Topological polarisation states

Abstract

Polarisation states are described by spin expectation values, known as Stokes parameters, the trajectories of which in a rotationally symmetric system form a sphere named after Poincaré. Here, we show that the trajectories of broken rotational symmetric systems can exhibit distinct topological structures in polarisation states. We use a phase-shifter to form a polarisation circle(S1), which interferes with the original input due to the phase change of the output state upon rotation. By rotating the circle using a rotator, the trajectories become a polarisation torus(S1×S1), which was experimentally confirmed in a simple setup using passive optical components together with the Mach–Zehnder interferometer. We also discuss the realisations of other topological features, such as a Möbius strip, a trefoil knot, Hopf links, and topological Dirac bosons, with a bulk-edge correspondence.