Optical knots and links have attracted great attention because of their exotic topological characteristics. Recent investigations have shown that the information encoding based on optical knots could possess robust features against external perturbations. However, as a superior coding scheme, it is also necessary to achieve a high capacity, which is hard to be fulfilled by existing knot-carriers owing to the limit number of associated topological invariants. Thus, how to realize the knot-based information coding with a high capacity is a key problem to be solved. Here, we create a type of nested vortex knot, and show that it can be used to fulfill the robust information coding with a high capacity assisted by a large number of intrinsic topological invariants. In experiments, we design and fabricate metasurface holograms to generate light fields sustaining different kinds of nested vortex links. Furthermore, we verify the feasibility of the high-capacity coding scheme based on those topological optical knots. Our work opens another way to realize the robust and high-capacity optical coding, which may have useful impacts on the field of information transfer and storage.

Researchers manipulation and measure the eight hyperentangled Bell-like state in eight-dimensional Hilbert space.

Holography provides an approach to reconstructing both intensity and phase information, and has many applications for microscopic imaging, optical security, and data storage. Recently, the azimuthal Laguerre-Gaussian (LG) mode index, orbital angular momentum (OAM), has been implemented in holography technologies as an independent degree of freedom for high-security encryption. The radial index (RI) of LG mode, however, has not been implemented as an information carrier in holography. Here we propose and demonstrate the RI holography by using strong RI selectivity in the spatial-frequency domain. Furthermore, the LG holography is realized theoretically and experimentally with the (RI, OAM) spanning from (1, -15) to (7, 15), which leads to a 26bit LG-multiplexing hologram for high-security optical encryption. Based on LG holography, a high-capacity holographic information system can be constructed. In our experiments, a LG-multiplexing holography with a span of 217 independent LG channels has been realized, which is inaccessible at present for the OAM holography.

The theory of knots and links focuses on the embedding mode of one or several closed curves in three-dimensional Euclidean space. In an electromagnetic field system, all-optical knots or links composed of phase or polarization singularities have been verified theoretically and experimentally. Recent studies have shown that robust topological all-optical coding can be achieved by using optical knots and links. However, in the current design of optical knots and links based on phase or polarization singularities, the amplitude of light between adjacent singularities is relatively weak. This brings great pressure to detection of optical knots and links and limits their applications. Here, we propose a new optimization method in theory. Compared with the existing design methods, our design method improves the relative intensity distribution of light between adjacent singularities. We verify the feasibility of our design results in experiments. Our study reduces the detection difficulty of optical knots and links, and has a positive significance for promotion of applications of optical knots and links.