An internationally joint research group between Singapore and Japan has unveiled a blueprint for arranging exotic, knot-like patterns of light into repeatable crystals that extend across both space and time. The work lays out how to build and control "hopfion" lattices using structured beams at two different colors, pointing to future systems for dense, robust information processing in photonics.
Hopfions are three-dimensional topological textures whose internal "spin" patterns weave into closed, interlinked loops. They have been observed or theorized in magnets and light fields, but previously they were mainly produced as isolated objects. The authors show how to assemble them into ordered arrays that repeat periodically, much like atoms in a crystal, only here the pattern repeats in time as well as in space.
The key is a two-color, or bichromatic, light field whose electric vector traces a changing polarization state over time. By carefully superimposing beams with different spatial modes and opposite circular polarizations, the team defines a "pseudospin" that evolves in a controlled rhythm. When the two colors are set to a simple ratio, the field beats with a fixed period, creating a chain of hopfions that recur every cycle.
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