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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.18232 |
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| _version_ | 1866912134731923456 |
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| author | Maxwell, Kerr Dennis, Mark R |
| author_facet | Maxwell, Kerr Dennis, Mark R |
| contents | We consider the jacobian of a random transverse polarisation field, from the transverse plane to the Poincaré 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 Poincaré 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_18232 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stochastic Stokes origami: folds, cusps and skyrmionic facets in random polarisation fields Maxwell, Kerr Dennis, Mark R Optics Mathematical Physics We consider the jacobian of a random transverse polarisation field, from the transverse plane to the Poincaré 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 Poincaré 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. |
| title | Stochastic Stokes origami: folds, cusps and skyrmionic facets in random polarisation fields |
| topic | Optics Mathematical Physics |
| url | https://arxiv.org/abs/2411.18232 |