Abstract
Diverging from traditional parity-time (PT)-symmetric paradigms, anti-PT (APT) symmetry provides an intriguing framework for harnessing non-Hermitian physics, offering the immense potential to control light-matter interactions in artificial photonic systems reliant on negative-index materials, typically realized with metamaterials. We report a specially configured Fabry-P & eacute;rot-type microcavity system by harnessing the unique anti-PT-symmetric constraints with negative-indexed background materials and meticulously balanced gain-loss distributions. We unveil the intriguing topological properties of a parametrically encircled third-order EP (EP3), emerging from two connected second-order EPs (EP2s) among three cavity states. We present a programmable adiabatic state-switching process and highlight the nuanced behaviors of second and third-order branch points by winding around embedded EPs within a 2D gain-loss parameter space. This work explores the theoretical foundations of the topological properties of EPs in negative-indexed media, paving the way for a novel class of metamaterial-based artificial photonic devices.