A joint team of researchers from Singapore and Japan has unveiled a theoretical design for arranging exotic, knot-like patterns of light into crystals called “hopfion lattices” that repeat not just in space but also in time.
Hopfions are three-dimensional topological structures in which internal spin-like patterns weave into closed, interlinked loops. They have been studied in magnetism and optics, but until now they mainly appeared as isolated curiosities. The new work shows how to assemble them into ordered arrays that behave like crystals, repeating periodically in both space and time.
The key lies in the use of a two-color, or bichromatic, light field. By overlapping beams of different spatial modes and opposite circular polarizations, the team created a pseudospin that evolves rhythmically. When the two colors are tuned to a simple ratio, the field produces a beat with a fixed period, generating a chain of hopfions that reappear every cycle. From this foundation, the researchers describe how more complex versions can be sculpted, with their topological “winding strength” increased, decreased, or even flipped simply by swapping the two wavelengths. Their simulations revealed that these structures can maintain near-perfect topological quality across an entire cycle.
Building on the one-dimensional chain of hopfions, the team extended their concept to true three-dimensional hopfion crystals. By arranging arrays of tiny emitters such as dipoles, grating couplers, or microwave antennas and driving them at two close colors, they sketched a method for producing lattices in which hopfions naturally alternate across space while maintaining an ordered pattern. Unlike earlier optical hopfions that relied on beam diffraction as light traveled forward, this design functions at a fixed plane, with the periodic beating of the light itself generating the structure. The researchers also examined how long these fields could maintain their integrity while propagating, and under what conditions diffraction would begin to degrade them.
The significance of this proposal lies in its potential applications. Topological textures like skyrmions have already inspired new approaches to data storage and signal routing, valued for their resilience against errors. Extending this concept to hopfion crystals in light could enable high-dimensional information encoding, more robust communication channels, advanced atom trapping methods, and novel regimes of light–matter interaction.
As the authors summarized, “The birth of spacetime hopfion crystals opens a path to condensed, robust topological information processing across optical, terahertz, and microwave domains.”
