The exquisite sensitivity of polarization

Recent insights into the time-development of quantum states driven by
nonhermitian 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 with the tracks exhibiting elaborate coilings and
loopings that would be very interesting to explore experimentally.
Underlying these dramatic violations of adiabatic intuition are the
disparity of exponentials and the Stokes phenomenon of asymptotics.