Optical polarization evolution near a non-Hermitian degeneracy

Recent insights into the time development of quantum states driven by non-Hermitian matrices, and an exactly solvable model, can be applied to the evolution of optical polarization in a stratified nontransparent dielectric medium twisted cyclically along the propagation direction. The twist is chosen to encircle a degeneracy (branch-point) in the plane of parameters describing the medium. Polarization evolutions are determined analytically and illustrated as tracks on the Poincaré sphere and the stereographic plane. Even when the twist is slow, the exact evolutions differ sharply from those of the local eigenpolarizations and can display extreme sensitivity to initial conditions. Underlying these dramatic violations of adiabatic intuition are the disparity of exponentials and the Stokes phenomenon of asymptotics.