Topological Polarisation States

TL;DR

This paper explores how broken rotational symmetry in polarization systems leads to complex topological structures like tori and Möbius strips, demonstrated through optical experiments with interferometers.

Contribution

It introduces a method to realize and observe various topological polarization states, including tori and Möbius strips, using simple optical components and interferometry.

Findings

Experimental confirmation of polarization torus (${ m S}^1 imes { m S}^1$) states.

Observation of topological structures such as Möbius strips and Hopf links.

Discussion of potential realizations of topological Dirac bosons.

Abstract

Polarisation states are described by spin expectation values, known as Stokes parameters, whose trajectories in a rotationally symmetric system form a sphere named after Poincar\'e. 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 (${\mathbb S}^1$), which interferes with the original input due to the phase change of the output state upon the rotation. By rotating the circle using a rotator, the trajectories become a polarisation torus (${\mathbb S}^1 \times {\mathbb S}^1$), which was experimentally confirmed in a simple set-up using passive optical components together with Mach-Zehnder interferometers. We also discuss about realisations of other topological features, such as M\"obius strip, Hopf-links, and topological Dirac bosons with a bulk-edge correspondence.