Incomplete chirality of exceptional points in asymmetric optical microcavity

A chiral exceptional point (EP) in an optical microcavity emerges from the coalescence of even and odd modes with identical azimuthal modal numbers under asymmetric perturbation. While the chirality of such EPs is well understood in circular disks with asymmetrically positioned Rayleigh scatterers, it becomes more intricate in asymmetric microcavities, where the contributing modes can exhibit nontrivial wave morphology according to chaotic deformation. To explore this, we consider a stand-alone microcavity composed of one half ellipse and two quarter ellipses, for which EPs exhibit incomplete chirality. Our analysis reveals that this incomplete chirality originates from prior mode coupling. After the prior mode coupling, only the quasinormal modes within each superposed mode pair that have identical azimuthal modal numbers but opposite parities contribute to the chirality at EPs. Consequently, the chirality of the EP modes remains incomplete, depending on the relative weight of the original mode pair. Finally, we analyze the formation of EPs and their chiral properties in a generic asymmetric microcavity, providing insights into the underlying mechanisms of incomplete chirality.