Knotted Hopfion Texture of Polarization States in Tightly Focused Light*

Topology is a key tool in engineering new states of matter, particularly in smooth configurations such as skyrmions and hopfions in nuclear physics, liquid crystals and magnetism [1, 2]. We find that the topology of optical polarization around a dark focus can be described in terms of space-filling topological hopfion textures, corresponding to the celebrated Hopf fibration or its generalizations. The textures consist of lines in the focal volume mapped to points on the Poincaré sphere of polarization; these lines are interlinked loops, which can be knotted [3]. These knotted hopfions arise naturally from linear interference of optical helicity eigenstates in the low-intensity focus, due to optical spin-orbit effects. We describe a potential experiment, which, if realized, could be used to imprint new topological stable states into soft or electronic matter, which might have application for information storage and processing, and opens the possibility of exploring new regimes of light-matter interaction.
[1] P J Ackerman & I I Smalyukh, Phys Rev X 7 011006 (2017).
[2] P Sutcliffe, Phys Rev Lett 118 247203 (2016).
[3] D Sugic & M R Dennis, in preparation.