Topological Polarimetry: Polarization Skyrmions and Vortices from Tissue Scattering

Abstract

The Stokes-Mueller description of tissue polarimetry is conventionally interpreted through local observables such as birefringence, depolarization, and helicity preservation. We show that tissue structure generates topology in the polarization field itself. Polarization-resolved measurements of unstained human breast tissue reveal polarization vortices and, where the tissue architecture provides coupled azimuthal and radial variation, Neel-type polarization skyrmions. These structures are quantified by the vortex winding number and skyrmion charge, integer-valued topological invariants that vanish for homogeneous media and therefore provide zero background readouts of tissue heterogeneity. Malignant ductal carcinoma exhibits non-trivial polarization topology, whereas adjacent healthy tissue remains topologically trivial. The results establish topological invariants of the polarization field as physically interpretable observables of tissue organization and motivate topological polarimetry as a field-based approach to tissue characterization.