Stochastic Stokes origami: folds, cusps and skyrmionic facets in random polarisation fields

TL;DR

This paper analyzes the geometric and topological properties of random polarization fields using concepts from origami, skyrmions, and topology, revealing statistical and percolation characteristics of patches and facets.

Contribution

It introduces a novel interpretation of random polarization patterns as origami-like structures with skyrmionic features, linking topology, geometry, and statistical analysis.

Findings

Identification of patches and facets as fold and cusp structures.

Statistical analysis of patch and facet properties.

Discussion of percolation and skyrmionic interpretations.

Abstract

We consider the jacobian of a random transverse polarisation field, from the transverse plane to the Poincar\'e sphere, as a Skyrme density partially covering the sphere. Connected domains of the plane where the jacobian has the same sign -- patches -- map to facets subtending some general solid angle on the Poincar\'e sphere. As a generic continuous mapping between surfaces, we interpret the polarisation pattern on the sphere in terms of fold lines (corresponding to the crease lines between neighbouring patches) and cusp points (where fold lines meet). We perform a basic statistical analysis of the properties of the patches and facets, including a brief discussion of the percolation properties of the jacobian domains. Connections with abstract origami manifolds are briefly considered. This analysis combines previous studies of structured skyrmionic polarisation patterns with random polarisation patterns, suggesting a particle-like interpretation of random patches as polarisation skyrmionic anyons.