Fractal modal encoding of multiscale Stokes-skyrmion networks with hierarchy-dependent Stokes-vector precession

Résumé fourni par la source

Optical Stokes skyrmions provide a route to polarization topology in structured vector beams, but most reported configurations are based on isolated textures, single-scale modal superpositions, or periodic arrays. Here we use a finite-order Sierpinski-hole hierarchy to organize a nonperiodic, multiscale assembly of mutually separated local domains, each carrying a Stokes-skyrmion unit formed by a locally confined Bessel–Gaussian-inspired modal pair in the circular polarization basis. The relative modal spinor ratio of the two circular components determines the wrapping of the normalized Stokes vector on the Poincaré sphere. For the uniform unit-winding case m g = +1, solid-angle integration gives total skyrmion numbers of Q = 1, 4, 13, and 40 for N = 1, 2, 3, and 4, respectively, in agreement with Q = (3 N − 1)/2. For the N = 4 network, simulated six-channel Stokes polarimetry reconstructs Q rec = 39.96. Under the prescribed modal phase evolution, the total and generation-resolved local charges remain unchanged, while the Stokes-vector precession rate scales as Ω g ∝ R g −2 . The results provide a modal route to self-similar, reconstructable, and programmable multiscale Stokes-skyrmion networks.