Topological transformation and free-space transport of photonic hopfions

Abstract

Structured light fields embody strong spatial variations of polarization, phase, and amplitude. Understanding, characterization, and exploitation of such fields can be achieved through their topological properties. Three-dimensional (3D) topological solitons, such as hopfions, are 3D localized continuous field configurations with nontrivial particle-like structures that exhibit a host of important topologically protected properties. Here, we propose and demonstrate photonic counterparts of hopfions with exact characteristics of Hopf fibration, Hopf index, and Hopf mapping from real-space vector beams to homotopic hyperspheres representing polarization states. We experimentally generate photonic hopfions with on-demand high-order Hopf indices and independently controlled topological textures, including Néel-, Bloch-, and antiskyrmionic types. We also demonstrate a robust free-space transport of photonic hopfions, thus showing the potential of hopfions for developing optical topological informatics and communications.

Reconfiguration of Nematic Dislocations

“…For example, Figure 1h illustrates a "nanoknot" in magnetization field ( Sutcliffe, 2017). Similar structures could be realised in optical vortex configuration (Shen et al, 2023). Related knotted and linked topologically protected structures are present in diverse tube-like structures in nature and seem to be a generic feature of complex pattern close to phase transitions and at the edge-of chaos conditions (Johnson, 2021).…”

Toward Arbitrary Spin‐Orbit Flat Optics Via Structured Geometric Phase Gratings

“…For quantum optics, the reciprocal SOC interface demonstrated here allows to implement a Bell measurement for arbitrary SOC states, which is the basis towards the teleportation scheme for SOC photon pairs [46]. Moreover, owing to the capability of full-field spatial mode control [58], the device also paves the way to quantum control of high-dimension photonic skyrmions [59,60]. Beyond single-beam vector mode control, this principle can further realize multiple vector mode control through the addition of a Dammann grating structure [12,61,62], see Supporting Information for an extended discussion on this.…”

“…[ 46 ] Moreover, owing to the capability of full‐field spatial mode control, [ 39 ] the device also paves the way to quantum control of high‐dimension photonic skyrmions. [ 58,59 ]…”

Building Paraxial Optical Skyrmions Using Rational Maps

“…[13] Combining phase information with the polarization profile of paraxial skyrmions has uncovered novel optical topological structures called Hopfions. [14,15] Initially, research efforts were focused on modeling paraxial optical skyrmions on their magnetic counterparts, [16] and an analogy justified because both represent "baby" skyrmions: skyrmion fields defined in a 2D space. [17,18] In the following, we will refer to such 2D skyrmions as skyrmions for simplicity.…”