Park et al.'s proposal (Photonics Research 2026) for a topologically protected optical mode-switching scheme that replaces the conventional dynamic encircling of a single exceptional point with a PAIR of exceptional points in a two-dimensional elliptical microcavity. The eigenvalue spectrum is treated as a two-sheeted branched Riemann surface (covering space) whose branch points coincide with the EP pair (modeled by omega^2 = (z - i)(z + i), ramification index 2); width bifurcation of the eigenvalues yields superradiant and subradiant branches. By lifting parameter-space control loops onto this covering space and classifying them via braid isotopy, the authors show that PURELY ADIABATIC encircling can switch modes and tune the cavity Q-factor with topological protection against noise and parametric perturbation — avoiding the nonlinear non-adiabatic transitions and path-dependent loss of prior single-EP schemes, and extending the model from Hermitian coupling into a non-Hermitian coupling regime (Im(g) > Re(g)) with new spectral topology.
Park et al. (Photonics Research 2026) propose a topologically protected optical mode-switching scheme built on a PAIR of exceptional points (EPs) in a two-dimensional elliptical microcavity, rather t…