Realization of geometric-phase topology induced by multiple exceptional points

Non-Hermitian systems have Riemann surface structures of complex eigenvalues that admit singularities known as exceptional points. Combining with geometric phases of eigenstates gives rise to unique properties of non-Hermitian systems, and their classifications have been studied recently. However, the physical realizations of classes of the classifications have been relatively limited because a small number of modes and exceptional points are involved. In this paper, we show in microcavities that all five classes [J.-W. Ryu et al., Commun. Phys. 7, 109 (2024)] of three modes can emerge with three exceptional points. In demonstrations, we identify various combinations of exceptional points within a two-dimensional parameter space of a single microcavity and define five distinct encircling loops based on three selected exceptional points. According to the classification, these loops facilitate different mode exchanges and the acquisition of additional geometric phases during the adiabatic encircling of exceptional points. Our results provide a broad description of the geometric phases-associated topology induced by multiple exceptional points in realistic physical systems.