Fig. 3: Generalized skyrmion adders.
From: Perturbation-resilient integer arithmetic using optical skyrmions
a, Concept of a generalized skyrmion photo-adder, which is a passive component that converts a skyrmion of degree n into a generalized skyrmion of degree (n + k1, n + k2, n + k3…). Note that the function of the adder is robust to perturbations in both input field and material parameters, with this robustness extending even to situations in which perturbations occur at the boundary. b, Given a polarization field, a single generalized skyrmion number (GSkyN) can be defined for each connected component of the Poincaré sphere carved out by the image of the boundary curve. A field with one component (left) and three components (right), along with the corresponding images of their boundary curves on the Poincaré sphere, is shown. A stereographically projected version of the boundary curve is also shown. Note that for a given boundary condition, any continuous extension of the boundary to the entire domain will have the same number of generalized skyrmion numbers. c, A generalized skyrmion adder works by manipulating the boundary to create new connected components. For each newly created component, the original skyrmion number (SkyN) is increased once for each time the boundary curve encircles the component, accounting for orientation. The figure depicts an example of an (n)↦(n + 1, n – 1, n) adder, with input field n = 2 and where the Stokes fields and stereographically projected boundary curves are shown. Finally, the skyrmion number and generalized skyrmion numbers of the two fields are provided.
