Fig. 1: Concept.
From: Skyrmions based on optical anisotropy for topological encoding
a Any vector field with a parameter space of \({S}^{2}\) can be used to construct a skyrmion. (Left) A Stokes vector field \({\boldsymbol{S}}(x,y) = [S_1, S_2, S_3]^{\mathsf{T}}\), which is commonly depicted by arrows or polarization ellipses. (Right) An arbitrary elliptical retarder array is characterized by its axis geometry \({\boldsymbol{A}}\) and retardance \(R\) (note induced phase and attenuation are not discussed throughout this work) and commonly depicted by elliptical cylinders, where the shape of the cylinder describes the axis geometry while the height describes the retardance. The axis geometry field of an arbitrary elliptical retarder array as defined in the main text, denoted as \({\boldsymbol{A}}(x,y)={[{A}_{1}(x,y),{A}_{2}(x,y),{A}_{3}(x,y)]}^{\mathsf{T}}\), maps the domain into \({S}^{2}\) and can thus be used to construct skyrmions. Additionally, vector fields are depicted using hue to indicate the azimuthal angle and saturation to represent \({S}_{3}\) and \({A}_{3}\). b An arbitrary elliptical retarder array can be formed by cascading multiple linear retarder arrays. Each linear retarder contributes a defined retardance and fast axis orientation, which together determine the overall axis geometry and net retardance of the synthesized elliptical retarder
