner boundary of the higher-order topological
insulator hosts a 2/3 fractional charge. We demonstrate that in the photonic
crystal such a fractional charge can be verified from the local density of
states of photons, through the concept of local spectral charge as an analog of
the local electric charge due to band filling anomaly in electronic systems.
Furthermore, we show that by introducing a disclination in the proposed
photonic crystal, localized states and a 2/3 fractional spectral charge emerge
around the disclination core, as the manifestation of the bulk disclination
correspondence. The predicted effects can be readily observed in the
state-of-the-art experiments and may lead to potential applications in
integrated and quantum photonics.
