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Whispering gallery modes (WGMs) in circularly symmetric opticalmicroresonators exhibit integer quantized angular momentum numbers due to theboundary condition imposed by the geometry. Here, we show that incorporating aphotonic crystal pattern in an integrated microring can result in WGMs withfractional optical angular momentum. By choosing the photonic crystalperiodicity to open a photonic bandgap with a band-edge momentum lying betweenthat of two WGMs of the unperturbed ring, we observe hybridized WGMs withhalf-integer quantized angular momentum numbers ($m \in \mathbb{Z}$ + 1/2).Moreover, we show that these modes with fractional angular momenta exhibit highoptical quality factors with good cavity-waveguide coupling and an order ofmagnitude reduced group velocity. Additionally, by introducing multipleartificial defects, multiple modes can be localized to small volumes within thering, while the relative orientation of the de-localized band-edge states canbe well-controlled. Our work unveils the renormalization of WGMs by thephotonic crystal, demonstrating novel fractional angular momentum states andnontrivial multi-mode orientation control arising from continuous rotationalsymmetry breaking. The findings are expected to be useful forsensing/metrology, nonlinear optics, and cavity quantum electrodynamics.

Fractional optical angular momentum and multi-defect-mediated mode re-normalization and orientation control in photonic crystal microring resonators