Asymmetric microcavities supporting Whispering-gallery modes (WGMs) are of great significance for on-chip optical information processing. We establish asymmetric microcavities on topologically curved surfaces, where the geodesic light trajectories completely reconstruct the cavity mode features. The curvature-mediated photon-lifetime engineering enables the enhancement of the quality factors of periodic island modes by up to 200 times. Strong and weak coupling between modes of very different origins occurs when the space curvature brings them into resonance, leading to fine tailoring of the cavity photon energy and lifetime and the observation of non-Hermitian exceptional point (EP). At large space curvatures, the role of the WGMs is replaced by high-Q periodic modes protected by the high stability of island-like light trajectory. Our work demonstrates interesting physical mechanisms at the crosspoint of optical chaotic dynamics, non-Hermitian physics, and geodesic optical devices, and would initiate the novel area of geodesic microcavity photonics.
© 2022. The Author(s).