Fractional vortex Hilbert's Hotel
Optics
2015-11-24 v1
Abstract
We demonstrate how the unusual mathematics of transfinite numbers, in particular a nearly perfect realization of Hilbert's famous hotel paradox, manifests in the propagation of light through fractional vortex plates. It is shown how a fractional vortex plate can be used, in principle, to create any number of "open rooms," i.e. topological charges, simultaneously. Fractional vortex plates are therefore demonstrated to create a singularity of topological charge, in which the vortex state is completely undefined and in fact arbitrary.
Keywords
Cite
@article{arxiv.1511.07339,
title = {Fractional vortex Hilbert's Hotel},
author = {Greg Gbur},
journal= {arXiv preprint arXiv:1511.07339},
year = {2015}
}