Light Beam Knots Allow Us to Store Information and Pass it Along

The mathematical knot theory explores structures of knots and the quantities they conserve. In this research, the knots and their conserved quantities were imprinted into light beams using electro-optical means, in a way that allows encoding information on one end, immediate transfer through optical fiber or free space, and decoding it on the other end.

Knots – performed by various types of bands, wires and strings – are used to save information due to their stability. For instance, testimonies from indigenous cultures around the world, mostly Inca remains in the Himalayas, show how knots were used to transfer information and maintain it.  Dr. Eliahu Cohen of BIU's Kofkin Faculty of Engineering was a partner in a research project in which complex knots were exhibited using light beams transferred through open space. In order to create the knots and control the light beam’s structure, the researchers used an electro-optical device called SLM (Spatial Light Modulator) to create holograms.

The SLM is similar to an extrusion device, like the mold used to form the shape of pasta by pushing the dough through a hole with the desired shape. The “dough,” in this case, is the light beam. The SLM controls the spatial modes of the light and its phase structure, that is the point where the wave begins (the wave has a high point and a low point, and the phase could be any one of them or any point in between). The holograms were attached to the two light polarizations, meaning the various fluctuation directions of the electric field from which the light is comprised (along with the magnetic field). Using polarization interference, an encounter of two waves carrying various holograms, the researchers created an optical “framed knot” for the first time ever.

The technology allowed actions to be performed on the light beams: braiding it and creating knots. The knots, as mentioned, contain information. The knots can be read anywhere and in any direction, they are stable and impervious to errors such as stretching, shrinking, rotating or translating them. Untying the knot allows the extraction of information, and generally, a special kind of calculation could also be performed, a topological one, based on the manipulation of the braids, which especially impervious to resistance to noise and errors.

The importance of this research, which offers a calculative-theoretical component, as well as a technological one, is that current-day communications are usually transferred via optical fibers. Once there is a correlation between the end that transfers the information through optical fibers and the receiving end, the application suggested in the research can be used for secure communication. The further vision is making use of this knowledge to build a quantum computer.

For the full article in Nature Communications